Msvd(Data: Array; Var U: Array; Var S: Array; Var V: Array);
Data. Input parameter, two-dimension array of the n×m size.
U. Input parameter, two-dimension array of the n×n size.
S. Output parameter, one-dimension array of the n size.
V. Output parameter, two-dimension array of the m×n size.
NOTE. The S parameter is a vector and contains items of main diagonal of the S matrix obtained via singular value decomposition.
The Msvd method returns the result of singular decomposition of a real matrix.
Singular value decomposition (SVD) is the decomposition of a rectangular float matrix into orthogonal matrices U and V and a diagonal matrix S, the product of U·S·V* results in the source matrix, where V* is a matrix transposed to V.
NOTE. Foresight Analytics Platform implements the economical version of SDV decomposition, due to which the condition of orthogonality of the U and V matrices may not be observed: the U and V matrices may be rectangular instead of square ones, and the products of the U·U* and V·V* may not result in a singular matrix. In this case a singular matrix is created only by means of the products U*·U and V*·V.
In general, the relation Data = U·S·V* does not have a unique solution. The Msvd method calculates one of the variants of solution.
To execute the example, add a link to the MathFin system assembly.
Sub UserProc;
Var
dimcol, dimrow: Integer;
matr: Array Of Double;
i, j : Integer;
U, S, V : Array Of Double;
str : String;
Begin
dimrow := 3;
dimcol := 5;
// Input matrix:
matr := New Double[dimrow, dimcol];
matr[0,0] := 1; matr[0,1] := 2; matr[0,2] := 0.2; matr[0,3] := 3; matr[0,4] := 8;
matr[1,0] := 0.5; matr[1,1] := -1; matr[1,2] := 2.2; matr[1,3] := 1.4; matr[1,4] := 2.1;
matr[2,0] := 0.7; matr[2,1] := 12; matr[2,2] := 10; matr[2,3] := 17; matr[2,4] := 0;
// Singular value decomposition of matrix:
math.Msvd(matr, U, S, V);
Debug.WriteLine("U = ");
For i:=0 To U.GetUpperBound(1) Do
str := "";
For j:=0 To U.GetUpperBound(2) Do
str := str + U[i,j].ToString + "; ";
End For;
Debug.WriteLine(str);
End For;
Debug.WriteLine("S = " );
str := "";
For i:=0 To S.GetUpperBound(1) Do
str := str + S[i].ToString + "; ";
End For;
Debug.WriteLine(str);
Debug.WriteLine("V = " );
For i:=0 To V.GetUpperBound(1) Do
str := "";
For j:=0 To V.GetUpperBound(2) Do
str := str + V[i,j].ToString + "; ";
End For;
Debug.WriteLine(str);
End For;
End Sub UserProc;
After executing the example the console window displays SVD decomposition of the source matrix.
U =
-0.165254675525592; 0.956389246351266; 0.240853693516601;
-0.0687713991903265; 0.232442607702064; -0.970175720567192;
-0.983850286817225; -0.176889919408434; 0.0273599989280314;
S =
23.4292158067414; 8.27738932394697; 2.55864664636389;
V =
-0.0379157195537407; 0.114624016244087; -0.0879692269494259;
-0.515080892728607; -0.053439935045388; 0.69575964983935;
-0.427792844804144; -0.128814480780358; -0.708427582151724;
-0.739141207464282; 0.0226470874442454; -0.0666621734228615;
-0.0625909699496861; 0.983310453119461; -0.0432023176062173;
See also: