# cgelyap - Man Page

## Name

cgelyap — C-Interface

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

## Synopsis

### Functions

void mepack_double_gelyap (const char *FACT, const char *TRANS, int M, double *A, int LDA, double *Q, int LDQ, double *X, int LDX, double *SCALE, double *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Standard Lyapunov Equations.
void mepack_single_gelyap (const char *FACT, const char *TRANS, int M, float *A, int LDA, float *Q, int LDQ, float *X, int LDX, float *SCALE, float *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Standard Lyapunov Equations.
void mepack_double_gestein (const char *FACT, const char *TRANS, int M, double *A, int LDA, double *Q, int LDQ, double *X, int LDX, double *SCALE, double *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Standard Stein Equations.
void mepack_single_gestein (const char *FACT, const char *TRANS, int M, float *A, int LDA, float *Q, int LDQ, float *X, int LDX, float *SCALE, float *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Standard Stein Equations.
void mepack_double_gelyap_refine (const char *TRANS, const char *GUESS, int M, double *A, int LDA, double *X, int LDX, double *Y, int LDY, double *AS, int LDAS, double *Q, int LDQ, int *MAXIT, double *TAU, double *CONVLOG, double *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Standard Lyapunov Equation.
void mepack_single_gelyap_refine (const char *TRANS, const char *GUESS, int M, float *A, int LDA, float *X, int LDX, float *Y, int LDY, float *AS, int LDAS, float *Q, int LDQ, int *MAXIT, float *TAU, float *CONVLOG, float *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Standard Lyapunov Equation.
void mepack_double_gestein_refine (const char *TRANS, const char *GUESS, int M, double *A, int LDA, double *X, int LDX, double *Y, int LDY, double *AS, int LDAS, double *Q, int LDQ, int *MAXIT, double *TAU, double *CONVLOG, double *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Standard Stein Equation.
void mepack_single_gestein_refine (const char *TRANS, const char *GUESS, int M, float *A, int LDA, float *X, int LDX, float *Y, int LDY, float *AS, int LDAS, float *Q, int LDQ, int *MAXIT, float *TAU, float *CONVLOG, float *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Standard Stein Equation.

## Detailed Description

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

The Fortran routines to solve standard Lyapunov and Stein equations with arbitrary 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. The only difference is that the C interface does not allow LAPACK-like work_space queries. For this purpose the mepack_memory_frontend function needs to be used.

## Function Documentation

### void mepack_double_gelyap (const char * FACT, const char * TRANS, int M, double * A, int LDA, double * Q, int LDQ, double * X, int LDX, double * SCALE, double * WORK, size_t LDWORK, int * INFO)

Frontend for the solution of Standard Lyapunov Equations.

Purpose:

mepack_double_gelyap solves a Lyapunov equation of the following forms

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

or

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

where A is a M-by-M general matrix.
The right hand side Y and the solution X are M-by-M matrices.  The matrix A
can be either supplied as general matrix or factorized in terms of its
Schur decomposition..fi

Remarks
This function is a wrapper around dla_gelyap.

dla_gelyap

Parameters
FACT

FACT is String
Specifies how the matrix A is given.
== 'N':  The matrix A is given as a general matrix and its Schur decomposition
A = Q*S*Q**T will be computed.
== 'F':  The matrix A is given as its Schur decomposition in terms of S and Q
form A = Q*S*Q**T

TRANS

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

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is DOUBLE PRECISION array, dimension (LDA,M)
If FACT == 'N', the matrix A is a general matrix and it is overwritten with its
schur decomposition S.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S being the
Schur decomposition of A.

LDA

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

Q

         Q is DOUBLE PRECISION array, dimension (LDQ,M)
If FACT == 'N', the matrix Q is an empty M-by-M matrix on input and contains the
Schur vectors of A on output.
If FACT == 'F', the matrix Q contains the Schur vectors of A.

LDQ

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

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)
Right hand side Y and the solution X are symmetric M-by-M 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 (MAX(1,LDWORK))
Workspace for the algorithm. The optimal workspace is given either by \ref mepack_memory_frontend.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm counted in floating point numbers of the actual precision.
The C interface does not support the workspace query by setting LDWORK == -1 on input. In this case,
the \ref mepack_memory_frontend function have to be used.

