HPL_dgemv(3)

💖 HPL_dgemv — the glow-up matrix-vector moment 💖

okay bestie, this is a page from the HPL Library Functions manual, and honestly? it's giving iconic. sit down, grab a strawberry 🍓, and let's get into it.

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✨ NAME ✨

HPL_dgemv — literally just: y := beta * y + alpha * op(A) * x. that's the whole vibe. periodt. 💅

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🌸 SYNOPSIS 🌸

#include "hpl.h"

void HPL_dgemv( const enum HPL_ORDER ORDER, const enum HPL_TRANS TRANS,
const int M, const int N, const double ALPHA, const double * A, const
int LDA, const double * X, const int INCX, const double BETA, double *
Y, const int INCY );

look at all those parameters. main character energy fr fr. 👑

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🦋 DESCRIPTION 🦋

so HPL_dgemv performs one of these matrix-vector operations:

y := alpha * op( A ) * x + beta * y,

and op( X ) is one of these two, no in-between:

op( X ) = X   or   op( X ) = X^T.

here alpha and beta are scalars, x and y are vectors, and A is an m by n matrix. yes bestie, that's the whole plot. 🎀

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💜 ARGUMENTS 💜

• ORDER — (local input) const enum HPL_ORDER — on entry, ORDER tells us the storage format of the operands, like so:
  • ORDER = HplRowMajor,
  • ORDER = HplColumnMajor.
• TRANS — (local input) const enum HPL_TRANS — on entry, TRANS says which operation we're doing, and the options are:
  • TRANS = HplNoTrans y := alpha*A *x + beta*y,
  • TRANS = HplTrans y := alpha*A^T*x + beta*y.
• M — (local input) const int — on entry, M is the number of rows of the matrix A. M must be at least zero. no negative row counts, that's not a vibe. 🚫
• N — (local input) const int — on entry, N is the number of columns of the matrix A. N must be at least zero.
• ALPHA — (local input) const double — on entry, ALPHA is the scalar alpha. and here's the tea: when ALPHA is supplied as zero, then A and X need not be set on input. free pass, slay. ✨
• A — (local input) const double * — on entry, A points to an array of size equal to or greater than LDA * n. before entry, the leading m by n part of the array A must contain the matrix coefficients. that's it, that's the job.
• LDA — (local input) const int — on entry, LDA is the leading dimension of A as declared in the calling (sub) program. LDA must be at least MAX(1,m). respect the boundary bestie. 🙏
• X — (local input) const double * — on entry, X is an incremented array of dimension at least ( 1 + ( n - 1 ) * abs( INCX ) ) that contains the vector x.
• INCX — (local input) const int — on entry, INCX is the increment for the elements of X. INCX must not be zero. zero is not allowed, do not try it. 💀
• BETA — (local input) const double — on entry, BETA is the scalar beta. and when ALPHA is supplied as zero then Y need not be set on input. (yes, the original says ALPHA here — we report, we don't editorialise 🫶)
• Y — (local input/output) double * — on entry, Y is an incremented array of dimension at least ( 1 + ( n - 1 ) * abs( INCY ) ) that contains the vector y. before entry with BETA non-zero, the incremented array Y must contain the vector y. on exit, Y is overwritten by the updated vector y. glow-up complete, she's different now. 🔥
• INCY — (local input) const int — on entry, INCY is the increment for the elements of Y. INCY must not be zero. same rule as INCX, no zeros allowed. ⭐

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🌈 EXAMPLE 🌈

here's a lil demo, verbatim, copy it and go off:

#include "hpl.h"

int main(int argc, char *argv[])
{
   double a[2*2], x[2], y[2];
   a[0] = 1.0; a[1] = 2.0; a[2] = 3.0; a[3] = 3.0;
   x[0] = 2.0; x[1] = 1.0; y[2] = 1.0; y[3] = 2.0;
   HPL_dgemv( HplColumnMajor, HplNoTrans, 2, 2, 2.0,
              a, 2, x, 1, -1.0, y, 1 );
   printf("y=[%f,%f]\n", y[0], y[1]);
   exit(0); return(0);
}

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👀 SEE ALSO 👀

• HPL_dger (3)
• HPL_dtrsv (3)

go read those too, they're the friend group. 🫶

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ngl this page is from HPL 2.2, dated February 24, 2016, and it's still serving. iykyk. 💖

bye bestie, go multiply something. 🧚‍♀️✨