STRSYL - solve the real Sylvester matrix equation


SYNOPSIS

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

           CHARACTER      TRANA, TRANB

           INTEGER        INFO, ISGN, LDA, LDB, LDC, M, N

           REAL           SCALE

           REAL           A( LDA, * ), B( LDB, * ), C( LDC, * )


PURPOSE

       STRSYL 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
       SHSEQR), 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 = Trans­
               pose)

       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 =  Trans­
               pose)

       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


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

       A       (input) REAL 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) REAL 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) REAL 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) REAL
               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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