Справочник MQL5Методы матриц и векторовOpenBLASLinear EquationsSylvesterEquationTriangular

SylvesterEquationTriangular

Solves Sylvester equation for real quasi-triangular or complex triangular matrices:

op(A)*X + X*op(B) = scale*C

op(A)*X - X*op(B) = scale*C

where op(A) = A or A**T or A**H, and A and B are both upper triangular. A is m-by-m and B is n-by-n; the right hand side C and the solution X are m-by-n; and scale is an output scale factor, set <= 1 to avoid overflow in X.

LAPACK function TRSYL.

Computing for type matrix<double>

bool  matrix::SylvesterEquationTriangular(
   ENUM_BLAS_TRANS      transa,       // specifies option op(A)
   ENUM_BLAS_TRANS      transb,       // specifies option op(B)
   ENUM_SYLVESTER_ISIGN isign,        // specifies the sign in the equation
   matrix&              B,            // upper triangular matrix B
   matrix&              C,            // right hand side matrix C
   matrix&              X,            // solution matrix X
   double&              scale         // scale factor
   );

Computing for type matrix<float>

bool  matrixf::SylvesterEquationTriangular(
   ENUM_BLAS_TRANS      transa,       // specifies option op(A)
   ENUM_BLAS_TRANS      transb,       // specifies option op(B)
   ENUM_SYLVESTER_ISIGN isign,        // specifies the sign in the equation
   matrixf&             B,            // upper triangular matrix B
   matrixf&             C,            // right hand side matrix C
   matrixf&             X,            // solution matrix X
   float&               scale         // scale factor
   );

Computing for type matrix<complex>

bool  matrix::SylvesterEquationTriangular(
   ENUM_BLAS_TRANS      transa,       // specifies option op(A)
   ENUM_BLAS_TRANS      transb,       // specifies option op(B)
   ENUM_SYLVESTER_ISIGN isign,        // specifies the sign in the equation
   matrixc&             B,            // upper triangular matrix B
   matrixc&             C,            // right hand side matrix C
   matrixc&             X,            // solution matrix X
   double&              scale         // scale factor
   );

Computing for type matrix<complexf>

bool  matrix::SylvesterEquationTriangular(
   ENUM_BLAS_TRANS      transa,       // specifies option op(A)
   ENUM_BLAS_TRANS      transb,       // specifies option op(B)
   ENUM_SYLVESTER_ISIGN isign,        // specifies the sign in the equation
   matrixcf&            B,            // upper triangular matrix B
   matrixcf&            C,            // right hand side matrix C
   matrixcf&            X,            // solution matrix X
   float&               scale         // scale factor
   );

Parameters

transa

[in] ENUM_BLAS_TRANS enumeration value which specifies option op(A).

transb

[in] ENUM_BLAS_TRANS enumeration value which specifies option op(B).

isign

[in] ENUM_SYLVESTER_ISIGN enumeration value which specifies the sign in the equation.

[in] Upper triangular matrix B.

[in] Matrix C whose columns are the right-hand sides for the systems of equations.

[out] Matrix X with solution of Sylvester equation.

scale

[out] The scale factor, set <= 1 to avoid overflow in X.

Return Value

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

Note

Output matrix X has the same sizes as input matrix C.

ENUM_BLAS_TRANS

An enumeration defining options op(A) and op(B).

ID	Description
BLASTRANS_N	'N': No transpose
BLASTRANS_T	'T': Transpose
BLASTRANS_C	'C': Conjugate transpose

In case of real matrices the value BLASTRANS_C assumed as Transpose.

In case of complex matrices the value BLASTRANS_T assumed as Conjugate transpose.

ENUM_SYLVESTER_ISIGN

An enumeration defining the sign in the equation.

ID	Description
ISIGN_PLUS	+1: solve op(A)X + Xop(B) = scale*C
ISIGN_MINUS	-1: solve op(A)X - Xop(B) = scale*C

LinearEquationsSolutionSyTridPD

SylvesterEquationTriangularBlocked