zcgesv.f (3) - Linux Man Pages

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)

ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

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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