ZCPOSV(1) LAPACK PROTOTYPE driver routine (version 3.2) ZCPOSV(1)NAME
ZCPOSV - computes the solution to a complex system of linear equations
A * X = B,
SYNOPSIS
SUBROUTINE ZCPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,
+ SWORK, RWORK, ITER, INFO )
CHARACTER UPLO
INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
DOUBLE PRECISION RWORK( * )
COMPLEX SWORK( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( N, * ),
+ X( LDX, * )
PURPOSE
ZCPOSV computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N Hermitian positive definite matrix
and X and B are N-by-NRHS matrices.
ZCPOSV 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
UPLO (input) CHARACTER
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 Hermitian matrix A. If UPLO =
'U', the leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper trian‐
gular part of A is not referenced. Note that the imaginary
parts of the diagonal elements need not be set and are assumed
to be zero. On exit, if iterative refinement has been success‐
fully 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 factor U or L from the Cholesky factoriza‐
tion A = U**H*U or A = L*L**H.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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 CPOTRF
-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, the leading minor of order i of (COMPLEX*16)
A is not positive definite, so the factorization could not be
completed, and the solution has not been computed. =========
LAPACK PROTOTYPE driver routine November 2008 ZCPOSV(1)
