PSLASCL(l)

📦 version 1.5, in ubuntu jammy

💖 PSLASCL 💖

okay bestie, gather round, because this is a LAPACK auxiliary routine (we're living in version 1.5 era, vintage queen) and she is so much simpler than she looks. it's PSLASCL, and no cap, her whole entire job is: take a distributed matrix and scale it. that's it. that's the girl. 🎀

✨ NAME ✨

PSLASCL multiplies the M-by-N real distributed matrix sub( A ) — which is shorthand for A(IA:IA+M-1,JA:JA+N-1) — by the real scalar CTO/CFROM. slay. 💅

🌸 SYNOPSIS 🌸

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

    CHARACTER       TYPE

    INTEGER         IA, INFO, JA, M, N

    REAL            CFROM, CTO

    INTEGER         DESCA( * )

    REAL            A( * )

🦋 PURPOSE 🦋

so PSLASCL multiplies the M-by-N real distributed matrix sub( A ) (aka A(IA:IA+M-1,JA:JA+N-1)) by the real scalar CTO/CFROM. and the iconic part? she does this without over/underflow — as long as the final result CTO * A(I,J) / CFROM doesn't over/underflow. that's the whole vibe. ✨

and TYPE tells her what shape sub( A ) is rocking: full, upper triangular, lower triangular, or upper Hessenberg. she's flexible, she contains multitudes. 👑

📝 Notes

okay so this is the part where we talk descriptors, and lowkey it's the most important lore. every global data object has an associated description vector, and that vector stores all the info you need to map an element of the object to its process and memory location. think of it as the object's ✨passport✨.

let A be a generic term for any 2D block cyclicly distributed array. that global array has an associated description vector DESCA. and in the following comments, whenever you see the character _, read it as "of the global array". iykyk. 🌈

  • 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)).

now let K be the number of rows or columns of a distributed matrix, and assume 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) REAL — and also CTO (global input) REAL. the distributed matrix sub( A ) gets 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. > heads up bestie: CFROM must be nonzero. dividing by zero is NOT the vibe, she will simply not do it. 💀
  • 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) REAL — 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. glow-up moment, honestly. ✨
  • 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. her passport, as established. 🛂
  • INFO (local output) INTEGER —
    • = 0: successful exit. we ate. 🔥
    • < 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. translation: negative INFO means somebody passed something illegal, and the number tells you exactly which argument and which entry snitched. 🙈

and that's the whole page, bestie. go forth and scale responsibly. mwah. 💖✨🦋

this queen dropped as part of LAPACK version 1.5, dated 12 May 1997 — vintage icon behavior, we stan a legacy routine. 👑

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