From 390cae2177623f40a15ce824e8cb767dab0d165a Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Sun, 8 Sep 2013 18:42:06 +0200
Subject: [PATCH] LA: Simplify Gram-Schmidt decomposition architecture

---
 .../LinearAlgebra/Complex/DenseMatrix.cs      |  2 +-
 .../Complex/Factorization/DenseGramSchmidt.cs | 57 +++++----------
 .../Complex/Factorization/GramSchmidt.cs      | 15 +++-
 .../Complex/Factorization/UserGramSchmidt.cs  | 69 +++++++------------
 src/Numerics/LinearAlgebra/Complex/Matrix.cs  |  2 +-
 .../LinearAlgebra/Complex32/DenseMatrix.cs    |  2 +-
 .../Factorization/DenseGramSchmidt.cs         | 57 +++++----------
 .../Complex32/Factorization/GramSchmidt.cs    | 15 +++-
 .../Factorization/UserGramSchmidt.cs          | 69 +++++++------------
 .../LinearAlgebra/Complex32/Matrix.cs         |  2 +-
 .../LinearAlgebra/Double/DenseMatrix.cs       |  2 +-
 .../Double/Factorization/DenseGramSchmidt.cs  | 57 +++++----------
 .../Double/Factorization/GramSchmidt.cs       | 16 +++--
 .../Double/Factorization/UserGramSchmidt.cs   | 67 +++++++-----------
 src/Numerics/LinearAlgebra/Double/Matrix.cs   |  2 +-
 .../Factorization/GramSchmidt.cs              | 11 ++-
 .../LinearAlgebra/Single/DenseMatrix.cs       |  2 +-
 .../Single/Factorization/DenseGramSchmidt.cs  | 57 +++++----------
 .../Single/Factorization/GramSchmidt.cs       | 16 +++--
 .../Single/Factorization/UserGramSchmidt.cs   | 67 +++++++-----------
 src/Numerics/LinearAlgebra/Single/Matrix.cs   |  2 +-
 .../Complex/Factorization/GramSchmidtTests.cs | 13 +---
 .../Factorization/UserGramSchmidtTests.cs     | 17 ++---
 .../Factorization/GramSchmidtTests.cs         | 13 +---
 .../Factorization/UserGramSchmidtTests.cs     | 19 ++---
 .../Double/Factorization/GramSchmidtTests.cs  | 13 +---
 .../Factorization/UserGramSchmidtTests.cs     | 18 ++---
 .../Single/Factorization/GramSchmidtTests.cs  | 13 +---
 .../Factorization/UserGramSchmidtTests.cs     | 18 ++---
 29 files changed, 257 insertions(+), 456 deletions(-)

diff --git a/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
index cb6b4391..ce1eea7c 100644
--- a/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
@@ -1026,7 +1026,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
 
         public override GramSchmidt<Complex> GramSchmidt()
         {
-            return new DenseGramSchmidt(this);
+            return DenseGramSchmidt.Create(this);
         }
 
         public override Svd<Complex> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Complex/Factorization/DenseGramSchmidt.cs b/src/Numerics/LinearAlgebra/Complex/Factorization/DenseGramSchmidt.cs
index c441e3be..a05ceda7 100644
--- a/src/Numerics/LinearAlgebra/Complex/Factorization/DenseGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Complex/Factorization/DenseGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,10 +28,9 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
 using MathNet.Numerics.Properties;
-using System;
-using MathNet.Numerics.Providers.LinearAlgebra;
 
 namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
 {
@@ -49,13 +48,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class DenseGramSchmidt : GramSchmidt
+    public sealed class DenseGramSchmidt : GramSchmidt
     {
-        /// <summary>
-        /// used for QR solve
-        /// </summary>
-        private readonly ILinearAlgebraProvider _provider = new ManagedLinearAlgebraProvider();
-
         /// <summary>
         /// Initializes a new instance of the <see cref="DenseGramSchmidt"/> class. This object creates an unitary matrix 
         /// using the modified Gram-Schmidt method.
@@ -64,21 +58,23 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public DenseGramSchmidt(DenseMatrix matrix)
+        public static DenseGramSchmidt Create(DenseMatrix matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
-            Factorize(((DenseMatrix)Q).Values, Q.RowCount, Q.ColumnCount, ((DenseMatrix)MatrixR).Values);
+            var q = (DenseMatrix)matrix.Clone();
+            var r = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            Factorize(q.Values, q.RowCount, q.ColumnCount, r.Values);
+
+            return new DenseGramSchmidt(q, r);
+        }
+
+        DenseGramSchmidt(Matrix<Complex> q, Matrix<Complex> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -138,17 +134,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<Complex> input, Matrix<Complex> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -179,7 +164,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense matrices at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
         }
 
