table of contents
PZGERFS(l) | LAPACK routine (version 1.5) | PZGERFS(l) |
NAME¶
PZGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutionsSYNOPSIS¶
- SUBROUTINE PZGERFS(
- TRANS, N, NRHS, A, IA, JA, DESCA, AF, IAF, JAF, DESCAF, IPIV, B, IB, JB, DESCB, X, IX, JX, DESCX, FERR, BERR, WORK, LWORK, RWORK, LRWORK, INFO )
- CHARACTER
- TRANS
- INTEGER
- IA, IAF, IB, IX, INFO, JA, JAF, JB, JX, LRWORK, LWORK, N, NRHS
- INTEGER
- DESCA( * ), DESCAF( * ), DESCB( * ), DESCX( * ), IPIV( * )
- DOUBLE
- PRECISION BERR( * ), FERR( * ), RWORK( * )
- COMPLEX*16
- A( * ), AF( * ), B( * ), WORK( * ), X( * )
PURPOSE¶
PZGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutions.DTYPE_A = 1.
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
array A.
array A.
the rows of the array.
the columns of the array.
row of the array A is distributed. CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
array. LLD_A >= MAX(1,LOCr(M_A)).
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). An upper bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
ARGUMENTS¶
- TRANS (global input) CHARACTER*1
- Specifies the form of the system of equations. = 'N': sub(
A ) * sub( X ) = sub( B ) (No transpose)
- N (global input) INTEGER
- The order of the matrix sub( A ). N >= 0.
- NRHS (global input) INTEGER
- The number of right hand sides, i.e., the number of columns of the matrices sub( B ) and sub( X ). NRHS >= 0.
- A (local input) COMPLEX*16 pointer into the local
- memory to an array of local dimension (LLD_A,LOCc(JA+N-1)). This array contains the local pieces of the distributed matrix sub( A ).
- IA (global input) INTEGER
- The row index in the global array A indicating the first row of sub( A ).
- JA (global input) INTEGER
- The column index in the global array A indicating the first column of sub( A ).
- DESCA (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix A.
- AF (local input) COMPLEX*16 pointer into the local
- memory to an array of local dimension (LLD_AF,LOCc(JA+N-1)). This array contains the local pieces of the distributed factors of the matrix sub( A ) = P * L * U as computed by PZGETRF.
- IAF (global input) INTEGER
- The row index in the global array AF indicating the first row of sub( AF ).
- JAF (global input) INTEGER
- The column index in the global array AF indicating the first column of sub( AF ).
- DESCAF (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix AF.
- IPIV (local input) INTEGER array of dimension LOCr(M_AF)+MB_AF.
- This array contains the pivoting information as computed by PZGETRF. IPIV(i) -> The global row local row i was swapped with. This array is tied to the distributed matrix A.
- B (local input) COMPLEX*16 pointer into the local
- memory to an array of local dimension (LLD_B,LOCc(JB+NRHS-1)). This array contains the local pieces of the distributed matrix of right hand sides sub( B ).
- IB (global input) INTEGER
- The row index in the global array B indicating the first row of sub( B ).
- JB (global input) INTEGER
- The column index in the global array B indicating the first column of sub( B ).
- DESCB (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix B.
- X (local input and output) COMPLEX*16 pointer into the
- local memory to an array of local dimension (LLD_X,LOCc(JX+NRHS-1)). On entry, this array contains the local pieces of the distributed matrix solution sub( X ). On exit, the improved solution vectors.
- IX (global input) INTEGER
- The row index in the global array X indicating the first row of sub( X ).
- JX (global input) INTEGER
- The column index in the global array X indicating the first column of sub( X ).
- DESCX (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix X.
- FERR (local output) DOUBLE PRECISION array of local dimension
- LOCc(JB+NRHS-1). The estimated forward error bound for each solution vector of sub( X ). If XTRUE is the true solution corresponding to sub( X ), FERR is an estimated upper bound for the magnitude of the largest element in (sub( X ) - XTRUE) divided by the magnitude of the largest element in sub( X ). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error. This array is tied to the distributed matrix X.
- BERR (local output) DOUBLE PRECISION array of local dimension
- LOCc(JB+NRHS-1). The componentwise relative backward error of each solution vector (i.e., the smallest re- lative change in any entry of sub( A ) or sub( B ) that makes sub( X ) an exact solution). This array is tied to the distributed matrix X.
- WORK (local workspace/local output) COMPLEX*16 array,
- dimension (LWORK) On exit, WORK(1) returns the minimal and optimal LWORK.
- LWORK (local or global input) INTEGER
- The dimension of the array WORK. LWORK is local input and
must be at least LWORK >= 2*LOCr( N + MOD(IA-1,MB_A) )
- RWORK (local workspace/local output) DOUBLE PRECISION array,
- dimension (LRWORK) On exit, RWORK(1) returns the minimal and optimal LRWORK.
- LRWORK (local or global input) INTEGER
- The dimension of the array RWORK. LRWORK is local input and
must be at least LRWORK >= LOCr( N + MOD(IB-1,MB_B) ).
- INFO (global output) INTEGER
- = 0: successful exit
PARAMETERS¶
ITMAX is the maximum number of steps of iterative refinement.12 May 1997 | LAPACK version 1.5 |