added thin qr

src/NativeWrappers/MKL/lapack.cpp

@@ -538,6 +538,27 @@ extern "C"{
 		return info;
 	}
 
+	DLLEXPORT MKL_INT s_qr_thin_factor(MKL_INT m, MKL_INT n, float q[], float tau[], float r[], float work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+		sgeqrf_(&m, &n, q, &m, tau, work, &len, &info);
+
+		for (MKL_INT i = 0; i < n; ++i)
+		{
+			for (MKL_INT j = 0; j < n; ++j)
+			{
+				if( i <= j) {
+					r[j * n + i] = q[j * m + i];
+				}
+			}
+		}
+
+		sorgqr_(&m, &n, &n, q, &m, tau, work, &len, &info);
+
+		return info;
+	}
+
+
 	DLLEXPORT MKL_INT d_qr_factor(MKL_INT m, MKL_INT n, double r[], double tau[], double q[], double work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
@@ -567,6 +588,26 @@ extern "C"{
 		return info;
 	}
 
+	DLLEXPORT MKL_INT d_qr_thin_factor(MKL_INT m, MKL_INT n, double q[], double tau[], double r[], double work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+		dgeqrf_(&m, &n, q, &m, tau, work, &len, &info);
+
+		for (MKL_INT i = 0; i < n; ++i)
+		{
+			for (MKL_INT j = 0; j < n; ++j)
+			{
+				if( i <= j) {
+					r[j * n + i] = q[j * m + i];
+				}
+			}
+		}
+
+		dorgqr_(&m, &n, &n, q, &m, tau, work, &len, &info);
+
+		return info;
+	}
+
 	DLLEXPORT MKL_INT c_qr_factor(MKL_INT m, MKL_INT n, MKL_Complex8 r[], MKL_Complex8 tau[], MKL_Complex8 q[], MKL_Complex8 work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
@@ -596,6 +637,26 @@ extern "C"{
 		return info;
 	}
 
+	DLLEXPORT MKL_INT c_qr_thin_factor(MKL_INT m, MKL_INT n, MKL_Complex8 q[], MKL_Complex8 tau[], MKL_Complex8 r[], MKL_Complex8 work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+		cgeqrf_(&m, &n, q, &m, tau, work, &len, &info);
+
+		for (MKL_INT i = 0; i < n; ++i)
+		{
+			for (MKL_INT j = 0; j < n; ++j)
+			{
+				if( i <= j) {
+					r[j * n + i] = q[j * m + i];
+				}
+			}
+		}
+
+		cungqr_(&m, &n, &n, q, &m, tau, work, &len, &info);
+
+		return info;
+	}
+
 	DLLEXPORT MKL_INT z_qr_factor(MKL_INT m, MKL_INT n, MKL_Complex16 r[], MKL_Complex16 tau[], MKL_Complex16 q[], MKL_Complex16 work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
@@ -625,29 +686,41 @@ extern "C"{
 		return info;
 	}
 
-	DLLEXPORT MKL_INT s_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, float r[], float b[], float x[], float work[], MKL_INT len)
+	DLLEXPORT MKL_INT z_qr_thin_factor(MKL_INT m, MKL_INT n, MKL_Complex16 q[], MKL_Complex16 tau[], MKL_Complex16 r[], MKL_Complex16 work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
-		float* clone_r = new float[m*n];
-		std::memcpy(clone_r, r, m*n*sizeof(float));
-
-		float* tau = new float[std::max(1, std::min(m,n))];
-		sgeqrf_(&m, &n, clone_r, &m, tau, work, &len, &info);
+		zgeqrf_(&m, &n, q, &m, tau, work, &len, &info);
 
-		if (info != 0)
+		for (MKL_INT i = 0; i < n; ++i)
 		{
-			delete[] clone_r;
-			delete[] tau;
-			return info;
+			for (MKL_INT j = 0; j < n; ++j)
+			{
+				if( i <= j) {
+					r[j * n + i] = q[j * m + i];
+				}
+			}
 		}
 
+		zungqr_(&m, &n, &n, q, &m, tau, work, &len, &info);
+
+		return info;
+	}
+
+	DLLEXPORT MKL_INT s_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, float a[], float b[], float x[], float work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+	    MKL_INT* jpvt = new MKL_INT[n];
+		MKL_INT rank = 0;
+		float cond = -1.0;
+
+		float* clone_a = new float[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(float));
+
 		float* clone_b = new float[m*bn];
 		std::memcpy(clone_b, b, m*bn*sizeof(float));
 
-		char side ='L';
-		char tran = 'T';
-		sormqr_(&side, &tran, &m, &bn, &n, clone_r, &m, tau, clone_b, &m, work, &len, &info);
-		cblas_strsm(CblasColMajor, CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, n, bn, 1.0, clone_r, m, clone_b, m);
+	    sgelsy_(&m, &n, &bn, clone_a, &m, clone_b, &m, jpvt, &cond, &rank, work, &len, &info);
+
 		for (MKL_INT i = 0; i < n; ++i)
 		{
 			for (MKL_INT j = 0; j < bn; ++j)
@@ -656,36 +729,57 @@ extern "C"{
 			}
 		}
 
-		delete[] clone_r;
-		delete[] tau;
+		delete[] jpvt;
+		delete[] clone_a;
 		delete[] clone_b;
 		return info;
 	}
 
-	DLLEXPORT MKL_INT d_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, double r[], double b[], double x[], double work[], MKL_INT len)
+	DLLEXPORT MKL_INT d_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, double a[], double b[], double x[], double work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
-		double* clone_r = new double[m*n];
-		std::memcpy(clone_r, r, m*n*sizeof(double));
+	    MKL_INT* jpvt = new MKL_INT[n];
+		MKL_INT rank = 0;
+		double cond = -1.0;
 
-		double* tau = new double[std::max(1, std::min(m,n))];
-		dgeqrf_(&m, &n, clone_r, &m, tau, work, &len, &info);
+		double* clone_a = new double[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(double));
 
-		if (info != 0)
+		double* clone_b = new double[m*bn];
+		std::memcpy(clone_b, b, m*bn*sizeof(double));
+
+	    dgelsy_(&m, &n, &bn, clone_a, &m, clone_b, &m, jpvt, &cond, &rank, work, &len, &info);
+
+		for (MKL_INT i = 0; i < n; ++i)
 		{
-			delete[] clone_r;
-			delete[] tau;
-			return info;
+			for (MKL_INT j = 0; j < bn; ++j)
+			{
+				x[j * n + i] = clone_b[j * m + i];
+			}
 		}
 
-		double* clone_b = new double[m*bn];
-		std::memcpy(clone_b, b, m*bn*sizeof(double));
+		delete[] jpvt;
+		delete[] clone_a;
+		delete[] clone_b;
+		return info;
+	}
 
-		char side ='L';
-		char tran = 'T';
+	DLLEXPORT MKL_INT c_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, MKL_Complex8 a[], MKL_Complex8 b[], MKL_Complex8 x[], MKL_Complex8 work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+	    MKL_INT* jpvt = new MKL_INT[n];
+		float* rwork = new float[2*n];
+		MKL_INT rank = 0;
+		float cond = -1.0;
+
+		MKL_Complex8* clone_a = new MKL_Complex8[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(MKL_Complex8));
+
+		MKL_Complex8* clone_b = new MKL_Complex8[m*bn];
+		std::memcpy(clone_b, b, m*bn*sizeof(MKL_Complex8));
+
+	    cgelsy_(&m, &n, &bn, clone_a, &m, clone_b, &m, jpvt, &cond, &rank, work, &len, rwork, &info);
 
-		dormqr_(&side, &tran, &m, &bn, &n, clone_r, &m, tau, clone_b, &m, work, &len, &info);
-		cblas_dtrsm(CblasColMajor, CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, n, bn, 1.0, clone_r, m, clone_b, m);
 		for (MKL_INT i = 0; i < n; ++i)
 		{
 			for (MKL_INT j = 0; j < bn; ++j)
@@ -694,37 +788,55 @@ extern "C"{
 			}
 		}
 
+		delete[] jpvt;
+		delete[] rwork;
+		delete[] clone_a;
 		delete[] clone_b;
-		delete[] tau;
-		delete[] clone_r;
 		return info;
 	}
 
-	DLLEXPORT MKL_INT c_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, MKL_Complex8 r[], MKL_Complex8 b[], MKL_Complex8 x[], MKL_Complex8 work[], MKL_INT len)
+	DLLEXPORT MKL_INT z_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, MKL_Complex16 a[], MKL_Complex16 b[], MKL_Complex16 x[], MKL_Complex16 work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
-		MKL_Complex8* clone_r = new MKL_Complex8[m*n];
-		std::memcpy(clone_r, r, m*n*sizeof(MKL_Complex8));
+	    MKL_INT* jpvt = new MKL_INT[n];
+		double* rwork = new double[2*n];
+		MKL_INT rank = 0;
+		double cond = -1.0;
+
+		MKL_Complex16* clone_a = new MKL_Complex16[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(MKL_Complex16));
+
+		MKL_Complex16* clone_b = new MKL_Complex16[m*bn];
+		std::memcpy(clone_b, b, m*bn*sizeof(MKL_Complex16));
 
-		MKL_Complex8* tau = new MKL_Complex8[std::min(m,n)];
-		cgeqrf_(&m, &n, clone_r, &m, tau, work, &len, &info);
+	    zgelsy_(&m, &n, &bn, clone_a, &m, clone_b, &m, jpvt, &cond, &rank, work, &len, rwork, &info);
 
-		if (info != 0)
+		for (MKL_INT i = 0; i < n; ++i)
 		{
-			delete[] clone_r;
-			delete[] tau;
-			return info;
+			for (MKL_INT j = 0; j < bn; ++j)
+			{
+				x[j * n + i] = clone_b[j * m + i];
+			}
 		}
 
-		char side ='L';
-		char tran = 'C';
+		delete[] jpvt;
+		delete[] rwork;
+		delete[] clone_a;
+		delete[] clone_b;
+		return info;
+	}
 
-		MKL_Complex8* clone_b = new MKL_Complex8[m*bn];
-		std::memcpy(clone_b, b, m*bn*sizeof(MKL_Complex8));
+	DLLEXPORT MKL_INT s_thin_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, float a[], float b[], float x[], float work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
 
-		cunmqr_(&side, &tran, &m, &bn, &n, clone_r, &m, tau, clone_b, &m, work, &len, &info);
-		MKL_Complex8 one = {1.0, 0.0};
-		cblas_ctrsm(CblasColMajor, CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, n, bn, &one, clone_r, m, clone_b, m);
+		float* clone_a = new float[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(float));
+
+		float* clone_b = new float[m*bn];
+		std::memcpy(clone_b, b, m*bn*sizeof(float));
+		char N = 'N';
+	    sgels_(&N, &m, &n, &bn, clone_a, &m, clone_b, &m, work, &len, &info);
 
 		for (MKL_INT i = 0; i < n; ++i)
 		{
@@ -734,37 +846,74 @@ extern "C"{
 			}
 		}
 
-		delete[] clone_r;
-		delete[] tau;
+		delete[] clone_a;
 		delete[] clone_b;
 		return info;
 	}
 
-	DLLEXPORT MKL_INT z_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, MKL_Complex16 r[], MKL_Complex16 b[], MKL_Complex16 x[], MKL_Complex16 work[], MKL_INT len)
+	DLLEXPORT MKL_INT d_thin_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, double a[], double b[], double x[], double work[], MKL_INT len)
 	{
 		MKL_INT info = 0;
-		MKL_Complex16* clone_r = new MKL_Complex16[m*n];
-		std::memcpy(clone_r, r, m*n*sizeof(MKL_Complex16));
 
-		MKL_Complex16* tau = new MKL_Complex16[std::min(m,n)];
-		zgeqrf_(&m, &n, clone_r, &m, tau, work, &len, &info);
+		double* clone_a = new double[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(double));
+
+		double* clone_b = new double[m*bn];
+		std::memcpy(clone_b, b, m*bn*sizeof(double));
 
-		if (info != 0)
+		char N = 'N';
+	    dgels_(&N, &m, &n, &bn, clone_a, &m, clone_b, &m, work, &len, &info);
+
+		for (MKL_INT i = 0; i < n; ++i)
 		{
-			delete[] clone_r;
-			delete[] tau;
-			return info;
+			for (MKL_INT j = 0; j < bn; ++j)
+			{
+				x[j * n + i] = clone_b[j * m + i];
+			}
 		}
 
-		char side ='L';
-		char tran = 'C';
+		delete[] clone_a;
+		delete[] clone_b;
+		return info;
+	}
+
+	DLLEXPORT MKL_INT c_thin_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, MKL_Complex8 a[], MKL_Complex8 b[], MKL_Complex8 x[], MKL_Complex8 work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+		MKL_Complex8* clone_a = new MKL_Complex8[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(MKL_Complex8));
+
+		MKL_Complex8* clone_b = new MKL_Complex8[m*bn];
+		std::memcpy(clone_b, b, m*bn*sizeof(MKL_Complex8));
+
+		char N = 'N';
+	    cgels_(&N, &m, &n, &bn, clone_a, &m, clone_b, &m, work, &len, &info);
+
+		for (MKL_INT i = 0; i < n; ++i)
+		{
+			for (MKL_INT j = 0; j < bn; ++j)
+			{
+				x[j * n + i] = clone_b[j * m + i];
+			}
+		}
+
+		delete[] clone_a;
+		delete[] clone_b;
+		return info;
+	}
+
+	DLLEXPORT MKL_INT z_thin_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, MKL_Complex16 a[], MKL_Complex16 b[], MKL_Complex16 x[], MKL_Complex16 work[], MKL_INT len)
+	{
+		MKL_INT info = 0;
+
+		MKL_Complex16* clone_a = new MKL_Complex16[m*n];
+		std::memcpy(clone_a, a, m*n*sizeof(MKL_Complex16));
 
 		MKL_Complex16* clone_b = new MKL_Complex16[m*bn];
 		std::memcpy(clone_b, b, m*bn*sizeof(MKL_Complex16));
 
-		zunmqr_(&side, &tran, &m, &bn, &n, clone_r, &m, tau, clone_b, &m, work, &len, &info);
-		MKL_Complex16 one = {1.0, 0.0};
-		cblas_ztrsm(CblasColMajor, CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, n, bn, &one, clone_r, m, clone_b, m);
+		char N = 'N';
+	    zgels_(&N, &m, &n, &bn, clone_a, &m, clone_b, &m, work, &len, &info);
 
 		for (MKL_INT i = 0; i < n; ++i)
 		{
@@ -774,8 +923,7 @@ extern "C"{
 			}
 		}
 
-		delete[] clone_r;
-		delete[] tau;
+		delete[] clone_a;
 		delete[] clone_b;
 		return info;
 	}

src/NativeWrappers/MKL/lapack.h

@@ -1,7 +1,7 @@
 #ifndef LAPACK_H
 #define LAPACK_H
 
-#include "blas.h"
+//#include "blas.h"
 #include "mkl_lapack.h"
 
 #endif 

src/NativeWrappers/Windows/ACMLWrapper/ACMKWrapper.vcxproj → src/NativeWrappers/Windows/ACML/ACMLWrapper.vcxproj

