SRC/dla_syamv.f(3)

💅 SRC/dla_syamv.f(3) — Library Functions Manual 🎀

okay bestie, sit down, hydrate, and let me tell you about SRC/dla_syamv.f from the Library Functions Manual. this one is a Fortran file and it's lowkey iconic. ✨

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✨ NAME ✨

SRC/dla_syamv.f — no cap, that's literally the whole name, she's mysterious like that 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine dla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — DLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. she's giving math AND she's giving error bounds, main character energy fr fr 👑

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🫶 Function/Subroutine Documentation 🫶

subroutine dla_syamv (integer uplo, integer n, double precision alpha, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

DLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. that's her whole job and she does it slayfully 💖

Purpose:

!>
!> DLA_SYAMV  performs the matrix-vector operation
!>
!>         y := alpha*abs(A)*abs(x) + beta*abs(y),
!>
!> where alpha and beta are scalars, x and y are vectors and A is an
!> n by n symmetric matrix.
!>
!> This function is primarily used in calculating error bounds.
!> To protect against underflow during evaluation, components in
!> the resulting vector are perturbed away from zero by (N+1)
!> times the underflow threshold.  To prevent unnecessarily large
!> errors for block-structure embedded in general matrices,
!>  zero components are not perturbed.  A zero
!> entry is considered  if all multiplications involved
!> in computing that entry have at least one zero multiplicand.
!>

like, the way she computes y := alpha*abs(A)*abs(x) + beta*abs(y)? obsessed. 😭 she's mostly out here calculating error bounds, and to keep underflow from ruining the vibe she perturbs components in the resulting vector away from zero by (N+1) times the underflow threshold — but bestie, zero components are not perturbed, because that would cause unnecessarily large errors for block-structure embedded in general matrices. a zero entry counts as zero if every multiplication involved in computing that entry has at least one zero multiplicand. iykyk 🧚

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⭐ Parameters ⭐

UPLO

!>          UPLO is INTEGER
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = BLAS_UPPER   Only the upper triangular part of A
!>                                  is to be referenced.
!>
!>              UPLO = BLAS_LOWER   Only the lower triangular part of A
!>                                  is to be referenced.
!>
!>           Unchanged on exit.
!>

so UPLO is an INTEGER and on entry it picks which triangle of A we're looking at: UPLO = BLAS_UPPER means only the upper triangular part of A gets referenced, and UPLO = BLAS_LOWER means only the lower triangular part of A gets referenced. she comes in unchanged on exit, queen of consistency 💅

N

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

N is an INTEGER, and on entry it's the number of columns of the matrix A. N must be at least zero (respect the boundary 🫶). unchanged on exit.

ALPHA

!>          ALPHA is DOUBLE PRECISION .
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>

ALPHA is DOUBLE PRECISION ✨ on entry it's the scalar alpha, and she stays unchanged on exit, periodt.

A

!>          A is DOUBLE PRECISION array, dimension ( LDA, n ).
!>           Before entry, the leading m by n part of the array A must
!>           contain the matrix of coefficients.
!>           Unchanged on exit.
!>

A is a DOUBLE PRECISION array with dimension ( LDA, n ). before entry, the leading m by n part of the array A must contain the matrix of coefficients. unchanged on exit 💜

yes bestie, the original really does say m by n here. i'm not fixing it, i'm just reporting the facts. 🙈

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the calling (sub) program. LDA must be at least
!>           max( 1, n ).
!>           Unchanged on exit.
!>

LDA is an INTEGER. on entry it's the first dimension of A as declared in the calling (sub) program, and it must be at least max( 1, n ) — no shortcuts, she checks. unchanged on exit.

X

!>          X is DOUBLE PRECISION array, dimension
!>           ( 1 + ( n - 1 )*abs( INCX ) )
!>           Before entry, the incremented array X must contain the
!>           vector x.
!>           Unchanged on exit.
!>

X is a DOUBLE PRECISION array with dimension ( 1 + ( n - 1 )*abs( INCX ) ). before entry, the incremented array X must contain the vector x. unchanged on exit 🌸

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, the increment for the elements of X. INCX must not be zero — like, do not do that, that's not the vibe 💀 unchanged on exit.

BETA

!>          BETA is DOUBLE PRECISION .
!>           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 DOUBLE PRECISION. on entry it's the scalar beta, and here's the cute part: when BETA is supplied as zero then Y need not be set on input 🎀 unchanged on exit.

Y

!>          Y is DOUBLE PRECISION array, dimension
!>           ( 1 + ( n - 1 )*abs( INCY ) )
!>           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.
!>

Y is a DOUBLE PRECISION array with dimension ( 1 + ( n - 1 )*abs( INCY ) ). 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 — she gets a whole glow-up 🔥

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, the increment for the elements of Y. INCY must not be zero — same rule, same energy 💀 unchanged on exit.

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👑 Author 👑

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

the whole squad showed up for this one, we love a collab 🌈

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🦋 Further Details: 🦋

!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>  -- Modified for the absolute-value product, April 2006
!>     Jason Riedy, UC Berkeley
!>

she's a Level 2 Blas routine, and her lore goes way back: written on 22-October-1986 by Jack Dongarra (Argonne National Lab), Jeremy Du Croz (Nag Central Office), Sven Hammarling (Nag Central Office) and Richard Hanson (Sandia National Labs) — then modified for the absolute-value product in April 2006 by Jason Riedy (UC Berkeley). ancestral icons honestly ⭐

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📍 Definition

Definition at line 175 of file dla_syamv.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (yes she was auto-generated and she still ate 💅)

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okay that's the whole page bestie, you're caught up 🫶

LAPACK · Version 3.12.0 · SRC/dla_syamv.f(3) — mwah, go forth and compute your error bounds, ily 💖✨🎀