INFO

         INFO is INTEGER
== 0:  successful exit
= 1:  DGEES failed
= 2:  DLA_SORT_EV failed
= 3:  Internal solver failed
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 160 of file gelyap.c.

### void mepack_double_gelyap_refine (const char * TRANS, const char * GUESS, int M, double * A, int LDA, double * X, int LDX, double * Y, int LDY, double * AS, int LDAS, double * Q, int LDQ, int * MAXIT, double * TAU, double * CONVLOG, double * WORK, size_t LDWORK, int * INFO)

Iterative Refinement for the Standard Lyapunov Equation.

Purpose:

mepack_double_GELYAP_refine solves a standard Lyapunov equation of the following forms

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

or

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

where A is a M-by-M matrix using iterative refinement.
The right hand side Y and the solution X are M-by-M matrices.
The matrix A needs to be provided as the original data
as well as in Schur decomposition since both are required in the
iterative refinement process..fi

Remarks
This function is a wrapper for dla_GELYAP_refine.

dla_GELYAP_refine

Parameters
TRANS

TRANS is String
Specifies the form of the system of equations with respect to A:
== 'N':  Equation (1) is solved
== 'T':  Equation (2) is solved

GUESS

         GUESS is String
Specifies whether X provides an initial guess or not.
= 'I': An initial guess is provided
== 'N': No initial guess is provided, X is set to zero.

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is DOUBLE PRECISION array, dimension (LDA,M)
The array A contains the original matrix A defining the equation.

LDA

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

X

         X is DOUBLE PRECISION array, dimension (LDX,M)
On input, the array X contains an initial guess.
On output, the array X contains the solution X.

LDX

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

Y

         Y is DOUBLE PRECISION array, dimension (LDY,M)
On input, the array Y contains the right hand side.

LDY

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

AS

         AS is DOUBLE PRECISION array, dimension (LDAS,M)
The array AS contains the Schur decomposition of A.

LDAS

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

Q

         Q is DOUBLE PRECISION array, dimension (LDQ,M)
The array Q contains the Schur vectors for A as returned by DGEES.

LDQ

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

MAXIT

         MAXIT is INTEGER
On input, MAXIT contains the maximum number of iteration that are performed, MAXIT <= 100
On exit, MAXIT contains the number of iteration steps taken by the algorithm.

TAU

         TAU is DOUBLE PRECISION
On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1
On exit, TAU contains the last relative residual when the stopping criterion got valid.

CONVLOG

         CONVLOG is DOUBLE PRECISION array, dimension (MAXIT)
The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum
relative residual before it is solved for the I-Th time.

WORK

         WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK))
Workspace for the algorithm.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend.

INFO

         INFO is INTEGER
== 0:  Success
> 0:  Iteration failed in step INFO
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 188 of file gelyap.c.

### void mepack_double_gestein (const char * FACT, const char * TRANS, int M, double * A, int LDA, double * Q, int LDQ, double * X, int LDX, double * SCALE, double * WORK, size_t LDWORK, int * INFO)

Frontend for the solution of Standard Stein Equations.

Purpose:

mepack_double_gestein solves a Stein equation of the following forms

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

or

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

where A is a M-by-M general matrix.
The right hand side Y and the solution X are M-by-M matrices.  The matrix A
can be either supplied as general matrix or factorized in terms of its
Schur decomposition..fi

Remarks
This function is a wrapper around dla_gestein.

dla_gestein

Parameters
FACT

FACT is String
Specifies how the matrix A is given.
== 'N':  The matrix A is given as a general matrix and its Schur decomposition
A = Q*S*Q**T will be computed.
== 'F':  The matrix A is given as its Schur decomposition in terms of S and Q
form A = Q*S*Q**T

TRANS

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

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is DOUBLE PRECISION array, dimension (LDA,M)
If FACT == 'N', the matrix A is a general matrix and it is overwritten with its
schur decomposition S.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S being the
Schur decomposition of A.

LDA

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

Q

         Q is DOUBLE PRECISION array, dimension (LDQ,M)
If FACT == 'N', the matrix Q is an empty M-by-M matrix on input and contains the
Schur vectors of A on output.
If FACT == 'F', the matrix Q contains the Schur vectors of A.

LDQ

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

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)
Right hand side Y and the solution X are symmetric M-by-M 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 (MAX(1,LDWORK))
Workspace for the algorithm. The optimal workspace is given either by \ref mepack_memory_frontend.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm counted in floating point numbers of the actual precision.
The C interface does not support the workspace query by setting LDWORK == -1 on input. In this case,
the \ref mepack_memory_frontend function have to be used.

