DTRSYL(l)		LAPACK routine (version	1.1)		    DTRSYL(l)

NAME
  DTRSYL - solve the real Sylvester matrix equation

SYNOPSIS

  SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE,
		     INFO )

      CHARACTER	     TRANA, TRANB

      INTEGER	     INFO, ISGN, LDA, LDB, LDC,	M, N

      DOUBLE	     PRECISION SCALE

      DOUBLE	     PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

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 ele-
  ments	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).