Provided by: scalapack-doc_1.5-10_all #### 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.
```