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 196 of file strsyl3.f.

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