Provided by: scalapack-doc_1.5-10_all 
NAME
PCGECON - estimate the reciprocal of the condition number of a general distributed complex
matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm, using the LU
factorization computed by PCGETRF
SYNOPSIS
SUBROUTINE PCGECON( NORM, N, A, IA, JA, DESCA, ANORM, RCOND, WORK, LWORK, RWORK, LRWORK,
INFO )
CHARACTER NORM
INTEGER IA, INFO, JA, LRWORK, LWORK, N
REAL ANORM, RCOND
INTEGER DESCA( * )
REAL RWORK( * )
COMPLEX A( * ), WORK( * )
PURPOSE
PCGECON estimates the reciprocal of the condition number of a general distributed complex
matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm, using the LU
factorization computed by PCGETRF.
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 as
RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) *
norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).
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
ARGUMENTS
NORM (global input) CHARACTER
Specifies whether the 1-norm condition number or the infinity-norm condition
number is required:
= '1' or 'O': 1-norm
= 'I': Infinity-norm
N (global input) INTEGER
The order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1). N >= 0.
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 and U from the factorization
A(IA:IA+N-1,JA:JA+N-1) = P*L*U; the unit diagonal elements of L are not stored.
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
If NORM = '1' or 'O', the 1-norm of the original distributed matrix
A(IA:IA+N-1,JA:JA+N-1). If NORM = 'I', the infinity-norm of the original
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
RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) *
norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).
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*CEIL(NPROW-1,NPCOL),LOCc(N+MOD(JA-1,NB_A)) + NB_A*CEIL(NPCOL-1,NPROW)) ).
LOCr and LOCc values can be computed using the ScaLAPACK tool function NUMROC;
NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.
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
< 0: If the i-th argument is an array and the j-entry had an illegal value, then
INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then
INFO = -i.