la_heamv(3)

📦

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🎀 la_heamv(3) 🎀

Okay bestie, welcome to the la_heamv(3) page from the Library Functions Manual. This is the main character doc for the |A| * |x| matrix-vector multiply with a Hermitian/symmetric twist, and it is lowkey all about error bounds. We are keeping every detail, no cap. 💖

✨ NAME ✨

la_heamv — la_heamv: matrix-vector multiply |A| * |x|, Hermitian/symmetric. That's the name, periodt. 👑

🦋 SYNOPSIS 🦋

🎀 Functions 🎀

subroutine cla_heamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.
subroutine cla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — CLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.
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.
subroutine sla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — SLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.
subroutine zla_heamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — ZLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.
subroutine zla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

🌈 Detailed Description 🌈

This is the part where the functions get their own little spotlights. Grab a snack and a beverage, bestie. 🍓

🧚 Function Documentation 🧚

💜 subroutine cla_heamv 💜

subroutine cla_heamv (integer uplo, integer n, real alpha, complex,
       dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer
       incx, real beta, real, dimension( * ) y, integer incy)

CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds. Slay.

🎯 Purpose: 🎯

!>
!> CLA_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.
!>

🌸 Parameters 🌸

UPLO — UPLO is INTEGER. On entry, UPLO is the little switch that tells the routine which triangle of A to look at: UPLO = BLAS_UPPER means only the upper triangular part of A is referenced, and UPLO = BLAS_LOWER means only the lower triangular part of A is referenced. It stays unchanged on exit. 💅
N — N is INTEGER. On entry, N is literally the number of columns of matrix A, and it must be at least zero. Unchanged on exit.
ALPHA — ALPHA is REAL. On entry, it's the scalar alpha, no notes, no drama. Unchanged on exit.
A — A is COMPLEX array, dimension ( LDA, n ). Before entry, the leading m by n part of A has to hold the matrix of coefficients. Unchanged on exit. Yes, it says m by n — keeping it exactly.
LDA — LDA is 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 ). Unchanged on exit.
X — X is COMPLEX array, dimension ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented X array has to contain vector x. Unchanged on exit.
INCX — INCX is INTEGER. On entry, it's the increment for the elements of X, and it must not be zero. Unchanged on exit.
BETA — BETA is REAL. On entry, it's the scalar beta. Cute detail: when BETA is supplied as zero, Y need not be set on input. Unchanged on exit.
Y — Y is REAL array, dimension ( 1 + ( n - 1 )*abs( INCY ) ). Before entry with BETA non-zero, the incremented Y array has to contain vector y. On exit, Y gets overwritten by the updated vector y. Bye original Y. 👋
INCY — INCY is INTEGER. On entry, it's the increment for the elements of Y, and it must not be zero. Unchanged on exit.

👑 Author 👑

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

🔥 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
!>

Definition at line 176 of file cla_heamv.f.

💙 subroutine cla_syamv 💙

subroutine cla_syamv (integer uplo, integer n, real alpha, complex,
       dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer
       incx, real beta, real, dimension( * ) y, integer incy)

CLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. Another icon.

🎯 Purpose: 🎯

!>
!> CLA_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.
!>

🌸 Parameters 🌸

UPLO — UPLO is INTEGER. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced: UPLO = BLAS_UPPER means only the upper triangular part of A is referenced, and UPLO = BLAS_LOWER means only the lower triangular part of A is referenced. 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.
ALPHA — ALPHA is REAL. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A — A is COMPLEX 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.
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.
X — X is COMPLEX array, 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.
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.
Y — Y is REAL 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.
INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

👑 Author 👑

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

🔥 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
!>

Definition at line 177 of file cla_syamv.f.

💚 subroutine dla_syamv 💚

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. Double precision, double slay.

🎯 Purpose: 🎯

...y := alpha*abs(A)*abs(x) + beta*abs(y) — that's the whole vibe, bestie. ✨

So like, where alpha and beta are scalars, x and y are vectors, and A is an n by n symmetric matrix. Write it out all pretty:

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

And why does this exist? Okay so this function is primarily used in calculating error bounds — it's the little safety net behind the scenes. To protect against underflow during evaluation, components in the resulting vector get perturbed away from zero by (N+1) times the underflow threshold. Lowkey dramatic but like, necessary 💅.

