MQL5 リファレンス行列とベクトルのメソッドOpenBLASEigen ValuesGeneral MatricesEigenSolver2Blocked

EigenSolver2Blocked

Compute generalized eigenvalues and eigenvectors for a pair of regular square matrices using a block algorithm (lapack function GGEV3). Both matrices must be the same size. The method parameters are exactly the same as EigenSolver2.

Computing for type matrix<double>

bool matrix::EigenSolver2Blocked(
matrix& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorc& alpha, // vector of computed eigenvalues
vector& beta, // vector of eigenvalue divisors
matrix& left_eigenvectors, // matrix of computed left vectors
matrix& right_eigenvectors // matrix of computed right vectors
);

Computing for type matrix<float>

bool matrixf::EigenSolver2Blocked(
matrix& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorcf& alpha, // vector of computed eigenvalues
vectorf& beta, // vector of eigenvalue divisors
matrixf& left_eigenvectors, // matrix of computed left vectors
matrixf& right_eigenvectors // matrix of computed right vectors
);

Computing for type matrix<complex>

bool matrix::EigenSolver2Blocked(
matrixc& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorc& alpha, // vector of computed eigenvalues
vectorc& beta, // vector of eigenvalue divisors
matrixc& left_eigenvectors, // matrix of computed left vectors
matrixc& right_eigenvectors // matrix of computed right vectors
);

Computing for type matrix<complexf>

bool matrixcf::EigenSolver2(
matrixcf& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorcf& alpha, // vector of computed eigenvalues
vectorcf& beta, // vector of eigenvalue divisors
matrixcf& left_eigenvectors, // matrix of computed left vectors
matrixcf& right_eigenvectors // matrix of computed right vectors
);

Parameters

[out] The second matrix in the pair.

jobv

[in] ENUM_EIG_VECTORS enumeration value which determines the method for computing left and right eigenvectors.

alpha

[out] Vector of eigenvalues.

beta

[out] Vector of eigenvalue divisors.

left_eigenvectors

[out] Matrix of left eigenvectors.

righeft_eigenvectors

[out] Matrix of right eigenvectors.

Return Value

The function returns 'true' on success or 'false' if an error occurs.

Note

Computation depends on the value of the jobv parameter.

A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero.

The right eigenvector v(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies:

A * v(j) = lambda(j) * B * v(j).

The left eigenvector u(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies:

u(j)**H * A = lambda(j) * u(j)**H * B .

where u(j)**H is the conjugate-transpose of u(j).

Real (non-complex) matrices can have a complex solution. Therefore, the input vector of eigenvalues must be complex. In case of a complex solution, the error code is set to 4019 (ERR_MATH_OVERFLOW). Otherwise, only the real parts of the complex values of the eigenvalue vector should be used.

ENUM_EIG_VECTORS

An enumeration defining the need to compute eigenvectors.

ID	Description
EIGVECTORS_N	Only eigenvalues are computed, without vectors.
EIGVECTORS_L	Only left eigenvectors are computed.
EIGVECTORS_R	Only right eigenvectors are computed.
EIGVECTORS_LR	Left and right eigenvectors are computed, eigenvalues are always computed.

EigenSolver2Shur

EigenSolver2ShurBlocked