ctglyap - Man Page

Name

ctglyap — C-Interface

— C-Interface for generalized Lyapunov and Stein equations with triangular coefficient matrices.

void mepack_double_tglyap_dag (const char *TRANS, int M, 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 Lyapunov equation with DAG scheduling.
void mepack_single_tglyap_dag (const char *TRANS, int M, 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 Lyapunov equation with DAG scheduling.
void mepack_double_tgstein_dag (const char *TRANS, int M, 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 Stein equation with DAG scheduling.
void mepack_single_tgstein_dag (const char *TRANS, int M, 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 Stein equation with DAG scheduling.
void mepack_double_tglyap_level2 (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_double_tglyap_level2_unopt (const char *TRANS, int M, 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 Lyapunov equation (Unoptimized)
void mepack_single_tglyap_level2 (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_single_tglyap_level2_unopt (const char *TRANS, int M, 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 Lyapunov equation (Unoptimized)
void mepack_double_tgstein_level2 (const char *TRANS, int M, 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 Stein equation.
void mepack_single_tgstein_level2 (const char *TRANS, int M, 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 Stein equation.
void mepack_double_tglyap_level3 (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_double_tglyap_level3_2stage (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_single_tglyap_level3 (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_single_tglyap_level3_2stage (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_double_tgstein_level3 (const char *TRANS, int M, 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 Stein equation.
void mepack_double_tgstein_level3_2stage (const char *TRANS, int M, 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 Stein equation.
void mepack_single_tgstein_level3 (const char *TRANS, int M, 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 Stein equation.
void mepack_single_tgstein_level3_2stage (const char *TRANS, int M, 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 Stein equation.
void mepack_double_tglyap_recursive (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_single_tglyap_recursive (const char *TRANS, int M, 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 Lyapunov equation.
void mepack_double_tgstein_recursive (const char *TRANS, int M, 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 Stein equation.
void mepack_single_tgstein_recursive (const char *TRANS, int M, 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 Stein equation.

Detailed Description

C-Interface for generalized Lyapunov and Stein equations with triangular coefficient matrices.

The Fortran routines to solve generalized Lyapunov and Stein equations 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_tglyap_dag (const char * TRANS, int M, 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 Lyapunov equation with DAG scheduling.

Purpose:

mepack_double_tglyap_dag solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tglyap_dag.

See also

dla_tglyap_dag

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tglyap.c.

void mepack_double_tglyap_level2 (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_double_tglyap_level2 solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tglyap_l2.

See also

dla_tglyap_l2

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tglyap.c.

void mepack_double_tglyap_level2_unopt (const char * TRANS, int M, 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 Lyapunov equation (Unoptimized)

Purpose:

mepack_double_tglyap_level2_unopt solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tglyap_l2_unopt.

See also

dla_tglyap_l2_unopt

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tglyap.c.

void mepack_double_tglyap_level3 (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_double_tglyap_level3 solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tglyap_l3.

See also

dla_tglyap_l3

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tglyap.c.

void mepack_double_tglyap_level3_2stage (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_double_tglyap_level3_2stage solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tglyap_l3_2s.

See also

dla_tglyap_l3_2s

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tglyap.c.

void mepack_double_tglyap_recursive (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_double_tglyap_recursive solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tglyap_recursive.

See also

dla_tglyap_recursive

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tglyap.c.

void mepack_double_tgstein_dag (const char * TRANS, int M, 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 Stein equation with DAG scheduling.

Purpose:

mepack_double_tgstein_dag solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tgstein_dag.

See also

dla_tgstein_dag

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tgstein.c.

void mepack_double_tgstein_level2 (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_double_tgstein_level2 solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tgstein_l2.

See also

dla_tgstein_l2

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tgstein.c.

void mepack_double_tgstein_level3 (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_double_tgstein_level3 solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tgstein_l3.

See also

dla_tgstein_l3

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tgstein.c.

void mepack_double_tgstein_level3_2stage (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_double_tgstein_level3_2stage solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tgstein_l3_2s.

See also

dla_tgstein_l3_2s

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tgstein.c.

void mepack_double_tgstein_recursive (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_double_tgstein_recursive solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by DGGES from LAPACK.

Remarks

This function is a wrapper around dla_tgstein_recursive.

See also

dla_tgstein_recursive

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is DOUBLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 146 of file tgstein.c.

void mepack_single_tglyap_dag (const char * TRANS, int M, 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 Lyapunov equation with DAG scheduling.

