PDLASCL(l)

📦 version 1.5, in ubuntu jammy

💖 PDLASCL — the LAPACK auxiliary routine (version 1.5) 💖

okay bestie, gather round, because this one is so useful and also kind of a vibe. it's a LAPACK auxiliary routine, and no cap, it does exactly one thing and does it gorgeously.

✨ NAME ✨

PDLASCL — 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. that's it, that's the whole girl. 💅

🌸 SYNOPSIS 🌸

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

    CHARACTER       TYPE

    INTEGER         IA, INFO, JA, M, N

    DOUBLE          PRECISION CFROM, CTO

    INTEGER         DESCA( * )

    DOUBLE          PRECISION A( * )

🦋 PURPOSE 🦋

so PDLASCL multiplies the M-by-N real distributed matrix sub( A ) — which is A(IA:IA+M-1,JA:JA+N-1) — by the real scalar CTO/CFROM. iconic behavior.

and here's the part that's lowkey genius: it does this without over/underflow as long as the final result CTO * A(I,J) / CFROM doesn't over/underflow. so like, it's careful. it's giving responsible main character. 🫶

TYPE tells it what shape sub( A ) is allowed to be: full, upper triangular, lower triangular, or upper Hessenberg. yes ma'am, all four.

💜 Notes 💜

every global data object gets described by an associated description vector. this vector stores all the info you need to establish the mapping between an object element and its corresponding process and memory location. it's basically the group chat roster for your array. ✨

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

here's the whole lineup, stored exactly where:

  • 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. she contains multitudes. 💀
  • 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.

and 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

slay. 🎀

👑 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, genuinely, do not pass a zero here, bestie, it's not the move. 😭
  • 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) DOUBLE PRECISION 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 confirmed. ✨
  • 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.
    • = 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.
💀 reminder: CFROM must be nonzero. that's the whole vibe check. also keep M >= 0 and N >= 0 or INFO will absolutely be snitching on you with that -(i*100+j) business.

🌈 SEE ALSO 🌈

NUMROC — go say hi, you'll need her. 🧚

that's the whole page, bestie. multiply responsibly, keep CFROM nonzero, and let the descriptor vectors do their thing. 💖

this was LAPACK version 1.5, dated 12 May 1997 — yeah she's vintage, she's an icon, she's been slaying since the 90s and she still runs. periodt. 👑💅✨

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