PCGETF2(l)

📦 version 1.5, in ubuntu jammy

✨ PCGETF2 — the LAPACK glow-up ✨

okay so bestie, welcome to PCGETF2 from LAPACK, version 1.5, chilling in manual section l. It's a ScaLAPACK routine, it's giving main character energy, and by the end of this page you're gonna understand it fr fr. 🫶

💖 NAME 💖

PCGETF2 — compute an LU factorization of a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. iconic behavior honestly ✨

🌸 SYNOPSIS 🌸

SUBROUTINE PCGETF2( M, N, A, IA, JA, DESCA, IPIV, INFO )

    INTEGER         IA, INFO, JA, M, N

    INTEGER         DESCA( * ), IPIV( * )

    COMPLEX         A( * )

🦋 PURPOSE 🦋

So what does PCGETF2 actually do, you ask? It computes an LU factorization of a general M-by-N distributed matrix

sub( A ) = A(IA:IA+M-1,JA:JA+N-1)

using partial pivoting with row interchanges. No cap. 💅

The factorization has the form

sub( A ) = P * L * U

where P is a permutation matrix, L is lower triangular with unit diagonal elements (and lower trapezoidal if m > n), and U is upper triangular (and upper trapezoidal if m < n). Slay. 🌈

This is the right-looking Parallel Level 2 BLAS version of the algorithm. That's the whole vibe. ⭐

📝 Notes 📝

Every global data object out here is described by an associated description vector, and that vector stores all the info you need to map an object element to its process and memory location. it's the group chat of data structures honestly 💜

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 whole roster, no one left 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
🚨 heads up bestie: this routine requires N <= NB_A-MOD(JA-1, NB_A) and square block decomposition (MB_A = NB_A). Don't come for me if you skip that, I literally told you. 😭

🎀 ARGUMENTS 🎀

  • 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 ). NB_A-MOD(JA-1, NB_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)). On entry, this array contains the local pieces of the M-by-N distributed matrix sub( A ). On exit, this array contains the local pieces of the factors L and U from the factorization sub( A ) = P*L*U; the unit diagonal elements of L are not stored. she contains multitudes, and also your factors ✨
  • 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.
  • IPIV — (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A ). This array contains the pivoting information. IPIV(i) -> the global row local row i was swapped with. This array is tied to the distributed matrix A. 🔥
  • INFO — (local output) INTEGER.
    • = 0: successful exit. we ate and left no crumbs 🍓
    • < 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.
    • > 0: if INFO = K, U(IA+K-1,JA+K-1) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. 💀 not the singular factor jumpscare

and that's the whole page, bestie, every flag, every index, every bound, all of it. iykyk. 🧚

okay love you, bye — this was LAPACK version 1.5, dated 12 May 1997. periodt. 💅✨

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