CGBTRS(3)

💅 cgbtrs.f(3) — Library Functions Manual 🎀

okay bestie so this is a page out of the Library Functions Manual, and it's literally just the docs for one Fortran subroutine, /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgbtrs.f. Yes the whole path, yes it's long, no we're not shortening it, it's the name, it's iconic like that. 🦋

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgbtrs.f — that's it, that's the name, that's the whole vibe. it's giving "my government name is a file path" and honestly? relatable. 💀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CGBTRS (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)

CGBTRS — the main character of this page 💫

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🔥 Function/Subroutine Documentation 🔥

subroutine CGBTRS (character trans, integer n, integer kl, integer ku,
    integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, integer,
    dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,
    integer info)

CGBTRS 🫶

💖 Purpose:

!>
!> CGBTRS solves a system of linear equations
!>    A * X = B,  A**T * X = B,  or  A**H * X = B
!> with a general band matrix A using the LU factorization computed
!> by CGBTRF.
!>

so basically: you've already got the LU factorization from CGBTRF, right? now CGBTRS comes in and actually solves the thing. three flavors available — A * X = B, A**T * X = B, or A**H * X = B — pick your fighter, the TRANS argument decides. no cap, that's the whole job. ✨

🎀 Parameters

• TRANS — CHARACTER*1, and it tells us what form of the system of equations we're doing. the options are, and I quote:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• N — INTEGER, the order of the matrix A. must be N >= 0. (zero is valid bestie, don't come for me.)
• KL — INTEGER, the number of subdiagonals within the band of A. must be KL >= 0.
• KU — INTEGER, the number of superdiagonals within the band of A. must be KU >= 0.
• NRHS — INTEGER, the number of right hand sides, i.e., the number of columns of the matrix B. must be NRHS >= 0.
• AB — COMPLEX array, dimension (LDAB,N). this bad boy holds the details of the LU factorization of the band matrix A, exactly as CGBTRF computed it. specifically:
  • U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1
  • the multipliers used during the factorization live in rows KL+KU+2 to 2*KL+KU+1
• LDAB — INTEGER, the leading dimension of the array AB. must be LDAB >= 2*KL+KU+1. not a suggestion, a requirement 💅
• IPIV — INTEGER array, dimension (N). the pivot indices. for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). it's giving "receipts of every swap" 🧾
• B — COMPLEX array, dimension (LDB,NRHS). on entry, this is the right hand side matrix B. on exit, it's the solution matrix X. same array, glow-up arc, we love a transformation ✨
• LDB — INTEGER, the leading dimension of the array B. must be LDB >= max(1,N). yes max(1,N), not just N — write it down. 📝
• INFO — INTEGER, the report card 📋:
  • = 0: successful exit — slay, you're done
  • < 0: if INFO = -i, the i-th argument had an illegal value — so INFO = -3 means arg number 3 was being messy. check your inputs bestie 😭

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👑 Author

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

Definition at line 136 of file cgbtrs.f. 🔖 (yes, line one-three-six, go look, it's right there)

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⭐ Author

Generated automatically by Doxygen for LAPACK from the source code. a bot wrote this and honestly it ate 🤖✨

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fair warning bestie: CGBTRS does not check that your factorization is nonsingular and it does not do the factorizing for you — that's CGBTRF's whole thing. this page only promises what it promises: it solves, given a factorization, and it reports INFO = -i for a bad argument. nothing more, nothing invented, periodt. 💜

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and that's the page!! 🦋 no notes. LAPACK, Version 3.12.0, footer said /home/abui...RC/cgbtrs.f(3) and we're not arguing with the manpage about a truncated path, we simply respect it. mwah 💋💖