SRC/dtrsyl3.f(3)

NAME
SRC/dtrsyl3.f

SYNOPSIS

  Functions/Subroutines
subroutine dtrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)
DTRSYL3

Function/Subroutine Documentation

  subroutine dtrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, * ) c, integer ldc, double precision scale, integer, dimension( * ) iwork, integer liwork, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)

DTRSYL3

Purpose

      DTRSYL3 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 DHSEQR), 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
              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 DOUBLE PRECISION 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 dtrsyl3.f.

Author

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