cgglyap - Man Page
Name
cgglyap — C-Interface
— C-Interface for generalized Lyapunov and Stein equation with general coefficient matrices.
Synopsis
Functions
void mepack_double_gglyap (const char *FACT, const char *TRANS, int M, double *A, int LDA, double *B, int LDB, double *Q, int LDQ, double *Z, int LDZ, double *X, int LDX, double *SCALE, double *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Generalized Lyapunov Equations.
void mepack_single_gglyap (const char *FACT, const char *TRANS, int M, float *A, int LDA, float *B, int LDB, float *Q, int LDQ, float *Z, int LDZ, float *X, int LDX, float *SCALE, float *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Generalized Lyapunov Equations.
void mepack_double_ggstein (const char *FACT, const char *TRANS, int M, double *A, int LDA, double *B, int LDB, double *Q, int LDQ, double *Z, int LDZ, double *X, int LDX, double *SCALE, double *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Generalized Stein Equations.
void mepack_single_ggstein (const char *FACT, const char *TRANS, int M, float *A, int LDA, float *B, int LDB, float *Q, int LDQ, float *Z, int LDZ, float *X, int LDX, float *SCALE, float *WORK, size_t LDWORK, int *INFO)
Frontend for the solution of Generalized Stein Equations.
void mepack_double_gglyap_refine (const char *TRANS, const char *GUESS, int M, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *Y, int LDY, double *AS, int LDAS, double *BS, int LDBS, double *Q, int LDQ, double *Z, int LDZ, int *MAXIT, double *TAU, double *CONVLOG, double *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Generalized Lyapunov Equation.
void mepack_single_gglyap_refine (const char *TRANS, const char *GUESS, int M, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *Y, int LDY, float *AS, int LDAS, float *BS, int LDBS, float *Q, int LDQ, float *Z, int LDZ, int *MAXIT, float *TAU, float *CONVLOG, float *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Generalized Lyapunov Equation.
void mepack_double_ggstein_refine (const char *TRANS, const char *GUESS, int M, double *A, int LDA, double *B, int LDB, double *X, int LDX, double *Y, int LDY, double *AS, int LDAS, double *BS, int LDBS, double *Q, int LDQ, double *Z, int LDZ, int *MAXIT, double *TAU, double *CONVLOG, double *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Generalized Stein Equation.
void mepack_single_ggstein_refine (const char *TRANS, const char *GUESS, int M, float *A, int LDA, float *B, int LDB, float *X, int LDX, float *Y, int LDY, float *AS, int LDAS, float *BS, int LDBS, float *Q, int LDQ, float *Z, int LDZ, int *MAXIT, float *TAU, float *CONVLOG, float *WORK, size_t LDWORK, int *INFO)
Iterative Refinement for the Generalized Stein Equation.
Detailed Description
C-Interface for generalized Lyapunov and Stein equation with general coefficient matrices.
The Fortran routines to solve generalized 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_gglyap (const char * FACT, const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * Q, int LDQ, double * Z, int LDZ, double * X, int LDX, double * SCALE, double * WORK, size_t LDWORK, int * INFO)
Frontend for the solution of Generalized Lyapunov Equations.
Purpose:
mepack_double_gglyap solves a generalized Lyapunov equation of the following forms
A * X * B^T + B * X * A^T = SCALE * Y (1)
or
A^T * X * B + B^T * X * A = SCALE * Y (2)
where (A,B) is a M-by-M matrix pencil. The right hand side Y and the solution X are
M-by-M matrices. The matrix pencil (A,B) is either in general form, in generalized
Hessenberg form, or in generalized Schur form where Q and Z also need to be provided.fi
Remarks
This function is a wrapper for dla_gglyap.
See also
dla_gglyap
Parameters
FACT
FACT is String
Specifies how the matrix A is given.
== 'N': The matrix pencil (A,B) is given as a general matrix pencil and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**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
== 'H': The matrix pencil (A,B) is given in generalized Hessenberg form and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**T will be computed.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 matrices A, B, Y and X. 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 then
quasi upper triangular matrix S of the generalized Schur decomposition.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the
generalized Schur decomposition of (A,B).
