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

EigenSolverX

Compute eigenvalues and eigenvectors of a regular square matrix in Expert mode, i.e. with the ability to influence the computation algorithm and the ability to obtain accompanying computation data (lapack function GEEVX).

Computing for type matrix<double>

bool  matrix::EigenSolverX(
  ENUM_EIG_BALANCE     balance,    // input matrix balancing method
  ENUM_EIG_VECTORS     jobv,        // determines computation of right and left eigenvectors
  ENUM_EIG_SENSE       sense,      // determines computation of reciprocal condition numbers
  vector&               EV,          // vector of computed eigenvectors
  matrix&               VL,          // matrix of computed left vectors
  matrix&               VR,         // matrix of computed right vectors
  matrix&               shur,       // balanced matrix in Schur form
  long&               ilo,        // subscript of balanced matrix
  long&               ihi,        // superscript of balanced matrix
  vector&               scale,      // details of permutations and scaling when balancing the input matrix
  double&               one_norm,   // one-norm of balanced matrix
  vector&               rconde,      // vector of reciprocal condition numbers for each eigenvalue
  vector&               rcondv      // vector of reciprocal condition numbers for each eigenvector
  );

Computing for type matrix<complex>

bool  matrix::EigenSolverX(
  ENUM_EIG_BALANCE     balance,    // input matrix balancing method
  ENUM_EIG_VECTORS     jobv,        // determines computation of right and left eigenvectors
  ENUM_EIG_SENSE       sense,      // determines computation of reciprocal condition numbers
  vector&               EV,          // vector of computed eigenvectors
  matrixc&               VL,          // matrix of computed left vectors
  matrixc&               VR,         // matrix of computed right vectors
  matrixc&               shur,       // balanced matrix in Schur form
  long&               ilo,        // subscript of balanced matrix
  long&               ihi,        // superscript of balanced matrix
  vector&               scale,      // details of permutations and scaling when balancing the input matrix
  double&               one_norm,   // one-norm of balanced matrix
  vector&               rconde,      // vector of reciprocal condition numbers for each eigenvalue
  vector&               rcondv      // vector of reciprocal condition numbers for each eigenvector
  );

Parameters

balance

[in]  Value from the ENUM_EIG_BALANCE enumeration which determines the need and method for balancing the input matrix; it is used to improve the conditioning of the eigenvalues and eigenvectors.

jobv

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

sense

[in]  Value from the ENUM_EIG_SENSE enumeration determining the need to compute reciprocal condition numbers.

EV

[out] Vector of eigenvalues.

VL

[out] Matrix of left eigenvectors.

VR

[out] Matrix of right eigenvectors.

shur

[out]  Balanced matrix in Schur form; the matrix is not filled if neither left nor right eigenvectors are computed.

ilo

[out]  Subscript of the balanced matrix; the matrix is not filled if no balancing is applied.

ihi

[out]  Superscript of the balanced matrix; the matrix is not filled if no balancing is applied.

scale

[out]  Vector of details of permutations and scaling when balancing the input matrix.

Details of the permutations and scaling factors applied when balancing A.

If P(j) is the index of the row and column interchanged with row and column j, and D(j) is the scaling factor applied to row and column j, then

scale(j) = P(j), for j = 1,...,ilo-1

= D(j), for j = ilo,...,ihi

= P(j) for j = ihi+1,..., n.

The order in which the interchanges are made is n to ihi+1, then 1 to ilo-1.

one_norm

[out]  One-norm of the balanced matrix (the maximum of the sum of absolute values of elements in any of the matrix columns).

rconde

[out]  Vector of reciprocal condition numbers for each eigenvalue; it is computed if the 'sense' parameter is set to 'E' or 'B'.

rcondv

[out]  Vector of reciprocal condition numbers for each eigenvector; it is computed if the 'sense' parameter is set to 'V' or 'B.

Return Value

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

Note

Input matrix balancing depends on the value of the 'balance' parameter.

Description of the GEEVX function: https://www.irya.unam.mx/computo/sites/manuales/fce12/mkl/mkl_manual/lse/functn_geevx.htm

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_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.

 

ENUM_EIG_SENSE

An enumeration defining the need to compute eigenvectors.

ID

Description

EIGSENSE_N

None of reciprocal condition numbers are computed

EIGSENSE_E

Computed for eigenvalues only

EIGSENSE_V

Computed for right eigenvectors only

EIGSENSE_B      

Computed for eigenvalues and right eigenvectors