PCTRRFS(l) | LAPACK routine (version 1.5) | PCTRRFS(l) |
NAME¶
PCTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrixSYNOPSIS¶
- SUBROUTINE PCTRRFS(
- UPLO, TRANS, DIAG, N, NRHS, A, IA, JA, DESCA, B, IB, JB, DESCB, X, IX, JX, DESCX, FERR, BERR, WORK, LWORK, RWORK, LRWORK, INFO )
- CHARACTER
- DIAG, TRANS, UPLO
- INTEGER
- INFO, IA, IB, IX, JA, JB, JX, LRWORK, LWORK, N, NRHS
- INTEGER
- DESCA( * ), DESCB( * ), DESCX( * )
- REAL
- BERR( * ), FERR( * ), RWORK( * )
- COMPLEX
- A( * ), B( * ), WORK( * ), X( * )
PURPOSE¶
PCTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix.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¶
- UPLO (global input) CHARACTER*1
- = 'U': sub( A ) is upper triangular;
- TRANS (global input) CHARACTER*1
- Specifies the form of the system of equations. = 'N': sub(
A ) * sub( X ) = sub( B ) (No transpose)
- DIAG (global input) CHARACTER*1
- = 'N': sub( A ) is non-unit triangular;
- 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 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 original triangular distributed matrix sub( A ). If UPLO = 'U', the leading N-by-N upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of sub( A ) contains the lower triangular part of the distribu- ted matrix, and its strictly upper triangular part is not referenced. If DIAG = 'U', the diagonal elements of sub( A ) are also not referenced and are assumed to be 1.
- 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.
- B (local input) COMPLEX pointer into the local memory
- to an array of local dimension (LLD_B, LOCc(JB+NRHS-1) ). On entry, this array contains the the local pieces of the 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) COMPLEX pointer into the local memory
- to an array of local dimension (LLD_X, LOCc(JX+NRHS-1) ). On entry, this array contains the the local pieces of the solution vectors sub( X ).
- 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) REAL array of local dimension
- LOCc(JB+NRHS-1). The estimated forward error bounds for each solution vector of sub( X ). If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (sub( X ) - XTRUE) divided by the magnitude of the largest entry 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) REAL 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 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) REAL 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
12 May 1997 | LAPACK version 1.5 |