BLAS/SRC/zgbmv.f(3)

✨ zgbmv — the band matrix girlie ✨

ok so this is BLAS/SRC/zgbmv.f, bestie 💖 she lives in the BLAS folder and she does band matrix-vector math and honestly? she ate.

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🎀 SYNOPSIS 🎀

Functions/Subroutines

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

ZGBMV 👑

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💜 Function/Subroutine Documentation 💜

subroutine zgbmv

subroutine zgbmv (character trans, integer m, integer n, integer kl, integer
    ku, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda,
    complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16,
    dimension(*) y, integer incy)

ZGBMV 💅

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🌸 Purpose 🌸

ok so ZGBMV performs one of these matrix-vector operations, pick your fighter:

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 (just lil numbers, no cap), x and y are vectors, and A is an m by n band matrix with kl sub-diagonals and ku super-diagonals. iconic honestly 🦋

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🌈 Parameters 🌈

• TRANS — TRANS is CHARACTER*1 — on entry, TRANS tells you which operation is happening, and it's giving choose-your-own-adventure:
  • 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 is the number of rows of the matrix A. M must be at least zero. (zero is allowed bestie, we don't judge 💖)
• N — N is INTEGER — on entry, N is the number of columns of the matrix A. N must be at least zero.
• KL — KL is INTEGER — on entry, KL is the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. (yes the .le. is Fortran-speak for ≤, we love her 🌸)
• KU — KU is INTEGER — on entry, KU is the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.
• ALPHA — ALPHA is COMPLEX*16 — on entry, ALPHA is the scalar alpha. main character scalar energy ✨
• A — A is COMPLEX*16 array, dimension ( LDA, N ) — okay this one's a whole situation, pay attention:
  • 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 don't correspond to elements in the band matrix (like the top left ku by ku triangle) are not referenced — they're just vibing, ignored, unbothered 💅
  • 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 COMPLEX*16 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)
• BETA — BETA is COMPLEX*16 — on entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. little treat for you 🍓
• Y — Y is COMPLEX*16 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 left 😭
• 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.

Definition at line 188 of file zgbmv.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. she's literally generated, she's literally that girl 🤖💖

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ok bye bestie, that's the whole page 🎀 this one came from Version 3.12.0, Tue Nov 28 2023 12:08:41, and the file is BLAS/SRC/zgbmv.f(3). slay, go call your band matrix, but like... with the right LDA. mwah 💅✨