dtrsyl man page on Scientific

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DTRSYL(1)		 LAPACK routine (version 3.2)		     DTRSYL(1)

NAME
       DTRSYL - solves 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-diag‐
       onal 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 matri‐
	       ces 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 routine (version 3.2)	 November 2008			     DTRSYL(1)
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