PCPOCON(l) | LAPACK routine (version 1.5) | PCPOCON(l) |
NAME¶
PCPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite distributed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by PCPOTRFSYNOPSIS¶
- SUBROUTINE PCPOCON(
- UPLO, N, A, IA, JA, DESCA, ANORM, RCOND, WORK, LWORK, RWORK, LRWORK, INFO )
PURPOSE¶
PCPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite distributed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by PCPOTRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and the reciprocal of the condition number is computed asRCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) *
norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ). Notes
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)). 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
- Specifies whether the factor stored in A(IA:IA+N-1,JA:JA+N-1) is upper or
lower triangular.
- N (global input) INTEGER
-
- A (local input) COMPLEX pointer into the local memory to
- an array of dimension ( LLD_A, LOCc(JA+N-1) ). On entry, this array contains the local pieces of the factors L or U from the Cholesky factorization A(IA:IA+N-1,JA:JA+N-1) = U'*U or L*L', as computed by PCPOTRF.
- 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.
- ANORM (global input) REAL
- The 1-norm (or infinity-norm) of the hermitian distributed matrix A(IA:IA+N-1,JA:JA+N-1).
- RCOND (global output) REAL
- The reciprocal of the condition number of the distributed matrix
A(IA:IA+N-1,JA:JA+N-1), computed as
- 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)) + MAX( 2, MAX(NB_A*MAX(1,CEIL(P-1,Q)),LOCc(N+MOD(JA-1,NB_A)) + NB_A*MAX(1,CEIL(Q-1,P))) ). 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) 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 >= 2*LOCc(N+MOD(JA-1,NB_A)). 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 |