PZTRRFS(l) | LAPACK routine (version 1.5) | PZTRRFS(l) |
NAME¶
PZTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrixSYNOPSIS¶
- SUBROUTINE PZTRRFS(
- UPLO, TRANS, DIAG, N, NRHS, A, IA, JA, DESCA, B, IB, JB, DESCB, X, IX, JX, DESCX, FERR, BERR, WORK, LWORK, RWORK, LRWORK, INFO )
PURPOSE¶
PZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by PZTRTRS or some other means before entering this routine. PZTRRFS does not do iterative refinement because doing so cannot improve the backward error. NotesDTYPE_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)). Let K be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q.
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*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 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*16 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*16 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) DOUBLE PRECISION 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) 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 ) ). If LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA.
- 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 ) ). If LRWORK = -1, then LRWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA.
- INFO (global output) INTEGER
- = 0: successful exit
12 May 1997 | LAPACK version 1.5 |