DTRSYL(l)								 )								 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 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).

LAPACK version 3.0						   15 June 2000 							 DTRSYL(l)