BLAS/SRC/sgbmv.f(3)

💖 BLAS/SRC/sgbmv.f — the sgbmv tea 💖

okay bestie, gather round, because we're talking about sgbmv from LAPACK's BLAS folder (BLAS/SRC/sgbmv.f), and honestly? it's giving band matrix main character energy. ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

SGBMV — that's the whole vibe, that's the name, periodt. 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine sgbmv (character trans, integer m, integer n, integer kl, integer
    ku, real alpha, real, dimension(lda,*) a, integer lda, real,
    dimension(*) x, integer incx, real beta, real, dimension(*) y, integer
    incy)

SGBMV 🫶

✨ Purpose ✨

so like, SGBMV 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. no cap, that's literally the whole job. 🔥

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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.

(yes bestie, 'C' does the same thing as 'T' here — conjugate-transpose who? not today 💀)

• 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 REAL. On entry, ALPHA specifies the scalar alpha. 🎀
• A — A is REAL 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

like, that snippet is iconic, don't @ me. 👑

• 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 REAL 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. 🚫
• 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. (free real estate, love that for you 💅)
• Y — Y is REAL 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. ✨ bye bestie, nothing to do here ✨

• 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.

the academic girlies really came through fr fr 🎓💖

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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.

the 1986 legends themselves, we stan an origin story 🫶

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🧚 Definition

Definition at line 186 of file sgbmv.f.

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👑 Author (of this page)

Generated automatically by Doxygen for LAPACK from the source code.

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aaaand that's the whole page bestie, no crumbs left. this lil writeup is Version 3.12.0, dated Tue Nov 28 2023 12:08:41, and it lives at BLAS/SRC/sgbmv.f(3) — slay, mwah, bye 💋🌸✨