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.
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.
Arguments
| TRANA |
(input) 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 |
(input) 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 |
(input) 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 |
(input) INTEGER
The order of the matrix A, and the number of rows in the
matrices X and C. M >= 0. |
| N |
(input) INTEGER
The order of the matrix B, and the number of columns in the
matrices X and C. N >= 0. |
| A |
(input) DOUBLE PRECISION array, dimension (LDA,M)
The upper quasi-triangular matrix A, in Schur canonical form.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
|
| B |
(input) DOUBLE PRECISION array, dimension (LDB,N)
The upper quasi-triangular matrix B, in Schur canonical form.
|
| LDB |
(input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
|
| C |
(input/output) 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 |
(input) INTEGER
The leading dimension of the array C. LDC >= max(1,M)
|
| SCALE |
(output) DOUBLE PRECISION
The scale factor, scale, set <= 1 to avoid overflow in X.
|
| INFO |
(output) 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). |