@@ -29,23 +29,27 @@
     <ConfigurationType>DynamicLibrary</ConfigurationType>
     <UseDebugLibraries>true</UseDebugLibraries>
     <CharacterSet>Unicode</CharacterSet>
+    <PlatformToolset>v110</PlatformToolset>
   </PropertyGroup>
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|x64'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
     <UseDebugLibraries>true</UseDebugLibraries>
     <CharacterSet>Unicode</CharacterSet>
+    <PlatformToolset>v110</PlatformToolset>
   </PropertyGroup>
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
     <UseDebugLibraries>false</UseDebugLibraries>
     <WholeProgramOptimization>true</WholeProgramOptimization>
     <CharacterSet>Unicode</CharacterSet>
+    <PlatformToolset>v110</PlatformToolset>
   </PropertyGroup>
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
     <UseDebugLibraries>false</UseDebugLibraries>
     <WholeProgramOptimization>true</WholeProgramOptimization>
     <CharacterSet>Unicode</CharacterSet>
+    <PlatformToolset>v110</PlatformToolset>
   </PropertyGroup>
   <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
   <ImportGroup Label="ExtensionSettings">

src/NativeWrappers/Windows/ACMLWrapper/ACMKWrapper.vcxproj.filters

@@ -1,33 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<Project ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
-  <ItemGroup>
-    <Filter Include="Source Files">
-      <UniqueIdentifier>{4FC737F1-C7A5-4376-A066-2A32D752A2FF}</UniqueIdentifier>
-      <Extensions>cpp;c;cc;cxx;def;odl;idl;hpj;bat;asm;asmx</Extensions>
-    </Filter>
-    <Filter Include="Header Files">
-      <UniqueIdentifier>{93995380-89BD-4b04-88EB-625FBE52EBFB}</UniqueIdentifier>
-      <Extensions>h;hpp;hxx;hm;inl;inc;xsd</Extensions>
-    </Filter>
-    <Filter Include="Resource Files">
-      <UniqueIdentifier>{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}</UniqueIdentifier>
-      <Extensions>rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms</Extensions>
-    </Filter>
-  </ItemGroup>
-  <ItemGroup>
-    <ResourceCompile Include="..\..\Common\resource.rc">
-      <Filter>Resource Files</Filter>
-    </ResourceCompile>
-  </ItemGroup>
-  <ItemGroup>
-    <ClCompile Include="..\..\Common\WindowsDLL.cpp">
-      <Filter>Source Files</Filter>
-    </ClCompile>
-    <ClCompile Include="..\..\ACML\blas.c">
-      <Filter>Source Files</Filter>
-    </ClCompile>
-    <ClCompile Include="..\..\ACML\lapack.cpp">
-      <Filter>Source Files</Filter>
-    </ClCompile>
-  </ItemGroup>
-</Project>

src/NativeWrappers/Windows/ACMLWrapperTests/ACMLWrapperTests.csproj

@@ -36,7 +36,7 @@
       <HintPath>..\..\..\..\out\debug\Net40\MathNet.Numerics.dll</HintPath>
     </Reference>
     <Reference Include="nunit.framework">
-      <HintPath>..\..\..\..\lib\NUnit.2.5.9\nunit.framework.dll</HintPath>
+      <HintPath>..\..\..\..\packages\NUnit.2.6.2\lib\nunit.framework.dll</HintPath>
     </Reference>
     <Reference Include="System" />
     <Reference Include="System.Core" />

src/NativeWrappers/Windows/MKL/MKLWrapper.vcxproj

@@ -25,23 +25,27 @@
   <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
+    <PlatformToolset>v110</PlatformToolset>
     <CharacterSet>MultiByte</CharacterSet>
     <WholeProgramOptimization>true</WholeProgramOptimization>
     <UseIntelMKL>Parallel</UseIntelMKL>
   </PropertyGroup>
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
+    <PlatformToolset>v110</PlatformToolset>
     <CharacterSet>MultiByte</CharacterSet>
     <UseIntelMKL>Parallel</UseIntelMKL>
   </PropertyGroup>
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
+    <PlatformToolset>v110</PlatformToolset>
     <CharacterSet>MultiByte</CharacterSet>
     <WholeProgramOptimization>true</WholeProgramOptimization>
     <UseIntelMKL>Parallel</UseIntelMKL>
   </PropertyGroup>
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|x64'" Label="Configuration">
     <ConfigurationType>DynamicLibrary</ConfigurationType>
+    <PlatformToolset>v110</PlatformToolset>
     <CharacterSet>MultiByte</CharacterSet>
     <UseIntelMKL>Parallel</UseIntelMKL>
   </PropertyGroup>
@@ -62,32 +66,28 @@
   </ImportGroup>
   <PropertyGroup Label="UserMacros" />
   <PropertyGroup>
-    <_ProjectFileVersion>10.0.30319.1</_ProjectFileVersion>
-    <OutDir Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
-    <IntDir Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">$(Platform)\$(Configuration)\</IntDir>
-    <OutDir Condition="'$(Configuration)|$(Platform)'=='Debug|x64'">$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
-    <IntDir Condition="'$(Configuration)|$(Platform)'=='Debug|x64'">$(Platform)\$(Configuration)\</IntDir>
-    <OutDir Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
-    <IntDir Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">$(Platform)\$(Configuration)\</IntDir>
-    <OutDir Condition="'$(Configuration)|$(Platform)'=='Release|x64'">$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
-    <IntDir Condition="'$(Configuration)|$(Platform)'=='Release|x64'">$(Platform)\$(Configuration)\</IntDir>
-    <CodeAnalysisRuleSet Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">AllRules.ruleset</CodeAnalysisRuleSet>
-    <CodeAnalysisRules Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'" />
-    <CodeAnalysisRuleAssemblies Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'" />
-    <CodeAnalysisRuleSet Condition="'$(Configuration)|$(Platform)'=='Debug|x64'">AllRules.ruleset</CodeAnalysisRuleSet>
-    <CodeAnalysisRules Condition="'$(Configuration)|$(Platform)'=='Debug|x64'" />
-    <CodeAnalysisRuleAssemblies Condition="'$(Configuration)|$(Platform)'=='Debug|x64'" />
-    <CodeAnalysisRuleSet Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">AllRules.ruleset</CodeAnalysisRuleSet>
-    <CodeAnalysisRules Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" />
-    <CodeAnalysisRuleAssemblies Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" />
-    <CodeAnalysisRuleSet Condition="'$(Configuration)|$(Platform)'=='Release|x64'">AllRules.ruleset</CodeAnalysisRuleSet>
-    <CodeAnalysisRules Condition="'$(Configuration)|$(Platform)'=='Release|x64'" />
-    <CodeAnalysisRuleAssemblies Condition="'$(Configuration)|$(Platform)'=='Release|x64'" />
+    <_ProjectFileVersion>11.0.50727.1</_ProjectFileVersion>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">
+    <OutDir>$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
+    <IntDir>$(Platform)\$(Configuration)\</IntDir>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|x64'">
+    <OutDir>$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
+    <IntDir>$(Platform)\$(Configuration)\</IntDir>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">
+    <OutDir>$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
+    <IntDir>$(Platform)\$(Configuration)\</IntDir>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'">
+    <OutDir>$(SolutionDir)$(Platform)\$(Configuration)\</OutDir>
+    <IntDir>$(Platform)\$(Configuration)\</IntDir>
   </PropertyGroup>
   <ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">
     <ClCompile>
       <Optimization>Disabled</Optimization>
-      <AdditionalIncludeDirectories>..\..\Common;..\..\MKL;C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\include;</AdditionalIncludeDirectories>
+      <AdditionalIncludeDirectories>$(ProjectDir)..\..\Common;$(ProjectDir)..\..\MKL;$(MKLIncludeDir);%(AdditionalIncludeDirectories)</AdditionalIncludeDirectories>
       <PreprocessorDefinitions>_WINDOWS;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <MinimalRebuild>true</MinimalRebuild>
       <BasicRuntimeChecks>EnableFastChecks</BasicRuntimeChecks>
@@ -99,12 +99,12 @@
     <Link>
       <AdditionalDependencies>mkl_intel_c.lib;mkl_intel_thread.lib;mkl_core.lib;libiomp5md.lib;%(AdditionalDependencies)</AdditionalDependencies>
       <OutputFile>$(OutDir)MathNET.Numerics.MKL.dll</OutputFile>
-      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\lib\ia32;C:\Program Files (x86)\Intel\ComposerXE-2011\compiler\lib\ia32;</AdditionalLibraryDirectories>
+      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\Compiler\11.1\046\lib\ia32;C:\Program Files (x86)\Intel\Compiler\11.1\046\mkl\ia32\lib;%(AdditionalLibraryDirectories)</AdditionalLibraryDirectories>
       <GenerateDebugInformation>true</GenerateDebugInformation>
       <TargetMachine>MachineX86</TargetMachine>
     </Link>
     <PostBuildEvent>
-      <Command>copy "C:\Program Files (x86)\Intel\Composer XE\redist\ia32\compiler\libiomp5md.dll" $(OutDir)</Command>
+      <Command>copy "$(CompilerPathForVC)\libiomp5md.dll" $(OutDir)</Command>
     </PostBuildEvent>
   </ItemDefinitionGroup>
   <ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='Debug|x64'">
@@ -113,7 +113,7 @@
     </Midl>
     <ClCompile>
       <Optimization>Disabled</Optimization>
-      <AdditionalIncludeDirectories>..\..\Common;..\..\MKL;C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\include;</AdditionalIncludeDirectories>
+      <AdditionalIncludeDirectories>$(ProjectDir)..\..\Common;$(ProjectDir)..\..\MKL;$(MKLIncludeDir);%(AdditionalIncludeDirectories)</AdditionalIncludeDirectories>
       <PreprocessorDefinitions>_WINDOWS;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <MinimalRebuild>true</MinimalRebuild>
       <BasicRuntimeChecks>EnableFastChecks</BasicRuntimeChecks>
@@ -125,19 +125,19 @@
     <Link>
       <AdditionalDependencies>mkl_intel_lp64.lib;mkl_intel_thread.lib;mkl_core.lib;libiomp5md.lib;%(AdditionalDependencies)</AdditionalDependencies>
       <OutputFile>$(OutDir)MathNET.Numerics.MKL.dll</OutputFile>
-      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\lib\intel64;C:\Program Files (x86)\Intel\ComposerXE-2011\compiler\lib\intel64</AdditionalLibraryDirectories>
+      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\Compiler\11.1\046\lib\intel64;C:\Program Files (x86)\Intel\Compiler\11.1\046\mkl\em64t\lib;%(AdditionalLibraryDirectories)</AdditionalLibraryDirectories>
       <GenerateDebugInformation>true</GenerateDebugInformation>
       <TargetMachine>MachineX64</TargetMachine>
     </Link>
     <PostBuildEvent>
-      <Command>copy "C:\Program Files (x86)\Intel\Composer XE\redist\intel64\compiler\libiomp5md.dll" $(OutDir)</Command>
+      <Command>copy "$(CompilerPathForVC)\libiomp5md.dll" $(OutDir)</Command>
     </PostBuildEvent>
   </ItemDefinitionGroup>
   <ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">
     <ClCompile>
       <Optimization>MaxSpeed</Optimization>
       <IntrinsicFunctions>true</IntrinsicFunctions>
-      <AdditionalIncludeDirectories>..\..\Common;..\..\MKL;C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\include;</AdditionalIncludeDirectories>
+      <AdditionalIncludeDirectories>$(ProjectDir)..\..\Common;$(ProjectDir)..\..\MKL;$(MKLIncludeDir);%(AdditionalIncludeDirectories)</AdditionalIncludeDirectories>
       <PreprocessorDefinitions>_WINDOWS;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <RuntimeLibrary>MultiThreaded</RuntimeLibrary>
       <FunctionLevelLinking>true</FunctionLevelLinking>
@@ -148,14 +148,14 @@
     <Link>
       <AdditionalDependencies>mkl_intel_c.lib;mkl_intel_thread.lib;mkl_core.lib;libiomp5md.lib;%(AdditionalDependencies)</AdditionalDependencies>
       <OutputFile>$(OutDir)MathNET.Numerics.MKL.dll</OutputFile>
-      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\lib\ia32;C:\Program Files (x86)\Intel\ComposerXE-2011\compiler\lib\ia32;</AdditionalLibraryDirectories>
+      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\Compiler\11.1\060\lib\ia32;C:\Program Files (x86)\Intel\Compiler\11.1\060\mkl\ia32\lib;%(AdditionalLibraryDirectories)</AdditionalLibraryDirectories>
       <GenerateDebugInformation>true</GenerateDebugInformation>
       <OptimizeReferences>true</OptimizeReferences>
       <EnableCOMDATFolding>true</EnableCOMDATFolding>
       <TargetMachine>MachineX86</TargetMachine>
     </Link>
     <PostBuildEvent>
-      <Command>copy "C:\Program Files (x86)\Intel\Composer XE\redist\ia32\compiler\libiomp5md.dll" $(OutDir)</Command>
+      <Command>copy "$(CompilerPathForVC)\libiomp5md.dll" $(OutDir)</Command>
     </PostBuildEvent>
   </ItemDefinitionGroup>
   <ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'">
@@ -165,7 +165,7 @@
     <ClCompile>
       <Optimization>MaxSpeed</Optimization>
       <IntrinsicFunctions>true</IntrinsicFunctions>
-      <AdditionalIncludeDirectories>..\..\Common;..\..\MKL;C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\include;</AdditionalIncludeDirectories>
+      <AdditionalIncludeDirectories>$(ProjectDir)..\..\Common;$(ProjectDir)..\..\MKL;$(MKLIncludeDir);%(AdditionalIncludeDirectories)</AdditionalIncludeDirectories>
       <PreprocessorDefinitions>_WINDOWS;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <RuntimeLibrary>MultiThreaded</RuntimeLibrary>
       <FunctionLevelLinking>true</FunctionLevelLinking>
@@ -176,26 +176,26 @@
     <Link>
       <AdditionalDependencies>mkl_intel_lp64.lib;mkl_intel_thread.lib;mkl_core.lib;libiomp5md.lib;%(AdditionalDependencies)</AdditionalDependencies>
       <OutputFile>$(OutDir)MathNET.Numerics.MKL.dll</OutputFile>
-      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\ComposerXE-2011\mkl\lib\intel64;C:\Program Files (x86)\Intel\ComposerXE-2011\compiler\lib\intel64</AdditionalLibraryDirectories>
+      <AdditionalLibraryDirectories>C:\Program Files (x86)\Intel\Compiler\11.1\060\lib\intel64;C:\Program Files (x86)\Intel\Compiler\11.1\060\mkl\em64t\lib;%(AdditionalLibraryDirectories)</AdditionalLibraryDirectories>
       <GenerateDebugInformation>true</GenerateDebugInformation>
       <OptimizeReferences>true</OptimizeReferences>
       <EnableCOMDATFolding>true</EnableCOMDATFolding>
       <TargetMachine>MachineX64</TargetMachine>
     </Link>
     <PostBuildEvent>
-      <Command>copy "C:\Program Files (x86)\Intel\Composer XE\redist\intel64\compiler\libiomp5md.dll" $(OutDir)</Command>
+      <Command>copy "$(CompilerPathForVC)\libiomp5md.dll" $(OutDir)</Command>
     </PostBuildEvent>
   </ItemDefinitionGroup>
-  <ItemGroup>
-    <ClInclude Include="..\..\Common\wrapper_common.h" />
-    <ClInclude Include="..\..\MKL\lapack.h" />
-  </ItemGroup>
   <ItemGroup>
     <ClCompile Include="..\..\Common\WindowsDLL.cpp" />
     <ClCompile Include="..\..\MKL\blas.c" />
     <ClCompile Include="..\..\MKL\lapack.cpp" />
     <ClCompile Include="..\..\MKL\vector_functions.c" />
   </ItemGroup>
+  <ItemGroup>
+    <ClInclude Include="..\..\Common\wrapper_common.h" />
+    <ClInclude Include="..\..\MKL\lapack.h" />
+  </ItemGroup>
   <ItemGroup>
     <ResourceCompile Include="..\..\Common\resource.rc" />
   </ItemGroup>

src/NativeWrappers/Windows/MKL/MKLWrapper.vcxproj.filters

@@ -15,17 +15,6 @@
     </Filter>
   </ItemGroup>
   <ItemGroup>
-    <ClInclude Include="..\..\Common\wrapper_common.h">
-      <Filter>Header Files</Filter>
-    </ClInclude>
-    <ClInclude Include="..\..\MKL\lapack.h">
-      <Filter>Header Files</Filter>
-    </ClInclude>
-  </ItemGroup>
-  <ItemGroup>
-    <ClCompile Include="..\..\Common\WindowsDLL.cpp">
-      <Filter>Source Files</Filter>
-    </ClCompile>
     <ClCompile Include="..\..\MKL\blas.c">
       <Filter>Source Files</Filter>
     </ClCompile>
@@ -35,6 +24,17 @@
     <ClCompile Include="..\..\MKL\vector_functions.c">
       <Filter>Source Files</Filter>
     </ClCompile>
+    <ClCompile Include="..\..\Common\WindowsDLL.cpp">
+      <Filter>Source Files</Filter>
+    </ClCompile>
+  </ItemGroup>
+  <ItemGroup>
+    <ClInclude Include="..\..\MKL\lapack.h">
+      <Filter>Header Files</Filter>
+    </ClInclude>
+    <ClInclude Include="..\..\Common\wrapper_common.h">
+      <Filter>Header Files</Filter>
+    </ClInclude>
   </ItemGroup>
   <ItemGroup>
     <ResourceCompile Include="..\..\Common\resource.rc">

src/NativeWrappers/Windows/MKLWrapperTests/MKLWrapperTests.csproj

@@ -59,8 +59,9 @@
       <SpecificVersion>False</SpecificVersion>
       <HintPath>..\..\..\..\out\debug\Net40\MathNet.Numerics.dll</HintPath>
     </Reference>
-    <Reference Include="nunit.framework">
-      <HintPath>..\..\..\..\lib\NUnit.2.5.9\nunit.framework.dll</HintPath>
+    <Reference Include="nunit.framework, Version=2.5.9.10348, Culture=neutral, PublicKeyToken=96d09a1eb7f44a77, processorArchitecture=MSIL">
+      <SpecificVersion>False</SpecificVersion>
+      <HintPath>..\..\..\..\packages\NUnit.2.6.2\lib\nunit.framework.dll</HintPath>
     </Reference>
     <Reference Include="System" />
     <Reference Include="System.Core">

