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trsyl3 - Man Page

trsyl3: Sylvester equation, level 3

subroutine ctrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)
CTRSYL3
subroutine ztrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)
ZTRSYL3

Detailed Description

Function Documentation

subroutine ctrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldc, * ) c, integer ldc, real scale, real, dimension( ldswork, * ) swork, integer ldswork, integer info)

CTRSYL3

Purpose

  CTRSYL3 solves the complex 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**H, and  A and B are both upper 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.

  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)
          = 'C': op(A) = A**H (Conjugate transpose)

TRANB

          TRANB is CHARACTER*1
          Specifies the option op(B):
          = 'N': op(B) = B    (No transpose)
          = 'C': op(B) = B**H (Conjugate 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 is INTEGER
          The order of the matrix A, and the number of rows in the
          matrices X and C. M >= 0.

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

          A is COMPLEX array, dimension (LDA,M)
          The upper triangular matrix A.

LDA

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

          B is COMPLEX array, dimension (LDB,N)
          The upper triangular matrix B.

LDB

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

          C is COMPLEX 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.

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 154 of file ctrsyl3.f.

subroutine ztrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ldc, ) c, integer ldc, double precision scale, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)

ZTRSYL3