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

SingularValueDecompositionQRPivot

Singular Value Decomposition, QR with pivoting algorithm (lapack function GESVDQ).

Computing for type matrix<double>

bool matrix::SingularValueDecompositionQRPivot(
ENUM_SVDQRP_A joba, // computation accuracy level
ENUM_SVDQRP_P jobp, // use row reversal to compute
ENUM_SVDQRP_R jobr, // use triangular matrix R to compute
ENUM_SVDQRP_U jobu, // how to compute left vectors
ENUM_SVDQRP_V jobv, // how to compute right vectors
vector S, // vector of computed singular values
matrix U, // matrix of computed left vectors U
matrix VT // transposed matrix of right vectors VT
);

Computing for type matrix<float>

bool matrix::SingularValueDecompositionQRPivot(
ENUM_SVDQRP_A joba, // computation accuracy level
ENUM_SVDQRP_P jobp, // use row reversal to compute
ENUM_SVDQRP_R jobr, // use triangular matrix R to compute
ENUM_SVDQRP_U jobu, // how to compute left vectors
ENUM_SVDQRP_V jobv, // how to compute right vectors
vectorf S, // vector of computed singular values
matrixf U, // matrix of computed left vectors U
matrixf VT // transposed matrix of right vectors VT
);

Computing for type matrix<complex>

bool matrix::SingularValueDecompositionQRPivot(
ENUM_SVDQRP_A joba, // computation accuracy level
ENUM_SVDQRP_P jobp, // use row reversal to compute
ENUM_SVDQRP_R jobr, // use triangular matrix R to compute
ENUM_SVDQRP_U jobu, // how to compute left vectors
ENUM_SVDQRP_V jobv, // how to compute right vectors
vector S, // vector of computed singular values
matrixc U, // matrix of computed left vectors U
matrixc VT // transposed matrix of right vectors VT
);

Parameters

joba

[in] ENUM_SVDQRP_A enumeration value defining the accuracy level of the SVD computation.

jobp

[in] ENUM_SVDQRP_P enumeration value defining the use of row reversal during the computation process.

jobr

[in] ENUM_SVDQRP_R enumeration value defining whether to transpose the triangular matrix R obtained as a result of the initial QR factorization.

jobu

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

jobv

[in] ENUM_SVDQRP_V enumeration value defining how the right singular vectors should be computed.

[out] Vector of singular values.

[out] Matrix of left singular vectors.

[out] Matrix of right singular vectors.

Return Value

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

Note

The number of matrix rows must not be less than the number of columns.

If both left and right singular vectors are computed, jobv must be set to SVDQRPV_R when jobu=SVDQRPU_R.

ENUM_SVDQRP_A

An enumeration that specifies the level of accuracy of the SVD computation.

ID	Description
SVDQRP_A	The requested accuracy corresponds to the inverse error limited by epsilon. This is an aggressive level of truncation.
SVDQRPA_M	Similar to SVDQRP_A, but the truncation is softer. This is the average level of truncation.
SVDQRPA_H	High accuracy is required.

ENUM_SVDQRP_P

An enumeration that specifies whether to use row reversal during calculation.

ID	Description
SVDQRPP_P	The rows of A are ordered in descending order. Recommended for numerical reliability.
SVDQRPP_N	No row reversal.

ENUM_SVDQRP_R

An enumeration that specifies whether to transpose the triangular matrix R obtained as a result of the initial QR factorization.

ID	Description
SVDQRPR_T	After the initial rotated QR factorization, GESVD is applied to the transpose R**T of the calculated triangular factor R.
SVDQRPR_N	The triangular factor R is given as input to GESVD.

ENUM_SVDQRP_U

An enumeration defining how left singular vectors should be computed.

ID	Description
SVDQRPU_A	All M left singular vectors are computed.
SVDQRPU_S	The min(M,N) left singular vectors are computed.
SVDQRPU_R	The numerical rank NUMRANK is determined and only the NUMRANK of the left singular vectors is computed.
SVDQRPU_F	N left singular vectors are returned.
SVDQRPU_N	Left singular vectors are not computed.

ENUM_SVDQRP_V

An enumeration defining how right singular vectors should be computed.

ID	Description
SVDQRPV_A	All N right singular vectors are computed.
SVDQRPV_R	The numerical rank NUMRANK is defined and only the NUMRANK of right singular vectors are computed.
SVDQRPV_N	Right singular vectors are not computed.