src/NativeWrappers/Windows/NativeWrappers.sln

@@ -1,6 +1,6 @@
 
-Microsoft Visual Studio Solution File, Format Version 11.00
-# Visual Studio 2010
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio 2012
 Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "Common", "Common", "{5A0892FF-82CE-40FC-BCE1-73810C615F52}"
 	ProjectSection(SolutionItems) = preProject
 		..\Common\resource.h = ..\Common\resource.h
@@ -13,14 +13,6 @@ Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "MKLWrapper", "MKL\MKLWrappe
 EndProject
 Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "MKLWrapperTests", "MKLWrapperTests\MKLWrapperTests.csproj", "{D0AD591B-0CE6-4A6D-8DEA-01777EE09BC3}"
 EndProject
-Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "GotoBLAS2Wrapper", "GotoBLAS2\GotoBLAS2Wrapper.vcxproj", "{507FF69E-32A6-495A-9DE2-20EC10EE8963}"
-EndProject
-Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "GotoBLAS2WrapperTests", "GotoBLAS2WrapperTests\GotoBLAS2WrapperTests.csproj", "{56FFAB18-CAA6-4913-8123-610872BFD60A}"
-EndProject
-Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "ACMLWrapper", "ACMLWrapper\ACMKWrapper.vcxproj", "{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}"
-EndProject
-Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "ACMLWrapperTests", "ACMLWrapperTests\ACMLWrapperTests.csproj", "{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}"
-EndProject
 Global
 	GlobalSection(SolutionConfigurationPlatforms) = preSolution
 		Debug|Any CPU = Debug|Any CPU
@@ -59,57 +51,6 @@ Global
 		{D0AD591B-0CE6-4A6D-8DEA-01777EE09BC3}.Release|Mixed Platforms.Build.0 = Release|Any CPU
 		{D0AD591B-0CE6-4A6D-8DEA-01777EE09BC3}.Release|Win32.ActiveCfg = Release|Any CPU
 		{D0AD591B-0CE6-4A6D-8DEA-01777EE09BC3}.Release|x64.ActiveCfg = Release|Any CPU
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|Any CPU.ActiveCfg = Debug|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|Mixed Platforms.ActiveCfg = Debug|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|Mixed Platforms.Build.0 = Debug|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|Win32.ActiveCfg = Debug|Win32
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|Win32.Build.0 = Debug|Win32
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|x64.ActiveCfg = Debug|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Debug|x64.Build.0 = Debug|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|Any CPU.ActiveCfg = Release|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|Mixed Platforms.ActiveCfg = Release|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|Mixed Platforms.Build.0 = Release|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|Win32.ActiveCfg = Release|Win32
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|Win32.Build.0 = Release|Win32
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|x64.ActiveCfg = Release|x64
-		{507FF69E-32A6-495A-9DE2-20EC10EE8963}.Release|x64.Build.0 = Release|x64
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Debug|Any CPU.Build.0 = Debug|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Debug|Mixed Platforms.ActiveCfg = Debug|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Debug|Mixed Platforms.Build.0 = Debug|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Debug|Win32.ActiveCfg = Debug|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Debug|x64.ActiveCfg = Debug|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Release|Any CPU.ActiveCfg = Release|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Release|Any CPU.Build.0 = Release|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Release|Mixed Platforms.ActiveCfg = Release|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Release|Win32.ActiveCfg = Release|Any CPU
-		{56FFAB18-CAA6-4913-8123-610872BFD60A}.Release|x64.ActiveCfg = Release|Any CPU
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|Any CPU.ActiveCfg = Debug|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|Mixed Platforms.ActiveCfg = Debug|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|Mixed Platforms.Build.0 = Debug|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|Win32.ActiveCfg = Debug|Win32
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|Win32.Build.0 = Debug|Win32
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|x64.ActiveCfg = Debug|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Debug|x64.Build.0 = Debug|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|Any CPU.ActiveCfg = Release|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|Mixed Platforms.ActiveCfg = Release|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|Mixed Platforms.Build.0 = Release|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|Win32.ActiveCfg = Release|Win32
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|Win32.Build.0 = Release|Win32
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|x64.ActiveCfg = Release|x64
-		{8774BCBE-27D0-44D2-A1B3-8ED705E252CB}.Release|x64.Build.0 = Release|x64
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Debug|Any CPU.Build.0 = Debug|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Debug|Mixed Platforms.ActiveCfg = Debug|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Debug|Mixed Platforms.Build.0 = Debug|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Debug|Win32.ActiveCfg = Debug|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Debug|x64.ActiveCfg = Debug|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Release|Any CPU.ActiveCfg = Release|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Release|Any CPU.Build.0 = Release|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Release|Mixed Platforms.ActiveCfg = Release|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Release|Mixed Platforms.Build.0 = Release|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Release|Win32.ActiveCfg = Release|Any CPU
-		{8A42A7F3-23C0-46D9-9DBA-B9039EB3C8EB}.Release|x64.ActiveCfg = Release|Any CPU
 	EndGlobalSection
 	GlobalSection(SolutionProperties) = preSolution
 		HideSolutionNode = FALSE

src/Numerics/Algorithms/LinearAlgebra/Acml/AcmlLinearAlgebraProvider.Complex.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Acml
 {
     using System;

src/Numerics/Algorithms/LinearAlgebra/Acml/AcmlLinearAlgebraProvider.Complex32.cs

@@ -32,6 +32,8 @@
    Last generated on UTC 2011-04-17 06:45:26Z
 */
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Acml
 {
     using System;

src/Numerics/Algorithms/LinearAlgebra/Acml/AcmlLinearAlgebraProvider.double.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Acml
 {
     using System;

src/Numerics/Algorithms/LinearAlgebra/Acml/AcmlLinearAlgebraProvider.float.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Acml
 {
     using System;

src/Numerics/Algorithms/LinearAlgebra/GotoBlas/GotoBlasLinearAlgebraProvider.Complex.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
 {
     using System;
@@ -541,7 +543,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// to be used by the QR solve routine.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
         [SecuritySafeCritical]
-        public override void QRFactor(Complex[] r, int rowsR, int columnsR, Complex[] q, Complex[] tau)
+        public override void QRFactor(Complex[] r, int rowsR, int columnsR, Complex[] q, Complex[] tau, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -747,8 +749,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// <summary>
         /// Solves A*X=B for X using a previously QR factored matrix.
         /// </summary>
-        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[])"/>.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[])"/>. </param>
+        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[],QRMethod)"/>.</param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
@@ -814,7 +816,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// </summary>
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[])"/>. </param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver

src/Numerics/Algorithms/LinearAlgebra/GotoBlas/GotoBlasLinearAlgebraProvider.Complex32.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
 {
     using System;
@@ -540,7 +542,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// to be used by the QR solve routine.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
         [SecuritySafeCritical]
-        public override void QRFactor(Complex32[] r, int rowsR, int columnsR, Complex32[] q, Complex32[] tau)
+        public override void QRFactor(Complex32[] r, int rowsR, int columnsR, Complex32[] q, Complex32[] tau, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -746,8 +748,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// <summary>
         /// Solves A*X=B for X using a previously QR factored matrix.
         /// </summary>
-        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[])"/>.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[])"/>. </param>
+        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[],QRMethod)"/>.</param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
@@ -813,7 +815,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// </summary>
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[])"/>. </param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver

src/Numerics/Algorithms/LinearAlgebra/GotoBlas/GotoBlasLinearAlgebraProvider.double.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
 {
     using System;
@@ -540,7 +542,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// to be used by the QR solve routine.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
         [SecuritySafeCritical]
-        public override void QRFactor(double[] r, int rowsR, int columnsR, double[] q, double[] tau)
+        public override void QRFactor(double[] r, int rowsR, int columnsR, double[] q, double[] tau, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -746,8 +748,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// <summary>
         /// Solves A*X=B for X using a previously QR factored matrix.
         /// </summary>
-        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>. </param>
+        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[],QRMethod)"/>.</param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
@@ -813,7 +815,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// </summary>
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>. </param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver

src/Numerics/Algorithms/LinearAlgebra/GotoBlas/GotoBlasLinearAlgebraProvider.float.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
 {
     using System;
@@ -540,7 +542,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// to be used by the QR solve routine.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
         [SecuritySafeCritical]
-        public override void QRFactor(float[] r, int rowsR, int columnsR, float[] q, float[] tau)
+        public override void QRFactor(float[] r, int rowsR, int columnsR, float[] q, float[] tau, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -746,8 +748,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// <summary>
         /// Solves A*X=B for X using a previously QR factored matrix.
         /// </summary>
-        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>. </param>
+        /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[],QRMethod)"/>.</param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
@@ -813,7 +815,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas
         /// </summary>
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
-        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>. </param>
+        /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[],QRMethod)"/>. </param>
         /// <param name="rowsR">The number of rows in the A matrix.</param>
         /// <param name="columnsR">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver

src/Numerics/Algorithms/LinearAlgebra/ILinearAlgebraProviderOfT.cs

@@ -25,6 +25,9 @@
 // </copyright>
 
 // INITIAL DRAFT MISSING EXCEPTION SPECIFICATIONS
+
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra
 {
     using System.Numerics;
@@ -313,27 +316,58 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         void CholeskySolveFactored(T[] a, int orderA, T[] b, int columnsB);
 
         /// <summary>
-        /// Computes the QR factorization of A.
+        /// Computes the full QR factorization of A.
         /// </summary>
-        /// <param name="r">On entry, it is the M by N A matrix to factor. On exit,
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
         /// it is overwritten with the R matrix of the QR factorization.</param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="q">On exit, A M by M matrix that holds the Q matrix of the
         /// QR factorization.</param>
         /// <param name="tau">A min(m,n) vector. On exit, contains additional information
         /// to be used by the QR solve routine.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
-        void QRFactor(T[] r, int rowsR, int columnsR, T[] q, T[] tau);
+        void QRFactor(T[] a, int rowsA, int columnsA, T[] q, T[] tau);
 
         /// <summary>
-        /// Computes the QR factorization of A.
+        /// Computes the full QR factorization of A.
         /// </summary>
-        /// <param name="r">On entry, it is the M by N A matrix to factor. On exit,
-        /// it is overwritten with the R matrix of the QR factorization. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
-        /// <param name="q">On exit, A M by M matrix that holds the Q matrix of the 
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the R matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="q">On exit, A M by M matrix that holds the Q matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <param name="work">The work array. The array must have a length of at least N,
+        /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
+        /// work size value.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        void QRFactor(T[] a, int rowsA, int columnsA, T[] q, T[] tau, T[] work);
+
+        /// <summary>
+        /// Computes the thin QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        void ThinQRFactor(T[] a, int rowsA, int columnsA, T[] r, T[] tau);
+
+        /// <summary>
+        /// Computes the thin QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
         /// QR factorization.</param>
         /// <param name="tau">A min(m,n) vector. On exit, contains additional information
         /// to be used by the QR solve routine.</param>
@@ -341,7 +375,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
-        void QRFactor(T[] r, int rowsR, int columnsR, T[] q, T[] tau, T[] work);
+        void ThinQRFactor(T[] a, int rowsA, int columnsA, T[] r, T[] tau, T[] work);
 
         /// <summary>
         /// Solves A*X=B for X using QR factorization of A.
@@ -352,8 +386,9 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        void QRSolve(T[] a, int rows, int columns, T[] b, int columnsB, T[] x);
+        void QRSolve(T[] a, int rows, int columns, T[] b, int columnsB, T[] x, QRMethod method = QRMethod.Full);
 
         /// <summary>
         /// Solves A*X=B for X using QR factorization of A.
@@ -367,8 +402,9 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        void QRSolve(T[] a, int rows, int columns, T[] b, int columnsB, T[] x, T[] work);
+        void QRSolve(T[] a, int rows, int columns, T[] b, int columnsB, T[] x, T[] work, QRMethod method = QRMethod.Full);
 
         /// <summary>
         /// Solves A*X=B for X using a previously QR factored matrix.
@@ -384,7 +420,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        void QRSolveFactored(T[] q, T[] r, int rowsR, int columnsR, T[] tau, T[] b, int columnsB, T[] x);
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
+        void QRSolveFactored(T[] q, T[] r, int rowsR, int columnsR, T[] tau, T[] b, int columnsB, T[] x, QRMethod method = QRMethod.Full);
 
         /// <summary>
         /// Solves A*X=B for X using a previously QR factored matrix.
@@ -403,7 +440,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        void QRSolveFactored(T[] q, T[] r, int rowsR, int columnsR, T[] tau, T[] b, int columnsB, T[] x, T[] work);
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
+        void QRSolveFactored(T[] q, T[] r, int rowsR, int columnsR, T[] tau, T[] b, int columnsB, T[] x, T[] work, QRMethod method = QRMethod.Full);
         
         /// <summary>
         /// Computes the singular value decomposition of A.

src/Numerics/Algorithms/LinearAlgebra/ManagedLinearAlgebraProvider.Complex.cs

@@ -23,6 +23,9 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
+
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra
 {
     using System;
@@ -1482,7 +1485,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            var work = new Complex[rowsR * rowsR];
+            var work = columnsR > rowsR ? new Complex[rowsR * rowsR] : new Complex[rowsR * columnsR];
             QRFactor(r, rowsR, columnsR, q, tau, work);
         }
 
@@ -1533,10 +1536,21 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            if (work.Length < rowsR * rowsR)
+            if (columnsR > rowsR)
             {
-                work[0] = rowsR * rowsR;
-                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                if (work.Length < rowsR * rowsR)
+                {
+                    work[0] = rowsR * rowsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
+            }
+            else
+            {
+                if (work.Length < rowsR * columnsR)
+                {
+                    work[0] = rowsR * columnsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
             }
 
             CommonParallel.For(0, rowsR, i => q[(i * rowsR) + i] = Complex.One);
@@ -1553,9 +1567,139 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 ComputeQR(work, i, q, i, rowsR, i, rowsR, Control.NumberOfParallelWorkerThreads);
             }
 
-            work[0] = rowsR * rowsR;
+            work[0] = columnsR > rowsR ? rowsR * rowsR : rowsR * columnsR;
+        }
+
+        /// <summary>
+        /// Computes the QR factorization of A.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(Complex[] a, int rowsA, int columnsA, Complex[] r, Complex[] tau)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("a");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            var work = new Complex[rowsA * columnsA];
+            ThinQRFactor(a, rowsA, columnsA, r, tau, work);
         }
 
+        /// <summary>
+        /// Computes the QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <param name="work">The work array. The array must have a length of at least N,
+        /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
+        /// work size value.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(Complex[] a, int rowsA, int columnsA, Complex[] r, Complex[] tau, Complex[] work)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (work == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            if (work.Length < rowsA * columnsA)
+            {
+                work[0] = rowsA * columnsA;
+                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+            }
+
+            var minmn = Math.Min(rowsA, columnsA);
+            for (var i = 0; i < minmn; i++)
+            {
+                GenerateColumn(work, a, rowsA, i, i);
+                ComputeQR(work, i, a, i, rowsA, i + 1, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            //copy R 
+            for (var j = 0; j < columnsA; j++)
+            {
+                var rIndex = j * columnsA;
+                var aIndex = j * rowsA;
+                for (var i = 0; i < columnsA; i++)
+                {
+                    r[rIndex + i] = a[aIndex + i];
+                }
+            }
+
+            //clear A and set diagonals to 1
+            Array.Clear(a, 0, a.Length);
+            for (var i = 0; i < columnsA; i++)
+            {
+                a[i * rowsA + i] = Complex.One;
+            }
+
+            for (var i = minmn - 1; i >= 0; i--)
+            {
+                ComputeQR(work, i, a, i, rowsA, i, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            work[0] = rowsA * columnsA;
+        }
+
+
         #region QR Factor Helper functions
 
         /// <summary>
@@ -1667,46 +1811,12 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x)
+        public virtual void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
-            var work = new Complex[rows * rows];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            var work = new Complex[rows * columns];
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -1721,8 +1831,9 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, Complex[] work)
+        public virtual void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, Complex[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -1764,19 +1875,29 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
             }
 
-            if (work.Length < rows * rows)
+            if (work.Length < rows * columns)
             {
-                work[0] = rows * rows;
+                work[0] = rows * columns;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
             var clone = new Complex[a.Length];
             a.Copy(clone);
-            var q = new Complex[rows * rows];
-            QRFactor(clone, rows, columns, q, work);
-            QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x);
 
-            work[0] = rows * rows;
+            if (method == QRMethod.Full)
+            {
+                var q = new Complex[rows * rows];
+                QRFactor(clone, rows, columns, q, work);
+                QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x, method);
+            }
+            else
+            {
+                var r = new Complex[columns * columns];
+                ThinQRFactor(clone, rows, columns, r, work);
+                QRSolveFactored(clone, r, rows, columns, null, b, columnsB, x, method);
+            }
+
+            work[0] = rows *  columns;
         }
 
         /// <summary>
@@ -1795,10 +1916,11 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(Complex[] q, Complex[] r, int rowsR, int columnsR, Complex[] tau, Complex[] b, int columnsB, Complex[] x, Complex[] work)
+        public virtual void QRSolveFactored(Complex[] q, Complex[] r, int rowsR, int columnsR, Complex[] tau, Complex[] b, int columnsB, Complex[] x, Complex[] work, QRMethod method = QRMethod.Full)
         {
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x);
+            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, method);
         }
 
         /// <summary>
@@ -1806,15 +1928,16 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// </summary>
         /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[])"/>.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(Complex[] q, Complex[] r, int rowsR, int columnsR, Complex[] tau, Complex[] b, int columnsB, Complex[] x)
+        public virtual void QRSolveFactored(Complex[] q, Complex[] r, int rowsA, int columnsA, Complex[] tau, Complex[] b, int columnsB, Complex[] x, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -1836,50 +1959,63 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentNullException("q");
             }
 
-            if (r.Length != rowsR * columnsR)
+            if (rowsA < columnsA)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (q.Length != rowsR * rowsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if( method == QRMethod.Full)
             {
-                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
+            }
+
+            if (r.Length != rowsR * columnsR)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (b.Length != rowsA * columnsB)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             var sol = new Complex[b.Length];
 