If FACT == 'H', the matrix A is an upper Hessenberg matrix of the generalized
Hessenberg form (A,B) and it is overwritten with the quasi upper triangular matrix S
of the generalized Schur decomposition.LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,M)
If FACT == 'N', the matrix B a general matrix and it is overwritten with the upper triangular
matrix of the generalized Schur decomposition.
If FACT == 'F', the matrix B contains its upper triangular matrix R of the generalized schur
Schur decomposition of (A,B).
If FACT == 'H', the matrix B is the upper triangular matrix of the generalized Hessenberg form
(A,B) and it is overwritten with the upper triangular matrix of the generalized Schur decomposition.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
left generalized Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Q contains the left generalized Schur vectors of (A,B).
If FACT == 'H', the matrix Q is an empty M-by-M matrix on input and contains the
left Schur vectors of (A,B) on output.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is DOUBLE PRECISION array, dimension (LDZ,M)
If FACT == 'N', the matrix Z is an empty M-by-M matrix on input and contains the
right generalized Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Z contains the right generalized Schur vectors of (A,B).
If FACT == 'H', the matrix Z is an empty M-by-M matrix on input and contains the
right Schur vectors of (A,B) on output.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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. 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 (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: DGGES failed
= 2: DLA_SORT_GEV failed
= 3: Inner 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
January 2024
Definition at line 199 of file gglyap.c.
void mepack_double_gglyap_refine (const char * TRANS, const char * GUESS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * Y, int LDY, double * AS, int LDAS, double * BS, int LDBS, double * Q, int LDQ, double * Z, int LDZ, int * MAXIT, double * TAU, double * CONVLOG, double * WORK, size_t LDWORK, int * INFO)
Iterative Refinement for the Generalized Lyapunov Equation.
Purpose:
mepack_double_gglyap_refine solves a generalized Lyapunov equation of the following forms
A * X * B^T + B * X * A^T = SCALE * Y (1)
or
A^T * X * B - B^T * 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 pencil (A,B) needs to be provided as the original data
as well as in generalized Schur decomposition since both are required in the
iterative refinement process..fi
Remarks
This function is a wrapper for dla_gglyap_refine.
See also
dla_gglyap_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 solvedGUESS
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).B
B is DOUBLE PRECISION array, dimension (LDB,M)
The array B contains the original matrix B defining the equation.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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 generalized Schur decomposition of the
matrix A.LDAS
LDAS is INTEGER
The leading dimension of the array AS. LDAS >= max(1,M).BS
BS is DOUBLE PRECISION array, dimension (LDBS,M)
The array BS contains the generalized Schur decomposition of the
matrix B.LDBS
LDBS is INTEGER
The leading dimension of the array BS. LDBS >= max(1,M).Q
Q is DOUBLE PRECISION array, dimension (LDQ,M)
The array Q contains the left generalized Schur vectors of
(A, B) as returned by DGGES3.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is DOUBLE PRECISION array, dimension (LDZ,M)
The array Z contains the right generalized Schur vectors of
(A,B) as returned by DGGES3.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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
January 2024
Definition at line 233 of file gglyap.c.
void mepack_double_ggstein (const char * FACT, const char * TRANS, int M, double * A, int LDA, double * B, int LDB, double * Q, int LDQ, double * Z, int LDZ, double * X, int LDX, double * SCALE, double * WORK, size_t LDWORK, int * INFO)
Frontend for the solution of Generalized Stein Equations.
Purpose:
mepack_double_ggstein 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,B) is a M-by-M matrix pencil. The right hand side Y and the solution X are
M-by-M matrices. The matrix pencil (A,B) is either in general form, in generalized
Hessenberg form, or in generalized Schur form where Q and Z also need to be provided..fi
Remarks
This function is a wrapper for dla_ggstein.
See also
dla_ggstein
Parameters
FACT
FACT is String
Specifies how the matrix A is given.
