BLAS/SRC/zgbmv.f(3)

💖 NAME 💖

Okay so this page is BLAS/SRC/zgbmv.f — section (3), bestie — from the Library Functions Manual, and it is all about the ZGBMV subroutine. It’s giving Level 2 BLAS, complex*16 band-matrix energy, and we are gonna get through every single parameter together. No cap. Periodt. 🫶

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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 (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 ✨

🎯 Purpose: 🎯

Bestie, ZGBMV performs one of these matrix-vector operations — yes, all three are on the menu:

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. 🦋

🧾 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. Respect the minimum, bestie.
• N — N is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Same vibe, zero is the floor.
• 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 COMPLEX*16. On entry, ALPHA specifies the scalar alpha. Main character scalar energy.
• A — A is COMPLEX*16 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 ). Do not play with this one.
• 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 Xmust contain the vectorx`. Vector x is ready for her close-up.
• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Like, genuinely not zero.
• 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. Zero beta means Y can chill.
• 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 Ymust contain the vectory. On exit, Yis overwritten by the updated vectory. If either mornis zero, thenY` is not referenced and the function performs a quick return. Quick return is a whole mood.
• INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Same rule, bestie: no zero increments.

🫶 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 zgbmv.f. ✨

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off, bestie: this whole page is from LAPACK Version 3.12.0, source BLAS/SRC/zgbmv.f(3), and the written-on date flex is 22-October-1986. Slay, band matrix, slay. 💖🎀🦋