LA: Matrix Rank calculation should use a tolerance based on the matrix size #334

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

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2015 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -71,7 +71,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
         {
             get
             {
-                return S.Count(t => !t.Magnitude.AlmostEqual(0.0));
+                double tolerance = Precision.DoublePrecision*Math.Max(U.RowCount, VT.RowCount);
+                return S.Count(t => t.Magnitude > tolerance);
             }
         }
 

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

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2015 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -39,13 +39,13 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 
     /// <summary>
     /// <para>A class which encapsulates the functionality of the singular value decomposition (SVD).</para>
-    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers. 
+    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers.
     /// Then there exists a factorization of the form M = UΣVT where:
     /// - U is an m-by-m unitary matrix;
     /// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
-    /// - VT denotes transpose of V, an n-by-n unitary matrix; 
-    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal 
-    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined 
+    /// - VT denotes transpose of V, an n-by-n unitary matrix;
+    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
+    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
     /// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.</para>
     /// </summary>
     /// <remarks>
@@ -66,7 +66,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
         {
             get
             {
-                return S.Count(t => !t.Magnitude.AlmostEqual(0.0f));
+                double tolerance = Precision.SinglePrecision*Math.Max(U.RowCount, VT.RowCount);
+                return S.Count(t => t.Magnitude > tolerance);
             }
         }
 

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

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2015 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -37,13 +37,13 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
     /// <summary>
     /// <para>A class which encapsulates the functionality of the singular value decomposition (SVD).</para>
-    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers. 
+    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers.
     /// Then there exists a factorization of the form M = UΣVT where:
     /// - U is an m-by-m unitary matrix;
     /// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
-    /// - VT denotes transpose of V, an n-by-n unitary matrix; 
-    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal 
-    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined 
+    /// - VT denotes transpose of V, an n-by-n unitary matrix;
+    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
+    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
     /// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.</para>
     /// </summary>
     /// <remarks>
@@ -64,7 +64,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
         {
             get
             {
-                return S.Count(t => !Math.Abs(t).AlmostEqual(0.0));
+                double tolerance = Precision.DoublePrecision*Math.Max(U.RowCount, VT.RowCount);
+                return S.Count(t => Math.Abs(t) > tolerance);
             }
         }
 

src/Numerics/LinearAlgebra/Factorization/Svd.cs

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2015 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -35,13 +35,13 @@ namespace MathNet.Numerics.LinearAlgebra.Factorization
 {
     /// <summary>
     /// <para>A class which encapsulates the functionality of the singular value decomposition (SVD).</para>
-    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers. 
+    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers.
     /// Then there exists a factorization of the form M = UΣVT where:
     /// - U is an m-by-m unitary matrix;
     /// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
-    /// - VT denotes transpose of V, an n-by-n unitary matrix; 
-    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal 
-    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined 
+    /// - VT denotes transpose of V, an n-by-n unitary matrix;
+    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
+    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
     /// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.</para>
     /// </summary>
     /// <remarks>

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

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2015 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -37,13 +37,13 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 {
     /// <summary>
     /// <para>A class which encapsulates the functionality of the singular value decomposition (SVD).</para>
-    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers. 
+    /// <para>Suppose M is an m-by-n matrix whose entries are real numbers.
     /// Then there exists a factorization of the form M = UΣVT where:
     /// - U is an m-by-m unitary matrix;
     /// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
-    /// - VT denotes transpose of V, an n-by-n unitary matrix; 
-    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal 
-    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined 
+    /// - VT denotes transpose of V, an n-by-n unitary matrix;
+    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
+    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
     /// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.</para>
     /// </summary>
     /// <remarks>
@@ -64,7 +64,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
         {
             get
             {
-                return S.Count(t => !Math.Abs(t).AlmostEqual(0.0f));
+                double tolerance = Precision.SinglePrecision*Math.Max(U.RowCount, VT.RowCount);
+                return S.Count(t => Math.Abs(t) > tolerance);
             }
         }