== 'N': The matrix pencil (A,B) is given as a general matrix pencil and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**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
== 'H': The matrix pencil (A,B) is given in generalized Hessenberg form and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**T will be computed.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 matrices A, B, Y and X. 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 the
quasi upper triangular matrix S of the generalized schur decomposition.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the
generalized Schur decomposition of (A,B).
If FACT == 'H', the matrix A is an upper Hessenberg matrix of the generalized
Hessenberg form (A,B) and it is overwritten with the quasi upper triangular matrix S
of the generalized Schur decomposition.LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).B
B is DOUBLE PRECISION array, dimension (LDB,M)
If FACT == 'N', the matrix B a general matrix and it is overwritten with the upper triangular
matrix of the generalized Schur decomposition.
If FACT == 'F', the matrix B contains its upper triangular matrix R of the generalized schur
Schur decomposition of (A,B).
If FACT == 'H', the matrix B is the upper triangular matrix of the generalized Hessenberg form
(A,B) and it is overwritten with the upper triangular matrix of the generalized Schur decomposition.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
left Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Q contains the left Schur vectors of (A,B).
If FACT == 'H', the matrix Q is an empty M-by-M matrix on input and contains the
left Schur vectors of (A,B) on output.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is DOUBLE PRECISION array, dimension (LDZ,M)
If FACT == 'N', the matrix Z is an empty M-by-M matrix on input and contains the
right Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Z contains the right Schur vectors of (A,B).
If FACT == 'H', the matrix Z is an empty M-by-M matrix on input and contains the
right Schur vectors of (A,B) on output.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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. 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 (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: DGGES failed
= 2: DLA_SORT_GEV failed
= 3: Inner 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
January 2024
Definition at line 201 of file ggstein.c.
void mepack_double_ggstein_refine (const char * TRANS, const char * GUESS, int M, double * A, int LDA, double * B, int LDB, double * X, int LDX, double * Y, int LDY, double * AS, int LDAS, double * BS, int LDBS, double * Q, int LDQ, double * Z, int LDZ, int * MAXIT, double * TAU, double * CONVLOG, double * WORK, size_t LDWORK, int * INFO)
Iterative Refinement for the Generalized Stein Equation.
Purpose:
mepack_double_ggstein_refine 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 matrix using iterative refinement.
The right hand side Y and the solution X are M-by-M matrices.
The matrix pencil (A,B) needs to be provided as the original data
as well as in generalized Schur decomposition since both are required in the
iterative refinement process..fi
Remarks
This function is a wrapper for dla_ggstein_refine.
See also
dla_ggstein_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 solvedGUESS
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).B
B is DOUBLE PRECISION array, dimension (LDB,M)
The array B contains the original matrix B defining the equation.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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 generalized Schur decomposition of
the matrix A.LDAS
LDAS is INTEGER
The leading dimension of the array AS. LDAS >= max(1,M).BS
BS is DOUBLE PRECISION array, dimension (LDBS,M)
The array AS contains the generalized Schur decomposition of
the matrix B.LDBS
LDBS is INTEGER
The leading dimension of the array BS. LDBS >= max(1,M).Q
Q is DOUBLE PRECISION array, dimension (LDQ,M)
The array Q contains the left generalized Schur vectors of
(A, B) as returned by DGGES3.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is DOUBLE PRECISION array, dimension (LDZ,M)
The array Z contains the right generalized Schur vectors of
(A,B) as returned by DGGES3.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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
January 2024
Definition at line 231 of file ggstein.c.
void mepack_single_gglyap (const char * FACT, const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * Q, int LDQ, float * Z, int LDZ, float * X, int LDX, float * SCALE, float * WORK, size_t LDWORK, int * INFO)
Frontend for the solution of Generalized Lyapunov Equations.
Purpose:
mepack_single_gglyap solves a generalized Lyapunov equation of the following forms
A * X * B^T + B * X * A^T = SCALE * Y (1)
or
A^T * X * B + B^T * X * A = SCALE * Y (2)
where (A,B) is a M-by-M matrix pencil. The right hand side Y and the solution X are
M-by-M matrices. The matrix pencil (A,B) is either in general form, in generalized
Hessenberg form, or in generalized Schur form where Q and Z also need to be provided..fi
Remarks
This function is a wrapper for sla_gglyap.