And 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. That's the rule, no cap. 🫶

🎀 Parameters (DLA_SYAMV)

UPLO — UPLO is INTEGER. On entry, UPLO tells us which triangle of the array A we're actually referencing, like this:
- 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. 🙈

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.
ALPHA — ALPHA is DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. ⭐
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. (yes bestie it says m by n, that's what the page says, we do not ask questions, we simply copy 💀)
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.
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. 🦋
INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. > Like fr fr, not zero, that's a whole undefined-behaviour situation, do not do it.
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. 🌸
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. 👑
INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

💜 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 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

Definition at line 175 of file dla_syamv.f.

🧚 subroutine sla_syamv

Okay bestie, now the REAL version, same energy, single precision this time:

subroutine sla_syamv (integer uplo, integer n, real alpha, real, dimension(
    lda, * ) a, integer lda, real, dimension( * ) x, integer incx, real
    beta, real, dimension( * ) y, integer incy)

SLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. That's the one-liner, iconic, no notes.

✨ Purpose:

SLA_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. 🎀

🫶 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.

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.
ALPHA — ALPHA is REAL . On entry, ALPHA specifies 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.
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.
X — X is REAL array, 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.
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. 🦋
Y — Y is REAL 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.
INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

💜 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 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

Definition at line 175 of file sla_syamv.f.

👑 subroutine zla_heamv

And now the complex one, she's fancy, DOUBLE PRECISION scalars, COMPLEX*16 matrix and vector, whole nine yards:

subroutine zla_heamv (integer uplo, integer n, double precision alpha,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
    ) x, integer incx, double precision beta, double precision, dimension( *
    ) y, integer incy)

ZLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds. 💅

✨ Purpose:

Okay so heads up, the source text here literally says ZLA_SYAMV — like, the SYAMV spelling. That's what's written on the page, bestie, so that's what I'm giving you. Not my typo, I'm just the messenger 🫶

ZLA_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.

🫶 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.

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.

and then ALPHA... yeah okay, we're literally about to get to it — keep scrolling bestie, it's right there 💀

okay so picking up the zla_heamv parameter list right where it left off, bestie: 💅

ALPHA — is DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A — is COMPLEX*16 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.
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.
X — is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. Unchanged on exit.
INCX — is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
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.
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.
INCY — is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Author 🫶

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

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

Definition at line 176 of file zla_heamv.f.

`zla_syamv` 🧚

okay next up is the sister routine, and she's giving error-bound realness: 🦋

subroutine zla_syamv (integer uplo, integer n, double precision alpha,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
    ) x, integer incx, double precision beta, double precision, dimension( *
    ) y, integer incy)

ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

Purpose 💖

ZLA_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.

Parameters 💅

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.
N — is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA — is DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A — is COMPLEX*16 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.
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.
X — is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. Unchanged on exit.
INCX — is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
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.
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.
INCY — is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Author 🫶

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

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

Definition at line 177 of file zla_syamv.f.

Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

Source/version check: LAPACK, Version 3.12.0 — la_heamv(3), and that's the whole vibe. Bye bestie 💅✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

la_heamv(3)

🎀 la_heamv(3) 🎀

✨ NAME ✨

🦋 SYNOPSIS 🦋

🎀 Functions 🎀

🌈 Detailed Description 🌈

🧚 Function Documentation 🧚

💜 subroutine cla_heamv 💜

🎯 Purpose: 🎯

🌸 Parameters 🌸

👑 Author 👑

🔥 Further Details: 🔥

💙 subroutine cla_syamv 💙

🎯 Purpose: 🎯

🌸 Parameters 🌸

👑 Author 👑

🔥 Further Details: 🔥

💚 subroutine dla_syamv 💚

🎯 Purpose: 🎯

🎀 Parameters (DLA_SYAMV)

💜 Author

🌈 Further Details:

🧚 subroutine sla_syamv

✨ Purpose:

🫶 Parameters

💜 Author

🌈 Further Details:

👑 subroutine zla_heamv

✨ Purpose:

🫶 Parameters

Author 🫶

Further Details 🌈

zla_syamv 🧚

Purpose 💖

Parameters 💅

Author 🫶

Further Details 🌈

Author 🤖

`zla_syamv` 🧚