PZLASCL(l)

📦 version 1.5, in ubuntu jammy

💖 PZLASCL — the LAPACK auxiliary routine, bestie edition 💖

okay so real quick, this is PZLASCL from the LAPACK auxiliary squad (manual page PZLASCL(l), version 1.5). It's the "scale a distributed matrix by a real number without blowing up your floats" routine. Let's get into it 🫶

✨ NAME ✨

PZLASCL — multiplie the M-by-N complex distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1) by the real scalar CTO/CFROM. 💅

✨ SYNOPSIS ✨

SUBROUTINE PZLASCL( TYPE, CFROM, CTO, M, N, A, IA, JA, DESCA, INFO )

    CHARACTER       TYPE

    INTEGER         IA, INFO, JA, M, N

    DOUBLE          PRECISION CFROM, CTO

    INTEGER         DESCA( * )

    COMPLEX*16      A( * )

✨ PURPOSE ✨

PZLASCL multiplies the M-by-N complex distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1) by the real scalar CTO/CFROM. The whole point, the moment, the reason she exists: this is done without over/underflow as long as the final result CTO * A(I,J) / CFROM does not over/underflow. So like, intermediate steps can be wild, but the final answer has to fit — that's the vibe check. ✨

TYPE specifies that sub( A ) may be full, upper triangular, lower triangular or upper Hessenberg. 🦋

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". iykyk 💜

Here's the whole lore, laid out:

  • 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

✨ ARGUMENTS ✨

  • TYPE — (global input) CHARACTER. TYPE indices the storage type of the input distributed matrix. 👑
    • = 'G': sub( A ) is a full matrix,
    • = 'L': sub( A ) is a lower triangular matrix,
    • = 'U': sub( A ) is an upper triangular matrix,
    • = 'H': sub( A ) is an upper Hessenberg matrix.
  • CFROM — (global input) DOUBLE PRECISION
  • CTO — (global input) DOUBLE PRECISION. The distributed matrix sub( A ) is multiplied by CTO/CFROM. A(I,J) is computed without over/underflow if the final result CTO * A(I,J) / CFROM can be represented without over/underflow. CFROM must be nonzero. 🚨 like fr fr, do not pass a zero here.
  • M — (global input) INTEGER. The number of rows to be operated on i.e the number of rows of the distributed submatrix sub( A ). 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 ). N >= 0.
  • A — (local input/local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). This array contains the local pieces of the distributed matrix sub( A ). On exit, this array contains the local pieces of the distributed matrix multiplied by CTO/CFROM. 🦋 she comes in as one thing and leaves scaled, main character transformation arc.
  • 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.
  • INFO — (local output) INTEGER. The receipts 📋
    • = 0: successful exit ✨
    • < 0: If the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i.
💀 note the < 0 case is literally "something you handed me was illegal" — negative INFO is not a slay, it's a "go fix your args" moment.

LAPACK version 1.5 · 12 May 1997 — that's the source, the version, and the date this page came from, and she's been iconic since. PZLASCL(l) out. 💖✨🎀

📦 where this page comes from