C# SV Decomp Example

← All NMath Code Examples

 

using System;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Matrix;

namespace CenterSpace.NMath.Matrix.Examples.CSharp
{
  /// <summary>
  /// A .NET example in C# demonstrating the features of the singular value decomposition (SVD) classes.
  /// </summary>
  class SVDecompExample
  {

    static void Main( string[] args )
    {
      // A general m x n system with random entries.
      var rng = new RandGenUniform( -1, 1 );
      rng.Reset( 0x124 );
      int rows = 6;
      int cols = 3;
      var A = new DoubleComplexMatrix( rows, cols, rng );

      // Construct a SV decomposition of A.
      var decomp = new DoubleComplexSVDecomp( A );

      Console.WriteLine();

      // Look at the components of the factorization A = USV'.
      Console.WriteLine( "U = " );
      Console.WriteLine( decomp.LeftVectors.ToTabDelimited( "G3" ) );

      Console.WriteLine( "B = " );
      Console.WriteLine( decomp.RightVectors.ToTabDelimited( "G3" ) );

      Console.WriteLine( "s = {0}", decomp.SingularValues );

      // U =
      // (-0.177,0.467)  (-0.204,0.0897) (0.0996,-0.151)
      // (0.102,0.0811)  (0.211,0.12)    (0.0504,-0.243)
      // (0.0774,-0.56)  (-0.261,0.0474) (0.133,0.382)
      // (0.247,-0.152)  (0.026,0.287)   (-0.449,-0.173)
      // (0.13,-0.513)   (0.165,-0.241)  (0.287,-0.644)
      // (-0.147,-0.168) (0.298,0.751)   (-0.0955,-0.0581)

      // B =
      // (0.556,0)       (0.674,0)       (-0.486,0)
      // (-0.644,-0.174) (0.512,-0.214)  (-0.0265,-0.496)
      // (-0.454,0.199)  (0.336,0.353)   (-0.0537,0.717)

      // s = [ 2.30473458507626 1.59555281597513 1.05912909184625 ]
      //
      // Note that the singular values, elements on the main diagonal of 
      // the diagonal matrix S, are returned as a vector.

      // The class DoubleComplexSVDecompServer allows more control over the 
      // computation. Suppose that you are only interested in the singular values,
      // not the vectors. You can configure a DoubleComplexSVDecompServer object
      // to compute just the singular values.
      var decompServer = new DoubleComplexSVDecompServer();
      decompServer.ComputeLeftVectors = false;
      decompServer.ComputeRightVectors = false;
      decomp = decompServer.GetDecomp( A );

      Console.WriteLine();
      Console.WriteLine( "Number of left vectors computed: {0}", decomp.NumberLeftVectors ); // 0

      Console.WriteLine();
      Console.WriteLine( "Number of right vectors computed: {0}", decomp.NumberRightVectors ); // 0

      // By default, the "reduced" SVD is computed; that is, if A is m x n, then U
      // is m x n. The "full" SVD is obtained by  adjoining an additional m-n
      // (assuming m > n) orthonormal columns to U making it a m x m unitary matrix. 
      // The singular value decomposition server object can be configured to
      // compute the full SVD as follows:
      decompServer.ComputeLeftVectors = true;
      decompServer.ComputeFull = true;
      decomp = decompServer.GetDecomp( A );

      Console.WriteLine();
      Console.WriteLine( "Full SVD, U = " );
      Console.WriteLine( decomp.LeftVectors.ToTabDelimited( "G5" ) );

      // Full SVD, U =
      // (-0.17729,0.46733)      (-0.20351,0.089678)     (0.099576,-0.15138)     (0.15718,-0.15252)      (0.62805,0.4364)        (-0.052634,-0.17958)
      // (0.10202,0.081075)      (0.21072,0.11971)       (0.0504,-0.2434)        (-0.1824,0.22817)       (-0.081697,0.34255)     (-0.60561,0.53516)
      // (0.077361,-0.55956)     (-0.26138,0.047439)     (0.13273,0.38226)       (0.038401,0.41859)      (0.431,0.038413)        (-0.2681,-0.10388)
      // (0.24748,-0.15212)      (0.026012,0.28707)      (-0.44923,-0.17313)     (0.70087,-0.030787)     (-0.1625,0.13184)       (-0.17238,-0.1873)
      // (0.12984,-0.51288)      (0.16486,-0.24073)      (0.28688,-0.64427)      (-0.073218,-0.25794)    (0.1492,0.089866)       (0.038802,-0.18397)
      // (-0.14678,-0.16813)     (0.29846,0.75096)       (-0.095458,-0.058056)   (-0.33519,0.11664)      (0.071816,0.15674)      (0.33872,-0.11948)
    
      // You can also set a tolerance for the singular values. Singular values 
      // whose value is less than the tolerance are set to zero. The number of
      // singular vectors are adjusted accordingly.
      // 
      // Make A rank deficient.
      A.Col( 0 )[Slice.All] = A.Col( 1 ); // Two equal columns.
      decompServer.ComputeFull = false;
      decompServer.ComputeLeftVectors = true;
      decompServer.ComputeRightVectors = true;
      decomp = decompServer.GetDecomp( A );

      Console.WriteLine( "Rank of A = {0}", decomp.Rank ); // 3

      // Apparently A has full rank. Let's look at the smallest
      // singular value. Singular values are arranged in descending
      // order, so the smallest value is the last value.
      Console.WriteLine();
      Console.WriteLine( "Smallest singular value = {0}", decomp.SingularValue( 2 ) ); //  5.48294957152069E-17

      // This singular value is equal to 0, which is within machine precision. Truncating 
      // the SVD will set this value to 0.
      double tolerance = 1e-16;
      decompServer.Tolerance = 1e-16;
      decomp = decompServer.GetDecomp( A );

      // Now look at the rank.
      Console.WriteLine( "Rank of A = {0}", decomp.Rank ); // 2

      // You can also truncate an existing decomp by calling its
      // truncate method with a specified tolerance.
      tolerance = 1e-12;
      decomp.Truncate( tolerance );

      Console.WriteLine();
      Console.WriteLine( "Press Enter Key" );
      Console.Read();
    }
  }
}

← All NMath Code Examples
Top