PSLASE2(l)

💖 NAME 💖

PSLASE2 — okay so, this is a LAPACK auxiliary routine (section l, the aux girlies, we love them) that initializes an M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1) to BETA on the diagonal and ALPHA on the offdiagonals. that's it. that's the whole job. and she does it flawlessly 💅

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🦋 SYNOPSIS 🦋

SUBROUTINE PSLASE2( UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )

    CHARACTER       UPLO

    INTEGER         IA, JA, M, N

    REAL            ALPHA, BETA

    INTEGER         DESCA( * )

    REAL            A( * )

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🌸 PURPOSE 🌸

PSLASE2 initializes an M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1) to BETA on the diagonal and ALPHA on the offdiagonals. and heads up bestie — PSLASE2 requires that only dimension of the matrix operand is distributed. 🫶

🎀 Notes 🎀

okay so this is the part where it gets real. 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. it's giving passport for your data 🛂

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".

NOTATION        STORED IN      EXPLANATION
--------------- -------------- --------------------------------------
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 distribu-
                               ted over. The context itself is glo-
                               bal, 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

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✨ ARGUMENTS ✨

• UPLO — (global input) CHARACTER. specifies the part of the distributed matrix sub( A ) to be set:
  • = 'U': upper triangular part is set; the strictly lower triangular part of sub( A ) is not changed;
  • = 'L': lower triangular part is set; the strictly upper triangular part of sub( A ) is not changed;
  • otherwise: all of the matrix sub( A ) is set.
• 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.
• ALPHA — (global input) REAL. the constant to which the offdiagonal elements are to be set. ✨
• BETA — (global input) REAL. the constant to which the diagonal elements are to be set. 💖
• A — (local output) REAL 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 ) to be set. on exit, the leading M-by-N submatrix sub( A ) is set as follows:

if UPLO = 'U', A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=j-1, 1<=j<=N,
if UPLO = 'L', A(IA+i-1,JA+j-1) = ALPHA, j+1<=i<=M, 1<=j<=N,
otherwise,     A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=M, 1<=j<=N,
               IA+i.NE.JA+j,
and, for all UPLO, A(IA+i-1,JA+i-1) = BETA, 1<=i<=min(M,N).

• 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. 👑

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not me writing a whole descriptor-vector dissertation and then the actual subroutine is just "fill the thing with two numbers." main character energy. 🦋

okay bestie that's the whole page, you ate, periodt. this one's from LAPACK version 1.5, dated 12 May 1997 — yes she's an elder but she still slays 💜🎀