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

# pdlacon(3)

estimate the 1-norm of a square, real distributed matrix A

## NAME

PDLACON - estimate the 1-norm of a square, real distributed matrix A

## SYNOPSIS

- SUBROUTINE PDLACON(

  N, V, IV, JV, DESCV, X, IX, JX, DESCX, ISGN, EST, KASE )

- INTEGER

  IV, IX, JV, JX, KASE, N

- DOUBLE

  PRECISION EST

- INTEGER

  DESCV( \* ), DESCX( \* ), ISGN( \* )

- DOUBLE

  PRECISION V( \* ), X( \* )

## PURPOSE

PDLACON estimates the 1-norm of a square, real distributed matrix A. Reverse communication is used for evaluating matrix-vector products. X and V are aligned with the distributed matrix A, this information is implicitly contained within IV, IX, DESCV, and DESCX.\

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

- N (global input) INTEGER

  The length of the distributed vectors V and X.  N \>= 0.

- V (local workspace) DOUBLE PRECISION pointer into the local

  memory to an array of dimension LOCr(N+MOD(IV-1,MB\_V)). On the final return, V = A\*W, where EST = norm(V)/norm(W) (W is not returned).

- IV (global input) INTEGER

  The row index in the global array V indicating the first row of sub( V ).

- JV (global input) INTEGER

  The column index in the global array V indicating the first column of sub( V ).

- DESCV (global and local input) INTEGER array of dimension DLEN\_.

  The array descriptor for the distributed matrix V.

- X (local input/local output) DOUBLE PRECISION pointer into the

  local memory to an array of dimension LOCr(N+MOD(IX-1,MB\_X)). On an intermediate return, X should be overwritten by A \* X,   if KASE=1, A' \* X,  if KASE=2, PDLACON must be re-called with all the other parameters unchanged.

- IX (global input) INTEGER

  The row index in the global array X indicating the first row of sub( X ).

- JX (global input) INTEGER

  The column index in the global array X indicating the first column of sub( X ).

- DESCX (global and local input) INTEGER array of dimension DLEN\_.

  The array descriptor for the distributed matrix X.

- ISGN (local workspace) INTEGER array, dimension

  LOCr(N+MOD(IX-1,MB\_X)). ISGN is aligned with X and V.

- EST (global output) DOUBLE PRECISION

  An estimate (a lower bound) for norm(A).

- KASE (local input/local output) INTEGER

  On the initial call to PDLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A \* X  or A' \* X. On the final return from PDLACON, KASE will again be 0.

## FURTHER DETAILS

The serial version DLACON has been contributed by Nick Higham, University of Manchester. It was originally named SONEST, dated March 16, 1988.\

Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.