MQL5 リファレンス行列とベクトルのメソッドOpenBLASSingular 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 left vectors
ENUM_BLAS_RANGE range, // subset of computed singular values
double lower, // lower limit of the subset
double upper, // upper limit of the subset
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 matrix::SingularValueDecompositionBidiagDC(
ENUM_SVDBIDIAG_Z jobz, // how to compute left vectors
ENUM_BLAS_RANGE range, // subset of computed singular values
double lower, // lower limit of the subset
double upper, // upper limit of the subset
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 left singular vectors should be computed.

range

[in] ENUM_BLAS_RANGE enumeration value that defines a subset of computable singular values and vectors.

lower

[in] The lower limit of singular values subset; specified depending on the value of the range parameter.

upper

[in] The upper limit of singular values subset; specified depending on the value of the range parameter.

[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.

ENUM_BLAS_RANGE

An enumeration defining how right singular vectors should be computed.

ID	Description
BLASRANGE_A	All singular or eigenvalues will be found.
BLASRANGE_V	All singular or eigenvalues in the half-open interval (VL,VU] will be found.
BLASRANGE_I	The IL-th through IU-th singular or eigenvalues will be found.