SRC/strsyl3.f(3)           Library Functions Manual           SRC/strsyl3.f(3)

NAME
       SRC/strsyl3.f

SYNOPSIS
   Functions/Subroutines
       subroutine strsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
           scale, iwork, liwork, swork, ldswork, info)
           STRSYL3

Function/Subroutine Documentation
   subroutine strsyl3 (character trana, character tranb, integer isgn, integer
       m, integer n, real, dimension( lda, * ) a, integer lda, real,
       dimension( ldb, * ) b, integer ldb, real, dimension( ldc, * ) c,
       integer ldc, real scale, integer, dimension( * ) iwork, integer liwork,
       real, dimension( ldswork, * ) swork, integer ldswork, integer info)
       STRSYL3

       Purpose


             STRSYL3 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.

             This is the block version of the algorithm.

       Parameters
           TRANA

                     TRANA is 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

                     TRANB is 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

                     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

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

           N

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

           A

                     A is REAL array, dimension (LDA,M)
                     The upper quasi-triangular matrix A, in Schur canonical form.

           LDA

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

           B

                     B is REAL array, dimension (LDB,N)
                     The upper quasi-triangular matrix B, in Schur canonical form.

           LDB

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

           C

                     C is 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

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

           SCALE

                     SCALE is REAL
                     The scale factor, scale, set <= 1 to avoid overflow in X.

           IWORK

                     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                     On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

           LIWORK

                     IWORK is INTEGER
                     The dimension of the array IWORK. LIWORK >=  ((M + NB - 1) / NB + 1)
                     + ((N + NB - 1) / NB + 1), where NB is the optimal block size.

                     If LIWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal dimension of the IWORK array,
                     returns this value as the first entry of the IWORK array, and
                     no error message related to LIWORK is issued by XERBLA.

           SWORK

                     SWORK is REAL array, dimension (MAX(2, ROWS),
                     MAX(1,COLS)).
                     On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS
                     and SWORK(2) returns the optimal COLS.

           LDSWORK

                     LDSWORK is INTEGER
                     LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1)
                     and NB is the optimal block size.

                     If LDSWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal dimensions of the SWORK matrix,
                     returns these values as the first and second entry of the SWORK
                     matrix, and no error message related LWORK is issued by XERBLA.

           INFO

                     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).

       Definition at line 178 of file strsyl3.f.

Author
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LAPACK                          Version 3.12.0                SRC/strsyl3.f(3)