INFO

         INFO is INTEGER
== 0:  successful exit
= 1:  DGEES failed
= 2:  DLA_SORT_EV failed
= 3:  Internal solver failed
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 159 of file gestein.c.

### void mepack_double_gestein_refine (const char * TRANS, const char * GUESS, int M, double * A, int LDA, double * X, int LDX, double * Y, int LDY, double * AS, int LDAS, double * Q, int LDQ, int * MAXIT, double * TAU, double * CONVLOG, double * WORK, size_t LDWORK, int * INFO)

Iterative Refinement for the Standard Stein Equation.

Purpose:

mepack_double_gestein_refine solves a standard Stein equation of the following forms

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

or

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

where A is a M-by-M matrix using iterative refinement.
The right hand side Y and the solution X are M-by-M matrices.
The matrix A needs to be provided as the original data
as well as in Schur decomposition since both are required in the
iterative refinement process..fi

Remarks
This function is a wrapper for dla_gestein_refine.

dla_gestein_refine

Parameters
TRANS

TRANS is String
Specifies the form of the system of equations with respect to A:
== 'N':  Equation (1) is solved
== 'T':  Equation (2) is solved

GUESS

         GUESS is String
Specifies whether X  contains an initial guess on input or not.
= 'I': X contains an initial guess for the solution
== 'N': No initial guess is provided. X is set to zero.

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is DOUBLE PRECISION array, dimension (LDA,M)
The array A contains the original matrix A defining the equation.

LDA

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

X

         X is DOUBLE PRECISION array, dimension (LDX,M)
On input, the array X contains the initial guess.
On output, the array X contains the solution X.

LDX

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

Y

         Y is DOUBLE PRECISION array, dimension (LDY,M)
On input, the array Y contains the right hand side.

LDY

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

AS

         AS is DOUBLE PRECISION array, dimension (LDAS,M)
The array AS contains the Schur decomposition of A.

LDAS

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

Q

         Q is DOUBLE PRECISION array, dimension (LDQ,M)
The array Q contains the Schur vectors for A as returned by DGEES.

LDQ

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

MAXIT

         MAXIT is INTEGER
On input, MAXIT contains the maximum number of iteration that are performed, MAXIT <= 100
On exit, MAXIT contains the number of iteration steps taken by the algorithm.

TAU

         TAU is DOUBLE PRECISION
On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1
On exit, TAU contains the last relative residual when the stopping criterion got valid.

CONVLOG

         CONVLOG is DOUBLE PRECISION array, dimension (MAXIT)
The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum
relative residual before it is solved for the I-Th time.

WORK

         WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK))
Workspace for the algorithm.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend.

INFO

         INFO is INTEGER
== 0:  Success
> 0:  Iteration failed in step INFO
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 192 of file gestein.c.

### void mepack_single_gelyap (const char * FACT, const char * TRANS, int M, float * A, int LDA, float * Q, int LDQ, float * X, int LDX, float * SCALE, float * WORK, size_t LDWORK, int * INFO)

Frontend for the solution of Standard Lyapunov Equations.

Purpose:

mepack_single_gelyap solves a Lyapunov equation of the following forms

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

or

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

where A is a M-by-M general matrix.
The right hand side Y and the solution X are M-by-M matrices.  The matrix A
can be either supplied as general matrix or factorized in terms of its
Schur decomposition..fi

Remarks
This function is a wrapper around sla_gelyap.

sla_gelyap

Parameters
FACT

FACT is String
Specifies how the matrix A is given.
== 'N':  The matrix A is given as a general matrix and its Schur decomposition
A = Q*S*Q**T will be computed.
== 'F':  The matrix A is given as its Schur decomposition in terms of S and Q
form A = Q*S*Q**T

TRANS

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

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is SINGLE PRECISION array, dimension (LDA,M)
If FACT == 'N', the matrix A is a general matrix and it is overwritten with its
schur decomposition S.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S being the
Schur decomposition of A.

LDA

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

Q

         Q is SINGLE PRECISION array, dimension (LDQ,M)
If FACT == 'N', the matrix Q is an empty M-by-M matrix on input and contains the
Schur vectors of A on output.
If FACT == 'F', the matrix Q contains the Schur vectors of A.

