- SUBROUTINE ZCGESV(
- 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, * )
PURPOSEZCGESV 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
o ITER is the number of the current iteration in the iterative
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
- N (input) INTEGER
- The number of linear equations, i.e., the order of the matrix A. N >= 0.
- NRHS (input) INTEGER
- The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
- A (input or input/ouptut) 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) INTEGER
- The leading dimension of the array A. LDA >= max(1,N).
- IPIV (output) 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) COMPLEX*16 array, dimension (LDB,NRHS)
- The N-by-NRHS right hand side matrix B.
- LDB (input) INTEGER
- The leading dimension of the array B. LDB >= max(1,N).
- X (output) COMPLEX*16 array, dimension (LDX,NRHS)
- If INFO = 0, the N-by-NRHS solution matrix X.
- LDX (input) INTEGER
- The leading dimension of the array X. LDX >= max(1,N).
- WORK (workspace) COMPLEX*16 array, dimension (N*NRHS)
- This array is used to hold the residual vectors.
- SWORK (workspace) 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 (workspace) DOUBLE PRECISION array, dimension (N)
- ITER (output) 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) 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. =========