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 =  Trans­
               pose)

       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 = Trans­
               pose)

       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

               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 eigenval­
               ues; perturbed values were used to solve the equa­
               tion (but the matrices A and B are unchanged).


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