PSLANGE(l)

📦 version 1.5, in ubuntu jammy

💅 PSLANGE 💅

okay so bestie, you typed man PSLANGE and here we are — this is the manual page PSLANGE(l), a LAPACK auxiliary routine, version 1.5. she's a REAL FUNCTION and she's booked and busy. let's get into it 🫶

✨ NAME ✨

PSLANGE — return the value of the one norm, or the Frobenius norm,

(yeah the title line cuts off there, but don't worry, she spills the whole menu down in PURPOSE, keep reading 💖)

🌸 SYNOPSIS 🌸

REAL FUNCTION PSLANGE( NORM, M, N, A, IA, JA, DESCA, WORK )

    CHARACTER NORM

    INTEGER   IA, JA, M, N

    INTEGER   DESCA( * )

    REAL      A( * ), WORK( * )

👑 PURPOSE 👑

ok so PSLANGE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a distributed matrix sub( A ) = A(IA:IA+M-1, JA:JA+N-1). she does it all, no cap 💅

Here's exactly what PSLANGE hands back, depending on NORM:

  • max(abs(A(i,j))) — when NORM = 'M' or 'm', with IA <= i <= IA+M-1, and JA <= j <= JA+N-1
  • norm1( sub( A ) ) — when NORM = '1', 'O' or 'o'
  • normI( sub( A ) ) — when NORM = 'I' or 'i'
  • normF( sub( A ) ) — when NORM = 'F', 'f', 'E' or 'e'

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares).

not me having to say this but: note that max(abs(A(i,j))) is not a matrix norm. she's a vibe, not a norm, 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".

the whole notation situation, laid out for you bestie:

  • 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

🎀 ARGUMENTS 🎀

  • NORM — (global input) CHARACTER. Specifies the value to be returned in PSLANGE as described above. she's the vibe selector ✨
  • M — (global input) INTEGER. The number of rows to be operated on i.e the number of rows of the distributed submatrix sub( A ). When M = 0, PSLANGE is set to zero. 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 ). When N = 0, PSLANGE is set to zero. N >= 0.
  • A — (local input) REAL pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the local pieces of the distributed matrix sub( A ).
  • 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.
  • WORK — (local workspace) REAL array dimension (LWORK).

ok so for WORK, listen closely bestie:

LWORK >= 0 if NORM = 'M' or 'm' (not referenced), Nq0 if NORM = '1', 'O' or 'o', Mp0 if NORM = 'I' or 'i', 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced), where

        IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW =
        INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA,
        NB_A, MYCOL, CSRC_A, NPCOL ), Mp0 = NUMROC( M+IROFFA, MB_A,
        MYROW, IAROW, NPROW ), Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL,
        IACOL, NPCOL ),

INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.

and that's the whole page, bestie 💖 she's PSLANGE(l) from LAPACK version 1.5, dated 12 May 1997, and honestly? iconic behavior. go forth and compute your norms, you absolute main character 👑✨🌸

📦 where this page comes from