         /// <summary>
@@ -189,16 +174,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<Complex> input, Vector<Complex> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
@@ -224,7 +199,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense vectors at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
         }
     }
 }
diff --git a/src/Numerics/LinearAlgebra/Complex/Factorization/GramSchmidt.cs b/src/Numerics/LinearAlgebra/Complex/Factorization/GramSchmidt.cs
index f57777aa..f5bfeda2 100644
--- a/src/Numerics/LinearAlgebra/Complex/Factorization/GramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Complex/Factorization/GramSchmidt.cs
@@ -3,7 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// Copyright (c) 2009-2010 Math.NET
+//
+// Copyright (c) 2009-2013 Math.NET
+//
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
 // files (the "Software"), to deal in the Software without
@@ -12,8 +14,10 @@
 // copies of the Software, and to permit persons to whom the
 // Software is furnished to do so, subject to the following
 // conditions:
+//
 // The above copyright notice and this permission notice shall be
 // included in all copies or substantial portions of the Software.
+//
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 // OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
@@ -24,12 +28,12 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
 {
-    using System;
-    using Properties;
 
 #if NOSYSNUMERICS
     using Complex = Numerics.Complex;
@@ -46,6 +50,11 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
     /// </remarks>
     public abstract class GramSchmidt : GramSchmidt<Complex>
     {
+        protected GramSchmidt(Matrix<Complex> q, Matrix<Complex> rFull)
+            : base(q, rFull)
+        {
+        }
+
         /// <summary>
         /// Gets the absolute determinant value of the matrix for which the QR matrix was computed.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Complex/Factorization/UserGramSchmidt.cs b/src/Numerics/LinearAlgebra/Complex/Factorization/UserGramSchmidt.cs
index cd30749e..6e7e873a 100644
--- a/src/Numerics/LinearAlgebra/Complex/Factorization/UserGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Complex/Factorization/UserGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,8 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-using MathNet.Numerics.Properties;
 using System;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
 {
@@ -47,7 +47,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class UserGramSchmidt : GramSchmidt
+    public sealed class UserGramSchmidt : GramSchmidt
     {
         /// <summary>
         /// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an unitary matrix 
@@ -57,51 +57,53 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public UserGramSchmidt(Matrix<Complex> matrix)
+        public static UserGramSchmidt Create(Matrix<Complex> matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            var q = matrix.Clone();
+            var r = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
 
-            for (var k = 0; k < Q.ColumnCount; k++)
+            for (var k = 0; k < q.ColumnCount; k++)
             {
-                var norm = Q.Column(k).L2Norm();
+                var norm = q.Column(k).L2Norm();
                 if (norm == 0.0)
                 {
                     throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
                 }
 
-                MatrixR.At(k, k, norm);
-                for (var i = 0; i < Q.RowCount; i++)
+                r.At(k, k, norm);
+                for (var i = 0; i < q.RowCount; i++)
                 {
-                    Q.At(i, k, Q.At(i, k) / norm);
+                    q.At(i, k, q.At(i, k) / norm);
                 }
 
-                for (var j = k + 1; j < Q.ColumnCount; j++)
+                for (var j = k + 1; j < q.ColumnCount; j++)
                 {
                     var dot = Complex.Zero;
-                    for (int i = 0; i < Q.RowCount; i++)
+                    for (int i = 0; i < q.RowCount; i++)
                     {
-                        dot += Q.Column(k)[i].Conjugate() * Q.Column(j)[i];
+                        dot += q.Column(k)[i].Conjugate() * q.Column(j)[i];
                     }
                     
-                    MatrixR.At(k, j, dot);
-                    for (var i = 0; i < Q.RowCount; i++)
+                    r.At(k, j, dot);
+                    for (var i = 0; i < q.RowCount; i++)
                     {
-                        var value = Q.At(i, j) - (Q.At(i, k) * dot);
-                        Q.At(i, j, value);
+                        var value = q.At(i, j) - (q.At(i, k) * dot);
+                        q.At(i, j, value);
                     }
                 }
             }
+
+            return new UserGramSchmidt(q, r);
+        }
+
+        UserGramSchmidt(Matrix<Complex> q, Matrix<Complex> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -111,17 +113,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<Complex> input, Matrix<Complex> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -196,16 +187,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<Complex> input, Vector<Complex> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
diff --git a/src/Numerics/LinearAlgebra/Complex/Matrix.cs b/src/Numerics/LinearAlgebra/Complex/Matrix.cs
index 96b1090d..2fde3cc5 100644
--- a/src/Numerics/LinearAlgebra/Complex/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/Matrix.cs
@@ -475,7 +475,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
 
         public override GramSchmidt<Complex> GramSchmidt()
         {
-            return new UserGramSchmidt(this);
+            return UserGramSchmidt.Create(this);
         }
 
         public override Svd<Complex> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
index 8c36d9cf..1d6f10d1 100644
--- a/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
@@ -1021,7 +1021,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
 
