2. EL 6 ELS
  3. lapack
  4. zcgesv(l)

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ZCGESV(1) LAPACK PROTOTYPE driver routine (version 3.2) ZCGESV(1)

NAME

ZCGESV - computes the solution to a complex system of linear equations A * X = B,

SYNOPSIS

N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,

+ SWORK, RWORK, ITER, INFO ) INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS INTEGER IPIV( * ) DOUBLE PRECISION RWORK( * ) COMPLEX SWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( N, * ), + X( LDX, * )

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

The number of linear equations, i.e., the order of the matrix A. N >= 0.
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
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.
The leading dimension of the array A. LDA >= max(1,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).
The N-by-NRHS right hand side matrix B.
The leading dimension of the array B. LDB >= max(1,N).
If INFO = 0, the N-by-NRHS solution matrix X.
The leading dimension of the array X. LDX >= max(1,N).
This array is used to hold the residual vectors.
This array is used to use the single precision matrix and the right-hand sides or solutions in single precision.
< 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
= 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. =========
November 2008 LAPACK PROTOTYPE driver routine (version 3.2)