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## NAME

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

```

## SYNOPSIS

```       DOUBLE PRECISION FUNCTION PDLANGE( NORM, M, N, A, IA, JA, DESCA, WORK )

CHARACTER    NORM

INTEGER      IA, JA, M, N

INTEGER      DESCA( * )

DOUBLE       PRECISION A( * ), WORK( * )

```

## PURPOSE

```       PDLANGE returns the value of the one norm, or the  Frobenius  norm,  or
the  infinity  norm,  or  the  element  of  largest absolute value of a
distributed matrix sub( A ) = A(IA:IA+M-1, JA:JA+N-1).

PDLANGE 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
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  PDLANGE  as  described
above.

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, PDLANGE 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,
PDLANGE 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 distributed matrix 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.
```