         public override GramSchmidt<Complex32> GramSchmidt()
         {
-            return new DenseGramSchmidt(this);
+            return DenseGramSchmidt.Create(this);
         }
 
         public override Svd<Complex32> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Complex32/Factorization/DenseGramSchmidt.cs b/src/Numerics/LinearAlgebra/Complex32/Factorization/DenseGramSchmidt.cs
index 0901e869..8c638910 100644
--- a/src/Numerics/LinearAlgebra/Complex32/Factorization/DenseGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/Factorization/DenseGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,10 +28,9 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
 using MathNet.Numerics.Properties;
-using System;
-using MathNet.Numerics.Providers.LinearAlgebra;
 
 namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 {
@@ -44,13 +43,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class DenseGramSchmidt : GramSchmidt
+    public sealed class DenseGramSchmidt : GramSchmidt
     {
-        /// <summary>
-        /// used for QR solve
-        /// </summary>
-        private readonly ILinearAlgebraProvider _provider = new ManagedLinearAlgebraProvider();
-
         /// <summary>
         /// Initializes a new instance of the <see cref="DenseGramSchmidt"/> class. This object creates an unitary matrix 
         /// using the modified Gram-Schmidt method.
@@ -59,21 +53,23 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public DenseGramSchmidt(DenseMatrix matrix)
+        public static DenseGramSchmidt Create(DenseMatrix matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
-            Factorize(((DenseMatrix)Q).Values, Q.RowCount, Q.ColumnCount, ((DenseMatrix)MatrixR).Values);
+            var q = (DenseMatrix)matrix.Clone();
+            var r = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            Factorize(q.Values, q.RowCount, q.ColumnCount, r.Values);
+
+            return new DenseGramSchmidt(q, r);
+        }
+
+        DenseGramSchmidt(Matrix<Complex32> q, Matrix<Complex32> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -133,17 +129,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<Complex32> input, Matrix<Complex32> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -174,7 +159,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense matrices at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
         }
 
         /// <summary>
@@ -184,16 +169,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<Complex32> input, Vector<Complex32> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
@@ -219,7 +194,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense vectors at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
         }
     }
 }
diff --git a/src/Numerics/LinearAlgebra/Complex32/Factorization/GramSchmidt.cs b/src/Numerics/LinearAlgebra/Complex32/Factorization/GramSchmidt.cs
index 0354c4d4..33bcd896 100644
--- a/src/Numerics/LinearAlgebra/Complex32/Factorization/GramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/Factorization/GramSchmidt.cs
@@ -3,7 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// Copyright (c) 2009-2010 Math.NET
+//
+// Copyright (c) 2009-2013 Math.NET
+//
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
 // files (the "Software"), to deal in the Software without
@@ -12,8 +14,10 @@
 // copies of the Software, and to permit persons to whom the
 // Software is furnished to do so, subject to the following
 // conditions:
+//
 // The above copyright notice and this permission notice shall be
 // included in all copies or substantial portions of the Software.
+//
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 // OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
@@ -24,13 +28,13 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 {
-    using System;
     using Numerics;
-    using Properties;
 
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition Modified Gram-Schmidt Orthogonalization.</para>
@@ -41,6 +45,11 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
     /// </remarks>
     public abstract class GramSchmidt : GramSchmidt<Complex32>
     {
+        protected GramSchmidt(Matrix<Complex32> q, Matrix<Complex32> rFull)
+            : base(q, rFull)
+        {
+        }
+
         /// <summary>
         /// Gets the absolute determinant value of the matrix for which the QR matrix was computed.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Complex32/Factorization/UserGramSchmidt.cs b/src/Numerics/LinearAlgebra/Complex32/Factorization/UserGramSchmidt.cs
index e2ac7284..e9614d9b 100644
--- a/src/Numerics/LinearAlgebra/Complex32/Factorization/UserGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/Factorization/UserGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,8 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-using MathNet.Numerics.Properties;
 using System;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 {
@@ -42,7 +42,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class UserGramSchmidt : GramSchmidt
+    public sealed class UserGramSchmidt : GramSchmidt
     {
         /// <summary>
         /// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an unitary matrix 
@@ -52,51 +52,53 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public UserGramSchmidt(Matrix<Complex32> matrix)
+        public static UserGramSchmidt Create(Matrix<Complex32> matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            var q = matrix.Clone();
+            var r = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
 
-            for (var k = 0; k < Q.ColumnCount; k++)
+            for (var k = 0; k < q.ColumnCount; k++)
             {
-                var norm = Q.Column(k).L2Norm().Real;
+                var norm = q.Column(k).L2Norm().Real;
                 if (norm == 0.0f)
                 {
                     throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
                 }
 
-                MatrixR.At(k, k, norm);
-                for (var i = 0; i < Q.RowCount; i++)
+                r.At(k, k, norm);
+                for (var i = 0; i < q.RowCount; i++)
                 {
-                    Q.At(i, k, Q.At(i, k) / norm);
+                    q.At(i, k, q.At(i, k) / norm);
                 }
 
