PZLANSY - return the value of the one norm, or the Frobenius norm,
- DOUBLE PRECISION
- FUNCTION PZLANSY( NORM, UPLO, N, A, IA, JA, DESCA, WORK )
CHARACTER NORM, UPLO INTEGER IA, JA, N INTEGER DESCA( * ) DOUBLE PRECISION WORK(
* ) COMPLEX*16 A( * )
PZLANSY returns the value of the one norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a real symmetric
distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).
PZLANSY 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 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 the value to be returned in PZLANSY as described above.
- UPLO (global input) CHARACTER
- Specifies whether the upper or lower triangular part of the symmetric
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, PZLANSY is
set to zero. N >= 0.
- A (local input) COMPLEX*16 pointer into the local memory
- to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the local pieces
of the symmetric 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 computed, and the strictly lower triangular
part of this matrix is not referenced. If UPLO = 'L', the leading N-by-N
lower triangular 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) DOUBLE PRECISION 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.