

SUBROUTINE PDGECON(  NORM, N, A, IA, JA, DESCA, ANORM, RCOND, WORK, LWORK, IWORK, LIWORK, INFO ) 
CHARACTER NORM  
INTEGER IA, INFO, JA, LIWORK, LWORK, N  
DOUBLE PRECISION ANORM, RCOND  
INTEGER DESCA( * ), IWORK( * )  
DOUBLE PRECISION A( * ), WORK( * )  
PDGECON estimates the reciprocal of the condition number of a general distributed real matrix A(IA:IA+N1,JA:JA+N1), in either the 1norm or the infinitynorm, using the LU factorization computed by PDGETRF. 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
NORM (global input) CHARACTER Specifies whether the 1norm condition number or the infinitynorm condition number is required:
= ’1’ or ’O’: 1norm
= ’I’: InfinitynormN (global input) INTEGER The order of the distributed matrix A(IA:IA+N1,JA:JA+N1). N >= 0. A (local input) DOUBLE PRECISION 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 and U from the factorization A(IA:IA+N1,JA:JA+N1) = 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) DOUBLE PRECISION If NORM = ’1’ or ’O’, the 1norm of the original distributed matrix A(IA:IA+N1,JA:JA+N1). If NORM = ’I’, the infinitynorm of the original distributed matrix A(IA:IA+N1,JA:JA+N1). RCOND (global output) DOUBLE PRECISION 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) DOUBLE PRECISION 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)) + 2*LOCc(N+MOD(JA1,NB_A)) + MAX( 2, MAX( NB_A*MAX( 1, CEIL(NPROW1,NPCOL) ), LOCc(N+MOD(JA1,NB_A)) + NB_A*MAX( 1, CEIL(NPCOL1,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.
IWORK (local workspace/local output) INTEGER array, dimension (LIWORK) On exit, IWORK(1) returns the minimal and optimal LIWORK. LIWORK (local or global input) INTEGER The dimension of the array IWORK. LIWORK is local input and must be at least LIWORK >= LOCr(N+MOD(IA1,MB_A)). If LIWORK = 1, then LIWORK 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.
ScaLAPACK version 1.7  PDGECON (l)  13 August 2001 
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