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dtrsyl

 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 = 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 canon-
              ical 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 canon-
              ical 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).