MQL5 リファレンス行列とベクトルのメソッドOpenBLASSingular Value DecompositionSingularValueDecompositionBidiagBisect

SingularValueDecompositionBidiagBisect

Singular Value Decomposition, bisection algorithm for bidiagonal matrices (lapack function BDSVDX).

Computing for type matrix<double>

bool matrix::SingularValueDecompositionBidiagBisect(
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::SingularValueDecompositionBidiagBisect(
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

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.