ctrsylv - Man Page
Name
ctrsylv — C-Interface
— C-Interface for triangular standard Sylvester equations.
Synopsis
Functions
void mepack_double_trsylv_dag (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
void mepack_single_trsylv_dag (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
void mepack_double_trsylv2_dag (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
void mepack_single_trsylv2_dag (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
void mepack_double_trsylv_level2 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_double_trsylv_level2_reorder (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
void mepack_double_trsylv_level2_unopt (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_double_trsylv_level2_local_copy (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
void mepack_double_trsylv_level2_local_copy_32 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32)
void mepack_double_trsylv_level2_local_copy_64 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
void mepack_double_trsylv_level2_local_copy_96 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N<=96)
void mepack_double_trsylv_level2_local_copy_128 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
void mepack_single_trsylv_level2 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_single_trsylv_level2_reorder (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
void mepack_single_trsylv_level2_unopt (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_single_trsylv_level2_local_copy (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
void mepack_single_trsylv_level2_local_copy_32 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32 )
void mepack_single_trsylv_level2_local_copy_64 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
void mepack_single_trsylv_level2_local_copy_96 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 96)
void mepack_single_trsylv_level2_local_copy_128 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
void mepack_double_trsylv2_level2 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_double_trsylv2_level2_reorder (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
void mepack_double_trsylv2_level2_unopt (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_double_trsylv2_level2_local_copy (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
void mepack_double_trsylv2_level2_local_copy_32 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32)
void mepack_double_trsylv2_level2_local_copy_64 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
void mepack_double_trsylv2_level2_local_copy_96 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N<=96)
void mepack_double_trsylv2_level2_local_copy_128 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
void mepack_single_trsylv2_level2 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_single_trsylv2_level2_reorder (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
void mepack_single_trsylv2_level2_unopt (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_single_trsylv2_level2_local_copy (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
void mepack_single_trsylv2_level2_local_copy_32 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32 )
void mepack_single_trsylv2_level2_local_copy_64 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
void mepack_single_trsylv2_level2_local_copy_96 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 96)
void mepack_single_trsylv2_level2_local_copy_128 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
void mepack_double_trsylv_level3 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_double_trsylv_level3_unopt (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_double_trsylv_level3_2stage (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm with sub-blocking for the generalized Sylvester equation.
void mepack_single_trsylv_level3 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_single_trsylv_level3_unopt (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_single_trsylv_level3_2stage (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm with blocking for the generalized Sylvester equation.
void mepack_double_trsylv2_level3 (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_double_trsylv2_level3_unopt (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_double_trsylv2_level3_2stage (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm with blocking for the generalized Sylvester equation.
void mepack_single_trsylv2_level3 (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_single_trsylv2_level3_unopt (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
void mepack_single_trsylv2_level3_2stage (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Level-3 Bartels-Stewart Algorithm with sub-blocking for the generalized Sylvester equation.
void mepack_double_trsylv_recursive (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_single_trsylv_recursive (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_double_trsylv2_recursive (const char *TRANSA, const char *TRANSB, double SGN, int M, int N, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *SCALE, double *WORK, int *INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
void mepack_single_trsylv2_recursive (const char *TRANSA, const char *TRANSB, float SGN, int M, int N, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *SCALE, float *WORK, int *INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Detailed Description
C-Interface for triangular standard Sylvester equations.
The Fortran routines to solve the standard Sylvester equation with triangular coefficients are wrapped in C to provide an easier access to them. All wrapper routines are direct wrappers to the corresponding Fortran subroutines without sanity checks. These are performed by the Fortran routines. Since the routines are using int values to pass sizes the work_space query will fail for large scale problems. For this reason the function mepack_memory should be used to query the required work_space from a C code. This function is aware of 64 bit integers if MEPACK is compiled with it.
Function Documentation
void mepack_double_trsylv2_dag (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
Purpose:
mepack_double_trsylv2_dag solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_dag.
- See also
dla_trsylv2_dag
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 166 of file trsylv2.c.
void mepack_double_trsylv2_level2 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv2_level2 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2.
- See also
dla_trsylv2_l2
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 165 of file trsylv2.c.
void mepack_double_trsylv2_level2_local_copy (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
Purpose:
mepack_double_trsylv2_level2_local_copy solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_local_copy.
