ZCGESV(3)      LAPACK routine of NEC Numeric Library Collection      ZCGESV(3)



NAME
       ZCGESV

SYNOPSIS
       SUBROUTINE ZCGESV (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK,
           RWORK, ITER, INFO)



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.




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

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

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

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

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

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

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

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

           SWORK     (output)
                     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     (output)
                     RWORK is DOUBLE PRECISION array, dimension (N)

           ITER      (output)
                     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      (output)
                     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.



LAPACK routine                  31 October 2017                      ZCGESV(3)