SRC/sla_geamv.f(3)

💅 SRC/sla_geamv.f

ok bestie, welcome to SRC/sla_geamv.f — a whole iconic LAPACK page, let's get into it ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine sla_geamv (trans, m, n, alpha, a, lda, x, incx, beta, y,
    incy)

SLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds. yes that's literally the whole job, and it does it flawlessly 🎀

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🦋 Function/Subroutine Documentation 🦋

subroutine sla_geamv (integer trans, integer m, integer n, real alpha, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) x, integer
    incx, real beta, real, dimension( * ) y, integer incy)

SLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds. no cap, that's the vibe 💖

⭐ Purpose

!> !> SLA_GEAMV performs one of the matrix-vector operations !> !> y := alpha*abs(A)*abs(x) + beta*abs(y), !> or y := alpha*abs(A)**T*abs(x) + beta*abs(y), !> !> where alpha and beta are scalars, x and y are vectors and A is an !> m by n 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. !>

So bestie, the tea is: this routine is primarily used in calculating error bounds (iykyk). To protect against underflow while it's evaluating, the components in the resulting vector get perturbed away from zero by (N+1) times the underflow threshold — lowkey a whole safety bubble 🫧. But to prevent unnecessarily large errors for block-structure embedded in general matrices, zero components are not perturbed. and a zero entry counts as zero if all the multiplications involved in computing that entry have at least one zero multiplicand. periodt 💅

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🔥 Parameters 🔥

TRANS

!> TRANS is INTEGER !> On entry, TRANS specifies the operation to be performed as !> follows: !> !> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) !> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) !> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) !> !> Unchanged on exit. !>

TRANS is INTEGER, and on entry it tells you which operation we're running: BLAS_NO_TRANS gives you y := alpha*abs(A)*abs(x) + beta*abs(y), BLAS_TRANS gives you y := alpha*abs(A**T)*abs(x) + beta*abs(y), and BLAS_CONJ_TRANS gives you y := alpha*abs(A**T)*abs(x) + beta*abs(y). Unchanged on exit 💜

M

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

M is INTEGER — number of rows of the matrix A. must be at least zero. Unchanged on exit ✨

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 INTEGER — number of columns of the matrix A. must be at least zero. Unchanged on exit 🌸

ALPHA

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

ALPHA is REAL and it's literally the scalar alpha. Unchanged on exit 🎀

A

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

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, m ). !> Unchanged on exit. !>

LDA is INTEGER — the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). Unchanged on exit 🦋

X

!> X is REAL array, dimension !> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' !> and at least !> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. !> Before entry, the incremented array X must contain the !> vector x. !> Unchanged on exit. !>

X is a REAL array with dimension ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n', and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. 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 INTEGER — the increment for the elements of X. INCX must not be zero (fr fr, don't do it). Unchanged on exit ⚠️

BETA

!> BETA is REAL !> 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 REAL and it's the scalar beta. When BETA is supplied as zero, then Y need not be set on input (slay, less work for you). Unchanged on exit 🌈

Y

!> Y is REAL array, !> dimension at least !> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' !> and at least !> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. !> 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. !> If either m or n is zero, then Y not referenced and the function !> performs a quick return. !>

Y is a REAL array with dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n', and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. 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. And if either m or n is zero, then Y is not referenced and the function performs a quick return — main character energy, it just leaves 😭

INCY

!> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> Unchanged on exit. !> !> Level 2 Blas routine. !>

INCY is INTEGER — the increment for the elements of Y. INCY must not be zero either 🫶

oh and also, this is a Level 2 Blas routine. noted 💀✨

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🧚 Author

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

Definition at line 174 of file sla_geamv.f. 🍓

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💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK · Version 3.12.0 · SRC/sla_geamv.f(3)

and that's the whole page bestie — go forth and compute those error bounds, you're gonna ate 💅👑🎀