LDQ

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

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)
Right hand side Y and the solution X are symmetric M-by-M 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 (MAX(1,LDWORK))
Workspace for the algorithm. The optimal workspace is given either by \ref mepack_memory_frontend
or a previous call to the this routine with LDWORK === -1.
On exit, WORK(1) contains the size of the workspace.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm counted in floating point numbers of the actual precision.
The C interface does not support the workspace query by setting LDWORK == -1 on input. In this case,
the \ref mepack_memory_frontend function have to be used.

INFO

         INFO is INTEGER
== 0:  successful exit
= 1:  DGEES failed
= 2:  DLA_SORT_EV failed
= 3:  Internal solver failed
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 315 of file gelyap.c.

### void mepack_single_gelyap_refine (const char * TRANS, const char * GUESS, int M, float * A, int LDA, float * X, int LDX, float * Y, int LDY, float * AS, int LDAS, float * Q, int LDQ, int * MAXIT, float * TAU, float * CONVLOG, float * WORK, size_t LDWORK, int * INFO)

Iterative Refinement for the Standard Lyapunov Equation.

Purpose:

mepack_single_gelyap_refine solves a standard Lyapunov equation of the following forms

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

or

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

where A is a M-by-M matrix using iterative refinement.
The right hand side Y and the solution X are M-by-M matrices.
The matrix A needs to be provided as the original data
as well as in Schur decomposition since both are required in the
iterative refinement process..fi

Remarks
This function is a wrapper for sla_gelyap_refine.

sla_gelyap_refine

Parameters
TRANS

TRANS is String
Specifies the form of the system of equations with respect to A:
== 'N':  Equation (1) is solved
== 'T':  Equation (2) is solved

M

         M is INTEGER
The order of the matrix A.  M >= 0.

GUESS

         GUESS is String
Specifies whether X provides an initial guess or not.
= 'I': An initial guess is provided
== 'N': No initial guess is provided, X is set to zero.

A

         A is SINGLE PRECISION array, dimension (LDA,M)
The array A contains the original matrix A defining the equation.

LDA

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

X

         X is SINGLE PRECISION array, dimension (LDX,M)
On input, the array X contains an initial guess.
On output, the array X contains the solution X.

LDX

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

Y

         Y is SINGLE PRECISION array, dimension (LDY,M)
On input, the array Y contains the right hand side.

LDY

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

AS

         AS is SINGLE PRECISION array, dimension (LDAS,M)
The array AS contains the Schur decomposition of A.

LDAS

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

Q

         Q is SINGLE PRECISION array, dimension (LDQ,M)
The array Q contains the Schur vectors for A as returned by DGEES.

LDQ

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

MAXIT

         MAXIT is INTEGER
On input, MAXIT contains the maximum number of iteration that are performed, MAXIT <= 100
On exit, MAXIT contains the number of iteration steps taken by the algorithm.

TAU

         TAU is SINGLE PRECISION
On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1
On exit, TAU contains the last relative residual when the stopping criterion got valid.

CONVLOG

         CONVLOG is SINGLE PRECISION array, dimension (MAXIT)
The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum
relative residual before it is solved for the I-Th time.

WORK

         WORK is SINGLE PRECISION array, dimension (MAX(1,LDWORK))
Workspace for the algorithm.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend.

INFO

         INFO is INTEGER
== 0:  Success
> 0:  Iteration failed in step INFO
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 374 of file gelyap.c.

### void mepack_single_gestein (const char * FACT, const char * TRANS, int M, float * A, int LDA, float * Q, int LDQ, float * X, int LDX, float * SCALE, float * WORK, size_t LDWORK, int * INFO)

Frontend for the solution of Standard Stein Equations.

Purpose:

mepack_single_gestein solves a Stein equation of the following forms

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

or

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

where A is a M-by-M general matrix.
The right hand side Y and the solution X are M-by-M matrices.  The matrix A
can be either supplied as general matrix or factorized in terms of its
Schur decomposition..fi

Remarks
This function is a wrapper around sla_gestein.

sla_gestein

Parameters
FACT

FACT is String
Specifies how the matrix A is given.
== 'N':  The matrix A is given as a general matrix and its Schur decomposition
A = Q*S*Q**T will be computed.
== 'F':  The matrix A is given as its Schur decomposition in terms of S and Q
form A = Q*S*Q**T

TRANS

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

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is SINGLE PRECISION array, dimension (LDA,M)
If FACT == 'N', the matrix A is a general matrix and it is overwritten with its
schur decomposition S.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S being the
Schur decomposition of A.

