SRC/zspmv.f(3)

💅 SRC/zspmv.f — from the Library Functions Manual ✨

okay so bestie, buckle up, because this is a single Fortran file's manpage and it ate. It lives in SRC/zspmv.f and it's the whole documentation vibe for one glorious BLAS routine. Let's get into it 🫶

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🌸 NAME 🌸

SRC/zspmv.f — literally just the filename, bestie, that's the name, that's the assignment 💀

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine zspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)

ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix — yes that's the whole vibe, no cap 💖

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👑 Function/Subroutine Documentation 👑

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)

Again, for the people in the back: ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix 🌈

🦋 Purpose 🦋

okay so here's the tea, here's what it actually does:

!>
!> 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.
!>

lowkey iconic, right? It's giving "I do one thing and I do it beautifully" 💅

🍓 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 you tell it 'U'/'u' for the upper triangle, 'L'/'l' for the lower triangle — and bestie, it comes out unchanged 🎀

N

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

the order of A, fr fr. Must be at least zero — don't come in here with negative chaos 🙈 Unchanged on exit.

ALPHA

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

that's the scalar alpha from the equation, she's a COMPLEX*16, and she stays exactly as she arrived 💜

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.
!>

okay this is the big one, the main character of the parameter list 👑 Dimensión at least ( ( N*( N + 1 ) )/2 ).

With UPLO = 'U' or 'u': upper triangular part, packed sequentially, column by column, so AP( 1 ) holds a( 1, 1 ), then AP( 2 ) and AP( 3 ) hold a( 1, 2 ) and a( 2, 2 ) respectively, and so on ✨

With UPLO = 'L' or 'l': lower triangular part, again packed sequentially, column by column, so AP( 1 ) holds a( 1, 1 ), then AP( 2 ) and AP( 3 ) hold a( 2, 1 ) and a( 3, 1 ) respectively, and so on ✨

Unchanged on exit — she does not get touched, periodt 💅

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.
!>

dimension at least ( 1 + ( N - 1 )*abs( INCX ) ), and before entry this incremented array must contain the N-element vector x. Unchanged on exit, she's just here to be read 🦋

INCX

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

the stride for X's elements. INCX must not be zero. 🚨 that's a hard no, bestie, zero stride is not it.

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.
!>

the other scalar! And here's the little shortcut: when BETA is supplied as zero then Y need not be set on input 😌 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.
!>

dimension at least ( 1 + ( N - 1 )*abs( INCY ) ). Before entry it holds the n element vector y. And on exit? Y is overwritten by the updated vector y — she gets a glow-up in place 🔥

INCY

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

Y's stride. INCY must not be zero 🚨 same energy as INCX, no zeros allowed.

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💖 Author 💖

slay, the whole squad showed up for this one:

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

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⭐ Definition ⭐

Definition at line 150 of file zspmv.f. go look at it, it's right there 👀

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🌺 Author (the meta one) 🌺

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing its little documentation dance 🤖🫶

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🎀 a friendly little reminder: this routine is pure BLAS energy — packed symmetric complex matrix, one product, no drama, and INCX/INCY absolutely cannot be zero, iykyk.

and that's the whole page, bestie — LAPACK, Version 3.12.0, straight out of SRC/zspmv.f(3). mwah 💋✨