ZGBMV(3)

ZGBMV(3) — LAPACK Library Functions Manual 💅

bestie, this is the zgbmv.f(3) page from the LAPACK Library Functions Manual, and it’s giving “complex band matrix realness” fr fr. Let’s break it down without losing a single detail. 🫶

🎀 NAME 🎀

The NAME is literally this file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/zgbmv.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

💅 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 — yes bestie, that’s the name. Iconic. 👑

🌸 Purpose 🌸

ZGBMV performs one of the matrix-vector operations, no cap:

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. Periodt. 💫

🎀 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.
• 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 COMPLEX*16. On entry, ALPHA specifies the scalar alpha.
• 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 ).
• 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.
• 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.
• 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.
• INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

👑 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.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bye bestie — kisses from LAPACK Version 3.12.0, page /home/abui...SRC/zgbmv.f(3) 💖✨🎀