table of contents
| trsyl(3) | LAPACK | trsyl(3) |
NAME¶
trsyl - trsyl: Sylvester equation
SYNOPSIS¶
Functions¶
subroutine ctrsyl (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, info)
CTRSYL subroutine dtrsyl (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, info)
DTRSYL subroutine strsyl (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, info)
STRSYL subroutine ztrsyl (trana, tranb, isgn, m, n, a, lda, b,
ldb, c, ldc, scale, info)
ZTRSYL
Detailed Description¶
Function Documentation¶
subroutine ctrsyl (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, integer info)¶
CTRSYL
Purpose:
CTRSYL 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.
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.
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
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dtrsyl (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 info)¶
DTRSYL
Purpose:
DTRSYL 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.
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.
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
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine strsyl (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 info)¶
STRSYL
Purpose:
STRSYL 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.
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.
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
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine ztrsyl (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, integer info)¶
ZTRSYL
Purpose:
ZTRSYL 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.
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.
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
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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