la_gbamv(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

NAME 💅

la_gbamv — la_gbamv: matrix-vector multiply |A| * |x|, general banded. That's the whole vibe. No transpose trickery at the caller level, no drama — just a banded matrix, absolute values everywhere, and a vector multiply that lives for error bounds. 🎀

SYNOPSIS ✨

Functions 🦋

cla_gbamv — the complex flavor. CLA_GBAMV performs a matrix-vector operation to calculate error bounds. 💖

subroutine cla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx,
    beta, y, incy)

dla_gbamv — the double precision one. DLA_GBAMV performs a matrix-vector operation to calculate error bounds. 🔥

subroutine dla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx,
    beta, y, incy)

sla_gbamv — single precision, same energy. SLA_GBAMV performs a matrix-vector operation to calculate error bounds. 🌸

subroutine sla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx,
    beta, y, incy)

zla_gbamv — double complex, main character energy. ZLA_GBAMV performs a matrix-vector operation to calculate error bounds. 👑

subroutine zla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx,
    beta, y, incy)

DETAILED DESCRIPTION 🫶

okay so Detailed Description is the section header, and everything juicy lives right below it in Function Documentation. no cap, that's where the good stuff is.

FUNCTION DOCUMENTATION 💜

subroutine `cla_gbamv` 🦋

subroutine cla_gbamv (integer trans, integer m, integer n, integer kl,
    integer ku, real alpha, complex, dimension( ldab, * ) ab, integer ldab,
    complex, dimension( * ) x, integer incx, real beta, real, dimension( * )
    y, integer incy)

CLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose 🎯

bestie, this routine does one of these two 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. literally the whole plot.

so like, 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. that's not optional, that's the safety net. but — and this is the iconic part — 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 🎀

TRANS — INTEGER. On entry, TRANS specifies the operation to be performed, like so:

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)

yep, BLAS_CONJ_TRANS produces the exact same line as BLAS_TRANS here — iykyk. Unchanged on exit. 💅

M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0. 🦋
KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0. 🦋
ALPHA — REAL. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
AB — COMPLEX array, dimension (LDAB,n). Before entry, the leading m by n part of the array AB must contain the matrix of coefficients. Unchanged on exit. the band storage icon.
LDAB — INTEGER. On entry, LDAB specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). Unchanged on exit.
X — COMPLEX 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. 🌈
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. fr fr, not zero. Unchanged on exit.
BETA — 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 — REAL array, dimension ( 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. shortcut era. ⭐
INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Level 2 Blas routine. 🫶

Author 👑

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

Definition at line 186 of file cla_gbamv.f.

subroutine `dla_gbamv` 🔥

subroutine dla_gbamv (integer trans, integer m, integer n, integer kl,
    integer ku, double precision alpha, double precision, dimension( ldab, *
    ) ab, integer ldab, double precision, dimension( * ) x, integer incx,
    double precision beta, double precision, dimension( * ) y, integer incy)

DLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose 🎯

same storyline, double precision edition. it performs one of these two 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. we been knew.

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. but 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 🎀

TRANS — 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. 💅

M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0. 🦋
KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0. 🦋
ALPHA — DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
AB — DOUBLE PRECISION array, dimension ( LDAB, n ). Before entry, the leading m by n part of the array AB must contain the matrix of coefficients. Unchanged on exit. band storage stays booked and busy.
LDAB — INTEGER. On entry, LDA specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). Unchanged on exit. (yes, it says LDA right there in the source — we don't edit the source, we respect it 🙈)
X — DOUBLE PRECISION 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. 🌈
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA — 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 — DOUBLE PRECISION array, dimension ( 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. quick return my beloved. ⭐
INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Level 2 Blas routine. 🫶

Author 👑

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

Definition at line 185 of file dla_gbamv.f.

(the s and z flavors are right behind this — same routine, same rules, different precision 💖)

🌀 `sla_gbamv` — the real-valued one

subroutine sla_gbamv (integer trans, integer m, integer n, integer kl,
    integer ku, real alpha, real, dimension( ldab, * ) ab, integer ldab,
    real, dimension( * ) x, integer incx, real beta, real, dimension( * ) y,
    integer incy)

SLA_GBAMV performs a matrix-vector operation to calculate error bounds. That's the whole gig, bestie.

✨ Purpose

SLA_GBAMV performs one of these 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. That's the whole safety mechanism, and yes it's giving "we padded it so it doesn't vanish into the void" 💅

🎀 Parameters

TRANS — 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.

M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
ALPHA — REAL. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
AB — REAL array, dimension ( LDAB, n ). Before entry, the leading m by n part of the array AB must contain the matrix of coefficients. Unchanged on exit.
LDAB — INTEGER. On entry, LDA specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). Unchanged on exit. Yes, it says LDA right there in the source — we don't make the rules, we just report them 💀
X — 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.
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA — 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 — REAL array, dimension ( 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.
INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Level 2 Blas routine. That's it, that's the note.

🌈 Author

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

Definition at line 185 of file sla_gbamv.f.

🌸 `zla_gbamv` — the complex*16 glow-up

subroutine zla_gbamv (integer trans, integer m, integer n, integer kl,
    integer ku, double precision alpha, complex*16, dimension( ldab, * ) ab,
    integer ldab, complex*16, dimension( * ) x, integer incx, double
    precision beta, double precision, dimension( * ) y, integer incy)

ZLA_GBAMV performs a matrix-vector operation to calculate error bounds. Same energy, different precision.

✨ Purpose

ZLA_GBAMV performs one of these 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. The underflow protection is lowkey the main character here 🫶

🎀 Parameters

TRANS — 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.

M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
ALPHA — DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
AB — COMPLEX*16 array, dimension ( LDAB, n ). Before entry, the leading m by n part of the array AB must contain the matrix of coefficients. Unchanged on exit.
LDAB — INTEGER. On entry, LDAB specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). Unchanged on exit. See? This one says LDAB. Character development 💅
X — COMPLEX*16 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.
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA — 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 — DOUBLE PRECISION array, dimension ( 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.
INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Level 2 Blas routine. Same note, same iconic status.

🌈 Author

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

Definition at line 186 of file zla_gbamv.f.

🦋 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. Not me being generated by Doxygen, that's so real 🎀

And that's the whole page, bestie. This was LAPACK Version 3.12.0, manual page la_gbamv(3) — go forth and compute those error bounds with main character energy. Periodt. 💖✨

📦 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_gbamv(3)

NAME 💅

SYNOPSIS ✨

Functions 🦋

DETAILED DESCRIPTION 🫶

FUNCTION DOCUMENTATION 💜

subroutine cla_gbamv 🦋

Purpose 🎯

Parameters 🎀

Author 👑

subroutine dla_gbamv 🔥

Purpose 🎯

Parameters 🎀

Author 👑

🌀 sla_gbamv — the real-valued one

✨ Purpose

🎀 Parameters

🌈 Author

🌸 zla_gbamv — the complex*16 glow-up

✨ Purpose

🎀 Parameters

🌈 Author

🦋 Author (the meta one)

subroutine `cla_gbamv` 🦋

subroutine `dla_gbamv` 🔥

🌀 `sla_gbamv` — the real-valued one

🌸 `zla_gbamv` — the complex*16 glow-up