PCLASCL(l)

📦 version 1.5, in ubuntu jammy

💖 PCLASCL 💖

okay bestie, sit DOWN, because we're about to talk about a LAPACK auxiliary routine and honestly? it's giving iconic. this one is PCLASCL, from the LAPACK fam (version 1.5, she's vintage, she's a legend). she scales a distributed complex matrix by a real scalar and she does it without over/underflow, which is the slay of it all. 🫶

✨ NAME ✨

PCLASCL multiplies the M-by-N complex distributed matrix sub( A ) — that's A(IA:IA+M-1,JA:JA+N-1) — by the real scalar CTO/CFROM. periodt. 💅

✨ SYNOPSIS ✨

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

    CHARACTER       TYPE

    INTEGER         IA, INFO, JA, M, N

    REAL            CFROM, CTO

    INTEGER         DESCA( * )

    COMPLEX         A( * )

✨ PURPOSE ✨

PCLASCL 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. and the way she does it?? without over/underflow, as long as the final result CTO * A(I,J) / CFROM doesn't over/underflow. literally main character energy. 🌟

TYPE specifies that sub( A ) may be full, upper triangular, lower triangular or upper Hessenberg. so many vibes, one routine. 💜

Notes 🌸

every 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. iykyk.

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". 🧚

here's the full rundown, and yes we're keeping every single one:

  • 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)).

okay so 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

math queen behavior, no cap. 👑

✨ 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. CTO — (global input) REAL. 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 zero. we're not doing that today.
  • 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 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 one way, she leaves another way. glow up. ✨
  • 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.
ngl bestie, that INFO < 0 encoding is doing the MOST, but it's fine, it's fine, we love a thorough error report.

and that's the whole page!! this manual page came from LAPACK version 1.5, dated 12 May 1997. literally an elder icon and we respect her. stay distributed, stay scaled, don't over/underflow. bye bestie!! 💅💖🎀🦋🌸🫶

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