STBTRS(3)

💅 STBTRS — like, the triangular band solver, bestie ✨

okay so real talk, this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stbtrs.f and it's from the LAPACK library functions manual, and honestly? it's giving "linear algebra but make it fashion" 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines, babes:

subroutine STBTRS (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb,
    info)
        STBTRS

🦋 Function/Subroutine Documentation 🦋

subroutine STBTRS (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer
    ldab, real, dimension( ldb, * ) b, integer ldb, integer info)

yep, that's the whole glow-up, STBTRS, right there in the function signature 💖

💜 Purpose 💜

so here's the vibe check, straight from the source:

!>
!> STBTRS solves a triangular system of the form
!>
!>    A * X = B  or  A**T * X = B,
!>
!> where A is a triangular band matrix of order N, and B is an
!> N-by NRHS matrix.  A check is made to verify that A is nonsingular.
!>

like, it literally solves your triangular system AND double-checks that A isn't singular. main character energy fr fr 👑

🌸 Parameters 🌸

okay bestie, here's the cast of characters, and yes every single one matters:

• UPLO — UPLO is CHARACTER*1, and it tells you which triangle of A we're working with:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — TRANS is CHARACTER*1, and it specifies the form the system of equations takes:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• DIAG — DIAG is CHARACTER*1:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — N is INTEGER, and it's the order of the matrix A. Constraint: N >= 0. no negative orders, that's a hard pass 😤
• KD — KD is INTEGER, aka the number of superdiagonals or subdiagonals of the triangular band matrix A. Constraint: KD >= 0.
• NRHS — NRHS is INTEGER, the number of right hand sides, i.e., the number of columns of the matrix B. Constraint: NRHS >= 0.
• AB — AB is REAL array, dimension (LDAB,N). this is the upper or lower triangular band matrix A, stored in the first kd+1 rows of AB. here's how the j-th column of A lands in the j-th column of the array AB:
  • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
  • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

and heads up: if DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. so don't come for me about what's in those slots 🙈

• LDAB — LDAB is INTEGER, the leading dimension of the array AB. Constraint: LDAB >= KD+1.
• B — B is REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. literal transformation arc ✨
• LDB — LDB is INTEGER, the leading dimension of the array B. Constraint: LDB >= max(1,N).
• INFO — INFO is INTEGER, the receipts:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed 💀

🧚 Author 🧚

the icons behind it all:

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

⭐ Definition location ⭐

Definition at line 144 of file stbtrs.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. — yes she was auto-generated and she still ate 💅

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ngl the short version: give her a triangular band matrix, a right hand side, and a dream, and she'll hand you back the solution — if the matrix isn't singular. otherwise INFO > 0 and it's a no from her 😭

LAPACK · Version 3.12.0 · file `/home/abui...RC/stbtrs.f(3) — mwah, that's the page, ily, go solve something triangular 🫶💖🌈