- DOUBLE PRECISION
- FUNCTION PDLANSY( NORM, UPLO, N, A, IA, JA, DESCA, WORK )
- CHARACTER NORM, UPLO
- INTEGER IA, JA, N
- INTEGER DESCA( * )
- DOUBLE PRECISION A( * ), WORK( * )
PURPOSEPDLANSY 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).
PDLANSY 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.
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
N_A (global) DESCA( N_ ) The number of columns in the global
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
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 PDLANSY 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, PDLANSY 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 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))
LDW = 0
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.