TMtx.SVDSolve Methods

Summary

Calculates the minimum norm solution to a real linear least squares problem.

Class
TMtx

Declaration

Function SVDSolve(B, X: TMtx; S: TVec; Threshold: TSample = 1E-9): integer;

Description

Matrix version of SVDSolve. Perfroms a SVDSolve for each U and V matrices columns in single pass.

Declaration

Function SVDSolve(B, X, S: TVec; Threshold: TSample = 1E-9): integer;

Description

Calculates the minimum norm solution to a real linear least squares problem.

Minimize 2-norm(| b - A*x |).

using the singular value decomposition (SVD) of the calling matrix A. A is an Rows-by-Cols matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call. The effective rank of A is determined by treating as zero those singular values which are less than Threshold times the largest singular value and is returned by the function. The S vector holds the singular values on the output.

See Also
SVD

Example 1

      var X,B,D: TVec;
        V: TMtx;
      begin
        CreateIt(X,B,D);
        CreateIt(V);
        try
          B.SetIt(false,[0,2,3]);
          V.SetIt(3,3,false,[1,2,3,
                             3,4,5,
                             6,7,7]);

          V.SVDSolve(B,X,D); // matrix V can be non-quadratic
        finally
          FreeIt(X,B,D);
          FreeIt(V);
        end;
      end;