BLAS/SRC/stbmv.f(3)

🦋 BLAS/SRC/stbmv.f — bestie, we're doing banded triangular matvecs today

okay so this page lives in the LAPACK manual (BLAS section, to be exact), and it's literally just one iconic little subroutine. no cap, she's small but she works. let's get into it 💖

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✨ NAME ✨

BLAS/SRC/stbmv.f — that's the whole name, that's her, that's the file 💅

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🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine stbmv (uplo, trans, diag, n, k, a, lda, x, incx) — STBMV

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🌸 Function/Subroutine Documentation 🌸

subroutine stbmv (character uplo, character trans, character diag, integer n, integer k, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx)

STBMV. that's the girl. 👑

💫 Purpose

STBMV performs one of the matrix-vector operations

   x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. fr fr that's the whole job. 🫶

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🌈 Parameters

• UPLO

UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:

• UPLO = 'U' or 'u' — A is an upper triangular matrix. ⬆️
• UPLO = 'L' or 'l' — A is a lower triangular matrix. ⬇️

• TRANS

TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:

• TRANS = 'N' or 'n' — x := A*x.
• TRANS = 'T' or 't' — x := A**T*x.
• TRANS = 'C' or 'c' — x := A**T*x.

• DIAG

DIAG is CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows:

• DIAG = 'U' or 'u' — A is assumed to be unit triangular. (the diagonal is all ones, we're just trusting you on that 🙈)
• DIAG = 'N' or 'n' — A is not assumed to be unit triangular.

• 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 with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K. ⭐

• 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 matrix of coefficients, 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. (she's not like other girls, she ignores that corner 💀)

The following program segment will transfer an upper triangular 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 matrix of coefficients, 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 a lower triangular 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

Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity. ✨

• 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 n element vector x. On exit, X is overwritten with the transformed vector x. she goes in, she comes out different. main character arc 🦋

• INCX

INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 🚫

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👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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🔥 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.

(the lore. the origin story. 1986, periodt 💜)

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Definition at line 185 of file stbmv.f.

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🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page bestie!! 💖 this one's Version 3.12.0, dated Tue Nov 28 2023 12:08:41, and the source is BLAS/SRC/stbmv.f(3). go forth and multiply your triangular band matrices, ily 🫶✨