zcposv zposv zposvx zppsv zppsvx

zcposv() void zcposv ( char  uplo, int  n, int  nrhs, int  lda, doublecomplex  a[], int  ldb, doublecomplex  b[], int  ldx, doublecomplex  x[], doublecomplex  work[], floatcomplex  swork[], double  rwork[], int *  iter, int *  info  ) (Simple driver) Solution to system of linear equations AX = B for a Hermitian positive definite matrix (mixed precision with iterative refinement) Purpose This routine computes the solution to a complex system of linear equations A * X = B, where A is an n x n Hermitian positive definite matrix and X and B are n x nrhs matrices. zcposv first attempts to factorize the matrix in single precision and use this factorization within an iterative refinement procedure to produce a solution with double precision normwise backward error quality (see below). If the approach fails the method switches to a double precision factorization and solve. The iterative refinement is not going to be a winning strategy if the ratio single precision performance over double precision performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. 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   iter is the number of the current iteration in the iterative refinement process   rnrm is the infinity-norm of the residual   xnrm is the infinity-norm of the solution   anrm is the infinity-operator-norm of the matrix A   eps is the machine epsilon returned by dlamch('E') The value itermax and bwdmax are fixed to 30 and 1.0D+00 respectively. Parameters [in] uplo = 'U': Upper triangle of A is stored. = 'L': Lower triangle of A is stored. [in] n Number of linear equations, i.e., order of the matrix A. (n >= 0) (If n = 0, returns without computation) [in] nrhs Number of right hand sides, i.e., number of columns of the matrix B. (nrhs >= 0) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, n)) [in,out] a[][] Array a[la][lda] (la >= n) [in] n x n Hermitian positove definite matrix A. The upper or lower triangular part is to be referenced in accordance with uplo. [out] If iterative refinement has been successfully used (info = 0 and iter >= 0, see description below), then a[][] is unchanged. If double precision factorization has been used (info = 0 and iter < 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. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in] b[][] Array b[lb][ldb] (lb >= nrhs) n x nrhs right hand side matrix B. [in] ldx Leading dimension of the two dimensional array x[][]. (ldx >= max(1, n)) [out] x[][] Array x[lx][ldx] (lx >= nrhs) If info = 0, n x nrhs solution matrix X. [out] work[] Array work[lwork] (lwork >= n*nrhs) This array is used to hold the residual vectors. [out] swork[] Array swork[lswork] (lswork >= n*(n + nrhs)) This array is used to use the single precision matrix and the right-hand sides or solutions in single precision. [out] rwork[] Array rwork[lrwork] (lrwork >= n) Work array. [out] iter < 0: Iterative refinement has failed, double precision 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 successfully used. Returns the number of iterations. [out] info = 0: Successful exit = -1: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -2: The argument n had an illegal value (n < 0) = -3: The argument nrhs had an illegal value (nrhs < 0) = -4: The argument lda had an illegal value (lda < max(1, n)) = -6: The argument ldb had an illegal value (ldb < max(1, n)) = -8: The argument ldx had an illegal value (ldx < max(1, n)) = i > 0: The leading minor of order i of (double precision) A is not positive definite, so the factorization could not be completed, and the solution has not been computed. Reference LAPACK