PCLANHE(3) ScaLAPACK routine of NEC Numeric Library Collection PCLANHE(3)
NAME
PCLANHE - return the value of the one norm, or the Frobenius norm,
SYNOPSIS
REAL FUNCTION PCLANHE( NORM, UPLO, N, A, IA, JA, DESCA, WORK )
CHARACTER NORM, UPLO
INTEGER IA, JA, N
INTEGER DESCA( * )
REAL WORK( * )
COMPLEX A( * )
PURPOSE
PCLANHE returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a com-
plex hermitian distributed matrix sub(A) = A(IA:IA+N-1,JA:JA+N-1).
PCLANHE returns the value
( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+N-1,
( and JA <= j <= JA+N-1,
(
( norm1( sub( A ) ), NORM = '1', 'O' or 'o'
(
( normI( sub( A ) ), NORM = 'I' or 'i'
(
( normF( sub( A ) ), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
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 the value to be returned in PCLANHE as described
above.
UPLO (global input) CHARACTER
Specifies whether the upper or lower triangular part of the
hermitian matrix sub( A ) is to be referenced. = 'U': Upper
triangular part of sub( A ) is referenced,
= 'L': Lower triangular part of sub( A ) is referenced.
N (global input) INTEGER
The number of rows and columns to be operated on i.e the number
of rows and columns of the distributed submatrix sub( A ). When
N = 0, PCLANHE is set to zero. N >= 0.
A (local input) COMPLEX pointer into the local memory
to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the
local pieces of the hermitian distributed matrix sub( A ). If
UPLO = 'U', the leading N-by-N upper triangular part of sub( A
) contains the upper triangular matrix which norm is to be com-
puted, and the strictly lower triangular part of this matrix is
not referenced. If UPLO = 'L', the leading N-by-N lower trian-
gular part of sub( A ) contains the lower triangular matrix
which norm is to be computed, and the strictly upper triangular
part of sub( A ) is not referenced.
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.
WORK (local workspace) REAL array dimension (LWORK)
LWORK >= 0 if NORM = 'M' or 'm' (not referenced), 2*Nq0+Np0+LDW
if NORM = '1', 'O', 'o', 'I' or 'i', where LDW is given by: IF(
NPROW.NE.NPCOL ) THEN LDW =
MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW)) ELSE LDW = 0 END IF 0 if
NORM = 'F', 'f', 'E' or 'e' (not referenced),
where LCM is the least common multiple of NPROW and NPCOL LCM =
ILCM( NPROW, NPCOL ) and CEIL denotes the ceiling operation
(ICEIL).
IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW =
INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA,
NB_A, MYCOL, CSRC_A, NPCOL ), Np0 = NUMROC( N+IROFFA, MB_A,
MYROW, IAROW, NPROW ), Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL,
IACOL, NPCOL ),
ICEIL, ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
MYROW, MYCOL, NPROW and NPCOL can be determined by calling the
subroutine BLACS_GRIDINFO.
ScaLAPACK routine 31 October 2017 PCLANHE(3)