PLASMA: PLASMA_zcposv

PLASMA 2.4.6

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PLASMA_zcgels
PLASMA_zcgesv
PLASMA_zcposv
PLASMA_zcungesv
PLASMA_zgebrd
PLASMA_zgelqf
PLASMA_zgelqs
PLASMA_zgels
PLASMA_zgemm
PLASMA_zgeqrf
PLASMA_zgeqrs
PLASMA_zgesv
PLASMA_zgesv_incpiv
PLASMA_zgesvd
PLASMA_zgetrf
PLASMA_zgetrf_incpiv
PLASMA_zgetri
PLASMA_zgetrs
PLASMA_zgetrs_incpiv
PLASMA_zheev
PLASMA_zheevd
PLASMA_zhegst
PLASMA_zhegv
PLASMA_zhegvd
PLASMA_zhemm
PLASMA_zher2k
PLASMA_zherk
PLASMA_zhetrd
PLASMA_zlacpy
PLASMA_zlange
PLASMA_zlanhe
PLASMA_zlansy
PLASMA_zLapack_to_Tile
PLASMA_zlaset
PLASMA_zlaswp
PLASMA_zlaswpc
PLASMA_zlauum
PLASMA_zplghe
PLASMA_zplgsy
PLASMA_zplrnt
PLASMA_zposv
PLASMA_zpotrf
PLASMA_zpotri
PLASMA_zpotrs
PLASMA_zsymm
PLASMA_zsyr2k
PLASMA_zsyrk
PLASMA_zTile_to_Lapack
PLASMA_ztrmm
PLASMA_ztrsm
PLASMA_ztrsmpl
PLASMA_ztrsmrv
PLASMA_ztrtri
PLASMA_zunglq
PLASMA_zungqr
PLASMA_zunmlq
PLASMA_zunmqr
int PLASMA_zcposv | ( | PLASMA_enum | uplo,
|  | int | N,
|  | int | NRHS,
|  | PLASMA_Complex64_t * | A,
|  | int | LDA,
|  | PLASMA_Complex64_t * | B,
|  | int | LDB,
|  | PLASMA_Complex64_t * | X,
|  | int | LDX,
|  | int * | ITER
| ) |  |
  PLASMA_zcposv - Computes the solution to a system of linear equations A * X = B, where A is an N-by-N symmetric positive definite (or Hermitian positive definite in the complex case) matrix and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as A = U**H * U, if uplo = PlasmaUpper, or A = L * L**H, if uplo = PlasmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. PLASMA_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 < 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('Epsilon'). Actually, in its current state (PLASMA 2.1.0), the test is slightly relaxed. The values ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively. Parameters
  [in] | uplo | Specifies whether the matrix A is upper triangular or lower triangular: = PlasmaUpper: Upper triangle of A is stored; = PlasmaLower: Lower triangle of A is stored.
  [in] | N | The number of linear equations, i.e., the order of the matrix A. N >= 0.
  [in] | NRHS | The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  [in] | A | The N-by-N symmetric positive definite (or Hermitian) coefficient matrix A. If uplo = PlasmaUpper, 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. This matrix is not modified.
  [in] | LDA | The leading dimension of the array A. LDA >= max(1,N).
  [in] | B | The N-by-NRHS matrix of right hand side matrix B.
  [in] | LDB | The leading dimension of the array B. LDB >= max(1,N).
  [out] | X | If return value = 0, the N-by-NRHS solution matrix X.
  [in] | LDX | The leading dimension of the array B. LDX >= max(1,N).
  [out] | ITER | The number of the current iteration in the iterative refinement process
  Returns Return values
  PLASMA_SUCCESS | successful exit
  <0 | if -i, the i-th argument had an illegal value
  >0 | if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.
See Also PLASMA_zcposv_Tile PLASMA_zcposv_Tile_Async PLASMA_dsposv PLASMA_zposv