BLAS/SRC/stbmv.f(3)

okay so this page is BLAS/SRC/stbmv.f(3) from the Library Functions Manual, and it’s giving major STBMV energy. 💅

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🌸 NAME 🌸

BLAS/SRC/stbmv.f — that’s the name, bestie. No cap. ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

STBMV — the icon itself. 👑

💖 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 — yes bestie, it’s the same star, full signature edition. 🫶

🎀 Purpose 🎀

Okay so 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. Literally the whole vibe. 💜

🦋 Parameters 🦋

💅 UPLO 💅

UPLO is CHARACTER*1. On entry, UPLO tells us whether the matrix is an upper or lower triangular matrix, like this:

• 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 says which operation to perform, like:

• 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 says whether or not A is unit triangular, like:

• DIAG = 'U' or 'u' — A is assumed to be unit triangular.
• 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.

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.

🫶 INCX 🫶

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

💖 Author 💖

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🌈 Further Details 🌈

Okay bestie, further details tea: this is a Level 2 Blas routine.

The vector and matrix arguments are not referenced when N = 0, or M = 0

It has the -- Written on 22-October-1986. line, with:

• Jack Dongarra, Argonne National Lab.
• Jeremy Du Croz, Nag Central Office.
• Sven Hammarling, Nag Central Office.
• Richard Hanson, Sandia National Labs.

Definition at line 185 of file stbmv.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Footer vibe check, bestie: LAPACK Version 3.12.0, source page BLAS/SRC/stbmv.f(3). The original footer didn’t give a date, so I’m not inventing one — just pure version/source truth. 💖✨🎀