LDA

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

Q

         Q is SINGLE PRECISION array, dimension (LDQ,M)
If FACT == 'N', the matrix Q is an empty M-by-M matrix on input and contains the
Schur vectors of A on output.
If FACT == 'F', the matrix Q contains the Schur vectors of A.

LDQ

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

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)
Right hand side Y and the solution X are symmetric M-by-M 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 (MAX(1,LDWORK))
Workspace for the algorithm. The optimal workspace is given either by \ref mepack_memory_frontend

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm counted in floating point numbers of the actual precision.
The C interface does not support the workspace query by setting LDWORK == -1 on input. In this case,
the \ref mepack_memory_frontend function have to be used.

INFO

         INFO is INTEGER
== 0:  successful exit
= 1:  DGEES failed
= 2:  DLA_SORT_EV failed
= 3:  Internal solver failed
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 312 of file gestein.c.

### void mepack_single_gestein_refine (const char * TRANS, const char * GUESS, int M, float * A, int LDA, float * X, int LDX, float * Y, int LDY, float * AS, int LDAS, float * Q, int LDQ, int * MAXIT, float * TAU, float * CONVLOG, float * WORK, size_t LDWORK, int * INFO)

Iterative Refinement for the Standard Stein Equation.

Purpose:

mepack_single_gestein_refine solves a standard Stein equation of the following forms

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

or

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

where A is a M-by-M matrix using iterative refinement.
The right hand side Y and the solution X are M-by-M matrices.
The matrix A needs to be provided as the original data
as well as in Schur decomposition since both are required in the
iterative refinement process..fi

Remarks
This function is a wrapper for sla_gestein_refine.

sla_gestein_refine

Parameters
TRANS

TRANS is String
Specifies the form of the system of equations with respect to A:
== 'N':  Equation (1) is solved
== 'T':  Equation (2) is solved

GUESS

         GUESS is String
Specifies whether X  contains an initial guess on input or not.
= 'I': X contains an initial guess for the solution
== 'N': No initial guess is provided. X is set to zero.

M

         M is INTEGER
The order of the matrix A.  M >= 0.

A

         A is SINGLE PRECISION array, dimension (LDA,M)
The array A contains the original matrix A defining the equation.

LDA

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

X

         X is SINGLE PRECISION array, dimension (LDX,M)
On input, the array X contains the initial guess.
On output, the array X contains the solution X.

LDX

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

Y

         Y is SINGLE PRECISION array, dimension (LDY,M)
On input, the array Y contains the right hand side.

LDY

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

AS

         AS is SINGLE PRECISION array, dimension (LDAS,M)
The array AS contains the Schur decomposition of A.

LDAS

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

Q

         Q is SINGLE PRECISION array, dimension (LDQ,M)
The array Q contains the Schur vectors for A as returned by DGEES.

LDQ

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

MAXIT

         MAXIT is INTEGER
On input, MAXIT contains the maximum number of iteration that are performed, MAXIT <= 100
On exit, MAXIT contains the number of iteration steps taken by the algorithm.

TAU

         TAU is SINGLE PRECISION
On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1
On exit, TAU contains the last relative residual when the stopping criterion got valid.

CONVLOG

         CONVLOG is SINGLE PRECISION array, dimension (MAXIT)
The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum
relative residual before it is solved for the I-Th time.

WORK

         WORK is SINGLE PRECISION array, dimension (MAX(1,LDWORK))
Workspace for the algorithm.

LDWORK

         LDWORK is INTEGER
Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend.

INFO

         INFO is INTEGER
== 0:  Success
> 0:  Iteration failed in step INFO
< 0:  if INFO == -i, the i-Th argument had an illegal value
Attention

The Fortran/LAPACK-like workspace query with setting LDWORK=-1 on input will not work in the C interface. One have to use the mepack_memory_frontend function for this purpose.

Author

Martin Koehler, MPI Magdeburg

Date

Januar 2023

Definition at line 380 of file gestein.c.

## Author

Generated automatically by Doxygen for MEPACK from the source code.

## Info

Tue Mar 7 2023 Version 1.0.3 MEPACK