---
name: "pdlange"
section: "3"
platform: "linux"
package: "scalapack-doc"
version: "1.5-11"
release: "Debian 11 (Bullseye)"
platforms: ["linux"]
url: "https://new.carta.tech/pdlange"
---

# pdlange(3)

return the value of the one norm, or the Frobenius norm,

## 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.