-                for (var j = k + 1; j < Q.ColumnCount; j++)
+                for (var j = k + 1; j < q.ColumnCount; j++)
                 {
                     var dot = Complex32.Zero;
-                    for (int i = 0; i < Q.RowCount; i++)
+                    for (int i = 0; i < q.RowCount; i++)
                     {
-                        dot += Q.Column(k)[i].Conjugate() * Q.Column(j)[i];
+                        dot += q.Column(k)[i].Conjugate() * q.Column(j)[i];
                     }
                     
-                    MatrixR.At(k, j, dot);
-                    for (var i = 0; i < Q.RowCount; i++)
+                    r.At(k, j, dot);
+                    for (var i = 0; i < q.RowCount; i++)
                     {
-                        var value = Q.At(i, j) - (Q.At(i, k) * dot);
-                        Q.At(i, j, value);
+                        var value = q.At(i, j) - (q.At(i, k) * dot);
+                        q.At(i, j, value);
                     }
                 }
             }
+
+            return new UserGramSchmidt(q, r);
+        }
+
+        UserGramSchmidt(Matrix<Complex32> q, Matrix<Complex32> rFull)
+            : base(q, rFull)
+        {
         }
         
         /// <summary>
@@ -106,17 +108,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<Complex32> input, Matrix<Complex32> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -191,16 +182,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<Complex32> input, Vector<Complex32> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
diff --git a/src/Numerics/LinearAlgebra/Complex32/Matrix.cs b/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
index 4ba57d64..156964b6 100644
--- a/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
@@ -470,7 +470,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
 
         public override GramSchmidt<Complex32> GramSchmidt()
         {
-            return new UserGramSchmidt(this);
+            return UserGramSchmidt.Create(this);
         }
 
         public override Svd<Complex32> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs
index 645650d3..87d3480e 100644
--- a/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs
@@ -1052,7 +1052,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
         public override GramSchmidt<double> GramSchmidt()
         {
-            return new DenseGramSchmidt(this);
+            return DenseGramSchmidt.Create(this);
         }
 
         public override Svd<double> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Double/Factorization/DenseGramSchmidt.cs b/src/Numerics/LinearAlgebra/Double/Factorization/DenseGramSchmidt.cs
index 44adebb0..70bf4cb8 100644
--- a/src/Numerics/LinearAlgebra/Double/Factorization/DenseGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Double/Factorization/DenseGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,10 +28,9 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
 using MathNet.Numerics.Properties;
-using System;
-using MathNet.Numerics.Providers.LinearAlgebra;
 
 namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
@@ -42,13 +41,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class DenseGramSchmidt : GramSchmidt
+    public sealed class DenseGramSchmidt : GramSchmidt
     {
-        /// <summary>
-        /// used for QR solve
-        /// </summary>
-        private readonly ILinearAlgebraProvider _provider = new ManagedLinearAlgebraProvider();
-
         /// <summary>
         /// Initializes a new instance of the <see cref="DenseGramSchmidt"/> class. This object creates an orthogonal matrix 
         /// using the modified Gram-Schmidt method.
@@ -57,21 +51,23 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public DenseGramSchmidt(DenseMatrix matrix)
+        public static DenseGramSchmidt Create(DenseMatrix matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
-            Factorize(((DenseMatrix)Q).Values, Q.RowCount, Q.ColumnCount, ((DenseMatrix)MatrixR).Values);
+            var q = (DenseMatrix)matrix.Clone();
+            var r = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            Factorize(q.Values, q.RowCount, q.ColumnCount, r.Values);
+
+            return new DenseGramSchmidt(q, r);
+        }
+
+        DenseGramSchmidt(Matrix<double> q, Matrix<double> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -131,17 +127,6 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<double> input, Matrix<double> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -172,7 +157,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense matrices at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
         }
 
