ZTRSYL (3lapack)

solve the complex Sylvester matrix equation

SYNOPSIS

  SUBROUTINE ZTRSYL( 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

      COMPLEX*16     A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE

  ZTRSYL solves the complex 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**H, and A and B are both upper 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.

ARGUMENTS

  TRANA   (input) CHARACTER*1
          Specifies the option op(A):
          = 'N': op(A) = A    (No transpose)
          = 'C': op(A) = A**H (Conjugate transpose)

  TRANB   (input) CHARACTER*1
          Specifies the option op(B):
          = 'N': op(B) = B    (No transpose)
          = 'C': op(B) = B**H (Conjugate 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) COMPLEX*16 array, dimension (LDA,M)
          The upper triangular matrix A.

  LDA     (input) INTEGER
          The leading dimension of the array A. LDA >= max(1,M).

  B       (input) COMPLEX*16 array, dimension (LDB,N)
          The upper triangular matrix B.

  LDB     (input) INTEGER
          The leading dimension of the array B. LDB >= max(1,N).

  C       (input/output) COMPLEX*16 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).