PDLANTR(3) ScaLAPACK routine of NEC Numeric Library Collection PDLANTR(3)
NAME
PDLANTR - return the value of the one norm, or the Frobenius norm,
SYNOPSIS
DOUBLE PRECISION FUNCTION PDLANTR( NORM, UPLO, DIAG, M, N, A, IA, JA,
DESCA, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER IA, JA, M, N
INTEGER DESCA( * )
DOUBLE PRECISION A( * ), WORK( * )
PURPOSE
PDLANTR returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a trape-
zoidal or triangular distributed matrix sub( A ) denoting A(IA:IA+M-1,
JA:JA+N-1).
PDLANTR returns the value
( max(abs(A(i,j))), NORM = 'M' or 'm' with ia <= i <= ia+m-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 PDLANTR as described
above.
UPLO (global input) CHARACTER
Specifies whether the matrix sub( A ) is upper or lower trape-
zoidal. = 'U': Upper trapezoidal
= 'L': Lower trapezoidal Note that sub( A ) is triangular
instead of trapezoidal if M = N.
DIAG (global input) CHARACTER
Specifies whether or not the distributed matrix sub( A ) has
unit diagonal. = 'N': Non-unit diagonal
= 'U': Unit diagonal
M (global input) INTEGER
The number of rows to be operated on i.e the number of rows of
the distributed submatrix sub( A ). When M = 0, PDLANTR is set
to zero. M >= 0.
N (global input) INTEGER
The number of columns to be operated on i.e the number of
columns of the distributed submatrix sub( A ). When N = 0,
PDLANTR is set to zero. N >= 0.
A (local input) DOUBLE PRECISION pointer into the local memory
to an array of dimension (LLD_A, LOCc(JA+N-1) ) containing the
local pieces of sub( A ).
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) DOUBLE PRECISION array dimension (LWORK)
LWORK >= 0 if NORM = 'M' or 'm' (not referenced), Nq0 if NORM
= '1', 'O' or 'o', Mp0 if NORM = 'I' or 'i', 0 if NORM = 'F',
'f', 'E' or 'e' (not referenced), where
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 ), Mp0 = NUMROC( M+IROFFA, MB_A,
MYROW, IAROW, NPROW ), Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL,
IACOL, NPCOL ),
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 PDLANTR(3)