         /// <summary>
@@ -182,16 +167,6 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<double> input, Vector<double> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
@@ -217,7 +192,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense vectors at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
         }
     }
 }
diff --git a/src/Numerics/LinearAlgebra/Double/Factorization/GramSchmidt.cs b/src/Numerics/LinearAlgebra/Double/Factorization/GramSchmidt.cs
index d4305f67..1e1b34a2 100644
--- a/src/Numerics/LinearAlgebra/Double/Factorization/GramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Double/Factorization/GramSchmidt.cs
@@ -3,7 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// Copyright (c) 2009-2010 Math.NET
+//
+// Copyright (c) 2009-2013 Math.NET
+//
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
 // files (the "Software"), to deal in the Software without
@@ -12,8 +14,10 @@
 // copies of the Software, and to permit persons to whom the
 // Software is furnished to do so, subject to the following
 // conditions:
+//
 // The above copyright notice and this permission notice shall be
 // included in all copies or substantial portions of the Software.
+//
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 // OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
@@ -24,13 +28,12 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
-    using System;
-    using Properties;
-
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition Modified Gram-Schmidt Orthogonalization.</para>
     /// <para>Any real square matrix A may be decomposed as A = QR where Q is an orthogonal mxn matrix and R is an nxn upper triangular matrix.</para>
@@ -40,6 +43,11 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
     /// </remarks>
     public abstract class GramSchmidt : GramSchmidt<double>
     {
+        protected GramSchmidt(Matrix<double> q, Matrix<double> rFull)
+            : base(q,rFull)
+        {
+        }
+
         /// <summary>
         /// Gets the absolute determinant value of the matrix for which the QR matrix was computed.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Double/Factorization/UserGramSchmidt.cs b/src/Numerics/LinearAlgebra/Double/Factorization/UserGramSchmidt.cs
index a0ec61c3..ba902841 100644
--- a/src/Numerics/LinearAlgebra/Double/Factorization/UserGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Double/Factorization/UserGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,8 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-using MathNet.Numerics.Properties;
 using System;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
@@ -40,7 +40,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class UserGramSchmidt : GramSchmidt
+    public sealed class UserGramSchmidt : GramSchmidt
     {
         /// <summary>
         /// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an orthogonal matrix 
@@ -50,46 +50,48 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public UserGramSchmidt(Matrix<double> matrix)
+        public static UserGramSchmidt Create(Matrix<double> matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            var q = matrix.Clone();
+            var r = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
 
-            for (var k = 0; k < Q.ColumnCount; k++)
+            for (var k = 0; k < q.ColumnCount; k++)
             {
-                var norm = Q.Column(k).L2Norm();
+                var norm = q.Column(k).L2Norm();
                 if (norm == 0.0)
                 {
                     throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
                 }
 
-                MatrixR.At(k, k, norm);
-                for (var i = 0; i < Q.RowCount; i++)
+                r.At(k, k, norm);
+                for (var i = 0; i < q.RowCount; i++)
                 {
-                    Q.At(i, k, Q.At(i, k) / norm);
+                    q.At(i, k, q.At(i, k) / norm);
                 }
 
-                for (var j = k + 1; j < Q.ColumnCount; j++)
+                for (var j = k + 1; j < q.ColumnCount; j++)
                 {
-                    var dot = Q.Column(k).DotProduct(Q.Column(j));
-                    MatrixR.At(k, j, dot);
-                    for (var i = 0; i < Q.RowCount; i++)
+                    var dot = q.Column(k).DotProduct(q.Column(j));
+                    r.At(k, j, dot);
+                    for (var i = 0; i < q.RowCount; i++)
                     {
-                        var value = Q.At(i, j) - (Q.At(i, k) * dot);
-                        Q.At(i, j, value);
+                        var value = q.At(i, j) - (q.At(i, k) * dot);
+                        q.At(i, j, value);
                     }
                 }
             }
+
+            return new UserGramSchmidt(q, r);
+        }
+
+        UserGramSchmidt(Matrix<double> q, Matrix<double> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -99,17 +101,6 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<double> input, Matrix<double> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -184,16 +175,6 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<double> input, Vector<double> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
diff --git a/src/Numerics/LinearAlgebra/Double/Matrix.cs b/src/Numerics/LinearAlgebra/Double/Matrix.cs
index e4b5d074..5ad949dd 100644
--- a/src/Numerics/LinearAlgebra/Double/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/Matrix.cs
@@ -476,7 +476,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
         public override GramSchmidt<double> GramSchmidt()
         {
-            return new UserGramSchmidt(this);
+            return UserGramSchmidt.Create(this);
         }
 
         public override Svd<double> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Factorization/GramSchmidt.cs b/src/Numerics/LinearAlgebra/Factorization/GramSchmidt.cs
index 68b09636..1cb59e1b 100644
--- a/src/Numerics/LinearAlgebra/Factorization/GramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Factorization/GramSchmidt.cs
@@ -3,7 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// Copyright (c) 2009-2010 Math.NET
+//
+// Copyright (c) 2009-2013 Math.NET
+//
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
 // files (the "Software"), to deal in the Software without
@@ -12,8 +14,10 @@
 // copies of the Software, and to permit persons to whom the
 // Software is furnished to do so, subject to the following
 // conditions:
+//
 // The above copyright notice and this permission notice shall be
 // included in all copies or substantial portions of the Software.
+//
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 // OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
@@ -39,5 +43,10 @@ namespace MathNet.Numerics.LinearAlgebra.Factorization
     public abstract class GramSchmidt<T> : QR<T>
     where T : struct, IEquatable<T>, IFormattable
     {
+        protected GramSchmidt(Matrix<T> q, Matrix<T> rFull)
+        {
+            Q = q;
+            MatrixR = rFull;
+        }
     }
 }
diff --git a/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs
index 99b1c773..88d2cb11 100644
--- a/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs
@@ -1052,7 +1052,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
 
