zcgesv.f(3)

NAME
zcgesv.f -

SYNOPSIS

  Functions/Subroutines
subroutine zcgesv (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)
ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Function/Subroutine Documentation

  subroutine zcgesv (integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( n, * )WORK, complex, dimension( * )SWORK, double precision, dimension( * )RWORK, integerITER, integerINFO)

Purpose:

     ZCGESV computes the solution to a complex system of linear equations
        A * X = B,
     where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
     ZCGESV first attempts to factorize the matrix in COMPLEX and use this
     factorization within an iterative refinement procedure to produce a
     solution with COMPLEX*16 normwise backward error quality (see below).
     If the approach fails the method switches to a COMPLEX*16
     factorization and solve.
     The iterative refinement is not going to be a winning strategy if
     the ratio COMPLEX performance over COMPLEX*16 performance is too
     small. A reasonable strategy should take the number of right-hand
     sides and the size of the matrix into account. This might be done
     with a call to ILAENV in the future. Up to now, we always try
     iterative refinement.
     The iterative refinement process is stopped if
         ITER > ITERMAX
     or for all the RHS we have:
         RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
     where
         o ITER is the number of the current iteration in the iterative
           refinement process
         o RNRM is the infinity-norm of the residual
         o XNRM is the infinity-norm of the solution
         o ANRM is the infinity-operator-norm of the matrix A
         o EPS is the machine epsilon returned by DLAMCH('Epsilon')
     The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
     respectively.

Parameters:
    N

              N is INTEGER
              The number of linear equations, i.e., the order of the
              matrix A.  N >= 0.

    NRHS

              NRHS is INTEGER
              The number of right hand sides, i.e., the number of columns
              of the matrix B.  NRHS >= 0.

    A

              A is COMPLEX*16 array,
              dimension (LDA,N)
              On entry, the N-by-N coefficient matrix A.
              On exit, if iterative refinement has been successfully used
              (INFO.EQ.0 and ITER.GE.0, see description below), then A is
              unchanged, if double precision factorization has been used
              (INFO.EQ.0 and ITER.LT.0, see description below), then the
              array A contains the factors L and U from the factorization
              A = P*L*U; the unit diagonal elements of L are not stored.

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices that define the permutation matrix P;
              row i of the matrix was interchanged with row IPIV(i).
              Corresponds either to the single precision factorization
              (if INFO.EQ.0 and ITER.GE.0) or the double precision
              factorization (if INFO.EQ.0 and ITER.LT.0).

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              The N-by-NRHS right hand side matrix B.

    LDB

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

    X

              X is COMPLEX*16 array, dimension (LDX,NRHS)
              If INFO = 0, the N-by-NRHS solution matrix X.

    LDX

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

    WORK

              WORK is COMPLEX*16 array, dimension (N*NRHS)
              This array is used to hold the residual vectors.

    SWORK

              SWORK is COMPLEX array, dimension (N*(N+NRHS))
              This array is used to use the single precision matrix and the
              right-hand sides or solutions in single precision.

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (N)

    ITER

              ITER is INTEGER
              < 0: iterative refinement has failed, COMPLEX*16
                   factorization has been performed
                   -1 : the routine fell back to full precision for
                        implementation- or machine-specific reasons
                   -2 : narrowing the precision induced an overflow,
                        the routine fell back to full precision
                   -3 : failure of CGETRF
                   -31: stop the iterative refinement after the 30th
                        iterations
              > 0: iterative refinement has been sucessfully used.
                   Returns the number of iterations

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, U(i,i) computed in COMPLEX*16 is exactly
                    zero.  The factorization has been completed, but the
                    factor U is exactly singular, so the solution
                    could not be computed.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 201 of file zcgesv.f.

Author

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