PZMAX1(l)

📦 version 1.5, in ubuntu jammy

🌟 NAME 🌟

PZMAX1 — bestie, this routine computes the global index of the maximum element in absolute value of a distributed vector sub( X ). It's a LAPACK auxiliary routine, version 1.5, and it is so iconic for that.

✨ SYNOPSIS ✨

SUBROUTINE PZMAX1( N, AMAX, INDX, X, IX, JX, DESCX, INCX )

    INTEGER        INDX, INCX, IX, JX, N

    COMPLEX*16     AMAX

    INTEGER        DESCX( * )

    COMPLEX*16     X( * )

💅 PURPOSE 💅

Okay so here's the whole vibe: PZMAX1 computes the global index of the maximum element in absolute value of a distributed vector sub( X ). The global index comes back in INDX, and the value comes back in AMAX,

where sub( X ) denotes

X(IX:IX+N-1,JX) if INCX = 1,
X(IX,JX:JX+N-1) if INCX = M_X.

🎀 Notes 🎀

Every global data object has an associated description vector, and that vector is holding all the info you need to map an object element to its process and memory location. It's giving organized.

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".

  • DTYPE_A (global) — stored in DESCA( DTYPE_ ) — the descriptor type. In this case, DTYPE_A = 1.
  • CTXT_A (global) — stored in DESCA( CTXT_ ) — the BLACS context handle, indicating the BLACS process grid A is distributed over. The context itself is global, but the handle (the integer value) may vary.
  • M_A (global) — stored in DESCA( M_ ) — the number of rows in the global array A.
  • N_A (global) — stored in DESCA( N_ ) — the number of columns in the global array A.
  • MB_A (global) — stored in DESCA( MB_ ) — the blocking factor used to distribute the rows of the array.
  • NB_A (global) — stored in DESCA( NB_ ) — the blocking factor used to distribute the columns of the array.
  • RSRC_A (global) — stored in DESCA( RSRC_ ) — the process row over which the first row of the array A is distributed.
  • CSRC_A (global) — stored in DESCA( CSRC_ ) — the process column over which the first column of the array A is distributed.
  • LLD_A (local) — stored in 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

Because vectors may be viewed as a subclass of matrices, a distributed vector is considered to be a distributed matrix. No cap. 🦋

When the result of a vector-oriented PBLAS call is a scalar, it will be made available only within the scope which owns the vector(s) being operated on. Let X be a generic term for the input vector(s). Then, the processes which receive the answer will be — and note that if an operation involves more than one vector, the processes which receive the result will be the union of the following calculation for each vector:

  • If N = 1, M_X = 1 and INCX = 1, then one can't determine if a process row or process column owns the vector operand, therefore only the process of coordinate {RSRC_X, CSRC_X} receives the result;
  • If INCX = M_X, then sub( X ) is a vector distributed over a process row. Each process part of this row receives the result;
  • If INCX = 1, then sub( X ) is a vector distributed over a process column. Each process part of this column receives the result;

Based on PZAMAX from Level 1 PBLAS. The change is to use the

The serial version was contributed to LAPACK by Nick Higham for use with ZLACON. 🫶

👑 ARGUMENTS 👑

  • N — (global input) pointer to INTEGER. The number of components of the distributed vector sub( X ). N >= 0.
  • AMAX — (global output) pointer to DOUBLE PRECISION. The absolute value of the largest entry of the distributed vector sub( X ) only in the scope of sub( X ).
  • INDX — (global output) pointer to INTEGER. The global index of the element of the distributed vector sub( X ) whose real part has maximum absolute value.
  • X — (local input) COMPLEX*16 array containing the local pieces of a distributed matrix of dimension of at least ( (JX-1)*M_X + IX + ( N - 1 )*abs( INCX ) ). This array contains the entries of the distributed vector sub( X ).
  • 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.
  • INCX — (global input) INTEGER. The global increment for the elements of X. Only two values of INCX are supported in this version, namely 1 and M_X.
🚨 INCX must not be zero. 🚨 Like, genuinely. Zero is not the moment.

That's the whole page, bestie. 💖 This was LAPACK version 1.5, dated 12 May 1997 — vintage, but she still ate. ✨

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