BLAS/SRC/cgbmv.f(3)

✨ BLAS/SRC/cgbmv.f ✨

okay bestie, gather round, we're doing complex band matrix-vector math and it's gonna be a whole moment 💅

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NAME

BLAS/SRC/cgbmv.f — yes that's literally the whole name, she's a file, she's iconic, that's it 🎀

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SYNOPSIS

Functions/Subroutines

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

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Function/Subroutine Documentation

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 👑

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Purpose:

so like, CGBMV performs one of the matrix-vector operations, and there are three (3) of them, 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. she's shaped like a band, she's got range 🌈

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Parameters

• TRANS — TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows, and bestie you literally have to pick one:
  • 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. On entry, ALPHA specifies the scalar alpha. she's just a little guy, a scalar, a queen 🫶
• 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

ngl that snippet is doing the most but it's doing it correctly, so.

• 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 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, zero is not the vibe here 💀
• 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. free pass, enjoy it ✨
• 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 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.

look at that roster. academic royalty. the avengers of linear algebra 👑

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Further Details:

• Level 2 Blas routine.
• The vector and matrix arguments are not referenced when N = 0, or M = 0

and now, the historical record, because we respect the elders 🎀

   -- 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.

1986?? they were doing this before the internet was cute and it still slays. respect. 💖

Definition at line 188 of file cgbmv.f.

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Author

Generated automatically by Doxygen for LAPACK from the source code. she didn't write herself, she was generated, and honestly? main character energy 😌

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Version 3.12.0 · Tue Nov 28 2023 12:08:41 · BLAS/SRC/cgbmv.f(3)

okay that's the whole page bestie, you understood all of it, I'm so proud of you, go forth and multiply your band matrices 💅🦋✨