dtrsyl3.f - Man Page

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

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.