PDZSUM1(l)

💖 PDZSUM1(l) — LAPACK auxiliary routine, version 1.5 💖

okay bestie, sit DOWN, because this one is a ScaLAPACK auxiliary routine and she is lowkey iconic. Her whole job? Add up absolute values. That's it. That's the gig. ✨

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🌸 NAME 🌸

PDZSUM1 — she returns the sum of absolute values of a complex distributed vector sub( X ) in ASUM. 🎀

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🦋 SYNOPSIS 🦋

SUBROUTINE PDZSUM1( N, ASUM, X, IX, JX, DESCX, INCX )

    INTEGER         IX, INCX, JX, N

    DOUBLE          PRECISION ASUM

    INTEGER         DESCX( * )

    COMPLEX*16      X( * )

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💅 PURPOSE 💅

PDZSUM1 returns the sum of absolute values of a complex distributed vector sub( X ) in ASUM,

where sub( X ) denotes

X(IX:IX+N-1,JX:JX), if INCX = 1,
X(IX:IX,JX:JX+N-1), if INCX = M_X.

Based on PDZASUM from the Level 1 PBLAS. The change is to use the 'genuine' absolute value. no cap, that's the whole glow-up. 💅

The serial version of this routine was originally contributed by Nick Higham for use with ZLACON. (shoutout Nick, king behavior 👑)

✨ 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".

• 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

Because vectors may be viewed as a subclass of matrices, a distributed vector is considered to be a distributed matrix. (she's giving matrix energy. because she literally is one. 💀)

When the result of a vector-oriented PBLAS call is a scalar, it will be made available only within the scope which owns the vector(s) being operated on. Let X be a generic term for the input vector(s). Then, the processes which receive the answer will be (note that if an operation involves more than one vector, the processes which receive the result will be the union of the following calculation for each vector):

• If N = 1, M_X = 1 and INCX = 1, then one can't determine if a process row or process column owns the vector operand, therefore only the process of coordinate {RSRC_X, CSRC_X} receives the result;
• If INCX = M_X, then sub( X ) is a vector distributed over a process row. Each process part of this row receives the result;
• If INCX = 1, then sub( X ) is a vector distributed over a process column. Each process part of this column receives the result;

🫶 bestie this scope thing is the part everyone forgets and then spends three hours debugging. the result does NOT go to everybody. read it twice, i'm begging. 😭

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🎀 PARAMETERS 🎀

• N — (global input) pointer to INTEGER. The number of components of the distributed vector sub( X ). N >= 0.
• ASUM — (local output) pointer to DOUBLE PRECISION. The sum of absolute values of the distributed vector sub( X ) only in its scope.
• X — (local input) COMPLEX*16 array containing the local pieces of a distributed matrix of dimension of at least ( (JX-1)*M_X + IX + ( N - 1 )*abs( INCX ) ). This array contains the entries of the distributed vector sub( X ).
• IX — (global input) pointer to INTEGER. The global row index of the submatrix of the distributed matrix X to operate on.
• JX — (global input) pointer to INTEGER. The global column index of the submatrix of the distributed matrix X to operate on.
• DESCX — (global and local input) INTEGER array of dimension 8. The array descriptor of the distributed matrix X.
• INCX — (global input) pointer to INTEGER. The global increment for the elements of X. Only two values of INCX are supported in this version, namely 1 and M_X.

💀 only 1 and M_X. do not get creative. she does not want your creative INCX. that's it, that's the whole range, periodt.

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and that's the whole page, bestie!! go forth and sum some absolute values 💖✨

🦋 cute little sign-off: this page is LAPACK version 1.5, dated 12 May 1997, and she is still serving looks. byeee 🎀💜