BLAS/SRC/ssbmv.f(3)

🌸 NAME 🌸

Okay bestie, this is the Library Functions Manual page for BLAS/SRC/ssbmv.f(3) — aka the ssbmv BLAS routine. It’s giving symmetric band matrix-vector realness, and we’re gonna get through every single detail together. 🫶

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

SSBMV. That’s the call, periodt. 💅

💅 Function/Subroutine Documentation 💅

subroutine ssbmv

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. Yes bestie, that’s the whole signature. 🦋

🎯 Purpose

okay so 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. Obsessed with the clarity. ✨

🌸 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 REAL. On entry, ALPHA specifies the scalar alpha.

A is REAL array, dimension ( LDA, N ). Okay, this one is the main character. 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 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 REAL 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 REAL. On entry, BETA specifies the scalar beta.

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 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

Definition at line 183 of file ssbmv.f. — periodt. 💅

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. No cap. ✨

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That’s the whole page, bestie 💖 — source/version footer vibes: LAPACK Version 3.12.0, file BLAS/SRC/ssbmv.f(3). Mwah 💋