DTRSYL (3lapack)

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).