BLAS/SRC/ssbmv.f(3)

🌸 BLAS/SRC/ssbmv.f 🌸

okay bestie, welcome to ssbmv — a Level 2 BLAS routine from the BLAS/SRC folder, and she is lowkey the moment 💅

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✨ NAME ✨

BLAS/SRC/ssbmv.f — the file, the icon, the legend 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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💖 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 ✨

🌟 Purpose:

not me about to explain this so it actually clicks 🧠

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. 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 )

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:

• 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.

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💜 Author 💜

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

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okay that's the whole page bestie, you ate 💅

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — from BLAS/SRC/ssbmv.f(3) 🎀 iykyk 🦋