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NAME

```       PDLANSY - return the value of the one norm, or the Frobenius norm,

```

SYNOPSIS

```       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( * )

```

PURPOSE

```       PDLANSY  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.

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

```

ARGUMENTS

```       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)) 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.
```