             // Copy B matrix to "sol", so B data will not be changed
-            CommonParallel.For(0, b.Length, index => sol[index] = b[index]);
+            Array.Copy(b, sol, b.Length);
 
             // Compute Y = transpose(Q)*B
-            var column = new Complex[rowsR];
+            var column = new Complex[rowsA];
             for (var j = 0; j < columnsB; j++)
             {
-                var jm = j * rowsR;
-                CommonParallel.For(0, rowsR, k => column[k] = sol[jm + k]);
+                var jm = j * rowsA;
+                CommonParallel.For(0, rowsA, k => column[k] = sol[jm + k]);
                 CommonParallel.For(
-                    0,
-                    rowsR,
+                    0, 
+                    columnsA, 
                     i =>
                     {
-                        var im = i * rowsR;
+                        var im = i * rowsA;
+
                         var sum = Complex.Zero;
-                        for (var k = 0; k < rowsR; k++)
+                        for (var k = 0; k < rowsA; k++)
                         {
                             sum += q[im + k].Conjugate() * column[k];
                         }
@@ -1889,19 +2025,19 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
             }
 
             // Solve R*X = Y;
-            for (var k = columnsR - 1; k >= 0; k--)
+            for (var k = columnsA - 1; k >= 0; k--)
             {
                 var km = k * rowsR;
                 for (var j = 0; j < columnsB; j++)
                 {
-                    sol[(j * rowsR) + k] /= r[km + k];
+                    sol[(j * rowsA) + k] /= r[km + k];
                 }
 
                 for (var i = 0; i < k; i++)
                 {
                     for (var j = 0; j < columnsB; j++)
                     {
-                        var jm = j * rowsR;
+                        var jm = j * rowsA;
                         sol[jm + i] -= sol[jm + k] * r[km + i];
                     }
                 }
@@ -1909,16 +2045,16 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
 
             // Fill result matrix
             CommonParallel.For(
-                0,
-                columnsR,
+                0, 
+                columnsR, 
                 row =>
                 {
                     for (var col = 0; col < columnsB; col++)
                     {
-                        x[(col * columnsR) + row] = sol[row + (col * rowsR)];
+                        x[(col * columnsA) + row] = sol[row + (col * rowsA)];
                     }
                 });
-        }
+        }        
 
         /// <summary>
         /// Computes the singular value decomposition of A.

src/Numerics/Algorithms/LinearAlgebra/ManagedLinearAlgebraProvider.Complex32.cs

@@ -23,6 +23,10 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
+
+using System.Numerics;
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra
 {
     using System;
@@ -1478,7 +1482,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            var work = new Complex32[rowsR * rowsR];
+            var work = columnsR > rowsR ? new Complex32 [rowsR * rowsR] : new Complex32[rowsR * columnsR];
             QRFactor(r, rowsR, columnsR, q, tau, work);
         }
 
@@ -1529,10 +1533,21 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            if (work.Length < rowsR * rowsR)
+            if (columnsR > rowsR)
             {
-                work[0] = rowsR * rowsR;
-                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                if (work.Length < rowsR * rowsR)
+                {
+                    work[0] = rowsR * rowsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
+            }
+            else
+            {
+                if (work.Length < rowsR * columnsR)
+                {
+                    work[0] = rowsR * columnsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
             }
 
             CommonParallel.For(0, rowsR, i => q[(i * rowsR) + i] = Complex32.One);
@@ -1549,9 +1564,139 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 ComputeQR(work, i, q, i, rowsR, i, rowsR, Control.NumberOfParallelWorkerThreads);
             }
 
-            work[0] = rowsR * rowsR;
+            work[0] = columnsR > rowsR ? rowsR * rowsR : rowsR * columnsR;
+        }
+
+        /// <summary>
+        /// Computes the QR factorization of A.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(Complex32[] a, int rowsA, int columnsA, Complex32[] r, Complex32[] tau)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("a");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            var work = new Complex32[rowsA * columnsA];
+            ThinQRFactor(a, rowsA, columnsA, r, tau, work);
+        }
+
+        /// <summary>
+        /// Computes the QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <param name="work">The work array. The array must have a length of at least N,
+        /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
+        /// work size value.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(Complex32[] a, int rowsA, int columnsA, Complex32[] r, Complex32[] tau, Complex32[] work)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (work == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            if (work.Length < rowsA * columnsA)
+            {
+                work[0] = rowsA * columnsA;
+                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+            }
+
+            var minmn = Math.Min(rowsA, columnsA);
+            for (var i = 0; i < minmn; i++)
+            {
+                GenerateColumn(work, a, rowsA, i, i);
+                ComputeQR(work, i, a, i, rowsA, i + 1, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            //copy R 
+            for (var j = 0; j < columnsA; j++)
+            {
+                var rIndex = j * columnsA;
+                var aIndex = j * rowsA;
+                for (var i = 0; i < columnsA; i++)
+                {
+                    r[rIndex + i] = a[aIndex + i];
+                }
+            }
+
+            //clear A and set diagonals to 1
+            Array.Clear(a, 0, a.Length);
+            for (var i = 0; i < columnsA; i++)
+            {
+                a[i * rowsA + i] = Complex32.One;
+            }
+
+            for (var i = minmn - 1; i >= 0; i--)
+            {
+                ComputeQR(work, i, a, i, rowsA, i, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            work[0] = rowsA * columnsA;
         }
 
+
         #region QR Factor Helper functions
 
         /// <summary>
@@ -1663,46 +1808,12 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x)
+        public virtual void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
-            var work = new Complex32[rows * rows];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            var work = new Complex32[rows * columns];
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -1717,8 +1828,9 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work)
+        public virtual void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -1760,19 +1872,29 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (work.Length < rows * rows)
+            if (work.Length < rows * columns)
             {
-                work[0] = rows * rows;
+                work[0] = rows * columns;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
             var clone = new Complex32[a.Length];
             a.Copy(clone);
-            var q = new Complex32[rows * rows];
-            QRFactor(clone, rows, columns, q, work);
-            QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x);
 
-            work[0] = rows * rows;
+            if (method == QRMethod.Full)
+            {
+                var q = new Complex32[rows * rows];
+                QRFactor(clone, rows, columns, q, work);
+                QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x, method);
+            }
+            else
+            {
+                var r = new Complex32[columns * columns];
+                ThinQRFactor(clone, rows, columns, r, work);
+                QRSolveFactored(clone, r, rows, columns, null, b, columnsB, x, method);
+            }
+
+            work[0] = rows * columns;
         }
 
         /// <summary>
@@ -1791,10 +1913,11 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsR, int columnsR, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work)
+        public virtual void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsR, int columnsR, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work, QRMethod method = QRMethod.Full)
         {
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x);
+            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, method);
         }
 
         /// <summary>
@@ -1802,15 +1925,16 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// </summary>
         /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[])"/>.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsR, int columnsR, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x)
+        public virtual void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsA, int columnsA, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -1832,50 +1956,63 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentNullException("q");
             }
 
-            if (r.Length != rowsR * columnsR)
+            if (rowsA < columnsA)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (q.Length != rowsR * rowsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if (method == QRMethod.Full)
             {
-                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
             }
 
-            if (rowsR < columnsR)
+            if (b.Length != rowsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
+            }
+
+            if (x.Length != columnsA * columnsB)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             var sol = new Complex32[b.Length];
 
             // Copy B matrix to "sol", so B data will not be changed
-            CommonParallel.For(0, b.Length, index => sol[index] = b[index]);
+            Array.Copy(b, sol, b.Length);
 
             // Compute Y = transpose(Q)*B
-            var column = new Complex32[rowsR];
+            var column = new Complex32[rowsA];
             for (var j = 0; j < columnsB; j++)
             {
-                var jm = j * rowsR;
-                CommonParallel.For(0, rowsR, k => column[k] = sol[jm + k]);
+                var jm = j * rowsA;
+                CommonParallel.For(0, rowsA, k => column[k] = sol[jm + k]);
                 CommonParallel.For(
                     0,
-                    rowsR,
+                    columnsA,
                     i =>
                     {
-                        var im = i * rowsR;
+                        var im = i * rowsA;
+
                         var sum = Complex32.Zero;
-                        for (var k = 0; k < rowsR; k++)
+                        for (var k = 0; k < rowsA; k++)
                         {
                             sum += q[im + k].Conjugate() * column[k];
                         }
@@ -1885,19 +2022,19 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
             }
 
             // Solve R*X = Y;
-            for (var k = columnsR - 1; k >= 0; k--)
+            for (var k = columnsA - 1; k >= 0; k--)
             {
                 var km = k * rowsR;
                 for (var j = 0; j < columnsB; j++)
                 {
-                    sol[(j * rowsR) + k] /= r[km + k];
+                    sol[(j * rowsA) + k] /= r[km + k];
                 }
 
                 for (var i = 0; i < k; i++)
                 {
                     for (var j = 0; j < columnsB; j++)
                     {
-                        var jm = j * rowsR;
+                        var jm = j * rowsA;
                         sol[jm + i] -= sol[jm + k] * r[km + i];
                     }
                 }
@@ -1911,7 +2048,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 {
                     for (var col = 0; col < columnsB; col++)
                     {
-                        x[(col * columnsR) + row] = sol[row + (col * rowsR)];
+                        x[(col * columnsA) + row] = sol[row + (col * rowsA)];
                     }
                 });
         }

src/Numerics/Algorithms/LinearAlgebra/ManagedLinearAlgebraProvider.Double.cs

@@ -23,6 +23,9 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
+
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra
 {
     using System;
@@ -1339,6 +1342,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// QR factorization.</param>
         /// <param name="tau">A min(m,n) vector. On exit, contains additional information
         /// to be used by the QR solve routine.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
         public virtual void QRFactor(double[] r, int rowsR, int columnsR, double[] q, double[] tau)
         {
@@ -1367,7 +1371,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            var work = new double[rowsR * rowsR];
+
+            var work = columnsR > rowsR ? new double[rowsR * rowsR] : new double[rowsR * columnsR];
             QRFactor(r, rowsR, columnsR, q, tau, work);
         }
 
@@ -1418,10 +1423,21 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            if (work.Length < rowsR * rowsR)
+            if (columnsR > rowsR)
             {
-                work[0] = rowsR * rowsR;
-                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                if (work.Length < rowsR * rowsR)
+                {
+                    work[0] = rowsR * rowsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
+            }
+            else
+            {
+                if (work.Length < rowsR * columnsR)
+                {
+                    work[0] = rowsR * columnsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
             }
 
             CommonParallel.For(0, rowsR, i => q[(i * rowsR) + i] = 1.0);
@@ -1438,7 +1454,136 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 ComputeQR(work, i, q, i, rowsR, i, rowsR, Control.NumberOfParallelWorkerThreads);
             }
 
-            work[0] = rowsR * rowsR;
+            work[0] = columnsR > rowsR ? rowsR * rowsR : rowsR * columnsR;
+        }
+
+        /// <summary>
+        /// Computes the QR factorization of A.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(double[] a, int rowsA, int columnsA, double[] r, double[] tau)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("a");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            var work = new double[rowsA * columnsA];
+            ThinQRFactor(a, rowsA, columnsA, r, tau, work);
+        }
+
+        /// <summary>
+        /// Computes the thin QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <param name="work">The work array. The array must have a length of at least N,
+        /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
+        /// work size value.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(double[] a, int rowsA, int columnsA, double[] r, double[] tau, double[] work)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (work == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            if (work.Length < rowsA * columnsA)
+            {
+                work[0] = rowsA*columnsA;
+                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+            }
+
+            var minmn = Math.Min(rowsA, columnsA);
+            for (var i = 0; i < minmn; i++)
+            {
+                GenerateColumn(work, a, rowsA, i, i);
+                ComputeQR(work, i, a, i, rowsA, i + 1, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            //copy R 
+            for (var j = 0; j < columnsA; j++ )
+            {
+                var rIndex = j * columnsA;
+                var aIndex = j * rowsA;
+                for (var i = 0; i < columnsA; i++)
+                {
+                    r[rIndex + i] = a[aIndex+i];
+                }
+            }
+
+            //clear A and set diagonals to 1
+            Array.Clear(a, 0, a.Length);
+            for (var i = 0; i < columnsA; i++ )
+            {
+                a[i * rowsA + i] = 1.0;
+            }
+
+            for (var i = minmn - 1; i >= 0; i--)
+            {
+                ComputeQR(work, i, a, i, rowsA, i, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            work[0] = rowsA * columnsA;
         }
 
         #region QR Factor Helper functions
@@ -1553,46 +1698,12 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x)
+        public virtual void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
-            var work = new double[rows * rows];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            var work = new double[rows * columns];
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -1607,8 +1718,9 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x, double[] work)
+        public virtual void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x, double[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -1650,19 +1762,28 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (work.Length < rows * rows)
+            if (work.Length < rows * columns)
             {
-                work[0] = rows * rows;
+                work[0] = rows * columns;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
             var clone = new double[a.Length];
-            a.Copy(clone); 
-            var q = new double[rows * rows];
-            QRFactor(clone, rows, columns, q, work);
-            QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x);
+            a.Copy(clone);
+
+           if (method == QRMethod.Full)
+            {
+                var q = new double[rows * rows];
+                QRFactor(clone, rows, columns, q, work);
+                QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x, method);
+            } else
+            {
+                var r = new double[columns * columns];
+                ThinQRFactor(clone, rows, columns, r, work);
+                QRSolveFactored(clone, r, rows, columns, null, b, columnsB, x, method);
+            }
 
-            work[0] = rows * rows;
+            work[0] = rows * columns;
         }
 
         /// <summary>
@@ -1671,8 +1792,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
@@ -1681,10 +1802,11 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(double[] q, double[] r, int rowsR, int columnsR, double[] tau, double[] b, int columnsB, double[] x, double[] work)
+        public virtual void QRSolveFactored(double[] q, double[] r, int rowsA, int columnsA, double[] tau, double[] b, int columnsB, double[] x, double[] work, QRMethod method = QRMethod.Full)
         {
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x);
+            QRSolveFactored(q, r, rowsA, columnsA, tau, b, columnsB, x, method);
         }
 
         /// <summary>
@@ -1692,15 +1814,16 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// </summary>
         /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(double[] q, double[] r, int rowsR, int columnsR, double[] tau, double[] b, int columnsB, double[] x)
+        public virtual void QRSolveFactored(double[] q, double[] r, int rowsA, int columnsA, double[] tau, double[] b, int columnsB, double[] x, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -1722,29 +1845,41 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentNullException("q");
             }
 
-            if (r.Length != rowsR * columnsR)
+            if (rowsA < columnsA)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (q.Length != rowsR * rowsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if( method == QRMethod.Full)
             {
-                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
+            }
+
+            if (b.Length != rowsA * columnsB)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             var sol = new double[b.Length];
@@ -1753,20 +1888,20 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
             Buffer.BlockCopy(b, 0, sol, 0, b.Length * Constants.SizeOfDouble);
 
             // Compute Y = transpose(Q)*B
-            var column = new double[rowsR];
+            var column = new double[rowsA];
             for (var j = 0; j < columnsB; j++)
             {
-                var jm = j * rowsR;
-                CommonParallel.For(0, rowsR, k => column[k] = sol[jm + k]);
+                var jm = j * rowsA;
+                CommonParallel.For(0, rowsA, k => column[k] = sol[jm + k]);
                 CommonParallel.For(
                     0, 
-                    rowsR, 
+                    columnsA, 
                     i =>
                     {
-                        var im = i * rowsR;
+                        var im = i * rowsA;
 
                         var sum = 0.0;
-                        for (var k = 0; k < rowsR; k++)
+                        for (var k = 0; k < rowsA; k++)
                         {
                             sum += q[im + k] * column[k];
                         }
@@ -1776,19 +1911,19 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
             }
 
             // Solve R*X = Y;
-            for (var k = columnsR - 1; k >= 0; k--)
+            for (var k = columnsA - 1; k >= 0; k--)
             {
                 var km = k * rowsR;
                 for (var j = 0; j < columnsB; j++)
                 {
-                    sol[(j * rowsR) + k] /= r[km + k];
+                    sol[(j * rowsA) + k] /= r[km + k];
                 }
 
                 for (var i = 0; i < k; i++)
                 {
                     for (var j = 0; j < columnsB; j++)
                     {
-                        var jm = j * rowsR;
+                        var jm = j * rowsA;
                         sol[jm + i] -= sol[jm + k] * r[km + i];
                     }
                 }
@@ -1802,7 +1937,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 {
                     for (var col = 0; col < columnsB; col++)
                     {
-                        x[(col * columnsR) + row] = sol[row + (col * rowsR)];
+                        x[(col * columnsA) + row] = sol[row + (col * rowsA)];
                     }
                 });
         }

src/Numerics/Algorithms/LinearAlgebra/ManagedLinearAlgebraProvider.Single.cs

@@ -23,6 +23,9 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
+
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra
 {
     using System;
@@ -1368,7 +1371,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            var work = new float[rowsR * rowsR];
+            var work = columnsR > rowsR ? new float[rowsR * rowsR] : new float[rowsR * columnsR];
             QRFactor(r, rowsR, columnsR, q, tau, work);
         }
 
