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SylvesterEquationTriangularBlocked

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

   op(A)*X + X*op(B) = scale*C

or

   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 TRSYL3. This is the block (BLAS level 3) version of TRSYL. Faster up to 5 times but not so accurate.

Computing for type matrix<double>

bool  matrix::SylvesterEquationTriangularBlocked(
   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::SylvesterEquationTriangularBlocked(
   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::SylvesterEquationTriangularBlocked(
   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::SylvesterEquationTriangularBlocked(
   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.

B

[in]  Upper triangular matrix B.

C

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

X

[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 B. Output vector X has the same size as input vector B.