dtrsyl3()

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

[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]	IWORK	!> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. !>
[in]	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. !>
[out]	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. !>
[in]	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. !>
[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). !>