@@ -1419,10 +1422,21 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
             }
 
-            if (work.Length < rowsR * rowsR)
+            if (columnsR > rowsR)
             {
-                work[0] = rowsR * rowsR;
-                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                if (work.Length < rowsR * rowsR)
+                {
+                    work[0] = rowsR * rowsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
+            }
+            else
+            {
+                if (work.Length < rowsR * columnsR)
+                {
+                    work[0] = rowsR * columnsR;
+                    throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+                }
             }
 
             CommonParallel.For(0, rowsR, i => q[(i * rowsR) + i] = 1.0f);
@@ -1439,9 +1453,139 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 ComputeQR(work, i, q, i, rowsR, i, rowsR, Control.NumberOfParallelWorkerThreads);
             }
 
-            work[0] = rowsR * rowsR;
+            work[0] = columnsR > rowsR ? rowsR * rowsR : rowsR * columnsR;
         }
 
+        /// <summary>
+        /// Computes the QR factorization of A.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(float[] a, int rowsA, int columnsA, float[] r, float[] tau)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("a");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            var work = new float[rowsA * columnsA];
+            ThinQRFactor(a, rowsA, columnsA, r, tau, work);
+        }
+
+        /// <summary>
+        /// Computes the QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="a">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <param name="work">The work array. The array must have a length of at least N,
+        /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
+        /// work size value.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        public virtual void ThinQRFactor(float[] a, int rowsA, int columnsA, float[] r, float[] tau, float[] work)
+        {
+            if (r == null)
+            {
+                throw new ArgumentNullException("r");
+            }
+
+            if (a == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (work == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (a.Length != rowsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "a");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
+            }
+
+            if (r.Length != columnsA * columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            if (work.Length < rowsA * columnsA)
+            {
+                work[0] = rowsA * columnsA;
+                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+            }
+
+            var minmn = Math.Min(rowsA, columnsA);
+            for (var i = 0; i < minmn; i++)
+            {
+                GenerateColumn(work, a, rowsA, i, i);
+                ComputeQR(work, i, a, i, rowsA, i + 1, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            //copy R 
+            for (var j = 0; j < columnsA; j++)
+            {
+                var rIndex = j * columnsA;
+                var aIndex = j * rowsA;
+                for (var i = 0; i < columnsA; i++)
+                {
+                    r[rIndex + i] = a[aIndex + i];
+                }
+            }
+
+            //clear A and set diagonals to 1
+            Array.Clear(a, 0, a.Length);
+            for (var i = 0; i < columnsA; i++)
+            {
+                a[i * rowsA + i] = 1.0f;
+            }
+
+            for (var i = minmn - 1; i >= 0; i--)
+            {
+                ComputeQR(work, i, a, i, rowsA, i, columnsA, Control.NumberOfParallelWorkerThreads);
+            }
+
+            work[0] = rowsA * columnsA;
+        }
+
+
         #region QR Factor Helper functions
 
         /// <summary>
@@ -1554,46 +1698,12 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x)
+        public virtual void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
-            var work = new float[rows * rows];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            var work = new float[rows * columns];
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -1608,8 +1718,9 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x, float[] work)
+        public virtual void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x, float[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -1651,19 +1762,29 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (work.Length < rows * rows)
+            if (work.Length < rows * columns)
             {
-                work[0] = rows * rows;
+                work[0] = rows * columns;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
             var clone = new float[a.Length];
-            a.Copy(clone); 
-            var q = new float[rows * rows];
-            QRFactor(clone, rows, columns, q, work);
-            QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x);
+            a.Copy(clone);
 
-            work[0] = rows * rows;
+            if (method == QRMethod.Full)
+            {
+                var q = new float[rows * rows];
+                QRFactor(clone, rows, columns, q, work);
+                QRSolveFactored(q, clone, rows, columns, null, b, columnsB, x, method);
+            }
+            else
+            {
+                var r = new float[columns * columns];
+                ThinQRFactor(clone, rows, columns, r, work);
+                QRSolveFactored(clone, r, rows, columns, null, b, columnsB, x, method);
+            }
+
+            work[0] = rows * columns;
         }
 
         /// <summary>
@@ -1672,8 +1793,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
@@ -1682,9 +1803,11 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
-        public virtual void QRSolveFactored(float[] q, float[] r, int rowsR, int columnsR, float[] tau, float[] b, int columnsB, float[] x, float[] work)
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
+        /// <remarks>Rows must be greater or equal to columns.</remarks>
+        public virtual void QRSolveFactored(float[] q, float[] r, int rowsA, int columnsA, float[] tau, float[] b, int columnsB, float[] x, float[] work, QRMethod method = QRMethod.Full)
         {
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x);
+            QRSolveFactored(q, r, rowsA, columnsA, tau, b, columnsB, x, method);
         }
 
         /// <summary>
@@ -1692,15 +1815,16 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
         /// </summary>
         /// <param name="q">The Q matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public virtual void QRSolveFactored(float[] q, float[] r, int rowsR, int columnsR, float[] tau, float[] b, int columnsB, float[] x)
+        public virtual void QRSolveFactored(float[] q, float[] r, int rowsA, int columnsA, float[] tau, float[] b, int columnsB, float[] x, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -1722,29 +1846,41 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 throw new ArgumentNullException("q");
             }
 
-            if (r.Length != rowsR * columnsR)
+            if (rowsA < columnsA)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                throw new ArgumentException(Resources.RowsLessThanColumns);
             }
 
-            if (q.Length != rowsR * rowsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if (method == QRMethod.Full)
             {
-                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * rowsR"), "q");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
+            }
+
+            if (b.Length != rowsA * columnsB)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             var sol = new float[b.Length];
@@ -1753,20 +1889,20 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
             Buffer.BlockCopy(b, 0, sol, 0, b.Length * Constants.SizeOfFloat);
 
             // Compute Y = transpose(Q)*B
-            var column = new float[rowsR];
+            var column = new float[rowsA];
             for (var j = 0; j < columnsB; j++)
             {
-                var jm = j * rowsR;
-                CommonParallel.For(0, rowsR, k => column[k] = sol[jm + k]);
+                var jm = j * rowsA;
+                CommonParallel.For(0, rowsA, k => column[k] = sol[jm + k]);
                 CommonParallel.For(
                     0,
-                    rowsR,
+                    columnsA,
                     i =>
                     {
-                        var im = i * rowsR;
+                        var im = i * rowsA;
 
                         var sum = 0.0f;
-                        for (var k = 0; k < rowsR; k++)
+                        for (var k = 0; k < rowsA; k++)
                         {
                             sum += q[im + k] * column[k];
                         }
@@ -1776,19 +1912,19 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
             }
 
             // Solve R*X = Y;
-            for (var k = columnsR - 1; k >= 0; k--)
+            for (var k = columnsA - 1; k >= 0; k--)
             {
                 var km = k * rowsR;
                 for (var j = 0; j < columnsB; j++)
                 {
-                    sol[(j * rowsR) + k] /= r[km + k];
+                    sol[(j * rowsA) + k] /= r[km + k];
                 }
 
                 for (var i = 0; i < k; i++)
                 {
                     for (var j = 0; j < columnsB; j++)
                     {
-                        var jm = j * rowsR;
+                        var jm = j * rowsA;
                         sol[jm + i] -= sol[jm + k] * r[km + i];
                     }
                 }
@@ -1802,7 +1938,7 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra
                 {
                     for (var col = 0; col < columnsB; col++)
                     {
-                        x[(col * columnsR) + row] = sol[row + (col * rowsR)];
+                        x[(col * columnsA) + row] = sol[row + (col * rowsA)];
                     }
                 });
         }

src/Numerics/Algorithms/LinearAlgebra/Mkl/MklLinearAlgebraProvider.Complex.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
 {
     using System;
@@ -666,46 +668,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(Complex[] a, int rows, int columns,  Complex[] b, int columnsB,  Complex[] x)
+        [SecuritySafeCritical]
+        public override void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
             var work = new Complex[columns * Control.BlockSize];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -720,8 +689,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, Complex[] work)
+        [SecuritySafeCritical]
+        public override void QRSolve(Complex[] a, int rows, int columns, Complex[] b, int columnsB, Complex[] x, Complex[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -769,7 +740,14 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.z_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+               SafeNativeMethods.z_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
+            else
+            {
+                SafeNativeMethods.z_thin_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
         }
 
         /// <summary>
@@ -784,57 +762,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
         [SecuritySafeCritical]
-        public override void QRSolveFactored(Complex[] q, Complex[] r, int rowsR, int columnsR, Complex[] tau, Complex[] b, int columnsB, Complex[] x)
+        public override void QRSolveFactored(Complex[] q, Complex[] r, int rowsR, int columnsR, Complex[] tau, Complex[] b, int columnsB, Complex[] x, QRMethod method = QRMethod.Full)
         {
-            if (r == null)
-            {
-                throw new ArgumentNullException("r");
-            }
-
-            if (q == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (r.Length != rowsR * columnsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
-            }
-
-            if (q.Length != rowsR * rowsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
-            }
-
-            if (b.Length != rowsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columnsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rowsR < columnsR)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-            
             var work = new Complex[columnsR * Control.BlockSize];
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work);
+            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -843,8 +777,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex[],int,int,Complex[],Complex[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
@@ -853,8 +787,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolveFactored(Complex[] q, Complex[] r, int rowsR, int columnsR, Complex[] tau, Complex[] b, int columnsB, Complex[] x, Complex[] work)
+        [SecuritySafeCritical]
+        public override void QRSolveFactored(Complex[] q, Complex[] r, int rowsA, int columnsA, Complex[] tau, Complex[] b, int columnsB, Complex[] x, Complex[] work, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -881,38 +817,54 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentNullException("work");
             }
 
-            if (r.Length != rowsR * columnsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if (method == QRMethod.Full)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (q.Length != rowsR * rowsR)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (b.Length != rowsA * columnsB)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             if (work.Length < 1)
             {
-                work[0] = rowsR * Control.BlockSize;
+                work[0] = rowsA * Control.BlockSize;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.z_qr_solve_factored(rowsR, columnsR, columnsB, r, b, tau, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.z_qr_solve_factored(rowsA, columnsA, columnsB, r, b, tau, x, work, work.Length);
+            }
+            else
+            {
+                // we don't have access to the raw Q matrix any more(it is stored in R in the full QR), need to think about this.
+                // let just call the managed version in the meantime. The heavy lifting has already been done. -marcus
+                base.QRSolveFactored(q, r, rowsA, columnsA, tau, b, columnsB, x, QRMethod.Thin);
+            }
         }
 
         /// <summary>

src/Numerics/Algorithms/LinearAlgebra/Mkl/MklLinearAlgebraProvider.Complex32.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
 {
     using System;
@@ -665,46 +667,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(Complex32[] a, int rows, int columns,  Complex32[] b, int columnsB,  Complex32[] x)
+        [SecuritySafeCritical]
+        public override void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
             var work = new Complex32[columns * Control.BlockSize];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -719,8 +688,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work)
+        [SecuritySafeCritical]
+        public override void QRSolve(Complex32[] a, int rows, int columns, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -768,7 +739,14 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.c_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.c_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
+            else
+            {
+                SafeNativeMethods.c_thin_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
         }
 
         /// <summary>
@@ -783,57 +761,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
         [SecuritySafeCritical]
-        public override void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsR, int columnsR, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x)
+        public override void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsR, int columnsR, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x, QRMethod method = QRMethod.Full)
         {
-            if (r == null)
-            {
-                throw new ArgumentNullException("r");
-            }
-
-            if (q == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (r.Length != rowsR * columnsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
-            }
-
-            if (q.Length != rowsR * rowsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
-            }
-
-            if (b.Length != rowsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columnsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rowsR < columnsR)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-            
             var work = new Complex32[columnsR * Control.BlockSize];
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work);
+            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -842,8 +776,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(Complex32[],int,int,Complex32[],Complex32[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
@@ -852,8 +786,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsR, int columnsR, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work)
+        [SecuritySafeCritical]
+        public override void QRSolveFactored(Complex32[] q, Complex32[] r, int rowsA, int columnsA, Complex32[] tau, Complex32[] b, int columnsB, Complex32[] x, Complex32[] work, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -880,38 +816,54 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentNullException("work");
             }
 
-            if (r.Length != rowsR * columnsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if (method == QRMethod.Full)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (q.Length != rowsR * rowsR)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (b.Length != rowsA * columnsB)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             if (work.Length < 1)
             {
-                work[0] = rowsR * Control.BlockSize;
+                work[0] = rowsA * Control.BlockSize;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.c_qr_solve_factored(rowsR, columnsR, columnsB, r, b, tau, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.c_qr_solve_factored(rowsA, columnsA, columnsB, r, b, tau, x, work, work.Length);
+            }
+            else
+            {
+                // we don't have access to the raw Q matrix any more(it is stored in R in the full QR), need to think about this.
+                // let just call the managed version in the meantime. The heavy lifting has already been done. -marcus
+                base.QRSolveFactored(q, r, rowsA, columnsA, tau, b, columnsB, x, QRMethod.Thin);
+            }
         }
 
         /// <summary>

src/Numerics/Algorithms/LinearAlgebra/Mkl/MklLinearAlgebraProvider.double.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
 {
     using System;
@@ -657,54 +659,125 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         }
 
         /// <summary>
-        /// Solves A*X=B for X using QR factorization of A.
+        /// Computes the thin QR factorization of A where M &gt; N.
         /// </summary>
-        /// <param name="a">The A matrix.</param>
-        /// <param name="rows">The number of rows in the A matrix.</param>
-        /// <param name="columns">The number of columns in the A matrix.</param>
-        /// <param name="b">The B matrix.</param>
-        /// <param name="columnsB">The number of columns of B.</param>
-        /// <param name="x">On exit, the solution matrix.</param>
-        /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(double[] a, int rows, int columns,  double[] b, int columnsB,  double[] x)
+        /// <param name="q">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        [SecuritySafeCritical]
+        public override void ThinQRFactor(double[] q, int rowsA, int columnsA, double[] r, double[] tau)
         {
-            if (a == null)
+            if (r == null)
             {
-                throw new ArgumentNullException("a");
+                throw new ArgumentNullException("r");
             }
 
-            if (b == null)
+            if (q == null)
             {
-                throw new ArgumentNullException("b");
+                throw new ArgumentNullException("q");
             }
 
-            if (x == null)
+            if (q.Length != rowsA * columnsA)
             {
-                throw new ArgumentNullException("x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "q");
             }
 
-            if (a.Length != rows * columns)
+            if (tau.Length < Math.Min(rowsA, columnsA))
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
             }
 
-            if (b.Length != rows * columnsB)
+            if (r.Length != columnsA*columnsA)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
             }
 
-            if (x.Length != columns * columnsB)
+            var work = new double[columnsA * Control.BlockSize];
+            SafeNativeMethods.d_qr_thin_factor(rowsA, columnsA, q, tau, r, work, work.Length);
+
+        }
+
+
+        /// <summary>
+        /// Computes the thin QR factorization of A where M &gt; N.
+        /// </summary>
+        /// <param name="q">On entry, it is the M by N A matrix to factor. On exit,
+        /// it is overwritten with the Q matrix of the QR factorization.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
+        /// <param name="r">On exit, A N by N matrix that holds the R matrix of the
+        /// QR factorization.</param>
+        /// <param name="tau">A min(m,n) vector. On exit, contains additional information
+        /// to be used by the QR solve routine.</param>
+        /// <param name="work">The work array. The array must have a length of at least N,
+        /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
+        /// work size value.</param>
+        /// <remarks>This is similar to the GEQRF and ORGQR LAPACK routines.</remarks>
+        [SecuritySafeCritical]
+        public override void ThinQRFactor(double[] q, int rowsA, int columnsA, double[] r, double[] tau, double[] work)
+        {
+            if (r == null)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentNullException("r");
             }
 
-            if (rows < columns)
+            if (q == null)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentNullException("q");
+            }
+
+            if (work == null)
+            {
+                throw new ArgumentNullException("q");
+            }
+
+            if (q.Length != rowsA*columnsA)
+            {
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, "rowsR * columnsR"), "q");
+            }
+
+            if (tau.Length < Math.Min(rowsA, columnsA))
+            {
+                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, "min(m,n)"), "tau");
             }
 
+            if (r.Length != columnsA*columnsA)
+            {
+                throw new ArgumentException(
+                    string.Format(Resources.ArgumentArrayWrongLength, "columnsA * columnsA"), "r");
+            }
+
+            if (work.Length < columnsA*Control.BlockSize)
+            {
+                work[0] = columnsA*Control.BlockSize;
+                throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
+            }
+
+            SafeNativeMethods.d_qr_thin_factor(rowsA, columnsA, q, tau, r, work, work.Length);
+        }
+
+        /// <summary>
+        /// Solves A*X=B for X using QR factorization of A.
+        /// </summary>
+        /// <param name="a">The A matrix.</param>
+        /// <param name="rows">The number of rows in the A matrix.</param>
+        /// <param name="columns">The number of columns in the A matrix.</param>
+        /// <param name="b">The B matrix.</param>
+        /// <param name="columnsB">The number of columns of B.</param>
+        /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
+        /// <remarks>Rows must be greater or equal to columns.</remarks>
+        [SecuritySafeCritical]
+        public override void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x, QRMethod method = QRMethod.Full)
+        {
             var work = new double[columns * Control.BlockSize];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -719,8 +792,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x, double[] work)
+        [SecuritySafeCritical]
+        public override void QRSolve(double[] a, int rows, int columns, double[] b, int columnsB, double[] x, double[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -768,7 +843,14 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.d_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.d_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
+            else
+            {
+                SafeNativeMethods.d_thin_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
         }
 
