BLAS/SRC/cgbmv.f(3)

okay so bestie, welcome to BLAS/SRC/cgbmv.f(3) — that's the page name — and it lives in the Library Functions Manual. it's giving linear algebra, it's giving band matrix, and honestly? CGBMV ate. 💅✨

🌸 NAME 🌸

BLAS/SRC/cgbmv.f — that's the file name, periodt. 🎀

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

💖 Function/Subroutine Documentation 💖

🌟 subroutine cgbmv 🌟

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

CGBMV

🎀 Purpose 🎀

okay so CGBMV performs one of these matrix-vector operations, and yes you need all three:

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

y := alpha*A**H*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. iconic band-matrix behavior, no cap. 👑

🌸 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**H*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. no negative row era, bestie. 🫶
• N — N is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. same energy: zero or more. ✨
• KL — KL is INTEGER. On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. keep it legal, okay? 💅
• KU — KU is INTEGER. On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. yes, super-diagonals need love too. 🦋
• ALPHA — ALPHA is COMPLEX. On entry, ALPHA specifies the scalar alpha. literally the scalar alpha, main character scalar. ⭐
• A — A is COMPLEX 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

• 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 ). don't skimp on the leading dimension, bestie. 💀
• X — X is COMPLEX 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. it's the vector, it's incremented, it's ready. 🔥
• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. zero increment is not the vibe. 🚫
• BETA — BETA is COMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. cute shortcut, lowkey. 🎀
• Y — Y is COMPLEX 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 is not referenced and the function performs a quick return. quick-return queen. 🌈
• INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. again: not zero, bestie. 💜

👑 Author 👑

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

🔥 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.

Definition at line 188 of file cgbmv.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💋 — this cutie comes from LAPACK, Version 3.12.0, on the BLAS/SRC/cgbmv.f(3) page. 🫶✨