MQL5 RiferimentoMetodi Matriciali e VettorialiOpenBLASSingular Value DecompositionSingularValueDecompositionBidiagDC

SingularValueDecompositionBidiagDC

Singular Value Decomposition, divide-and-conquer algorithm for bidiagonal matrices (LAPACK function BDSDC).

Computing for type matrix<double>

bool  matrix::SingularValueDecompositionBidiagDC(
   ENUM_SVDBIDIAG_Z    jobz,       // how to compute singular vectors
   vector&             S,          // vector of computed singular values
   matrix&             U,          // U matrix of computed left vectors
   matrix&             VT          // VT transposed matrix of right vectors
   );

Computing for type matrix<float>

bool  matrixf::SingularValueDecompositionBidiagDC(
   ENUM_SVDBIDIAG_Z    jobz,       // how to compute singular vectors
   vectorf&            S,          // vector of computed singular values
   matrixf&            U,          // U matrix of computed left vectors
   matrixf&            VT          // VT transposed matrix of right vectors
   );

Parameters

jobz

[in] ENUM_SVDBIDIAG_Z enumeration value that determines how the singular vectors should be computed.

[out] Vector of singular values.

[out] Matrix of left singular vectors.

[out] Transposed matrix of right singular vectors.

Return Value

Return true if successful, otherwise false in case of an error.

Note

Computation depends on the values of the jobz and range parameters.

When BLASRANGE_A is set, all singular values are computed, and the lower and upper parameters are ignored.

With the BLASRANGE_V value, only those singular values (and their vectors) that fall within the range of real values specified by the 'lower' and 'upper' parameters are computed.

With the BLASRANGE_I value, only those singular values (and their vectors) that fall within the range of integer indices specified by the 'lower' and 'upper' parameters are computed. For example, with lower=0 and upper=2, only the first three singular values are computed.

A bidiagonal matrix is a square matrix with non-zero main diagonal and one of the sub-diagonals.

Upper bidiagonal matrix

[[x, x, 0, 0, 0],
[0, x, x, 0, 0],
[0, 0, x, x, 0],
[0, 0, 0, x, x],
[0, 0, 0, 0, x]]

Lower bidiagonal matrix

[[x, 0, 0, 0, 0],
[x, x, 0, 0, 0],
[0, x, x, 0, 0],
[0, 0, x, x, 0],
[0, 0, 0, x, x]]

ENUM_SVDBIDIAG_Z

An enumeration defining how left singular vectors should be computed.

ID	Description
SVDJOBZ_V	Compute singular values and singular vectors.
SVDJOBZ_N	Compute singular values only.