         /// <summary>
@@ -783,57 +865,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
         [SecuritySafeCritical]
-        public override void QRSolveFactored(double[] q, double[] r, int rowsR, int columnsR, double[] tau, double[] b, int columnsB, double[] x)
+        public override void QRSolveFactored(double[] q, double[] r, int rowsR, int columnsR, double[] tau, double[] b, int columnsB, double[] x, QRMethod method = QRMethod.Full)
         {
-            if (r == null)
-            {
-                throw new ArgumentNullException("r");
-            }
-
-            if (q == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (r.Length != rowsR * columnsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
-            }
-
-            if (q.Length != rowsR * rowsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
-            }
-
-            if (b.Length != rowsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columnsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rowsR < columnsR)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-            
             var work = new double[columnsR * Control.BlockSize];
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work);
+            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -842,8 +880,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(double[],int,int,double[],double[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
@@ -852,8 +890,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolveFactored(double[] q, double[] r, int rowsR, int columnsR, double[] tau, double[] b, int columnsB, double[] x, double[] work)
+        [SecuritySafeCritical]
+        public override void QRSolveFactored(double[] q, double[] r, int rowsA, int columnsA, double[] tau, double[] b, int columnsB, double[] x, double[] work, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -880,38 +920,54 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentNullException("work");
             }
 
-            if (r.Length != rowsR * columnsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if( method == QRMethod.Full)
+            {
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (q.Length != rowsR * rowsR)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (b.Length != rowsA * columnsB)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             if (work.Length < 1)
             {
-                work[0] = rowsR * Control.BlockSize;
+                work[0] = rowsA * Control.BlockSize;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.d_qr_solve_factored(rowsR, columnsR, columnsB, r, b, tau, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.d_qr_solve_factored(rowsA, columnsA, columnsB, r, b, tau, x, work, work.Length);
+            }
+            else
+            {
+                // we don't have access to the raw Q matrix any more(it is stored in R in the full QR), need to think about this.
+                // let just call the managed version in the meantime. The heavy lifting has already been done. -marcus
+                base.QRSolveFactored(q, r, rowsA, columnsA, tau, b, columnsB, x, QRMethod.Thin);
+            }
         }
 
         /// <summary>

src/Numerics/Algorithms/LinearAlgebra/Mkl/MklLinearAlgebraProvider.float.cs

@@ -32,6 +32,8 @@
    Last generated on UTC 2011-04-17 06:45:23Z
 */
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
 {
     using System;
@@ -669,46 +671,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(float[] a, int rows, int columns,  float[] b, int columnsB,  float[] x)
+        [SecuritySafeCritical]
+        public override void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x, QRMethod method = QRMethod.Full)
         {
-            if (a == null)
-            {
-                throw new ArgumentNullException("a");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("b");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("x");
-            }
-
-            if (a.Length != rows * columns)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "a");
-            }
-
-            if (b.Length != rows * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columns * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rows < columns)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-
             var work = new float[columns * Control.BlockSize];
-            QRSolve(a, rows, columns, b, columnsB, x, work);
+            QRSolve(a, rows, columns, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -723,8 +692,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x, float[] work)
+        [SecuritySafeCritical]
+        public override void QRSolve(float[] a, int rows, int columns, float[] b, int columnsB, float[] x, float[] work, QRMethod method = QRMethod.Full)
         {
             if (a == null)
             {
@@ -772,7 +743,14 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.s_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.s_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
+            else
+            {
+                SafeNativeMethods.s_thin_qr_solve(rows, columns, columnsB, a, b, x, work, work.Length);
+            }
         }
 
         /// <summary>
@@ -787,57 +765,13 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="b">The B matrix.</param>
         /// <param name="columnsB">The number of columns of B.</param>
         /// <param name="x">On exit, the solution matrix.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
         [SecuritySafeCritical]
-        public override void QRSolveFactored(float[] q, float[] r, int rowsR, int columnsR, float[] tau, float[] b, int columnsB, float[] x)
+        public override void QRSolveFactored(float[] q, float[] r, int rowsR, int columnsR, float[] tau, float[] b, int columnsB, float[] x, QRMethod method = QRMethod.Full)
         {
-            if (r == null)
-            {
-                throw new ArgumentNullException("r");
-            }
-
-            if (q == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (b == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (x == null)
-            {
-                throw new ArgumentNullException("q");
-            }
-
-            if (r.Length != rowsR * columnsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
-            }
-
-            if (q.Length != rowsR * rowsR)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
-            }
-
-            if (b.Length != rowsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
-            }
-
-            if (x.Length != columnsR * columnsB)
-            {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
-            }
-
-            if (rowsR < columnsR)
-            {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
-            }
-            
             var work = new float[columnsR * Control.BlockSize];
-            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work);
+            QRSolveFactored(q, r, rowsR, columnsR, tau, b, columnsB, x, work, method);
         }
 
         /// <summary>
@@ -846,8 +780,8 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="q">The Q matrix obtained by QR factor. This is only used for the managed provider and can be
         /// <c>null</c> for the native provider. The native provider uses the Q portion stored in the R matrix.</param>
         /// <param name="r">The R matrix obtained by calling <see cref="QRFactor(float[],int,int,float[],float[])"/>. </param>
-        /// <param name="rowsR">The number of rows in the A matrix.</param>
-        /// <param name="columnsR">The number of columns in the A matrix.</param>
+        /// <param name="rowsA">The number of rows in the A matrix.</param>
+        /// <param name="columnsA">The number of columns in the A matrix.</param>
         /// <param name="tau">Contains additional information on Q. Only used for the native solver
         /// and can be <c>null</c> for the managed provider.</param>
         /// <param name="b">On entry the B matrix; on exit the X matrix.</param>
@@ -856,8 +790,10 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         /// <param name="work">The work array - only used in the native provider. The array must have a length of at least N,
         /// but should be N*blocksize. The blocksize is machine dependent. On exit, work[0] contains the optimal
         /// work size value.</param>
+        /// <param name="method">The type of QR factorization to perform. <seealso cref="QRMethod"/></param>
         /// <remarks>Rows must be greater or equal to columns.</remarks>
-        public override void QRSolveFactored(float[] q, float[] r, int rowsR, int columnsR, float[] tau, float[] b, int columnsB, float[] x, float[] work)
+        [SecuritySafeCritical]
+        public override void QRSolveFactored(float[] q, float[] r, int rowsA, int columnsA, float[] tau, float[] b, int columnsB, float[] x, float[] work, QRMethod method = QRMethod.Full)
         {
             if (r == null)
             {
@@ -884,38 +820,54 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
                 throw new ArgumentNullException("work");
             }
 
-            if (r.Length != rowsR * columnsR)
+            int rowsQ, columnsQ, rowsR, columnsR;
+            if (method == QRMethod.Full)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "r");
+                rowsQ = columnsQ = rowsR = rowsA;
+                columnsR = columnsA;
+            }
+            else
+            {
+                rowsQ = rowsA;
+                columnsQ = rowsR = columnsR = columnsA;
             }
 
-            if (q.Length != rowsR * rowsR)
+            if (r.Length != rowsR * columnsR)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "q");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsR * columnsR), "r");
             }
 
-            if (b.Length != rowsR * columnsB)
+            if (q.Length != rowsQ * columnsQ)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "b");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsQ * columnsQ), "q");
             }
 
-            if (x.Length != columnsR * columnsB)
+            if (b.Length != rowsA * columnsB)
             {
-                throw new ArgumentException(Resources.ArgumentArraysSameLength, "x");
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, rowsA * columnsB), "b");
             }
 
-            if (rowsR < columnsR)
+            if (x.Length != columnsA * columnsB)
             {
-                throw new ArgumentException(Resources.RowsLessThanColumns);
+                throw new ArgumentException(string.Format(Resources.ArgumentArrayWrongLength, columnsA * columnsB), "x");
             }
 
             if (work.Length < 1)
             {
-                work[0] = rowsR * Control.BlockSize;
+                work[0] = rowsA * Control.BlockSize;
                 throw new ArgumentException(Resources.WorkArrayTooSmall, "work");
             }
 
-            SafeNativeMethods.s_qr_solve_factored(rowsR, columnsR, columnsB, r, b, tau, x, work, work.Length);
+            if (method == QRMethod.Full)
+            {
+                SafeNativeMethods.s_qr_solve_factored(rowsA, columnsA, columnsB, r, b, tau, x, work, work.Length);
+            }
+            else
+            {
+                // we don't have access to the raw Q matrix any more(it is stored in R in the full QR), need to think about this.
+                // let just call the managed version in the meantime. The heavy lifting has already been done. -marcus
+                base.QRSolveFactored(q, r, rowsA, columnsA, tau, b, columnsB, x, QRMethod.Thin);
+            }
         }
 
         /// <summary>

src/Numerics/Algorithms/LinearAlgebra/Mkl/SafeNativeMethods.cs

@@ -218,6 +218,18 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
         internal static extern int z_qr_factor(int m, int n, [In, Out] Complex[] r, [In, Out] Complex[] tau, [In, Out] Complex[] q, [In, Out] Complex[] work, int len);
 
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int s_qr_thin_factor(int m, int n, [In, Out] float[] q, [In, Out] float[] tau, [In, Out] float[] r, [In, Out] float[] work, int len);
+
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int d_qr_thin_factor(int m, int n, [In, Out] double[] q, [In, Out] double[] tau, [In, Out] double[] r, [In, Out] double[] work, int len);
+
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int c_qr_thin_factor(int m, int n, [In, Out] Complex32[] q, [In, Out] Complex32[] tau, [In, Out] Complex32[] r, [In, Out] Complex32[] work, int len);
+
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int z_qr_thin_factor(int m, int n, [In, Out] Complex[] q, [In, Out] Complex[] tau, [In, Out] Complex[] r, [In, Out] Complex[] work, int len);
+
         [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
         internal static extern int s_qr_solve(int m, int n, int bn, float[] r, float[] b, [In, Out] float[] x, [In, Out] float[] work, int len);
 
@@ -230,6 +242,18 @@ namespace MathNet.Numerics.Algorithms.LinearAlgebra.Mkl
         [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
         internal static extern int z_qr_solve(int m, int n, int bn, Complex[] r, Complex[] b, [In, Out] Complex[] x, [In, Out] Complex[] work, int len);
 
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int s_thin_qr_solve(int m, int n, int bn, float[] r, float[] b, [In, Out] float[] x, [In, Out] float[] work, int len);
+
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int d_thin_qr_solve(int m, int n, int bn, double[] r, double[] b, [In, Out] double[] x, [In, Out] double[] work, int len);
+
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int c_thin_qr_solve(int m, int n, int bn, Complex32[] r, Complex32[] b, [In, Out] Complex32[] x, [In, Out] Complex32[] work, int len);
+
+        [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
+        internal static extern int z_thin_qr_solve(int m, int n, int bn, Complex[] r, Complex[] b, [In, Out] Complex[] x, [In, Out] Complex[] work, int len);
+
         [DllImport(DllName, ExactSpelling = true, SetLastError = false, CallingConvention = CallingConvention.Cdecl)]
         internal static extern int s_qr_solve_factored(int m, int n, int bn, float[] r, float[] b, float[] tau, [In, Out] float[] x, [In, Out] float[] work, int len);
 

src/Numerics/LinearAlgebra/Complex/ExtensionMethods.cs

@@ -60,10 +60,11 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Computes the QR decomposition for a matrix.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <returns>The QR decomposition object.</returns>
-        public static QR QR(this Matrix<Complex> matrix)
+        public static QR QR(this Matrix<Complex> matrix, QRMethod method = QRMethod.Full)
         {
-            return (QR)QR<Complex>.Create(matrix);
+            return (QR)QR<Complex>.Create(matrix, method);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Complex/Factorization/DenseQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
 {
     using System;
@@ -60,9 +62,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
-        public DenseQR(DenseMatrix matrix)
+        public DenseQR(DenseMatrix matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -74,10 +77,22 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = new DenseMatrix(matrix.RowCount);
             Tau = new Complex[Math.Min(matrix.RowCount, matrix.ColumnCount)];
-            Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount, ((DenseMatrix)MatrixQ).Data, Tau);
+
+            if (method == QRMethod.Full)
+            {
+                MatrixR = matrix.Clone();
+                MatrixQ = new DenseMatrix(matrix.RowCount);
+                Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixQ).Data, Tau);
+            }
+            else
+            {
+                MatrixQ = matrix.Clone();
+                MatrixR = new DenseMatrix(matrix.ColumnCount);
+                Control.LinearAlgebraProvider.ThinQRFactor(((DenseMatrix)MatrixQ).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixR).Data, Tau);
+            }
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Complex/Factorization/QR.cs

@@ -33,12 +33,15 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
 
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition.</para>
-    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
-    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix 
+    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix
+    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix 
     /// (also called right triangular matrix).</para>
     /// </summary>
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by Householder transformation.
+    /// If a <seealso cref="QRMethod.Full"/> factorization is peformed, the resulting Q matrix is an m x m matrix 
+    /// and the R matrix is an m x n matrix. If a <seealso cref="QRMethod.Thin"/> factorization is performed, the 
+    /// resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.     
     /// </remarks>
     public abstract class QR : QR<Complex>
     {

src/Numerics/LinearAlgebra/Complex/Factorization/UserQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
 {
     using System;
@@ -53,8 +55,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The QR factorization method to use.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
-        public UserQR(Matrix<Complex> matrix)
+        public UserQR(Matrix<Complex> matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -66,25 +69,57 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
-
-            for (var i = 0; i < matrix.RowCount; i++)
-            {
-                MatrixQ.At(i, i, 1.0);
-            }
-
             var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount);
             var u = new Complex[minmn][];
-            for (var i = 0; i < minmn; i++)
+
+            if (method == QRMethod.Full)
             {
-                u[i] = GenerateColumn(MatrixR, i, i);
-                ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads);
-            }
+                MatrixR = matrix.Clone();
+                MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
 
-            for (var i = minmn - 1; i >= 0; i--)
+                for (var i = 0; i < matrix.RowCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0f);
+                }
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixR, i, i);
+                    ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+            }
+            else
             {
-                ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads);
+                MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+                MatrixQ = matrix.Clone();
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixQ, i, i);
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                MatrixR = MatrixQ.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount);
+                MatrixQ.Clear();
+
+                for (var i = 0; i < matrix.ColumnCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0f);
+                }
+
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
             }
         }
 

src/Numerics/LinearAlgebra/Complex32/ExtensionMethods.cs

@@ -60,10 +60,11 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Computes the QR decomposition for a matrix.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <returns>The QR decomposition object.</returns>
-        public static QR QR(this Matrix<Complex32> matrix)
+        public static QR QR(this Matrix<Complex32> matrix, QRMethod method = QRMethod.Full)
         {
-            return (QR)QR<Complex32>.Create(matrix);
+            return (QR)QR<Complex32>.Create(matrix, method);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Complex32/Factorization/DenseQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 {
     using System;
@@ -60,9 +62,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The QR factorization method to use.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
-        public DenseQR(DenseMatrix matrix)
+        public DenseQR(DenseMatrix matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -74,10 +77,22 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = new DenseMatrix(matrix.RowCount);
             Tau = new Complex32[Math.Min(matrix.RowCount, matrix.ColumnCount)];
-            Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount, ((DenseMatrix)MatrixQ).Data, Tau);
+
+            if (method == QRMethod.Full)
+            {
+                MatrixR = matrix.Clone();
+                MatrixQ = new DenseMatrix(matrix.RowCount);
+                Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixQ).Data, Tau);
+            }
+            else
+            {
+                MatrixQ = matrix.Clone();
+                MatrixR = new DenseMatrix(matrix.ColumnCount);
+                Control.LinearAlgebraProvider.ThinQRFactor(((DenseMatrix)MatrixQ).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixR).Data, Tau);
+            }
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Complex32/Factorization/QR.cs

@@ -33,12 +33,15 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition.</para>
-    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
-    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix 
+    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix
+    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix 
     /// (also called right triangular matrix).</para>
     /// </summary>
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by Householder transformation.
+    /// If a <seealso cref="QRMethod.Full"/> factorization is peformed, the resulting Q matrix is an m x m matrix 
+    /// and the R matrix is an m x n matrix. If a <seealso cref="QRMethod.Thin"/> factorization is performed, the 
+    /// resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.     
     /// </remarks>
     public abstract class QR : QR<Complex32>
     {

src/Numerics/LinearAlgebra/Complex32/Factorization/UserQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 {
     using System;
@@ -53,8 +55,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The QR factorization method to use.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
-        public UserQR(Matrix<Complex32> matrix)
+        public UserQR(Matrix<Complex32> matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -66,25 +69,57 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
-
-            for (var i = 0; i < matrix.RowCount; i++)
-            {
-                MatrixQ.At(i, i, 1.0f);
-            }
-
             var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount);
             var u = new Complex32[minmn][];
-            for (var i = 0; i < minmn; i++)
+
+            if (method == QRMethod.Full)
             {
-                u[i] = GenerateColumn(MatrixR, i, i);
-                ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads);
-            }
+                MatrixR = matrix.Clone();
+                MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
 
