MQL5 リファレンス行列とベクトルのメソッドOpenBLASMatrix BalanceEigenVectorsBackward

EigenVectorsBackward

Forms the right or left eigenvectors of a real or complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by MatrixBalance. LAPACK function GEBAK.

Computing for type matrix<double>

bool matrix::EigenVectorsBackward(
ENUM_EIG_BALANCE job, // matrix balancing method
ENUM_EIG_SIDE side, // right or left eigenvectors
long ilo, // subscript of balanced matrix
long ihi, // superscript of balanced matrix
vector& scale, // details of permutations and scaling when balancing the input matrix
matrix& V // eigenvectors
);

Computing for type matrix<float>

bool matrixf::EigenVectorsBackward(
ENUM_EIG_BALANCE job, // input matrix balancing method
ENUM_EIG_SIDE side, // right or left eigenvectors
long ilo, // subscript of balanced matrix
long ihi, // superscript of balanced matrix
vectorf& scale, // details of permutations and scaling when balancing the input matrix
matrixf& V // eigenvectors
);

Computing for type matrix<complex>

bool matrixc::EigenVectorsBackward(
ENUM_EIG_BALANCE job, // input matrix balancing method
ENUM_EIG_SIDE side, // right or left eigenvectors
long ilo, // subscript of balanced matrix
long ihi, // superscript of balanced matrix
vector& scale, // details of permutations and scaling when balancing the input matrix
matrixc& V // eigenvectors
);

Computing for type matrix<complexf>

bool matrixcf::EigenVectorsBackward(
ENUM_EIG_BALANCE job, // input matrix balancing method
ENUM_EIG_SIDE side, // right or left eigenvectors
long ilo, // subscript of balanced matrix
long ihi, // superscript of balanced matrix
vectorf& scale, // details of permutations and scaling when balancing the input matrix
matrixcf& V // eigenvectors
);

Parameters

job

[in] Value from the ENUM_EIG_BALANCE enumeration which determines the need and method for balancing the input matrix.

side

[in] Value from the ENUM_EIG_SIDE enumeration which determines the need and method for balancing the input matrix.

ilo

[in] Subscript of the balanced matrix. As returned by MatrixBalance.

ihi

[in] Superscript of the balanced matrix. As returned by MatrixBalance.

scale

[in] Vector of details of permutations and scaling when balancing the input matrix. As returned by MatrixBalance.

[out] Right or left eigenvectors backtransformed from the input eigenvectors.

Return Value

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

Note

When computing eigenvalues and eigenvectors, matrix balancing (scaling of rows and columns) is often used to improve numerical stability. This balancing is performed by the GEBAL function, which transforms the matrix into a "nicer" form.

After balancing and computing the eigenvectors of the transformed matrix, the result does not correspond to the original matrix. In this case, GEBAK is called to transform the eigenvectors back into the space of the original (unbalanced) matrix.

This method is applied to the matrix of right or left eigenvectors of balanced matrix. They can be produced by some eigen solver.

ENUM_EIG_BALANCE

An enumeration defining the need to compute eigenvectors.

ID	Description
EIGBALANCE_N	Do not diagonally scale or permute
EIGBALANCE_P	Perform permutations to make the matrix more nearly upper triangular. Do not diagonally scale
EIGBALANCE_S	Diagonally scale the matrix. Do not permute
EIGBALANCE_B	Both diagonally scale and permute

ENUM_EIG_SIDE

An enumeration defining the need to compute right or left eigenvectors.

ID	Description
EIGSIDE_R	'R': right eigenvectors
EIGSIDE_L	'L': left eigenvectors

MatrixBalance

ReduceToHessenbergBalanced