- See also
dla_trsylv2_l2_local_copy
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 637 of file trsylv2.c.
void mepack_double_trsylv2_level2_local_copy_128 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
Purpose:
mepack_double_trsylv2_level2_local_copy_128 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_local_copy_128.
- See also
dla_trsylv2_l2_local_copy_128
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1269 of file trsylv2.c.
void mepack_double_trsylv2_level2_local_copy_32 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32)
Purpose:
mepack_double_trsylv2_level2_local_copy_32 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_local_copy_32.
- See also
dla_trsylv2_l2_local_copy_32
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 795 of file trsylv2.c.
void mepack_double_trsylv2_level2_local_copy_64 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
Purpose:
mepack_double_trsylv2_level2_local_copy_64 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_local_copy_64.
- See also
dla_trsylv2_l2_local_copy_64
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 953 of file trsylv2.c.
void mepack_double_trsylv2_level2_local_copy_96 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N<=96)
Purpose:
mepack_double_trsylv2_level2_local_copy_96 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_local_copy_96.
- See also
dla_trsylv2_l2_local_copy_96
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1111 of file trsylv2.c.
void mepack_double_trsylv2_level2_reorder (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
Purpose:
mepack_double_trsylv2_level2_reorder solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_reorder.
- See also
dla_trsylv2_l2_reorder
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 323 of file trsylv2.c.
void mepack_double_trsylv2_level2_unopt (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_double_trsylv2_level2_unopt solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_unopt.
- See also
dla_trsylv2_l2_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 480 of file trsylv2.c.
void mepack_double_trsylv2_level3 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv2_level3 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l3.
- See also
dla_trsylv2_l3
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 168 of file trsylv2.c.
void mepack_double_trsylv2_level3_2stage (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm with blocking for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv2_level3_2stage solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l3_2s.
- See also
dla_trsylv2_l3_2s
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 483 of file trsylv2.c.
void mepack_double_trsylv2_level3_unopt (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_double_trsylv2_level3_unopt solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l3_unopt.
- See also
dla_trsylv2_l3_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 326 of file trsylv2.c.
void mepack_double_trsylv2_recursive (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv2_recursive solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_recursive.
- See also
dla_trsylv2_recursive
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 168 of file trsylv2.c.
void mepack_double_trsylv_dag (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
Purpose:
mepack_double_trsylv_dag solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_dag.
- See also
dla_trsylv_dag
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 166 of file trsylv.c.
void mepack_double_trsylv_level2 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv_level2 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2.
- See also
dla_trsylv_l2
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 165 of file trsylv.c.
void mepack_double_trsylv_level2_local_copy (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
Purpose:
mepack_double_trsylv_level2_local_copy solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_local_copy.
- See also
dla_trsylv_l2_local_copy
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 637 of file trsylv.c.
void mepack_double_trsylv_level2_local_copy_128 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
Purpose:
mepack_double_trsylv_level2_local_copy_128 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_local_copy_128.
- See also
dla_trsylv_l2_local_copy_128
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1269 of file trsylv.c.
void mepack_double_trsylv_level2_local_copy_32 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32)
Purpose:
mepack_double_trsylv_level2_local_copy_32 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_local_copy_32.
- See also
dla_trsylv_l2_local_copy_32
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 795 of file trsylv.c.
void mepack_double_trsylv_level2_local_copy_64 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
Purpose:
mepack_double_trsylv_level2_local_copy_64 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_local_copy_64.
- See also
dla_trsylv_l2_local_copy_64
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 953 of file trsylv.c.
void mepack_double_trsylv_level2_local_copy_96 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N<=96)
Purpose:
mepack_double_trsylv_level2_local_copy_96 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_local_copy_96.
- See also
dla_trsylv_l2_local_copy_96
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1111 of file trsylv.c.
void mepack_double_trsylv_level2_reorder (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
Purpose:
mepack_double_trsylv_level2_reorder solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_reorder.
- See also
dla_trsylv_l2_reorder
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 323 of file trsylv.c.
void mepack_double_trsylv_level2_unopt (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_double_trsylv_level2_unopt solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_unopt.
- See also
dla_trsylv_l2_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 480 of file trsylv.c.
void mepack_double_trsylv_level3 (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv_level3 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l3.
- See also
dla_trsylv_l3
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 168 of file trsylv.c.
void mepack_double_trsylv_level3_2stage (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm with sub-blocking for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv_level3_2stage solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l3_2s.