-            for (var i = minmn - 1; i >= 0; i--)
+                for (var i = 0; i < matrix.RowCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0f);
+                }
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixR, i, i);
+                    ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+            }
+            else
             {
-                ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads);
+                MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+                MatrixQ = matrix.Clone();
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixQ, i, i);
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                MatrixR = MatrixQ.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount);
+                MatrixQ.Clear();
+
+                for (var i = 0; i < matrix.ColumnCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0f);
+                }
+
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
             }
         }
 

src/Numerics/LinearAlgebra/Double/ExtensionMethods.cs

@@ -59,10 +59,11 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Computes the QR decomposition for a matrix.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <returns>The QR decomposition object.</returns>
-        public static QR QR(this Matrix<double> matrix)
+        public static QR QR(this Matrix<double> matrix, QRMethod method = QRMethod.Full)
         {
-            return (QR)QR<double>.Create(matrix);
+            return (QR)QR<double>.Create(matrix, method);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Double/Factorization/DenseQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
     using System;
@@ -59,9 +61,10 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
-        public DenseQR(DenseMatrix matrix)
+        public DenseQR(DenseMatrix matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -73,10 +76,23 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = new DenseMatrix(matrix.RowCount);
             Tau = new double[Math.Min(matrix.RowCount, matrix.ColumnCount)];
-            Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount, ((DenseMatrix)MatrixQ).Data, Tau);
+
+            if (method == QRMethod.Full)
+            {
+                MatrixR = matrix.Clone();
+                MatrixQ = new DenseMatrix(matrix.RowCount);
+                Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixQ).Data, Tau);
+            }
+            else
+            {
+                MatrixQ = matrix.Clone();
+                MatrixR = new DenseMatrix(matrix.ColumnCount);
+                Control.LinearAlgebraProvider.ThinQRFactor(((DenseMatrix) MatrixQ).Data, matrix.RowCount,
+                                                           matrix.ColumnCount,
+                                                           ((DenseMatrix) MatrixR).Data, Tau);
+            }
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Double/Factorization/QR.cs

@@ -32,12 +32,15 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition.</para>
-    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
-    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix 
+    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix
+    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix 
     /// (also called right triangular matrix).</para>
     /// </summary>
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by Householder transformation.
+    /// If a <seealso cref="QRMethod.Full"/> factorization is performed, the resulting Q matrix is an m x m matrix 
+    /// and the R matrix is an m x n matrix. If a <seealso cref="QRMethod.Thin"/> factorization is performed, the 
+    /// resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.     
     /// </remarks>
     public abstract class QR : QR<double>
     {

src/Numerics/LinearAlgebra/Double/Factorization/UserQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
     using System;
@@ -52,8 +54,9 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The QR factorization method to use.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
-        public UserQR(Matrix<double> matrix)
+        public UserQR(Matrix<double> matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -65,25 +68,58 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
-
-            for (var i = 0; i < matrix.RowCount; i++)
-            {
-                MatrixQ.At(i, i, 1.0);
-            }
-
             var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount);
             var u = new double[minmn][];
-            for (var i = 0; i < minmn; i++)
+
+            if (method == QRMethod.Full)
             {
-                u[i] = GenerateColumn(MatrixR, i, i);
-                ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads);
-            }
+                MatrixR = matrix.Clone();
+                MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
+
+                for (var i = 0; i < matrix.RowCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0);
+                }
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixR, i, i);
+                    ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
 
-            for (var i = minmn - 1; i >= 0; i--)
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+            }
+            else
             {
-                ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads);
+                MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+                MatrixQ = matrix.Clone();
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixQ, i, i);
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                MatrixR = MatrixQ.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount);
+                MatrixQ.Clear();
+                
+                for (var i = 0; i < matrix.ColumnCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0);
+                }
+                
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
             }
         }
         

src/Numerics/LinearAlgebra/Generic/Factorization/GramSchmidt.cs

@@ -47,7 +47,7 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
         /// <returns>A QR factorization object.</returns>
-        new internal static GramSchmidt<T> Create(Matrix<T> matrix)
+        internal static GramSchmidt<T> Create(Matrix<T> matrix)
         {
             if (typeof(T) == typeof(double))
             {

src/Numerics/LinearAlgebra/Generic/Factorization/QR.cs

@@ -31,14 +31,33 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
     using Generic;
     using Numerics;
 
+    /// <summary>
+    /// The type of QR factorization go perform.
+    /// </summary>
+    public enum QRMethod
+    {
+        /// <summary>
+        /// Compute the full QR factorization of a matrix.
+        /// </summary>
+        Full = 0,
+
+        /// <summary>
+        /// Compute the thin QR factorixation of a matrix.
+        /// </summary>
+        Thin = 1
+    }
+
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition.</para>
-    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
-    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix 
+    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix
+    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix 
     /// (also called right triangular matrix).</para>
     /// </summary>
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by Householder transformation.
+    /// If a <seealso cref="QRMethod.Full"/> factorization is performed, the resulting Q matrix is an m x m matrix 
+    /// and the R matrix is an m x n matrix. If a <seealso cref="QRMethod.Thin"/> factorization is performed, the 
+    /// resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.     
     /// </remarks>
     /// <typeparam name="T">Supported data types are double, single, <see cref="Complex"/>, and <see cref="Complex32"/>.</typeparam>
     public abstract class QR<T> : ISolver<T>
@@ -66,18 +85,19 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
         /// Internal method which routes the call to perform the QR factorization to the appropriate class.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <returns>A QR factorization object.</returns>
-        internal static QR<T> Create(Matrix<T> matrix)
+        internal static QR<T> Create(Matrix<T> matrix, QRMethod method = QRMethod.Full)
         {
             if (typeof(T) == typeof(double))
             {
                 var dense = matrix as LinearAlgebra.Double.DenseMatrix;
                 if (dense != null)
                 {
-                    return new LinearAlgebra.Double.Factorization.DenseQR(dense) as QR<T>;
+                    return new LinearAlgebra.Double.Factorization.DenseQR(dense, method) as QR<T>;
                 }
 
-                return new LinearAlgebra.Double.Factorization.UserQR(matrix as Matrix<double>) as QR<T>;
+                return new LinearAlgebra.Double.Factorization.UserQR(matrix as Matrix<double>, method) as QR<T>;
             }
 
             if (typeof(T) == typeof(float))
@@ -85,10 +105,10 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
                 var dense = matrix as LinearAlgebra.Single.DenseMatrix;
                 if (dense != null)
                 {
-                    return new LinearAlgebra.Single.Factorization.DenseQR(dense) as QR<T>;
+                    return new LinearAlgebra.Single.Factorization.DenseQR(dense, method) as QR<T>;
                 }
 
-                return new LinearAlgebra.Single.Factorization.UserQR(matrix as Matrix<float>) as QR<T>;
+                return new LinearAlgebra.Single.Factorization.UserQR(matrix as Matrix<float>, method) as QR<T>;
             }
 
             if (typeof(T) == typeof(Complex))
@@ -96,10 +116,10 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
                 var dense = matrix as LinearAlgebra.Complex.DenseMatrix;
                 if (dense != null)
                 {
-                    return new LinearAlgebra.Complex.Factorization.DenseQR(dense) as QR<T>;
+                    return new LinearAlgebra.Complex.Factorization.DenseQR(dense, method) as QR<T>;
                 }
 
-                return new LinearAlgebra.Complex.Factorization.UserQR(matrix as Matrix<Complex>) as QR<T>;
+                return new LinearAlgebra.Complex.Factorization.UserQR(matrix as Matrix<Complex>, method) as QR<T>;
             }
 
             if (typeof(T) == typeof(Complex32))
@@ -107,10 +127,10 @@ namespace MathNet.Numerics.LinearAlgebra.Generic.Factorization
                 var dense = matrix as LinearAlgebra.Complex32.DenseMatrix;
                 if (dense != null)
                 {
-                    return new LinearAlgebra.Complex32.Factorization.DenseQR(dense) as QR<T>;
+                    return new LinearAlgebra.Complex32.Factorization.DenseQR(dense, method) as QR<T>;
                 }
 
-                return new LinearAlgebra.Complex32.Factorization.UserQR(matrix as Matrix<Complex32>) as QR<T>;
+                return new LinearAlgebra.Complex32.Factorization.UserQR(matrix as Matrix<Complex32>, method) as QR<T>;
             }
 
             throw new NotSupportedException();

src/Numerics/LinearAlgebra/Single/ExtensionMethods.cs

@@ -59,10 +59,11 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Computes the QR decomposition for a matrix.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The type of QR factorization to perform.</param>
         /// <returns>The QR decomposition object.</returns>
-        public static QR QR(this Matrix<float> matrix)
+        public static QR QR(this Matrix<float> matrix, QRMethod method = QRMethod.Full)
         {
-            return (QR)QR<float>.Create(matrix);
+            return (QR)QR<float>.Create(matrix, method);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Single/Factorization/DenseQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 {
     using System;
@@ -59,9 +61,10 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The QR factorization method to use.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
-        public DenseQR(DenseMatrix matrix)
+        public DenseQR(DenseMatrix matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -73,10 +76,22 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = new DenseMatrix(matrix.RowCount);
             Tau = new float[Math.Min(matrix.RowCount, matrix.ColumnCount)];
-            Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount, ((DenseMatrix)MatrixQ).Data, Tau);
+
+            if (method == QRMethod.Full)
+            {
+                MatrixR = matrix.Clone();
+                MatrixQ = new DenseMatrix(matrix.RowCount);
+                Control.LinearAlgebraProvider.QRFactor(((DenseMatrix)MatrixR).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixQ).Data, Tau);
+            }
+            else
+            {
+                MatrixQ = matrix.Clone();
+                MatrixR = new DenseMatrix(matrix.ColumnCount);
+                Control.LinearAlgebraProvider.ThinQRFactor(((DenseMatrix)MatrixQ).Data, matrix.RowCount, matrix.ColumnCount,
+                                                       ((DenseMatrix)MatrixR).Data, Tau);
+            }
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Single/Factorization/QR.cs

@@ -32,12 +32,15 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition.</para>
-    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
-    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix 
+    /// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix
+    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix 
     /// (also called right triangular matrix).</para>
     /// </summary>
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by Householder transformation.
+    /// If a <seealso cref="QRMethod.Full"/> factorization is peformed, the resulting Q matrix is an m x m matrix 
+    /// and the R matrix is an m x n matrix. If a <seealso cref="QRMethod.Thin"/> factorization is performed, the 
+    /// resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.     
     /// </remarks>
     public abstract class QR : QR<float>
     {

src/Numerics/LinearAlgebra/Single/Factorization/UserQR.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 {
     using System;
@@ -52,8 +54,9 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// QR factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
+        /// <param name="method">The QR factorization method to use.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
-        public UserQR(Matrix<float> matrix)
+        public UserQR(Matrix<float> matrix, QRMethod method = QRMethod.Full)
         {
             if (matrix == null)
             {
@@ -65,25 +68,57 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            MatrixR = matrix.Clone();
-            MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
-
-            for (var i = 0; i < matrix.RowCount; i++)
-            {
-                MatrixQ.At(i, i, 1.0f);
-            }
-
             var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount);
             var u = new float[minmn][];
-            for (var i = 0; i < minmn; i++)
+
+            if (method == QRMethod.Full)
             {
-                u[i] = GenerateColumn(MatrixR, i, i);
-                ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads);
-            }
+                MatrixR = matrix.Clone();
+                MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount);
 
-            for (var i = minmn - 1; i >= 0; i--)
+                for (var i = 0; i < matrix.RowCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0f);
+                }
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixR, i, i);
+                    ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+            }
+            else
             {
-                ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads);
+                MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+                MatrixQ = matrix.Clone();
+
+                for (var i = 0; i < minmn; i++)
+                {
+                    u[i] = GenerateColumn(MatrixQ, i, i);
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i + 1, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
+
+                MatrixR = MatrixQ.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount);
+                MatrixQ.Clear();
+
+                for (var i = 0; i < matrix.ColumnCount; i++)
+                {
+                    MatrixQ.At(i, i, 1.0f);
+                }
+
+                for (var i = minmn - 1; i >= 0; i--)
+                {
+                    ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.ColumnCount,
+                              Control.NumberOfParallelWorkerThreads);
+                }
             }
         }
 

src/Numerics/Numerics.csproj

@@ -85,22 +85,6 @@
     <Reference Include="System.Xml" />
   </ItemGroup>
   <ItemGroup>
-    <Compile Include="Algorithms\LinearAlgebra\Acml\AcmlLinearAlgebraProvider.Complex.cs">
-    </Compile>
-    <Compile Include="Algorithms\LinearAlgebra\Acml\AcmlLinearAlgebraProvider.Complex32.cs">
-    </Compile>
-    <Compile Include="Algorithms\LinearAlgebra\Acml\AcmlLinearAlgebraProvider.double.cs">
-    </Compile>
-    <Compile Include="Algorithms\LinearAlgebra\Acml\AcmlLinearAlgebraProvider.float.cs">
-    </Compile>
-    <Compile Include="Algorithms\LinearAlgebra\Acml\SafeNativeMethods.cs">
-    </Compile>
-    <Compile Include="Algorithms\LinearAlgebra\GotoBlas\GotoBlasLinearAlgebraProvider.Common.cs" />
-    <Compile Include="Algorithms\LinearAlgebra\GotoBlas\GotoBlasLinearAlgebraProvider.Complex.cs" />
-    <Compile Include="Algorithms\LinearAlgebra\GotoBlas\GotoBlasLinearAlgebraProvider.Complex32.cs" />
-    <Compile Include="Algorithms\LinearAlgebra\GotoBlas\GotoBlasLinearAlgebraProvider.double.cs" />
-    <Compile Include="Algorithms\LinearAlgebra\GotoBlas\GotoBlasLinearAlgebraProvider.float.cs" />
-    <Compile Include="Algorithms\LinearAlgebra\GotoBlas\SafeNativeMethods.cs" />
     <Compile Include="Algorithms\LinearAlgebra\ManagedLinearAlgebraProvider.Complex32.cs" />
     <Compile Include="Algorithms\LinearAlgebra\ManagedLinearAlgebraProvider.Complex.cs" />
     <Compile Include="Algorithms\LinearAlgebra\ManagedLinearAlgebraProvider.Single.cs" />

src/UnitTests/LinearAlgebraProviderTests/Complex/LinearAlgebraProviderTests.cs

@@ -789,6 +789,115 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Complex
             }
         }
 
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex[3];
+            var q = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex[3];
+            var q = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix using a work array.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex[3];
+            var q = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix using a work matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex[3];
+            var q = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve Ax=b using QR factorization with a square A matrix.
         /// </summary>
@@ -807,7 +916,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Complex
 
             var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
             var mb = matrix * mx;
-
+            Console.WriteLine(mx);
             AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
             AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
             AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
@@ -1015,6 +1124,232 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Complex
             AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
         }
 
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            var work = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            var work = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex[matrix.ColumnCount];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex[matrix.ColumnCount];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex[matrix.ColumnCount];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new Complex[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex[matrix.ColumnCount];
+            var r = new Complex[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new Complex[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { new Complex(1.0, 0), 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new Complex[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
         /// <summary>
         /// Can compute the SVD factorization of a square matrix.
         /// </summary>

src/UnitTests/LinearAlgebraProviderTests/Complex32/LinearAlgebraProviderTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Complex32
 {
     using System;
@@ -796,6 +798,115 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Complex32
             }
         }
 
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex32[3];
+            var q = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex32[3];
+            var q = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix using a work array.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex32[3];
+            var q = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix using a work matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new Complex32[3];
+            var q = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve Ax=b using QR factorization with a square A matrix.
         /// </summary>
@@ -1022,6 +1133,232 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Complex32
             AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
         }
 
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            var work = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            var work = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex32[matrix.ColumnCount];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex32[matrix.ColumnCount];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex32[matrix.ColumnCount];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new Complex32[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new Complex32[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new Complex32[matrix.ColumnCount];
+            var r = new Complex32[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new Complex32[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new Complex32[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
         /// <summary>
         /// Can compute the SVD factorization of a square matrix.
         /// </summary>

src/UnitTests/LinearAlgebraProviderTests/Double/LinearAlgebraProviderTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Double
 {
     using System;
@@ -787,11 +789,121 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Double
             }
         }
 
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new double[3];
+            var q = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new double[3];
+            var q = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix using a work array.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new double[3];
+            var q = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new double[matrix.ColumnCount * Control.BlockSize];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix using a work matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new double[3];
+            var q = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new double[matrix.ColumnCount * Control.BlockSize];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 14);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve Ax=b using QR factorization with a square A matrix.
         /// </summary>
         [Test]
-        public void CanSolveUsingQRSquareMatrix()
+        public void  CanSolveUsingQRSquareMatrix()
         {
             var matrix = _matrices["Square3x3"];
             var a = new double[matrix.RowCount * matrix.ColumnCount];
@@ -852,7 +964,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Double
 
             var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
             var x = new double[matrix.ColumnCount * 2];
-            var work = new double[matrix.RowCount * matrix.RowCount];
+            var work = new double[matrix.RowCount * Control.BlockSize];
             Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work);
 
