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| trsyl3(3) | LAPACK | trsyl3(3) |
NAME
trsyl3 - trsyl3: Sylvester equation, level 3
SYNOPSIS
Functions
subroutine ctrsyl3 (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, swork, ldswork, info)
CTRSYL3 subroutine ztrsyl3 (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, swork, ldswork, info)
ZTRSYL3
Detailed Description
Function Documentation
subroutine ctrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldc, * ) c, integer ldc, real scale, real, dimension( ldswork, * ) swork, integer ldswork, integer info)
CTRSYL3
Purpose
CTRSYL3 solves the complex Sylvester matrix equation:
op(A)*X + X*op(B) = scale*C or
op(A)*X - X*op(B) = scale*C,
where op(A) = A or A**H, and A and B are both upper triangular. A is
M-by-M and B is N-by-N; the right hand side C and the solution X are
M-by-N; and scale is an output scale factor, set <= 1 to avoid
overflow in X.
This is the block version of the algorithm.
Parameters
TRANA
TRANA is CHARACTER*1
Specifies the option op(A):
= 'N': op(A) = A (No transpose)
= 'C': op(A) = A**H (Conjugate transpose)
TRANB
TRANB is CHARACTER*1
Specifies the option op(B):
= 'N': op(B) = B (No transpose)
= 'C': op(B) = B**H (Conjugate transpose)
ISGN
ISGN is INTEGER
Specifies the sign in the equation:
= +1: solve op(A)*X + X*op(B) = scale*C
= -1: solve op(A)*X - X*op(B) = scale*C
M
M is INTEGER
The order of the matrix A, and the number of rows in the
matrices X and C. M >= 0.
N
N is INTEGER
The order of the matrix B, and the number of columns in the
matrices X and C. N >= 0.
A
A is COMPLEX array, dimension (LDA,M)
The upper triangular matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is COMPLEX array, dimension (LDB,N)
The upper triangular matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C
C is COMPLEX array, dimension (LDC,N)
On entry, the M-by-N right hand side matrix C.
On exit, C is overwritten by the solution matrix X.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M)
SCALE
SCALE is REAL
The scale factor, scale, set <= 1 to avoid overflow in X.
SWORK
SWORK is REAL array, dimension (MAX(2, ROWS), MAX(1,COLS)).
On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS
and SWORK(2) returns the optimal COLS.
LDSWORK
LDSWORK is INTEGER
LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1)
and NB is the optimal block size.
If LDSWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal dimensions of the SWORK matrix,
returns these values as the first and second entry of the SWORK
matrix, and no error message related LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: A and B have common or very close eigenvalues; perturbed
values were used to solve the equation (but the matrices
A and B are unchanged).
Definition at line 154 of file ctrsyl3.f.
subroutine ztrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldc, * ) c, integer ldc, double precision scale, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)
ZTRSYL3
Purpose
ZTRSYL3 solves the complex Sylvester matrix equation:
op(A)*X + X*op(B) = scale*C or
op(A)*X - X*op(B) = scale*C,
where op(A) = A or A**H, and A and B are both upper triangular. A is
M-by-M and B is N-by-N; the right hand side C and the solution X are
M-by-N; and scale is an output scale factor, set <= 1 to avoid
overflow in X.
This is the block version of the algorithm.
Parameters
TRANA
TRANA is CHARACTER*1
Specifies the option op(A):
= 'N': op(A) = A (No transpose)
= 'C': op(A) = A**H (Conjugate transpose)
TRANB
TRANB is CHARACTER*1
Specifies the option op(B):
= 'N': op(B) = B (No transpose)
= 'C': op(B) = B**H (Conjugate transpose)
ISGN
ISGN is INTEGER
Specifies the sign in the equation:
= +1: solve op(A)*X + X*op(B) = scale*C
= -1: solve op(A)*X - X*op(B) = scale*C
M
M is INTEGER
The order of the matrix A, and the number of rows in the
matrices X and C. M >= 0.
N
N is INTEGER
The order of the matrix B, and the number of columns in the
matrices X and C. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,M)
The upper triangular matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is COMPLEX*16 array, dimension (LDB,N)
The upper triangular matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C
C is COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N right hand side matrix C.
On exit, C is overwritten by the solution matrix X.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M)
SCALE
SCALE is DOUBLE PRECISION
The scale factor, scale, set <= 1 to avoid overflow in X.
SWORK
SWORK is DOUBLE PRECISION array, dimension (MAX(2, ROWS),
MAX(1,COLS)).
On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS
and SWORK(2) returns the optimal COLS.
LDSWORK
LDSWORK is INTEGER
LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1)
and NB is the optimal block size.
If LDSWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal dimensions of the SWORK matrix,
returns these values as the first and second entry of the SWORK
matrix, and no error message related LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: A and B have common or very close eigenvalues; perturbed
values were used to solve the equation (but the matrices
A and B are unchanged).
Definition at line 155 of file ztrsyl3.f.
Author
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