MQL5 リファレンス行列とベクトルのメソッドOpenBLASEigen ValuesGeneral MatricesEigenSolver2Shur

EigenSolver2Shur

Compute a pair of ordinary square matrices of generalized eigenvalues, generalized eigenvectors, generalized Schur forms, as well as left and right Schur vectors (lapack function GGES).

Сomputes the generalized eigenvalues, the generalized real/complex Schur form (S,T), optionally, the left and/or right matrices of Schur vectors (vsl and vsr) for a pair of n-by-n real/complex nonsymmetric matrices (A,B). This gives the generalized Schur factorization:

(A,B) = ( vsl*S *vsrH, vsl*T*vsrH )

Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T. The leading columns of vsl and vsr then form an orthonormal/unitary basis for the corresponding left and right eigenspaces (deflating subspaces).

Computing for type matrix<double>

bool matrix::EigenSolver2Shur(
matrix& B, // second matrix in the pair
ENUM_EIG_VECTORS jobvs, // method to compute left and right vectors
vector& alpha, // vector of computed eigenvalues
vector& beta, // vector of eigenvalue divisors
matrix& shur_s, // matrix S in Schur form
matrix& shur_t, // matrix T in Schur form
matrix& vsl, // matrix of left Schur vectors vsl
matrix& vsr // matrix of right Schur vectors vsr
);

Computing for type matrix<float>

bool matrixf::EigenSolver2Shur(
matrixf& B, // second matrix in the pair
ENUM_EIG_VECTORS jobvs, // method to compute left and right vectors
vectorcf& alpha, // vector of computed eigenvalues
vectorf& beta, // vector of eigenvalue divisors
matrixf& shur_s, // matrix S in Schur form
matrixf& shur_t, // matrix T in Schur form
matrixf& vsl, // matrix of left Schur vectors vsl
matrixf& vsr // matrix of right Schur vectors vsr
);

Computing for type matrix<complex>

bool matrix::EigenSolver2Shur(
matrixc& B, // second matrix in the pair
ENUM_EIG_VECTORS jobvs, // method to compute left and right vectors
vectorc& alpha, // vector of computed eigenvalues
vectorc& beta, // vector of eigenvalue divisors
matrixc& shur_s, // matrix S in Schur form
matrixc& shur_t, // matrix T in Schur form
matrixc& vsl, // matrix of left Schur vectors vsl
matrixc& vsr // matrix of right Schur vectors vsr
);

Вычисления для типа matrix<complexf>

bool matrixcf::EigenSolver2Shur(
matrixcf& B, // second matrix in the pair
ENUM_EIG_VECTORS jobvs, // method to compute left and right vectors
vectorcf& alpha, // vector of computed eigenvalues
vectorcf& beta, // vector of eigenvalue divisors
matrixcf& shur_s, // matrix S in Schur form
matrixcf& shur_t, // matrix T in Schur form
matrixcf& vsl, // matrix of left Schur vectors vsl
matrixcf& vsr // matrix of right Schur vectors vsr
);

Parameters

[out] The second matrix in the pair.

jobvs

[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.

shur_s

[out] Matrix S, block upper triangular Schur matrix (Schur form for the input matrix).

shur_t

[out] Matrix T, block upper triangular Schur matrix (Schur form for the second matrix in the pair).

vsl

[out] Matrix of left Schur vectors.

vsr

[out] Matrix of right Schur vectors.

Return Value

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

Note

Computation depends on the jobvs parameter values.

The second matrix in the pair must be the same size as the first (input) one.

Real (non-complex) matrices can have a complex solution. Therefore, the 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.

EigenSolverShur

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.

EigenSolver2X

EigenSolver2Blocked