Purpose:

mepack_single_tglyap_dag solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tglyap_dag.

See also

sla_tglyap_dag

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tglyap.c.

void mepack_single_tglyap_level2 (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_single_tglyap_level2 solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tglyap_l2.

See also

sla_tglyap_l2

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 420 of file tglyap.c.

void mepack_single_tglyap_level2_unopt (const char * TRANS, int M, 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 Lyapunov equation (Unoptimized)

Purpose:

mepack_single_tglyap_level2_unopt solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tglyap_l2_unopt.

See also

sla_tglyap_l2_unopt

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 557 of file tglyap.c.

void mepack_single_tglyap_level3 (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_single_tglyap_level3 solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tglyap_l3.

See also

sla_tglyap_l3

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 416 of file tglyap.c.

void mepack_single_tglyap_level3_2stage (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_single_tglyap_level3_2stage solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tglyap_l3_2s.

See also

sla_tglyap_l3_2s

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 551 of file tglyap.c.

void mepack_single_tglyap_recursive (const char * TRANS, int M, 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 Lyapunov equation.

Purpose:

mepack_single_tglyap_recursive solves a generalized Lyapunov  equation of the following forms

   A * X * B^T + A * X * B^T = SCALE * Y                                              (2)

or

   A^T * X * B + A^T * X * B =  SCALE * Y                                             (1)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tglyap_recursive.

See also

sla_tglyap_recursive

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tglyap.c.

void mepack_single_tgstein_dag (const char * TRANS, int M, 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 Stein equation with DAG scheduling.

Purpose:

mepack_single_tgstein_dag solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tgstein_dag.

See also

sla_tgstein_dag

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tgstein.c.

void mepack_single_tgstein_level2 (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_single_tgstein_level2 solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tgstein_l2.

See also

sla_tgstein_l2

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 282 of file tgstein.c.

void mepack_single_tgstein_level3 (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_single_tgstein_level3 solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tgstein_l3.

See also

sla_tgstein_l3

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 416 of file tgstein.c.

void mepack_single_tgstein_level3_2stage (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_single_tgstein_level3_2stage solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tgstein_l3_2s.

See also

sla_tgstein_l3_2s

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 551 of file tgstein.c.

void mepack_single_tgstein_recursive (const char * TRANS, int M, 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 Stein equation.

Purpose:

mepack_single_tgstein_recursive solves a generalized Stein  equation of the following forms

   A * X * A^T - B * X * B^T = SCALE * Y                                              (1)

or

   A^T * X * A - B^T * X * B =  SCALE * Y                                             (2)

where A is a M-by-M quasi upper triangular matrix, B is a M-by-M upper triangular,
and X and Y are symmetric  M-by-M matrices.
Typically the matrix pencil (A,B) is created by SGGES from LAPACK.

Remarks

This function is a wrapper around sla_tgstein_recursive.

See also

sla_tgstein_recursive

Parameters

TRANS

         TRANS is a string
         Specifies the form of the system of equations with respect to A and B:
         == 'N':  Equation (1) is solved.
         == 'T':  Equation (2) is solved.

         M is INTEGER
         The order of the matrices A and B.  M >= 0.

         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 is SINGLE PRECISION array, dimension (LDB,M)
         The matrix B must be upper triangular.

LDB

         LDB is INTEGER
         The leading dimension of the array B.  LDB >= max(1,M).

         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.  LDX >= 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 281 of file tgstein.c.

Author

Generated automatically by Doxygen for MEPACK from the source code.

Info

Fri Oct 25 2024 00:00:00 Version 1.1.1 MEPACK

ctglyap - Man Page

Name

Synopsis

Functions

Detailed Description

Function Documentation

void mepack_double_tglyap_dag (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tglyap_level2 (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tglyap_level2_unopt (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tglyap_level3 (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tglyap_level3_2stage (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tglyap_recursive (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tgstein_dag (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tgstein_level2 (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tgstein_level3 (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tgstein_level3_2stage (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_double_tgstein_recursive (const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * SCALE, double * WORK, int * INFO)

void mepack_single_tglyap_dag (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tglyap_level2 (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tglyap_level2_unopt (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tglyap_level3 (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tglyap_level3_2stage (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tglyap_recursive (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tgstein_dag (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tgstein_level2 (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tgstein_level3 (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tgstein_level3_2stage (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

void mepack_single_tgstein_recursive (const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * SCALE, float * WORK, int * INFO)

Author

Info