See also
sla_gglyap
Parameters
FACT
FACT is String
Specifies how the matrix A is given.
== 'N': The matrix pencil (A,B) is given as a general matrix pencil and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**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
== 'H': The matrix pencil (A,B) is given in generalized Hessenberg form and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**T will be computed.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 matrices A, B, Y and X. 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 the
quasi upper triangular matrix S of the generalized Schur decomposition.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the
generalized Schur decomposition of (A,B).
If FACT == 'H', the matrix A is an upper Hessenberg matrix of the generalized
Hessenberg form (A,B) and it is overwritten with the quasi upper triangular matrix S
of the generalized Schur decomposition.LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,M)
If FACT == 'N', the matrix B a general matrix and it is overwritten with the upper triangular
matrix of the generalized Schur decomposition.
If FACT == 'F', the matrix B contains its upper triangular matrix R of the generalized schur
Schur decomposition of (A,B).
If FACT == 'H', the matrix B is the upper triangular matrix of the generalized Hessenberg form
(A,B) and it is overwritten with the upper triangular matrix of the generalized Schur decomposition.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
left generalized Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Q contains the left Schur vectors of (A,B).
If FACT == 'H', the matrix Q is an empty M-by-M matrix on input and contains the
left Schur vectors of (A,B) on output.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is SINGLE PRECISION array, dimension (LDZ,M)
If FACT == 'N', the matrix Z is an empty M-by-M matrix on input and contains the
right generalized Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Z contains the right Schur vectors of (A,B).
If FACT == 'H', the matrix Z is an empty M-by-M matrix on input and contains the
right Schur vectors of (A,B) on output.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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. 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 (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: DGGES failed
= 2: DLA_SORT_GEV failed
= 3: Inner 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
January 2024
Definition at line 395 of file gglyap.c.
void mepack_single_gglyap_refine (const char * TRANS, const char * GUESS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * Y, int LDY, float * AS, int LDAS, float * BS, int LDBS, float * Q, int LDQ, float * Z, int LDZ, int * MAXIT, float * TAU, float * CONVLOG, float * WORK, size_t LDWORK, int * INFO)
Iterative Refinement for the Generalized Lyapunov Equation.
Purpose:
mepack_single_gglyap_refine solves a generalized Lyapunov equation of the following forms
A * X * B^T + B * X * A^T = SCALE * Y (1)
or
A^T * X * B + B^T * 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 pencil (A,B) needs to be provided as the original data
as well as in generalized Schur decomposition since both are required in the
iterative refinement process..fi
Remarks
This function is a wrapper for dla_gglyap_refine.
See also
dla_gglyap_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 solvedGUESS
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).B
B is SINGLE PRECISION array, dimension (LDB,M)
The array B contains the original matrix B defining the equation.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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 generalized Schur decomposition of the
matrix A.LDAS
LDAS is INTEGER
The leading dimension of the array AS. LDAS >= max(1,M).BS
BS is SINGLE PRECISION array, dimension (LDBS,M)
The array BS contains the generalized Schur decomposition of the
matrix B.LDBS
LDBS is INTEGER
The leading dimension of the array BS. LDBS >= max(1,M).Q
Q is SINGLE PRECISION array, dimension (LDQ,M)
The array Q contains the left generalized Schur vectors of
(A, B) as returned by SGGES3.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is SINGLE PRECISION array, dimension (LDZ,M)
The array Z contains the right generalized Schur vectors of
(A,B) as returned by SGGES3.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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
January 2024
Definition at line 468 of file gglyap.c.
void mepack_single_ggstein (const char * FACT, const char * TRANS, int M, float * A, int LDA, float * B, int LDB, float * Q, int LDQ, float * Z, int LDZ, float * X, int LDX, float * SCALE, float * WORK, size_t LDWORK, int * INFO)
Frontend for the solution of Generalized Stein Equations.