- See also
dla_trsylv_l3_2s
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 483 of file trsylv.c.
void mepack_double_trsylv_level3_unopt (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_double_trsylv_level3_unopt solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l3_unopt.
- See also
dla_trsylv_l3_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 326 of file trsylv.c.
void mepack_double_trsylv_recursive (const char * TRANSA, const char * TRANSB, double SGN, int M, int N, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_double_trsylv_recursive solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_recursive.
- See also
dla_trsylv_recursive
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 168 of file trsylv.c.
void mepack_single_trsylv2_dag (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
Purpose:
mepack_single_trsylv2_dag solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_dag.
- See also
sla_trsylv2_dag
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 324 of file trsylv2.c.
void mepack_single_trsylv2_level2 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv2_level2 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2.
- See also
sla_trsylv2_l2
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1428 of file trsylv2.c.
void mepack_single_trsylv2_level2_local_copy (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
Purpose:
mepack_single_trsylv2_level2_local_copy solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2_local_copy.
- See also
sla_trsylv2_l2_local_copy
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1903 of file trsylv2.c.
void mepack_single_trsylv2_level2_local_copy_128 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
Purpose:
mepack_single_trsylv2_level2_local_copy_128 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2_local_copy_128.
- See also
sla_trsylv2_l2_local_copy_128
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2535 of file trsylv2.c.
void mepack_single_trsylv2_level2_local_copy_32 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32 )
Purpose:
mepack_single_trsylv2_level2_local_copy_32 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2_local_copy_32.
- See also
sla_trsylv2_l2_local_copy_32
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2060 of file trsylv2.c.
void mepack_single_trsylv2_level2_local_copy_64 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
Purpose:
mepack_double_trsylv2_level2_local_copy_64 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv2_l2_local_copy_64.
- See also
dla_trsylv2_l2_local_copy_64
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2217 of file trsylv2.c.
void mepack_single_trsylv2_level2_local_copy_96 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 96)
Purpose:
mepack_single_trsylv2_level2_local_copy_96 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2_local_copy_96.
- See also
sla_trsylv2_l2_local_copy_96
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2376 of file trsylv2.c.
void mepack_single_trsylv2_level2_reorder (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
Purpose:
mepack_single_trsylv2_level2_reorder solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2_reorder.
- See also
sla_trsylv2_l2_reorder
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1587 of file trsylv2.c.
void mepack_single_trsylv2_level2_unopt (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_single_trsylv2_level2_unopt solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l2_unopt.
- See also
sla_trsylv2_l2_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1744 of file trsylv2.c.
void mepack_single_trsylv2_level3 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv2_level3 solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l3.
- See also
sla_trsylv2_l3
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 640 of file trsylv2.c.
void mepack_single_trsylv2_level3_2stage (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm with sub-blocking for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv2_level3_2stage solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l3_2s.
- See also
sla_trsylv2_l3_2s
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 956 of file trsylv2.c.
void mepack_single_trsylv2_level3_unopt (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_single_trsylv2_level3_unopt solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_l3_unopt.
- See also
sla_trsylv2_l3_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 799 of file trsylv2.c.
void mepack_single_trsylv2_recursive (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv2_recursive solves a Sylvester equation of the following forms op1(A) * X * op2(B) + X = SCALE * Y (1) or op1(A) * X * op2(B) - X = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv2_recursive.
- See also
sla_trsylv2_recursive
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 327 of file trsylv2.c.
void mepack_single_trsylv_dag (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation with DAG parallelization.
Purpose:
mepack_single_trsylv_dag solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_dag.
- See also
sla_trsylv_dag
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 324 of file trsylv.c.
void mepack_single_trsylv_level2 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv_level2 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2.
- See also
sla_trsylv_l2
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1428 of file trsylv.c.
void mepack_single_trsylv_level2_local_copy (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant)
Purpose:
mepack_single_trsylv_level2_local_copy solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2_local_copy.
- See also
sla_trsylv_l2_local_copy
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1903 of file trsylv.c.
void mepack_single_trsylv_level2_local_copy_128 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 128)
Purpose:
mepack_single_trsylv_level2_local_copy_128 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2_local_copy_128.
- See also
sla_trsylv_l2_local_copy_128
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2535 of file trsylv.c.
void mepack_single_trsylv_level2_local_copy_32 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 32 )
Purpose:
mepack_single_trsylv_level2_local_copy_32 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2_local_copy_32.