             NotModified(3, 3, a, matrix);
@@ -1013,6 +1125,232 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Double
             AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
         }
 
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            var work = new double[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            var work = new double[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new double[matrix.ColumnCount];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new double[matrix.ColumnCount];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new double[matrix.ColumnCount];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new double[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 14);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 14);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 14);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 14);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 14);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 14);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new double[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new double[matrix.ColumnCount];
+            var r = new double[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new double[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
+            var x = new double[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin );
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 14);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 14);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 14);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 14);
+        }
+        
         /// <summary>
         /// Can compute the SVD factorization of a square matrix.
         /// </summary>

src/UnitTests/LinearAlgebraProviderTests/Single/LinearAlgebraProviderTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Single
 {
     using System;
@@ -795,6 +797,115 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Single
             }
         }
 
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new float[3];
+            var q = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new float[3];
+            var q = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a square matrix using a work array.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorSquareMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new float[3];
+            var q = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new float[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can compute thin QR factorization of a tall matrix using a work matrix.
+        /// </summary>
+        [Test]
+        public void CanComputeThinQRFactorTallMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            var tau = new float[3];
+            var q = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, q, q.Length);
+
+            var work = new float[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
+            var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
+            var a = mq * mr;
+            for (var row = 0; row < matrix.RowCount; row++)
+            {
+                for (var col = 0; col < matrix.ColumnCount; col++)
+                {
+                    AssertHelpers.AlmostEqual(matrix[row, col], a[row, col], 6);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve Ax=b using QR factorization with a square A matrix.
         /// </summary>
@@ -1021,6 +1132,232 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraProviderTests.Single
             AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
         }
 
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            var work = new float[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 3, a, matrix);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixUsingWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            var work = new float[matrix.RowCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work, QRMethod.Thin);
+
+            NotModified(3, 2, a, matrix);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new float[matrix.ColumnCount];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrix()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new float[matrix.ColumnCount];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a square A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRSquareMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Square3x3"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new float[matrix.ColumnCount];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new float[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
+            var mb = matrix * mx;
+
+            AssertHelpers.AlmostEqual(mb[0, 0], b[0], 5);
+            AssertHelpers.AlmostEqual(mb[1, 0], b[1], 5);
+            AssertHelpers.AlmostEqual(mb[2, 0], b[2], 5);
+            AssertHelpers.AlmostEqual(mb[0, 1], b[3], 5);
+            AssertHelpers.AlmostEqual(mb[1, 1], b[4], 5);
+            AssertHelpers.AlmostEqual(mb[2, 1], b[5], 5);
+        }
+
+        /// <summary>
+        /// Can solve Ax=b using thin QR factorization with a tall A matrix
+        /// using a factored A matrix with a work array.
+        /// </summary>
+        [Test]
+        public void CanSolveUsingThinQRTallMatrixOnFactoredMatrixWithWorkArray()
+        {
+            var matrix = _matrices["Tall3x2"];
+            var a = new float[matrix.RowCount * matrix.ColumnCount];
+            Array.Copy(matrix.Data, a, a.Length);
+
+            var tau = new float[matrix.ColumnCount];
+            var r = new float[matrix.ColumnCount * matrix.ColumnCount];
+            var work = new float[2048];
+            Control.LinearAlgebraProvider.ThinQRFactor(a, matrix.RowCount, matrix.ColumnCount, r, tau, work);
+
+            var b = new[] { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f };
+            var x = new float[matrix.ColumnCount * 2];
+            Control.LinearAlgebraProvider.QRSolveFactored(a, r, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x, work, QRMethod.Thin);
+
+            var mb = new DenseMatrix(matrix.RowCount, 2, b);
+            var test = (matrix.Transpose() * matrix).Inverse() * matrix.Transpose() * mb;
+
+            AssertHelpers.AlmostEqual(test[0, 0], x[0], 6);
+            AssertHelpers.AlmostEqual(test[1, 0], x[1], 6);
+            AssertHelpers.AlmostEqual(test[0, 1], x[2], 6);
+            AssertHelpers.AlmostEqual(test[1, 1], x[3], 6);
+        }
+
         /// <summary>
         /// Can compute the SVD factorization of a square matrix.
         /// </summary>

src/UnitTests/LinearAlgebraTests/Complex/Factorization/QRTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="QRTests.cs" company="Math.NET">
+// <copyright file="QRTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -88,6 +88,38 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = DenseMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.ColumnCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(1.0, r[i, j].Magnitude);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(Complex.Zero, r[i, j]);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -151,6 +183,64 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(Complex.Zero, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q is unitary --> (Q*)x(Q) = I
+            var matrixQсtQ = q.ConjugateTranspose() * q;
+            for (var i = 0; i < matrixQсtQ.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQсtQ.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(matrixQсtQ[i, j].Real, 1.0f, 1e-3f);
+                        Assert.AreEqual(matrixQсtQ[i, j].Imaginary, 0.0f, 1e-3f);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(matrixQсtQ[i, j].Real, 0.0f, 1e-3f);
+                        Assert.AreEqual(matrixQсtQ[i, j].Imaginary, 0.0f, 1e-3f);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>
@@ -339,5 +429,194 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
                 }
             }
         }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random vector (Ax=b).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
+            var resultx = factorQR.Solve(vectorb);
+
+            Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < order; i++)
+            {
+                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
+            var matrixX = factorQR.Solve(matrixB);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 9);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve for a random vector into a result vector.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
+            var vectorbCopy = vectorb.Clone();
+            var resultx = new DenseVector(order);
+            factorQR.Solve(vectorb, resultx);
+
+            Assert.AreEqual(vectorb.Count, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure b didn't change.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
+            var matrixBCopy = matrixB.Clone();
+
+            var matrixX = new DenseMatrix(order, order);
+            factorQR.Solve(matrixB, matrixX);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 9);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure B didn't change.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
+                }
+            }
+        }
     }
 }

src/UnitTests/LinearAlgebraTests/Complex/Factorization/UserQRTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
 {
     using System;
@@ -88,6 +90,38 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = UserDefinedMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.RowCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(-Complex.One, r[i, j]);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(Complex.Zero, r[i, j]);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -151,6 +185,55 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(Complex.Zero, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q*R is the original matrix.
+            var matrixQfromR = q * r;
+            for (var i = 0; i < matrixQfromR.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
+                {
+                    AssertHelpers.AlmostEqual(matrixA[i, j], matrixQfromR[i, j], 9);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>
@@ -339,5 +422,194 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
                 }
             }
         }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random vector (Ax=b).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var resultx = factorQR.Solve(vectorb);
+
+            Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < order; i++)
+            {
+                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixX = factorQR.Solve(matrixB);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 9);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve for a random vector into a result vector.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var vectorbCopy = vectorb.Clone();
+            var resultx = new UserDefinedVector(order);
+            factorQR.Solve(vectorb, resultx);
+
+            Assert.AreEqual(vectorb.Count, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure b didn't change.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixBCopy = matrixB.Clone();
+
+            var matrixX = new UserDefinedMatrix(order, order);
+            factorQR.Solve(matrixB, matrixX);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 9);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure B didn't change.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
+                }
+            }
+        }
     }
 }

src/UnitTests/LinearAlgebraTests/Complex32/Factorization/QRTests.cs

@@ -88,6 +88,39 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = DenseMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.ColumnCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(1.0, r[i, j].Magnitude);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(Complex32.Zero, r[i, j]);
+                    }
+                }
+            }
+        }
+
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -171,6 +204,64 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(Complex32.Zero, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q is unitary --> (Q*)x(Q) = I
+            var matrixQсtQ = q.ConjugateTranspose() * q;
+            for (var i = 0; i < matrixQсtQ.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQсtQ.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(matrixQсtQ[i, j].Real, 1.0f, 1e-3f);
+                        Assert.AreEqual(matrixQсtQ[i, j].Imaginary, 0.0f, 1e-3f);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(matrixQсtQ[i, j].Real, 0.0f, 1e-3f);
+                        Assert.AreEqual(matrixQсtQ[i, j].Imaginary, 0.0f, 1e-3f);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>

src/UnitTests/LinearAlgebraTests/Complex32/Factorization/UserQRTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
 {
     using System;
@@ -87,6 +89,38 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = UserDefinedMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.RowCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(-Complex32.One, r[i, j]);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(Complex32.Zero, r[i, j]);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -170,6 +204,56 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(Complex32.Zero, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q*R is the original matrix.
+            var matrixQfromR = q * r;
+            for (var i = 0; i < matrixQfromR.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixA[i, j].Real, matrixQfromR[i, j].Real, 1e-3f);
+                    Assert.AreEqual(matrixA[i, j].Imaginary, matrixQfromR[i, j].Imaginary, 1e-3f);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>
@@ -362,5 +446,198 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
                 }
             }
         }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random vector (Ax=b).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var resultx = factorQR.Solve(vectorb);
+
+            Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < order; i++)
+            {
+                Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-3f);
+                Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, 1e-3f);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixX = factorQR.Solve(matrixB);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 1e-3f);
+                    Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 1e-3f);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve for a random vector into a result vector.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var vectorbCopy = vectorb.Clone();
+            var resultx = new UserDefinedVector(order);
+            factorQR.Solve(vectorb, resultx);
+
+            Assert.AreEqual(vectorb.Count, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-3f);
+                Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, 1e-3f);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure b didn't change.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixBCopy = matrixB.Clone();
+
+            var matrixX = new UserDefinedMatrix(order, order);
+            factorQR.Solve(matrixB, matrixX);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 1e-3f);
+                    Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 1e-3f);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure B didn't change.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
+                }
+            }
+        }
     }
 }

src/UnitTests/LinearAlgebraTests/Double/Factorization/QRTests.cs

@@ -87,6 +87,38 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = DenseMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.ColumnCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(1.0, Math.Abs(r[i, j]));
+                    }
+                    else
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -150,6 +182,55 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q*R is the original matrix.
+            var matrixQfromR = q * r;
+            for (var i = 0; i < matrixQfromR.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixA[i, j], matrixQfromR[i, j], 1.0e-11);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>

src/UnitTests/LinearAlgebraTests/Double/Factorization/UserQRTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
 {
     using System;
@@ -86,6 +88,38 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = UserDefinedMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.RowCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(-1.0, r[i, j]);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -149,6 +183,55 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q*R is the original matrix.
+            var matrixQfromR = q * r;
+            for (var i = 0; i < matrixQfromR.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixA[i, j], matrixQfromR[i, j], 1.0e-11);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>
@@ -337,5 +420,194 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
                 }
             }
         }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random vector (Ax=b).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var resultx = factorQR.Solve(vectorb);
+
+            Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < order; i++)
+            {
+                Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1.0e-11);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixX = factorQR.Solve(matrixB);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1.0e-11);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve for a random vector into a result vector.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var vectorbCopy = vectorb.Clone();
+            var resultx = new UserDefinedVector(order);
+            factorQR.Solve(vectorb, resultx);
+
+            Assert.AreEqual(vectorb.Count, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1.0e-11);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure b didn't change.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixBCopy = matrixB.Clone();
+
+            var matrixX = new UserDefinedMatrix(order, order);
+            factorQR.Solve(matrixB, matrixX);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1.0e-11);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure B didn't change.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
+                }
+            }
+        }
     }
 }

src/UnitTests/LinearAlgebraTests/Single/Factorization/QRTests.cs

@@ -87,6 +87,39 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = DenseMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.ColumnCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(1.0, Math.Abs(r[i, j]));
+                    }
+                    else
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+        }
+
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -150,6 +183,55 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q*R is the original matrix.
+            var matrixQfromR = q * r;
+            for (var i = 0; i < matrixQfromR.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixA[i, j], matrixQfromR[i, j], 1.0e-4);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>

src/UnitTests/LinearAlgebraTests/Single/Factorization/UserQRTests.cs

@@ -24,6 +24,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
 {
     using System;
@@ -86,6 +88,38 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize identity matrix using thin QR.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(10)]
+        [TestCase(100)]
+        public void CanFactorizeIdentityUsingThinQR(int order)
+        {
+            var matrixI = UserDefinedMatrix.Identity(order);
+            var factorQR = matrixI.QR(QRMethod.Thin);
+            var r = factorQR.R;
+
+            Assert.AreEqual(matrixI.RowCount, r.RowCount);
+            Assert.AreEqual(matrixI.ColumnCount, r.ColumnCount);
+
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(-1.0, r[i, j]);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+        }
+
         /// <summary>
         /// Identity determinant is one.
         /// </summary>
@@ -149,6 +183,55 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
             }
         }
 
+        /// <summary>
+        /// Can factorize a random matrix using thin QR.
+        /// </summary>
+        /// <param name="row">Matrix row number.</param>
+        /// <param name="column">Matrix column number.</param>
+        [TestCase(1, 1)]
+        [TestCase(2, 2)]
+        [TestCase(5, 5)]
+        [TestCase(10, 6)]
+        [TestCase(50, 48)]
+        [TestCase(100, 98)]
+        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(row, column);
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var q = factorQR.Q;
+            var r = factorQR.R;
+
+            // Make sure the R has the right dimensions.
+            Assert.AreEqual(column, r.RowCount);
+            Assert.AreEqual(column, r.ColumnCount);
+
+            // Make sure the Q has the right dimensions.
+            Assert.AreEqual(row, q.RowCount);
+            Assert.AreEqual(column, q.ColumnCount);
+
+            // Make sure the R factor is upper triangular.
+            for (var i = 0; i < r.RowCount; i++)
+            {
+                for (var j = 0; j < r.ColumnCount; j++)
+                {
+                    if (i > j)
+                    {
+                        Assert.AreEqual(0.0, r[i, j]);
+                    }
+                }
+            }
+
+            // Make sure the Q*R is the original matrix.
+            var matrixQfromR = q * r;
+            for (var i = 0; i < matrixQfromR.RowCount; i++)
+            {
+                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixA[i, j], matrixQfromR[i, j], 1.0e-4);
+                }
+            }
+        }
+
         /// <summary>
         /// Can solve a system of linear equations for a random vector (Ax=b).
         /// </summary>
@@ -337,5 +420,194 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
                 }
             }
         }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random vector (Ax=b).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var resultx = factorQR.Solve(vectorb);
+
+            Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < order; i++)
+            {
+                Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1e-4);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B).
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixX = factorQR.Solve(matrixB);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1e-4);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can solve for a random vector into a result vector.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
+            var vectorbCopy = vectorb.Clone();
+            var resultx = new UserDefinedVector(order);
+            factorQR.Solve(vectorb, resultx);
+
+            Assert.AreEqual(vectorb.Count, resultx.Count);
+
+            var matrixBReconstruct = matrixA * resultx;
+
+            // Check the reconstruction.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1e-4);
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure b didn't change.
+            for (var i = 0; i < vectorb.Count; i++)
+            {
+                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
+            }
+        }
+
+        /// <summary>
+        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
+        /// </summary>
+        /// <param name="order">Matrix order.</param>
+        [TestCase(1)]
+        [TestCase(2)]
+        [TestCase(5)]
+        [TestCase(10)]
+        [TestCase(50)]
+        [TestCase(100)]
+        public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinAR(int order)
+        {
+            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixACopy = matrixA.Clone();
+            var factorQR = matrixA.QR(QRMethod.Thin);
+
+            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
+            var matrixBCopy = matrixB.Clone();
+
+            var matrixX = new UserDefinedMatrix(order, order);
+            factorQR.Solve(matrixB, matrixX);
+
+            // The solution X row dimension is equal to the column dimension of A
+            Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
+
+            // The solution X has the same number of columns as B
+            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
+
+            var matrixBReconstruct = matrixA * matrixX;
+
+            // Check the reconstruction.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1e-4);
+                }
+            }
+
+            // Make sure A didn't change.
+            for (var i = 0; i < matrixA.RowCount; i++)
+            {
+                for (var j = 0; j < matrixA.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
+                }
+            }
+
+            // Make sure B didn't change.
+            for (var i = 0; i < matrixB.RowCount; i++)
+            {
+                for (var j = 0; j < matrixB.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
+                }
+            }
+        }
     }
 }

src/UnitTests/Setup.cs

@@ -45,13 +45,5 @@ public class Setup
         {
             MathNet.Numerics.Control.LinearAlgebraProvider = new MathNet.Numerics.Algorithms.LinearAlgebra.Mkl.MklLinearAlgebraProvider();
         }
-        else if (provider.Contains("gotoblas"))
-        {
-            MathNet.Numerics.Control.LinearAlgebraProvider = new MathNet.Numerics.Algorithms.LinearAlgebra.GotoBlas.GotoBlasLinearAlgebraProvider();
-        }
-        else if (provider.Contains("acml"))
-        {
-            MathNet.Numerics.Control.LinearAlgebraProvider = new MathNet.Numerics.Algorithms.LinearAlgebra.Acml.AcmlLinearAlgebraProvider();
-        }
     }
 }