BLAS/SRC/chbmv.f(3)

💖 NAME 💖

BLAS/SRC/chbmv.f — okay so this is the file, bestie, and inside it lives one whole subroutine called chbmv. That's it, that's the file. 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine chbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
  • CHBMV — yup, that's her 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine chbmv (character uplo, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy)

CHBMV

Purpose:

So what she actually does: CHBMV performs the matrix-vector operation

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

where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals. No cap. 💅

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🌸 Parameters 🌸

• UPLO — this one's CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows:
  • UPLO = 'U' or 'u' — the upper triangular part of A is being supplied.
  • UPLO = 'L' or 'l' — the lower triangular part of A is being supplied.
• N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. (Zero is fine, she's chill like that.)
• K — K is INTEGER. On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.
• ALPHA — ALPHA is COMPLEX. On entry, ALPHA specifies the scalar alpha. Just a lil scalar. 🍓
• A — A is COMPLEX array, dimension ( LDA, N ). Okay this one's the long one, sit down, hydrate:

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced.

The following program segment will transfer the upper triangular part of a hermitian band matrix from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         M = K + 1 - J
         DO 10, I = MAX( 1, J - K ), J
            A( M + I, J ) = matrix( I, J )
   10    CONTINUE
   20 CONTINUE

Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced.

The following program segment will transfer the lower triangular part of a hermitian band matrix from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         M = 1 - J
         DO 10, I = J, MIN( N, J + K )
            A( M + I, J ) = matrix( I, J )
   10    CONTINUE
   20 CONTINUE

Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. (Iconic behaviour honestly. ✨)

• 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 ( k + 1 ).
• X — X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). 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. On entry, BETA specifies the scalar beta.
• Y — Y is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. (not me saying goodbye to your old y... she's gone, bestie)
• 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.

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📍 Definition at line 186 of file chbmv.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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Not me, not you, but Doxygen wrote that last bit. She's the main character, we're just living in her house. 🙈

And that's the whole vibe check, bestie — Version 3.12.0, dated Tue Nov 28 2023 12:08:41, straight from BLAS/SRC/chbmv.f(3). Slay, ate, left no crumbs, and every single parameter survived the trip. Periodt. 💖✨🎀