dtrsyl()

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

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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

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