TESTING/LIN/zsbmv.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

🌸 NAME 🌸

TESTING/LIN/zsbmv.f — okay so bestie, this page is from the Library Functions Manual, and it's literally the documentation home for zsbmv.f in TESTING/LIN. It's giving "niche band-matrix subroutine with main character energy" 💅✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine zsbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) — the one and only ZSBMV baddie on this page, no cap 🌟
subroutine zsbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
    ZSBMV

💅 Function/Subroutine Documentation 💅

🎀 Purpose 🎀

Okay so <pink>ZSBMV</pink> performs the matrix-vector operation:

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors, and A is an n by n symmetric band matrix, with k super-diagonals. Obsessed with the band-matrix lore, honestly 🦋

🫶 Arguments 🫶

  • UPLO — CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows:

UPLO = 'U' or 'u': the upper triangular part of A is being supplied.

UPLO = 'L' or 'l': the lower triangular part of A is being supplied.

Unchanged on exit. 💖

  • N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ✨
  • K — INTEGER. On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit. 🎀
  • ALPHA — COMPLEX*16. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. 💫
  • A — COMPLEX*16 array, dimension( LDA, N ).

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced.

The following program segment will transfer the upper triangular part of a symmetric band matrix from conventional full matrix storage to band storage:

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

Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced.

The following program segment will transfer the lower triangular part of a symmetric band matrix from conventional full matrix storage to band storage:

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

Unchanged on exit. 🫶

  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). Unchanged on exit. 🌈
  • X — COMPLEX*16 array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). 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 — COMPLEX*16. On entry, BETA specifies the scalar beta. Unchanged on exit. 💜
  • Y — COMPLEX*16 array, dimension at least ( 1 + ( N - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. 👑
  • INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. 🌸

🌟 Author 🌟

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

📜 Definition 📜

Definition at line 150 of file zsbmv.f.

🧚 Author (generated) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie, that's the whole page — footer vibe check: LAPACK Version 3.12.0, page TESTING/LIN/zsbmv.f(3), and no fake date energy from me because the footer literally doesn't list one 🙈💖✨🫶

📦 where this page comes from