ZTRSYL(3)      LAPACK routine of NEC Numeric Library Collection      ZTRSYL(3)



NAME
       ZTRSYL

SYNOPSIS
       SUBROUTINE ZTRSYL (TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC,
           SCALE, INFO)



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

           TRANB     (input)
                     TRANB is CHARACTER*1
                     Specifies the option op(B):
                     = 'N': op(B) = B    (No transpose)
                     = 'C': op(B) = B**H (Conjugate transpose)

           ISGN      (input)
                     ISGN is 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)
                     M is INTEGER
                     The order of the matrix A, and the number of rows in the
                     matrices X and C. M >= 0.

           N         (input)
                     N is INTEGER
                     The order of the matrix B, and the number of columns in the
                     matrices X and C. N >= 0.

           A         (input)
                     A is COMPLEX*16 array, dimension (LDA,M)
                     The upper triangular matrix A.

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

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

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

           C         (input/output)
                     C is 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)
                     LDC is INTEGER
                     The leading dimension of the array C. LDC >= max(1,M)

           SCALE     (output)
                     SCALE is DOUBLE PRECISION
                     The scale factor, scale, set <= 1 to avoid overflow in X.

           INFO      (output)
                     INFO is 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).



LAPACK routine                  31 October 2017                      ZTRSYL(3)