BLAS/SRC/dgbmv.f(3)

💖 BLAS/SRC/dgbmv.f(3) — the dgbmv glow-up 💖

okay bestie, welcome to the LAPACK manual page for BLAS/SRC/dgbmv.f ✨ this is the whole thing, every crumb, no skips. grab a snack, we're doing banded matrix-vector math 🍓

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✨ NAME ✨

BLAS/SRC/dgbmv.f — that's it, that's the name, she's mysterious like that 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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🌸 Function/Subroutine Documentation 🌸

subroutine dgbmv

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

okay so DGBMV performs one of these two matrix-vector operations, pick your fighter:

   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. band matrix representation, we stan a memory-saving queen 👑

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🎀 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*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. (zero is allowed, bestie, we love a flexible icon)
• 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. ✨
• 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 vibing, we don't touch them 🙈. 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 ).
• 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. 🚫 (fr fr, 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. that's a little shortcut for you, you're welcome 💅
• 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 — she said "not today" and bounced 😭
• INCY — INCY is INTEGER. on entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

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👑 Author

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

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🔥 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.

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⭐ Definition

Definition at line 186 of file dgbmv.f.

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. (the robots did this one, not me 🧚)

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Version 3.12.0 · Tue Nov 28 2023 12:08:41 · BLAS/SRC/dgbmv.f(3)

okay that's the whole page, every flag, every parameter, every line, nothing left out 💖 now go forth and multiply your band matrices, bestie, you ate 🫶✨