DGBMV(3)

💅 DGBMV(3) — or: the band-matrix glow-up, bestie 🎀

okay so first things first, this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/dgbmv.f — that's the whole NAME section, yes really, it's just a path, the LAPACK docs are Like That 💀. Anyway. It's a Library Functions Manual situation and we're about to get into it.

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✨ SYNOPSIS ✨

Functions/Subroutines 🌸

subroutine DGBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y,
    incy)

DGBMV — that's the whole description, she contains multitudes 💅

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🦋 Function/Subroutine Documentation 🦋

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 🎯

ok so get this — DGBMV does 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. she's banded, she's built different, periodt 👑

Parameters 🫶

• TRANS — TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed, like so:
  • TRANS = 'N' or 'n' → y := alpha*A*x + beta*y.
  • TRANS = 'T' or 't' → y := alpha*A**T*x + beta*y.
  • TRANS = 'C' or 'c' → y := alpha*A**T*x + beta*y.
• M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero.
• N — N is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero.
• KL — KL is INTEGER. On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 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.
• ALPHA — ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. our little scalar icon 💖
• 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 — they're just there, vibing, ignored 🙈. And 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

• 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 ). no shortcuts bestie ✨
• 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.
• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. like, do NOT. 🚫
• 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 — zero beta means free real estate, you can leave Y a mess 💀
• 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 — she gets a whole new identity, main character energy 💅. If either m or n is zero, then Y is not referenced and the function performs a quick return. bye bestie 👋
• INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. same rule, no zeroes, we don't do that here 🎀

Author 👑

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

the whole squad, shoutout 🫶

Further Details 🔥

• Level 2 Blas routine.
• The vector and matrix arguments are not referenced when N = 0, or M = 0 — they literally don't get looked at. not even a glance 😭
• -- 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.

1986!! they were doing banded matrix-vector products before it was cool, no cap ⭐

Definition at line 186 of file dgbmv.f.

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Author (again, the auto one) 🌈

Generated automatically by Doxygen for LAPACK from the source code. yes, a robot wrote this part, and honestly? she ate 🤖✨

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and that's the whole page bestie — LAPACK Version 3.12.0, from /home/abui...SRC/dgbmv.f(3), which is where we came in and where we're leaving 💜 go forth and multiply (matrices) 🦋