MQL5 ReferenceMatrix and Vector MethodsOpenBLASEigen 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
   vectorc&              eigen_values,            // vector of computed eigenvalues
   matrix&               left_eigenvectors,       // matrix of computed left vectors
   matrix&               right_eigenvectors       // matrix of computed right vectors
   matrix&               shur_matrix,             // 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&               ab_norm,                 // 1-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<float>

bool  matrixf::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
   vectorcf&             eigen_values,            // vector of computed eigenvalues
   matrixf&              left_eigenvectors,       // matrix of computed left vectors
   matrixf&              right_eigenvectors       // matrix of computed right vectors
   matrixf&              shur_matrix,             // balanced matrix in Schur form
   long&                 ilo,                     // subscript of balanced matrix
   long&                 ihi,                     // superscript of balanced matrix
   vectorf&              scale,                   // details of permutations and scaling when balancing the input matrix
   float&                ab_norm,                 // 1-norm of balanced matrix
   vectorf&              rconde,                  // vector of reciprocal condition numbers for each eigenvalue
   vectorf&              rcondv                   // vector of reciprocal condition numbers for each eigenvector
   );

Computing for type matrix<complex>

bool  matrixc::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
   vectorc&              eigen_values,            // vector of computed eigenvalues
   matrixc&              left_eigenvectors,       // matrix of computed left vectors
   matrixc&              right_eigenvectors       // matrix of computed right vectors
   matrixc&              shur_matrix,             // 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&               ab_norm,                 // 1-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<complexf>

bool  matrixcf::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
   vectorcf&             eigen_values,            // vector of computed eigenvalues
   matrixcf&             left_eigenvectors,       // matrix of computed left vectors
   matrixcf&             right_eigenvectors       // matrix of computed right vectors
   matrixcf&             shur_matrix,             // balanced matrix in Schur form
   long&                 ilo,                     // subscript of balanced matrix
   long&                 ihi,                     // superscript of balanced matrix
   vectorf&              scale,                   // details of permutations and scaling when balancing the input matrix
   float&                ab_norm,                 // 1-norm of balanced matrix
   vectorf&              rconde,                  // vector of reciprocal condition numbers for each eigenvalue
   vectorf&              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.

eigen_values

[out] Vector of eigenvalues.

left_eigenvectors

[out] Matrix of left eigenvectors.

right_eigenvectors

[out] Matrix of right eigenvectors.

shur_matrix

[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.

ab_norm

[out] 1-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.

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

EigenSolver

EigenSolverShur