         public override GramSchmidt<float> GramSchmidt()
         {
-            return new DenseGramSchmidt(this);
+            return DenseGramSchmidt.Create(this);
         }
 
         public override Svd<float> Svd(bool computeVectors)
diff --git a/src/Numerics/LinearAlgebra/Single/Factorization/DenseGramSchmidt.cs b/src/Numerics/LinearAlgebra/Single/Factorization/DenseGramSchmidt.cs
index 16579149..c5b803ff 100644
--- a/src/Numerics/LinearAlgebra/Single/Factorization/DenseGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Single/Factorization/DenseGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,10 +28,9 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
 using MathNet.Numerics.Properties;
-using System;
-using MathNet.Numerics.Providers.LinearAlgebra;
 
 namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 {
@@ -42,13 +41,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class DenseGramSchmidt : GramSchmidt
+    public sealed class DenseGramSchmidt : GramSchmidt
     {
-        /// <summary>
-        /// used for QR solve
-        /// </summary>
-        private readonly ILinearAlgebraProvider _provider = new ManagedLinearAlgebraProvider();
-
         /// <summary>
         /// Initializes a new instance of the <see cref="DenseGramSchmidt"/> class. This object creates an orthogonal matrix 
         /// using the modified Gram-Schmidt method.
@@ -57,21 +51,23 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public DenseGramSchmidt(DenseMatrix matrix)
+        public static DenseGramSchmidt Create(DenseMatrix matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
-            Factorize(((DenseMatrix)Q).Values, Q.RowCount, Q.ColumnCount, ((DenseMatrix)MatrixR).Values);
+            var q = (DenseMatrix)matrix.Clone();
+            var r = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            Factorize(q.Values, q.RowCount, q.ColumnCount, r.Values);
+
+            return new DenseGramSchmidt(q, r);
+        }
+
+        DenseGramSchmidt(Matrix<float> q, Matrix<float> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -131,17 +127,6 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<float> input, Matrix<float> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -172,7 +157,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense matrices at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
         }
 
         /// <summary>
@@ -182,16 +167,6 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<float> input, Vector<float> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
@@ -217,7 +192,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
                 throw new NotSupportedException("Can only do GramSchmidt factorization for dense vectors at the moment.");
             }
 
-            _provider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
+            Control.LinearAlgebraProvider.QRSolveFactored(((DenseMatrix)Q).Values, ((DenseMatrix)MatrixR).Values, Q.RowCount, MatrixR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
         }
     }
 }
diff --git a/src/Numerics/LinearAlgebra/Single/Factorization/GramSchmidt.cs b/src/Numerics/LinearAlgebra/Single/Factorization/GramSchmidt.cs
index 9b26dc26..f58ae735 100644
--- a/src/Numerics/LinearAlgebra/Single/Factorization/GramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Single/Factorization/GramSchmidt.cs
@@ -3,7 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// Copyright (c) 2009-2010 Math.NET
+//
+// Copyright (c) 2009-2013 Math.NET
+//
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
 // files (the "Software"), to deal in the Software without
@@ -12,8 +14,10 @@
 // copies of the Software, and to permit persons to whom the
 // Software is furnished to do so, subject to the following
 // conditions:
+//
 // The above copyright notice and this permission notice shall be
 // included in all copies or substantial portions of the Software.
+//
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 // OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
@@ -24,13 +28,12 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Factorization;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 {
-    using System;
-    using Properties;
-
     /// <summary>
     /// <para>A class which encapsulates the functionality of the QR decomposition Modified Gram-Schmidt Orthogonalization.</para>
     /// <para>Any real square matrix A may be decomposed as A = QR where Q is an orthogonal mxn matrix and R is an nxn upper triangular matrix.</para>
@@ -40,6 +43,11 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
     /// </remarks>
     public abstract class GramSchmidt : GramSchmidt<float>
     {
+        protected GramSchmidt(Matrix<float> q, Matrix<float> rFull)
+            : base(q, rFull)
+        {
+        }
+
         /// <summary>
         /// Gets the absolute determinant value of the matrix for which the QR matrix was computed.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Single/Factorization/UserGramSchmidt.cs b/src/Numerics/LinearAlgebra/Single/Factorization/UserGramSchmidt.cs
index 21773ed0..bf983bdd 100644
--- a/src/Numerics/LinearAlgebra/Single/Factorization/UserGramSchmidt.cs
+++ b/src/Numerics/LinearAlgebra/Single/Factorization/UserGramSchmidt.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,8 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-using MathNet.Numerics.Properties;
 using System;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 {
@@ -40,7 +40,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
     /// <remarks>
     /// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
     /// </remarks>
-    public class UserGramSchmidt : GramSchmidt
+    public sealed class UserGramSchmidt : GramSchmidt
     {
         /// <summary>
         /// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an orthogonal matrix 
@@ -50,46 +50,48 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// <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>
         /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
-        public UserGramSchmidt(Matrix<float> matrix)
+        public static UserGramSchmidt Create(Matrix<float> matrix)
         {
-            if (matrix == null)
-            {
-                throw new ArgumentNullException("matrix");
-            }
-
             if (matrix.RowCount < matrix.ColumnCount)
             {
                 throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
             }
 
