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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 dtrsyl3 (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)
DTRSYL3 subroutine strsyl3 (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)
STRSYL3 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).
subroutine dtrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, * ) c, integer ldc, double precision scale, integer, dimension( * ) iwork, integer liwork, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)¶
DTRSYL3
Purpose:
DTRSYL3 solves the real 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**T, and A and B are both upper quasi-
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.
A and B must be in Schur canonical form (as returned by DHSEQR), that
is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
each 2-by-2 diagonal block has its diagonal elements equal and its
off-diagonal elements of opposite sign.
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)
= 'T': op(A) = A**T (Transpose)
= 'C': op(A) = A**H (Conjugate transpose = Transpose)
TRANB
TRANB is CHARACTER*1
Specifies the option op(B):
= 'N': op(B) = B (No transpose)
= 'T': op(B) = B**T (Transpose)
= 'C': op(B) = B**H (Conjugate transpose = 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 DOUBLE PRECISION array, dimension (LDA,M)
The upper quasi-triangular matrix A, in Schur canonical form.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N)
The upper quasi-triangular matrix B, in Schur canonical form.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C
C is DOUBLE PRECISION 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.
IWORK
IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK
IWORK is INTEGER
The dimension of the array IWORK. LIWORK >= ((M + NB - 1) / NB + 1)
+ ((N + NB - 1) / NB + 1), where NB is the optimal block size.
If LIWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal dimension of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
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).
subroutine strsyl3 (character trana, character tranb, integer isgn, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldc, * ) c, integer ldc, real scale, integer, dimension( * ) iwork, integer liwork, real, dimension( ldswork, * ) swork, integer ldswork, integer info)¶
STRSYL3
Purpose:
STRSYL3 solves the real 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**T, and A and B are both upper quasi-
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.
A and B must be in Schur canonical form (as returned by SHSEQR), that
is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
each 2-by-2 diagonal block has its diagonal elements equal and its
off-diagonal elements of opposite sign.
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)
= 'T': op(A) = A**T (Transpose)
= 'C': op(A) = A**H (Conjugate transpose = Transpose)
TRANB
TRANB is CHARACTER*1
Specifies the option op(B):
= 'N': op(B) = B (No transpose)
= 'T': op(B) = B**T (Transpose)
= 'C': op(B) = B**H (Conjugate transpose = 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 REAL array, dimension (LDA,M)
The upper quasi-triangular matrix A, in Schur canonical form.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is REAL array, dimension (LDB,N)
The upper quasi-triangular matrix B, in Schur canonical form.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C
C is REAL 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.
IWORK
IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK
IWORK is INTEGER
The dimension of the array IWORK. LIWORK >= ((M + NB - 1) / NB + 1)
+ ((N + NB - 1) / NB + 1), where NB is the optimal block size.
If LIWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal dimension of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
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).
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).
Author¶
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| Tue Jan 14 2025 16:19:47 | Version 3.12.0 |