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zcposv.f(3) LAPACK zcposv.f(3)

zcposv.f -


subroutine zcposv (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)
 
ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices

ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices
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.
Parameters:
UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
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 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
          triangular 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 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 factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.
LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
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 CPOTRF
               -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, 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 209 of file zcposv.f.

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