BLAS/SRC/dtbsv.f(3)

💖 BLAS/SRC/dtbsv.f(3) — the LAPACK manual, bestie edition 💖

okay so this is a page straight out of the LAPACK manual (that's the Linear Algebra PACKage, iykyk) and it lives at BLAS/SRC/dtbsv.f(3). it's a BLAS Level 2 routine. it's giving ✨legacy numerical linear algebra✨ and honestly? iconic. let's get into it 🫶

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🌸 NAME 🌸

BLAS/SRC/dtbsv.f — that's the file, that's the girl 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine dtbsv (uplo, trans, diag, n, k, a, lda, x, incx) — DTBSV

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🦋 Function/Subroutine Documentation 🦋

subroutine dtbsv (character uplo, character trans, character diag, integer n, integer k, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx)

DTBSV 💫

🎀 Purpose 🎀

okay bestie, listen up: DTBSV solves one of the systems of equations

A*x = b,   or   A**T*x = b,

where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. slay.

⚠️ not me warning you: No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. so like… she will NOT catch you if your matrix is singular, that's on you, no cap 😭 do your own vibe check first fr fr.

🌈 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 equations to be solved as follows:

TRANS = 'N' or 'n'   A*x = b.

TRANS = 'T' or 't'   A**T*x = b.

TRANS = 'C' or 'c'   A**T*x = b.

• 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.

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 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 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. (she just knows they're 1, don't argue 💅)

• 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 DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x. main character energy: she goes in as b, she comes out as x ✨

• INCX

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

👑 Author 👑

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

💜 Further Details: 💜

Level 2 Blas routine.

-- 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 188 of file dtbsv.f. 📍

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. (yes she was born in a doc generator and she's still serving looks, we love that for her 🌸)

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okay that's the whole page, bestie!! every flag, every default, every DO 20 loop, all of it. go forth and solve your triangular band systems responsibly 🫶

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/dtbsv.f(3) ✨ that's the version, that's the date, that's the file, and that's the tea 💅💖