- See also
sla_trsylv_l2_local_copy_32
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2060 of file trsylv.c.
void mepack_single_trsylv_level2_local_copy_64 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 64)
Purpose:
mepack_double_trsylv_level2_local_copy_64 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via DGEES form LAPACK.
- Remarks
This function is a wrapper around dla_trsylv_l2_local_copy_64.
- See also
dla_trsylv_l2_local_copy_64
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is DOUBLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is DOUBLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2217 of file trsylv.c.
void mepack_single_trsylv_level2_local_copy_96 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Local copy variant, M,N <= 96)
Purpose:
mepack_single_trsylv_level2_local_copy_96 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2_local_copy_96.
- See also
sla_trsylv_l2_local_copy_96
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 2376 of file trsylv.c.
void mepack_single_trsylv_level2_reorder (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Reordered variant)
Purpose:
mepack_single_trsylv_level2_reorder solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2_reorder.
- See also
sla_trsylv_l2_reorder
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1587 of file trsylv.c.
void mepack_single_trsylv_level2_unopt (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-2 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_single_trsylv_level2_unopt solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l2_unopt.
- See also
sla_trsylv_l2_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 1744 of file trsylv.c.
void mepack_single_trsylv_level3 (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv_level3 solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l3.
- See also
sla_trsylv_l3
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 640 of file trsylv.c.
void mepack_single_trsylv_level3_2stage (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm with blocking for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv_level3_2stage solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l3_2s.
- See also
sla_trsylv_l3_2s
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 956 of file trsylv.c.
void mepack_single_trsylv_level3_unopt (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation. (Unoptimized variant)
Purpose:
mepack_single_trsylv_level3_unopt solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_l3_unopt.
- See also
sla_trsylv_l3_unopt
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 799 of file trsylv.c.
void mepack_single_trsylv_recursive (const char * TRANSA, const char * TRANSB, float SGN, int M, int N, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)
Recursive blocking Level-3 Bartels-Stewart Algorithm for the generalized Sylvester equation.
Purpose:
mepack_single_trsylv_recursive solves a Sylvester equation of the following forms op1(A) * X + X * op2(B) = SCALE * Y (1) or op1(A) * X - X * op2(B) = SCALE * Y (2) where A is a M-by-M quasi upper triangular matrix, B is a N-by-N quasi upper triangular matrix. The right hand side Y and the solution X are M-by-N matrices. Typically the matrices A and B are generated via SGEES form LAPACK.
- Remarks
This function is a wrapper around sla_trsylv_recursive.
- See also
sla_trsylv_recursive
- Parameters
TRANSA
TRANSA is string Specifies the form of the system of equations with respect to A: == 'N': op1(A) = A == 'T': op1(A) = A**TTRANSB
TRANSB is string Specifies the form of the system of equations with respect to B: == 'N': op2(B) = B, == 'T': op2(B) = B**TSGN
SGN is SINGLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)M
M is INTEGER The order of the matrices A and C. M >= 0.N
N is INTEGER The order of the matrices B and D. N >= 0.A
A is SINGLE PRECISION array, dimension (LDA,M) The matrix A must be (quasi-) upper triangular.LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,N) The matrix B must be (quasi-) upper triangular.LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).X
X is SINGLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) as selected by TRANSA, TRANSB, and SGN. Right hand side Y and the solution X are M-by-N matrices.LDX
LDX is INTEGER The leading dimension of the array X. LDB >= max(1,M).SCALE
SCALE is SINGLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.WORK
WORK is SINGLE PRECISION array, dimension LDWORK Workspace for the algorithm. The workspace needs to queried before the running the computation. The query is performed by calling the subroutine with INFO == -1 on input. The required workspace is then returned in INFO.INFO
INFO is INTEGER On input: == -1 : Perform a workspace query <> -1 : normal operation On exit, workspace query: < 0 : if INFO == -i, the i-Th argument had an illegal value >= 0: The value of INFO is the required number of elements in the workspace. On exit, normal operation: == 0: successful exit < 0: if INFO == -i, the i-Th argument had an illegal value > 0: The equation is not solved correctly. One of the arising inner system got singular.- Author
Martin Koehler, MPI Magdeburg
- Date
January 2024
Definition at line 327 of file trsylv.c.
Author
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