Purpose:
mepack_single_ggstein 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,B) is a M-by-M matrix pencil. The right hand side Y and the solution X are
M-by-M matrices. The matrix pencil (A,B) is either in general form, in generalized
Hessenberg form, or in generalized Schur form where Q and Z also need to be provided..fi
Remarks
This function is a wrapper for sla_ggstein.
See also
sla_ggstein
Parameters
FACT
FACT is String
Specifies how the matrix A is given.
== 'N': The matrix pencil (A,B) is given as a general matrix pencil and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**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
== 'H': The matrix pencil (A,B) is given in generalized Hessenberg form and its Schur decomposition
A = Q*S*Z**T, B = Q*R*Z**T will be computed.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 matrices A, B, Y and X. 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 the
quasi upper triangular matrix S of the generalized schur decomposition.
If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the
generalized Schur decomposition of (A,B).
If FACT == 'H', the matrix A is an upper Hessenberg matrix of the generalized
Hessenberg form (A,B) and it is overwritten with the quasi upper triangular matrix S
of the generalized Schur decomposition.LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).B
B is SINGLE PRECISION array, dimension (LDB,M)
If FACT == 'N', the matrix B a general matrix and it is overwritten with the upper triangular
matrix of the generalized Schur decomposition.
If FACT == 'F', the matrix B contains its upper triangular matrix R of the generalized schur
Schur decomposition of (A,B).
If FACT == 'H', the matrix B is the upper triangular matrix of the generalized Hessenberg form
(A,B) and it is overwritten with the upper triangular matrix of the generalized Schur decomposition.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
left Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Q contains the left Schur vectors of (A,B).
If FACT == 'H', the matrix Q is an empty M-by-M matrix on input and contains the
left Schur vectors of (A,B) on output.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is SINGLE PRECISION array, dimension (LDZ,M)
If FACT == 'N', the matrix Z is an empty M-by-M matrix on input and contains the
right Schur vectors of (A,B) on output.
If FACT == 'F', the matrix Z contains the right Schur vectors of (A,B).
If FACT == 'H', the matrix Z is an empty M-by-M matrix on input and contains the
right Schur vectors of (A,B) on output.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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. 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 (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: DGGES failed
= 2: DLA_SORT_GEV failed
= 3: Inner 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
January 2024
Definition at line 397 of file ggstein.c.
void mepack_single_ggstein_refine (const char * TRANS, const char * GUESS, int M, float * A, int LDA, float * B, int LDB, float * X, int LDX, float * Y, int LDY, float * AS, int LDAS, float * BS, int LDBS, float * Q, int LDQ, float * Z, int LDZ, int * MAXIT, float * TAU, float * CONVLOG, float * WORK, size_t LDWORK, int * INFO)
Iterative Refinement for the Generalized Stein Equation.
Purpose:
mepack_single_ggstein_refine 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 matrix using iterative refinement.
The right hand side Y and the solution X are M-by-M matrices.
The matrix pencil (A,B) needs to be provided as the original data
as well as in generalized Schur decomposition since both are required in the
iterative refinement process..fi
Remarks
This function is a wrapper for sla_ggstein_refine.
See also
sla_ggstein_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 solvedGUESS
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).B
B is SINGLE PRECISION array, dimension (LDB,M)
The array B contains the original matrix B defining the equation.LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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 generalized Schur decomposition of
the matrix A.LDAS
LDAS is INTEGER
The leading dimension of the array AS. LDAS >= max(1,M).BS
BS is SINGLE PRECISION array, dimension (LDBS,M)
The array AS contains the generalized Schur decomposition of
the matrix B.LDBS
LDBS is INTEGER
The leading dimension of the array BS. LDBS >= max(1,M).Q
Q is SINGLE PRECISION array, dimension (LDQ,M)
The array Q contains the left generalized Schur vectors of
(A,B) as returned by SGEES3.LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).Z
Z is SINGLE PRECISION array, dimension (LDZ,M)
The array Z contains the right generalized Schur vectors
of (A,B) as returned by SGGES3.LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 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
January 2024
Definition at line 464 of file ggstein.c.
Author
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