PCPOCON  estimate the reciprocal of the condition number (in the 1norm) of a
complex Hermitian positive definite distributed matrix using the Cholesky
factorization A = U**H*U or A = L*L**H computed by PCPOTRF
 SUBROUTINE PCPOCON(
 UPLO, N, A, IA, JA, DESCA, ANORM, RCOND, WORK, LWORK, RWORK, LRWORK, INFO
)
CHARACTER UPLO INTEGER IA, INFO, JA, LRWORK, LWORK, N REAL ANORM, RCOND INTEGER
DESCA( * ) REAL RWORK( * ) COMPLEX A( * ), WORK( * )
PCPOCON estimates the reciprocal of the condition number (in the 1norm) 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+N1,JA:JA+N1))), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm( A(IA:IA+N1,JA:JA+N1) ) *
norm( inv(A(IA:IA+N1,JA:JA+N1)) ) ).
Notes
=====
Each global data object is described by an associated description vector. This
vector stores the information required to establish the mapping between an
object element and its corresponding process and memory location.
Let A be a generic term for any 2D block cyclicly distributed array. Such a
global array has an associated description vector DESCA. In the following
comments, the character _ should be read as "of the global array".
NOTATION STORED IN EXPLANATION
  
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu
ted over. The context itself is glo
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
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.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
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( K ) denotes the number of elements of K that a process would receive if K
were distributed over the p processes of its process column.
Similarly, LOCc( K ) denotes the number of elements of K that a process would
receive if K were distributed over the q processes of its process row.
The values of LOCr() and LOCc() may be determined via a call to the ScaLAPACK
tool function, NUMROC:
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
 UPLO (global input) CHARACTER
 Specifies whether the factor stored in A(IA:IA+N1,JA:JA+N1) is upper or
lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
 N (global input) INTEGER

The order of the distributed matrix A(IA:IA+N1,JA:JA+N1). N >= 0.
 A (local input) COMPLEX pointer into the local memory to
 an array of dimension ( LLD_A, LOCc(JA+N1) ). On entry, this array
contains the local pieces of the factors L or U from the Cholesky
factorization A(IA:IA+N1,JA:JA+N1) = 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 1norm (or infinitynorm) of the hermitian distributed matrix
A(IA:IA+N1,JA:JA+N1).
 RCOND (global output) REAL
 The reciprocal of the condition number of the distributed matrix
A(IA:IA+N1,JA:JA+N1), computed as
RCOND = 1 / ( norm( A(IA:IA+N1,JA:JA+N1) ) *
norm( inv(A(IA:IA+N1,JA:JA+N1)) ) ).
 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(IA1,MB_A)) + MAX( 2,
MAX(NB_A*MAX(1,CEIL(P1,Q)),LOCc(N+MOD(JA1,NB_A)) +
NB_A*MAX(1,CEIL(Q1,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(JA1,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
< 0: If the ith argument is an array and the jentry had an illegal
value, then INFO = (i*100+j), if the ith argument is a scalar and had an
illegal value, then INFO = i.