PSLACON(l)

📦 version 1.5, in ubuntu jammy

💖 PSLACON(l) — the LAPACK auxiliary routine that clocks your matrix's 1-norm 💖

okay bestie, sit down, hydrate, because we're talking about PSLACON from LAPACK auxiliary routine (version 1.5) and she is that girl. Parallel ScaLAPACK energy, reverse communication, descriptor vectors everywhere — it's giving "I understand BLACS and I'm not sorry about it." 🦋

✨ NAME ✨

PSLACON — estimates the 1-norm of a square, real distributed matrix A. no cap, that's the whole job, and she does it flawlessly. 💅

🎀 SYNOPSIS 🎀

SUBROUTINE PSLACON( N, V, IV, JV, DESCV, X, IX, JX, DESCX, ISGN, EST,
                    KASE )

    INTEGER         IV, IX, JV, JX, KASE, N

    REAL            EST

    INTEGER         DESCV( * ), DESCX( * ), ISGN( * )

    REAL            V( * ), X( * )

look at her. eleven arguments. main character energy fr fr. 🌟

🌸 PURPOSE 🌸

So PSLACON estimates the 1-norm of a square, real distributed matrix A. Reverse communication is used for evaluating matrix-vector products — yes bestie, she calls you back, that's the whole bit. 🔁

X and V are aligned with the distributed matrix A, and this information is implicitly contained within IV, IX, DESCV, and DESCX. iykyk. 💜

🧚 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". periodt. 💫

  • DTYPE_A (global) — DESCA( DTYPE_ ) — The descriptor type. In this case, DTYPE_A = 1.
  • CTXT_A (global) — 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) — DESCA( M_ ) — The number of rows in the global array A.
  • N_A (global) — DESCA( N_ ) — The number of columns in the global array A.
  • MB_A (global) — DESCA( MB_ ) — The blocking factor used to distribute the rows of the array.
  • NB_A (global) — DESCA( NB_ ) — The blocking factor used to distribute the columns of the array.
  • RSRC_A (global) — DESCA( RSRC_ ) — The process row over which the first row of the array A is distributed.
  • CSRC_A (global) — DESCA( CSRC_ ) — The process column over which the first column of the array A is distributed.
  • LLD_A (local) — 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 💅

  • N — (global input) INTEGER. The length of the distributed vectors V and X. N >= 0. she does not do negative lengths, don't even try it. 🙈
  • V — (local workspace) REAL pointer into the local memory to an array of dimension LOCr(N+MOD(IV-1,MB_V)). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned). rip W, she was never invited back. 😭
  • IV — (global input) INTEGER. The row index in the global array V indicating the first row of sub( V ).
  • JV — (global input) INTEGER. The column index in the global array V indicating the first column of sub( V ).
  • DESCV — (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix V.
  • X — (local input/local output) REAL pointer into the local memory to an array of dimension LOCr(N+MOD(IX-1,MB_X)). On an intermediate return, X should be overwritten by A * X, if KASE=1, A' * X, if KASE=2, PSLACON must be re-called with all the other parameters unchanged. ⚠️ yes bestie, all the other parameters — do not freestyle.
  • 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.
  • ISGN — (local workspace) INTEGER array, dimension LOCr(N+MOD(IX-1,MB_X)). ISGN is aligned with X and V. 🫶
  • EST — (global output) REAL. An estimate (a lower bound) for norm(A). she's humble — a lower bound — but she is correct. 👑
  • KASE — (local input/local output) INTEGER. On the initial call to PSLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A' * X. On the final return from PSLACON, KASE will again be 0. the full circle moment, we love a returning queen. 🔥

🌈 FURTHER DETAILS 🌈

The serial version SLACON has been contributed by Nick Higham, University of Manchester. It was originally named SONEST, dated March 16, 1988. a legend, honestly. 💐

Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

✨ and that's the whole page bestie ✨

this was LAPACK version 1.5, dated 12 May 1997, and it's still serving looks. mwah. 💋 🎀💖

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