/home/abui...RC/zspmv.f(3)

💅 ZSPMV — the packed-symmetric-matrix girlie 💅

Okay bestie, welcome to the glow-up zone. This is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zspmv.f, straight out of the LAPACK library functions squad. It's a Fortran file, it's iconic, and it does exactly one thing beautifully. Let's get into it 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine ZSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy) — bestie, this one computes a matrix-vector product for complex vectors using a complex symmetric packed matrix. Periodt.

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🌸 Function/Subroutine Documentation 🌸

subroutine ZSPMV — the full signature, no cap 👑

subroutine ZSPMV (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) ap, complex*16, dimension( * ) x, integer incx, complex*16 beta, complex*16, dimension( * ) y, integer incy)

ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix. That's the whole vibe. 💜

🫶 Purpose

Okay so here's the actual math, and it's lowkey gorgeous:

!>
!> ZSPMV  performs the matrix-vector operation
!>
!>    y := alpha*A*x + beta*y,
!>
!> where alpha and beta are scalars, x and y are n element vectors and
!> A is an n by n symmetric matrix, supplied in packed form.
!>

Translation: A is n by n, symmetric, and it's living its best compact life in "packed form" — which is the aesthetic, honestly. 🧚

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🎀 Parameters 🎀

UPLO

!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP.
!>
!>           Unchanged on exit.

So UPLO is a CHARACTER*1 and it's basically asking you: upper girlie or lower girlie? ⬆️⬇️ Pick 'U' / 'u' and the upper triangular part of A gets supplied in AP. Pick 'L' / 'l' and it's the lower triangular part in AP. Either way it comes back to you unchanged on exit — she does not get altered by this whole ordeal, respect. 💅

N

!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>           Unchanged on exit.

N is an INTEGER and on entry it specifies the order of the matrix A. Rule: N must be at least zero — no negative chaos allowed, we don't do that here. And yep, unchanged on exit. ⭐

ALPHA

!>          ALPHA is COMPLEX*16
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.

ALPHA is COMPLEX*16 and on entry it specifies the scalar alpha. That's it, that's the whole personality. Unchanged on exit. ✨

AP

!>          AP is COMPLEX*16 array, dimension at least
!>           ( ( N*( N + 1 ) )/2 ).
!>           Before entry, with UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on.
!>           Before entry, with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on.
!>           Unchanged on exit.

AP is a COMPLEX*16 array, dimension at least ( ( N*( N + 1 ) )/2 ). It's the main character of this whole operation, ngl.

Before entry, with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix, packed sequentially column by column, so that:

• AP( 1 ) contains a( 1, 1 )
• AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively
• and so on 👑

Before entry, with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix, packed sequentially column by column, so that:

• AP( 1 ) contains a( 1, 1 )
• AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively
• and so on 💀

Unchanged on exit. She literally just sits there being packed and perfect. 🍓

X

!>          X is COMPLEX*16 array, dimension at least
!>           ( 1 + ( N - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the N-
!>           element vector x.
!>           Unchanged on exit.

X is a COMPLEX*16 array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N-element vector x. Unchanged on exit — she gives her energy and stays exactly as she was. 🦋

INCX

!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>           Unchanged on exit.

INCX is an INTEGER and on entry it specifies the increment for the elements of X. INCX must not be zero — hard pass on that, fr fr. Unchanged on exit. 🌈

BETA

!>          BETA is COMPLEX*16
!>           On entry, BETA specifies the scalar beta. When BETA is
!>           supplied as zero then Y need not be set on input.
!>           Unchanged on exit.

BETA is COMPLEX*16 and on entry it specifies the scalar beta. Important glow-up detail: when BETA is supplied as zero, then Y need not be set on input — she's flexible like that. 🧚 Unchanged on exit.

Y

!>          Y is COMPLEX*16 array, dimension at least
!>           ( 1 + ( N - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y. On exit, Y is overwritten by the updated
!>           vector y.

Y is a COMPLEX*16 array, dimension at least ( 1 + ( N - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. And on exit? Y is overwritten by the updated vector y — full transformation arc, we love a main character moment. 😭🔥

INCY

!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>           Unchanged on exit.

INCY is an INTEGER and on entry it specifies the increment for the elements of Y. INCY must not be zero — same energy as above, no zeros allowed bestie. 🙈 Unchanged on exit. ⭐

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👑 Author 👑

The absolute legends behind this:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Icons only, no notes. 💅

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📖 Definition 📖

Definition at line 150 of file zspmv.f. Yes bestie, that's where the magic is written. ✨

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🌸 Sign-off 🌸

This page was generated automatically by Doxygen for LAPACK from the source code — so if you're obsessed, thank the automation pipeline too. This whole serve is courtesy of LAPACK, Version 3.12.0. 💖🫶🎀

Go forth and slay those matrix-vector products, iykyk. 🦋🌈👑