PZGECON(3) ScaLAPACK routine of NEC Numeric Library Collection PZGECON(3)
NAME
PZGECON - 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 PZGETRF
SYNOPSIS
SUBROUTINE PZGECON( NORM, N, A, IA, JA, DESCA, ANORM, RCOND, WORK,
LWORK, RWORK, LRWORK, INFO )
CHARACTER NORM
INTEGER IA, INFO, JA, LRWORK, LWORK, N
DOUBLE PRECISION ANORM, RCOND
INTEGER DESCA( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), WORK( * )
PURPOSE
PZGECON 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 PZGETRF.
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 vec-
tor. This vector stores the information required to establish the map-
ping 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 col-
umn.
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*16 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) DOUBLE PRECISION
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) DOUBLE PRECISION
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*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)) + 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) 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 >= 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.
ScaLAPACK routine 31 October 2017 PZGECON(3)