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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, * )



     #include <sunperf.h>

     void dtrsyl(char trana, char tranb, int isgn, int m, int  n,
               double  *da,  int lda, double *db, int ldb, double
               *dc, int ldc, double *dscale, int *info) ;

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  =  Tran-
               spose)

     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  =  Tran-
               spose)

     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  over-
               flow in X.

     INFO      (output) INTEGER
               = 0: successful exit
               < 0: if INFO = -i, the i-th argument had an  ille-
               gal value
               = 1: A and B have  common  or  very  close  eigen-
               values;  perturbed  values  were used to solve the
               equation (but the matrices A and B are unchanged).

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