/home/abui...RC/cptsv.f(3)

💅 CPTSV 💅

ok so bestie, this one's from /home/abui...RC/cptsv.f(3) — it's a section 3 library functions manual page, and the actual file it documents is this whole journey:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cptsv.f

It's LAPACK, it's Fortran, it's giving big computational main character energy. Let's get into it 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cptsv.f — like, that's the file, that's the name, that's the whole vibe. no notes 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CPTSV (n, nrhs, d, e, b, ldb, info)

CPTSV computes the solution to system of linear equations A * X = B for PT matrices — that's the official one-liner, and honestly? she ate. 🔥

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💖 Function/Subroutine Documentation 💖

subroutine CPTSV (integer n, integer nrhs, real, dimension( * ) d, complex,
    dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer
    info)

So like, restating for the people in the back: CPTSV computes the solution to system of linear equations A * X = B for PT matrices. periodt. 👑

🌸 Purpose 🌸

!> !> CPTSV computes the solution to a complex system of linear equations !> A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal !> matrix, and X and B are N-by-NRHS matrices. !> !> A is factored as A = L*D*L**H, and the factored form of A is then !> used to solve the system of equations. !>

so basically bestie, A is a complex Hermitian positive definite tridiagonal matrix, dimensions N-by-N, and X and B are N-by-NRHS matrices. the routine factors A as A = L*D*L**H, and then uses that factored form to actually solve the system. it's giving ✨prep work pays off✨ — factor first, solve second. no cap. 🧚

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🎀 Parameters 🎀

N

!> N is INTEGER !> The order of the matrix A. N >= 0. !>

N is INTEGER — it's the order of the matrix A. the rule is N >= 0, and we respect the rule. 🫡

NRHS

!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !>

NRHS is INTEGER — the number of right hand sides, like, the number of columns of the matrix B. and yes, NRHS >= 0. she's flexible but not that flexible 💅

D

!> D is REAL array, dimension (N) !> On entry, the n diagonal elements of the tridiagonal matrix !> A. On exit, the n diagonal elements of the diagonal matrix !> D from the factorization A = L*D*L**H. !>

D is a REAL array, dimension (N). on entry, it's the n diagonal elements of the tridiagonal matrix A. on exit, it's the n diagonal elements of that diagonal matrix D from the factorization A = L*D*L**H. so she comes in as one thing and leaves as another — glow-up arc fr fr. 🌈

E

!> E is COMPLEX array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix A. On exit, the (n-1) subdiagonal elements of the !> unit bidiagonal factor L from the L*D*L**H factorization of !> A. E can also be regarded as the superdiagonal of the unit !> bidiagonal factor U from the U**H*D*U factorization of A. !>

E is a COMPLEX array, dimension (N-1). on entry it holds the (n-1) subdiagonal elements of the tridiagonal matrix A; on exit it holds the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. and here's the fun part — E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A. it's giving versatile icon, one array two readings, we love a multitasker 😭💜

B

!> B is COMPLEX array, dimension (LDB,NRHS) !> On entry, the N-by-NRHS right hand side matrix B. !> On exit, if INFO = 0, the N-by-NRHS solution matrix X. !>

B is a COMPLEX array, dimension (LDB,NRHS). on entry, it's the N-by-NRHS right hand side matrix B. on exit, if INFO = 0, it's the N-by-NRHS solution matrix X. so like, conditional transformation — that INFO = 0 clause is doing a LOT of heavy lifting there bestie, don't skip it 🙈

LDB

!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>

LDB is INTEGER — the leading dimension of the array B, and the requirement is LDB >= max(1,N). that max(1,N) is not decorative, she's protecting you from yourself 💀

INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the leading principal minor of order i !> is not positive, and the solution has not been !> computed. The factorization has not been completed !> unless i = N. !>

INFO is INTEGER — the status report, the receipts, the ~vibe check~ of the whole operation:

• = 0 → successful exit. slay, we're done, go home. ✨
• < 0 → if INFO = -i, the i-th argument had an illegal value. somebody passed something cursed. 😬
• > 0 → if INFO = i, the leading principal minor of order i is not positive, and the solution has not been computed. also, the factorization has not been completed unless i = N. so like... you don't get an answer. read that again. no answer. 🫠

⚠️ okay genuine heads up bestie: that INFO > 0 case means no solution was computed at all, and unless i = N the factorization is sitting there unfinished too. don't ignore INFO. do not. ignore. INFO. 🙏

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👑 Author 👑

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

absolute legends, all four, no cap. 🫶

⭐ Definition at line 114 of file cptsv.f.

that's the location. line 114. go look, she's there. 💅

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this bad boy — the robots did it. iconic behavior honestly. 🤖✨

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and that's the whole page, bestie — every flag, every array bound, every INFO branch, all of it, still intact, just with 200% more personality 💖

LAPACK — Version 3.12.0 — /home/abui...RC/cptsv.f(3) 🎀🦋🌸