BLAS/SRC/dgbmv.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💅 BLAS/SRC/dgbmv.f(3) — like, the Library Functions Manual energy ✨

okay bestie, so this is a page from the Library Functions Manual (yes, the actual manual name, she's fancy) and it's about a little Fortran icon called dgbmv. no cap, she does band matrix-vector math and she slays.

🎀 NAME 🎀

BLAS/SRC/dgbmv.f — that's it, that's the name. short, sweet, iconic. 🫶

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

  • subroutine dgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy) — the whole squad, assembled. this is the one. DGBMV, the main character.
subroutine dgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)

👑 Function/Subroutine Documentation 👑

okay so, here's the full signature, exactly as she is, no edits, no vibes-based alterations:

subroutine dgbmv (character trans, integer m, integer n, integer kl, integer
    ku, 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)

DGBMV 🔥

💖 Purpose: 💖

DGBMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

so literally: she multiplies a band matrix by a vector and mixes in scaled versions of y. that's the whole personality. 💅

🌸 Parameters 🌸

TRANS

TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*AT*x + beta*y. TRANS = 'C' or 'c' y := alpha*AT*x + beta*y.

picking 'N'/'n' means no transpose, bestie. 'T'/'t' and 'C'/'c' both give you the A**T version — lowercase counts too, she's not picky about case. 🦋

M

M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero.

rows. at least zero. no negatives, periodt. ✨

N

N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero.

columns. also at least zero. keep the streak alive. 🎀

KL

KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL.

how many sub-diagonals she's got going on. requirement: 0 .le. KL. 🫶

KU

KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.

how many super-diagonals. requirement: 0 .le. KU. same energy, different diagonal direction. 💜

ALPHA

ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.

just a scalar. she's DOUBLE PRECISION and she's doing her best. 😌

A

A is DOUBLE PRECISION array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE

okay this one is the ✨lore✨. the leading ( kl + ku + 1 ) by n chunk holds the coefficients, packed column by column, and the diagonal placement is very specific — leading diagonal in row ( ku + 1 ), first super-diagonal starting at position 2 in row ku, first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. the bits of A that aren't in the band matrix (like that top-left ku by ku triangle, she's just filler 💀) are not referenced. the doctored loop up there is the exact glow-up from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         K = KU + 1 - J
         DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
            A( K + I, J ) = matrix( I, J )
       10    CONTINUE
       20 CONTINUE

clone that, don't freestyle it. 🙈

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 ( kl + ku + 1 ).

leading dimension, as declared in the calling (sub) program. minimum: ( kl + ku + 1 ). don't skimp. 💅

X

X is DOUBLE PRECISION array, dimension at least ( 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.

so the size flips depending on TRANS: ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n', and ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. before entry, the incremented array X has to contain the vector x. 🔥

INCX

INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

stride for X. must not be zero. not a drill, bestie. 💀

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.

the other scalar. and lowkey the best part: when BETA is supplied as zero, Y need not be set on input. you get to skip that setup, iykyk. 🎀

Y

Y is DOUBLE PRECISION 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, 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.

note how Y mirrors X but swapped: ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n', ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. on entry it's the vector y, on exit it's overwritten by the updated vector y. and if either m or n is zero, Y is not referenced and the function performs a quick return — she leaves early, respectfully. 🧚

INCY

INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

stride for Y. must not be zero either. two zero-stride crimes, zero tolerance. ⭐

🌈 Author 🌈

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

look at this collective. absolute icons, all of them. 👑

💜 Further Details: 💜

Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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.

she's a Level 2 Blas routine, and the vector and matrix arguments are not referenced when N = 0, or M = 0. written 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). vintage but still ate. 🍓

🫶 Definition 🫶

Definition at line 186 of file dgbmv.f.

⭐ Author (the meta one) ⭐

Generated automatically by Doxygen for LAPACK from the source code.

that's the whole page, bestie, every last flag and caveat intact, nothing dropped, nothing invented 💖

LAPACK — Version 3.12.0 🌸 and the header up top was BLAS/SRC/dgbmv.f(3) from the Library Functions Manual, if you were wondering. mwah, go call dgbmv responsibly 😭✨💅

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