PLASMA: PLASMA_zcungesv

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_zcungesv | ( | PLASMA_enum | trans,
|  | 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_zcungesv - Solves overdetermined or underdetermined linear systems involving an M-by-N matrix A using the QR or the LQ factorization of A. It is assumed that A has full rank. The following options are provided: # trans = PlasmaNoTrans and M >= N: find the least squares solution of an overdetermined system, i.e., solve the least squares problem: minimize || B - A*X ||. # trans = PlasmaNoTrans and M < N: find the minimum norm solution of an underdetermined system A * X = B. Several right hand side vectors B and solution vectors X can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. PLASMA_zcungesv 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. We follow Bjorck's algorithm proposed in "Iterative Refinement of Linear Least Squares solutions I", BIT, 7:257-278, 1967.4 Parameters
  [in] | trans | Intended usage: = PlasmaNoTrans: the linear system involves A; = PlasmaConjTrans: the linear system involves A**H. Currently only PlasmaNoTrans is supported.
  [in] | N | The number of columns of the matrix A. N >= 0.
  [in] | NRHS | The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
  [in] | A | The M-by-N matrix A. This matrix is not modified.
  [in] | LDA | The leading dimension of the array A. LDA >= max(1,M).
  [in] | B | The M-by-NRHS matrix B of right hand side vectors, stored columnwise. Not modified.
  [in] | LDB | The leading dimension of the array B. LDB >= MAX(1,M,N).
  [out] | X | If return value = 0, the solution vectors, stored columnwise. if M >= N, rows 1 to N of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements N+1 to M in that column; if M < N, rows 1 to N of B contain the minimum norm solution vectors;
  [in] | LDX | The leading dimension of the array B. LDB >= MAX(1,M,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
See Also PLASMA_zcungesv_Tile PLASMA_zcungesv_Tile_Async PLASMA_dsungesv PLASMA_zgels