SSBMV(3)

okay so bestie, this is the ssbmv.f(3) page in the Library Functions Manual — we’re folding the manual name in right here at the top instead of copying that header line, because we’re extra like that 💅✨

🎀 NAME 🎀

The NAME on this page is literally the full path, no cute nickname, no cap:

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

✨ SYNOPSIS ✨

Functions/Subroutines

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

💖 Function/Subroutine Documentation 💖

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

🎯 Purpose

The source doc-comment literally says this, so here it is verbatim, bestie:

!>
!> SSBMV  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 symmetric band matrix, with k super-diagonals.
!>

Translation: it does 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 symmetric band matrix with k super-diagonals. Periodt. 🔥

🧩 Parameters

UPLO

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

N is INTEGER.

On entry, N specifies the order of the matrix A. N must be at least zero.

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 REAL.

On entry, ALPHA specifies the scalar alpha.

A

A is REAL array, dimension ( LDA, N ).

Okay so this one is the main character, let’s break it down gently 🫶

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 symmetric 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 symmetric 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 symmetric 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 symmetric 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

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 REAL 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 REAL.

On entry, BETA specifies the scalar beta.

Y

Y is REAL 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

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:

The source doc-comment says this, verbatim, and it is lowkey iconic:

!>
!>  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 183 of file ssbmv.f.

---

📝 Author 📝

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okay bye bestie — this footer gives us LAPACK Version 3.12.0 and the page path /home/abui...SRC/ssbmv.f(3), so that’s the whole sign-off 🌈✨🫶