DSBMV(3)

💖 DSBMV(3) 💖

okay so bestie, welcome to the Library Functions Manual page for dsbmv.f(3) — yes, we're doing symmetric band matrix-vector math and it's lowkey iconic. 💅

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

Functions/Subroutines

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

💖 Function/Subroutine Documentation 💖

subroutine DSBMV (character uplo, integer n, integer k, double precision
    alpha, double precision, dimension(lda,*) a, integer lda, double
    precision, dimension(*) x, integer incx, double precision beta, double
    precision, dimension(*) y, integer incy)
    DSBMV

🎯 Purpose

DSBMV 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. ✨

🧚 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.

💜 A

A is DOUBLE PRECISION 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 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 DOUBLE PRECISION 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.

bestie, INCX being zero is not a vibe. 🫶

💜 BETA

BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta.

💜 Y

Y is DOUBLE PRECISION 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.

and same energy for INCY, okay? Not zero. Periodt. 💀

👑 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 183 of file dsbmv.f.

🩷 Author

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 bestie, that's the whole page. Footer tea: LAPACK Version 3.12.0, source tag /home/abui...SRC/dsbmv.f(3). 🫶