-            Q = matrix.Clone();
-            MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
+            var q = matrix.Clone();
+            var r = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
 
-            for (var k = 0; k < Q.ColumnCount; k++)
+            for (var k = 0; k < q.ColumnCount; k++)
             {
-                var norm = Q.Column(k).L2Norm();
+                var norm = q.Column(k).L2Norm();
                 if (norm == 0.0)
                 {
                     throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
                 }
 
-                MatrixR.At(k, k, norm);
-                for (var i = 0; i < Q.RowCount; i++)
+                r.At(k, k, norm);
+                for (var i = 0; i < q.RowCount; i++)
                 {
-                    Q.At(i, k, Q.At(i, k) / norm);
+                    q.At(i, k, q.At(i, k) / norm);
                 }
 
-                for (var j = k + 1; j < Q.ColumnCount; j++)
+                for (var j = k + 1; j < q.ColumnCount; j++)
                 {
-                    var dot = Q.Column(k).DotProduct(Q.Column(j));
-                    MatrixR.At(k, j, dot);
-                    for (var i = 0; i < Q.RowCount; i++)
+                    var dot = q.Column(k).DotProduct(q.Column(j));
+                    r.At(k, j, dot);
+                    for (var i = 0; i < q.RowCount; i++)
                     {
-                        var value = Q.At(i, j) - (Q.At(i, k) * dot);
-                        Q.At(i, j, value);
+                        var value = q.At(i, j) - (q.At(i, k) * dot);
+                        q.At(i, j, value);
                     }
                 }
             }
+
+            return new UserGramSchmidt(q, r);
+        }
+
+        UserGramSchmidt(Matrix<float> q, Matrix<float> rFull)
+            : base(q, rFull)
+        {
         }
 
         /// <summary>
@@ -99,17 +101,6 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
         public override void Solve(Matrix<float> input, Matrix<float> result)
         {
-            // Check for proper arguments.
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // The solution X should have the same number of columns as B
             if (input.ColumnCount != result.ColumnCount)
             {
@@ -184,16 +175,6 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
         public override void Solve(Vector<float> input, Vector<float> result)
         {
-            if (input == null)
-            {
-                throw new ArgumentNullException("input");
-            }
-
-            if (result == null)
-            {
-                throw new ArgumentNullException("result");
-            }
-
             // Ax=b where A is an m x n matrix
             // Check that b is a column vector with m entries
             if (Q.RowCount != input.Count)
diff --git a/src/Numerics/LinearAlgebra/Single/Matrix.cs b/src/Numerics/LinearAlgebra/Single/Matrix.cs
index 109d9419..8ba5eb8e 100644
--- a/src/Numerics/LinearAlgebra/Single/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/Matrix.cs
@@ -476,7 +476,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
 
         public override GramSchmidt<float> GramSchmidt()
         {
-            return new UserGramSchmidt(this);
+            return UserGramSchmidt.Create(this);
         }
 
         public override Svd<float> Svd(bool computeVectors)
diff --git a/src/UnitTests/LinearAlgebraTests/Complex/Factorization/GramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Complex/Factorization/GramSchmidtTests.cs
index 861051f4..e154f359 100644
--- a/src/UnitTests/LinearAlgebraTests/Complex/Factorization/GramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Complex/Factorization/GramSchmidtTests.cs
@@ -24,10 +24,10 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Complex;
 using MathNet.Numerics.LinearAlgebra.Complex.Factorization;
 using NUnit.Framework;
-using System;
 
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
 {
@@ -38,22 +38,13 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
     /// </summary>
     public class GramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        [Test]
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new DenseGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new DenseGramSchmidt(new DenseMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => DenseGramSchmidt.Create(new DenseMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Complex/Factorization/UserGramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Complex/Factorization/UserGramSchmidtTests.cs
index 9b249b43..0af16ed7 100644
--- a/src/UnitTests/LinearAlgebraTests/Complex/Factorization/UserGramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Complex/Factorization/UserGramSchmidtTests.cs
@@ -24,33 +24,26 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
+using MathNet.Numerics.LinearAlgebra.Complex.Factorization;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
 {
-    using System;
     using System.Numerics;
-    using LinearAlgebra.Complex.Factorization;
-    using NUnit.Framework;
 
