CHBMV(3)

bestie, welcome to the chbmv.f(3) page from the Library Functions Manual 💅 the header/footer path is /home/abui...SRC/chbmv.f(3), and this whole page is a Doxygen-generated LAPACK situation. ok so let’s get into it ✨

🎀 NAME 🎀

literally just the source file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/chbmv.f — that’s the whole NAME section, no cap.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine CHBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) — this is the subroutine, also labeled CHBMV.

subroutine CHBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
    CHBMV

💖 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 🌸

ok so the purpose is this, bestie:

!>
!> 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.
!>

🫶 Parameters 🫶

• UPLO — is 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 — is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
• K — is INTEGER. On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.
• ALPHA — is COMPLEX. On entry, ALPHA specifies the scalar alpha.
• A — is COMPLEX array, dimension ( LDA, N ). 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.

• 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 — is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x.
• INCX — is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
• BETA — is COMPLEX. On entry, BETA specifies the scalar beta.
• 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.
• 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 186 of file chbmv.f.

💀 Author 💀

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ok bye bestie 🫶 — this page is from LAPACK Version 3.12.0 and the source path is /home/abui...SRC/chbmv.f(3). 💖