ZTRSYL - 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 trian­
       gular.  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.

               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  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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