     /// <summary>
     /// GramSchmidt factorization tests for a user matrix.
     /// </summary>
     public class UserGramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new UserGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new UserGramSchmidt(new UserDefinedMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => UserGramSchmidt.Create(new UserDefinedMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/GramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/GramSchmidtTests.cs
index 0eb3cc08..5f2ba889 100644
--- a/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/GramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/GramSchmidtTests.cs
@@ -24,10 +24,10 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Complex32;
 using MathNet.Numerics.LinearAlgebra.Complex32.Factorization;
 using NUnit.Framework;
-using System;
 
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
 {
@@ -38,22 +38,13 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
     /// </summary>
     public class GramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        [Test]
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new DenseGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new DenseGramSchmidt(new DenseMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => DenseGramSchmidt.Create(new DenseMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/UserGramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/UserGramSchmidtTests.cs
index 363339b1..fd6f7be2 100644
--- a/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/UserGramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Complex32/Factorization/UserGramSchmidtTests.cs
@@ -24,33 +24,26 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
+using MathNet.Numerics.LinearAlgebra.Complex32.Factorization;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Factorization
 {
-    using System;
-    using LinearAlgebra.Complex32.Factorization;
-    using NUnit.Framework;
-    using Complex32 = Numerics.Complex32;
+    using Numerics;
 
     /// <summary>
     /// GramSchmidt factorization tests for a user matrix.
     /// </summary>
     public class UserGramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new UserGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new UserGramSchmidt(new UserDefinedMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => UserGramSchmidt.Create(new UserDefinedMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Double/Factorization/GramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Double/Factorization/GramSchmidtTests.cs
index 881371fc..743ab268 100644
--- a/src/UnitTests/LinearAlgebraTests/Double/Factorization/GramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Double/Factorization/GramSchmidtTests.cs
@@ -24,10 +24,10 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Double;
 using MathNet.Numerics.LinearAlgebra.Double.Factorization;
 using NUnit.Framework;
-using System;
 
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
 {
@@ -36,22 +36,13 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
     /// </summary>
     public class GramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        [Test]
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new DenseGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new DenseGramSchmidt(new DenseMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => DenseGramSchmidt.Create(new DenseMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserGramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserGramSchmidtTests.cs
index 2b9c1859..431a29c4 100644
--- a/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserGramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Double/Factorization/UserGramSchmidtTests.cs
@@ -24,32 +24,24 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
+using MathNet.Numerics.LinearAlgebra.Double.Factorization;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
 {
-    using System;
-    using LinearAlgebra.Double.Factorization;
-    using NUnit.Framework;
-
     /// <summary>
     /// GramSchmidt factorization tests for a user matrix.
     /// </summary>
     public class UserGramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new UserGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new UserGramSchmidt(new UserDefinedMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => UserGramSchmidt.Create(new UserDefinedMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Single/Factorization/GramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Single/Factorization/GramSchmidtTests.cs
index f987eaed..413c8493 100644
--- a/src/UnitTests/LinearAlgebraTests/Single/Factorization/GramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Single/Factorization/GramSchmidtTests.cs
@@ -24,10 +24,10 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using MathNet.Numerics.LinearAlgebra.Single;
 using MathNet.Numerics.LinearAlgebra.Single.Factorization;
 using NUnit.Framework;
-using System;
 
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
 {
@@ -36,22 +36,13 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
     /// </summary>
     public class GramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        [Test]
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new DenseGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new DenseGramSchmidt(new DenseMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => DenseGramSchmidt.Create(new DenseMatrix(3, 4)));
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Single/Factorization/UserGramSchmidtTests.cs b/src/UnitTests/LinearAlgebraTests/Single/Factorization/UserGramSchmidtTests.cs
index 36a54e31..331acb85 100644
--- a/src/UnitTests/LinearAlgebraTests/Single/Factorization/UserGramSchmidtTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Single/Factorization/UserGramSchmidtTests.cs
@@ -24,32 +24,24 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
+using MathNet.Numerics.LinearAlgebra.Single.Factorization;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
 {
-    using System;
-    using LinearAlgebra.Single.Factorization;
-    using NUnit.Framework;
-
     /// <summary>
     /// GramSchmidt factorization tests for a user matrix.
     /// </summary>
     public class UserGramSchmidtTests
     {
-        /// <summary>
-        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
-        /// </summary>
-        public void ConstructorNullThrowsArgumentNullException()
-        {
-            Assert.Throws<ArgumentNullException>(() => new UserGramSchmidt(null));
-        }
-
         /// <summary>
         /// Constructor with wide matrix throws <c>ArgumentException</c>.
         /// </summary>
         [Test]
         public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
         {
-            Assert.Throws<ArgumentException>(() => new UserGramSchmidt(new UserDefinedMatrix(3, 4)));
+            Assert.Throws<ArgumentException>(() => UserGramSchmidt.Create(new UserDefinedMatrix(3, 4)));
         }
 
         /// <summary>