BLAS/SRC/dsbmv.f(3)

💖 NAME 💖

BLAS/SRC/dsbmv.f — okay bestie, this is the file for dsbmv, a Level 2 BLAS routine, and it's literally that girl 💅

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

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

DSBMV

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🌸 Function/Subroutine Documentation 🌸

🎀 subroutine dsbmv

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 — bestie, this is a 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 — an INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
• K — an INTEGER. On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.
• ALPHA — a DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 💫
• A — a 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 — an 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 — a DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. 🦋
• INCX — an INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 🚫
• BETA — a DOUBLE PRECISION. On entry, BETA specifies the scalar beta. ✨
• Y — a 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 — an 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 183 of file dsbmv.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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ok that's the whole page bestie, no cap 💖 this is Version 3.12.0, dated Tue Nov 28 2023 12:08:41 — go forth and multiply your band matrices, you absolute icon 🫶✨💅