SRC/sgeqrt2.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🌸 SRC/sgeqrt2.f — bestie, let me introduce you to the QR glow-up function 🌸

Okay so like, this is the manual page for SRC/sgeqrt2.f, part of the LAPACK Library Functions Manual, and it's literally the blueprint for sgeqrt2 — a subroutine that does QR factorization using the compact WY representation of Q. It's giving linear algebra main character energy and I'm obsessed. Let me walk you through it, no cap. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine sgeqrt2 (m, n, a, lda, t, ldt, info)

SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Periodt. 🔥

🦋 Function/Subroutine Documentation 🦋

subroutine sgeqrt2 (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Yes bestie, that's the whole vibe.

🎀 Purpose 🎀

!> !> SGEQRT2 computes a QR factorization of a real M-by-N matrix A, !> using the compact WY representation of Q. !>

Like, it takes a real M-by-N matrix A and factorizes it into Q and R, but it stores Q in that iconic compact WY form instead of building the whole thing. Efficiency slay. 💖

💜 Parameters 💜

  • M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= N. Gotta have at least as many rows as columns, bestie, that's the rule. ✨
  • N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0. Zero columns is valid, but like, why would you? 🙈
  • A — A is REAL array, dimension (LDA,N). On entry, this is the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details — and bestie, the details are juicy. 🍓
  • LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,M). Don't skimp on this or the compiler will literally come for you. 💀
  • T — T is REAL array, dimension (LDT,N). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. Like, they're just vibing there, ignored. 💅
  • LDT — LDT is INTEGER. The leading dimension of the array T. Constraint: LDT >= max(1,N). Same energy as LDA — respect the leading dimension. 👑
  • INFO — INFO is INTEGER. Exit status, and it's giving binary icon:
    • = 0: successful exit, slay! ✅
    • < 0: if INFO = -i, the i-th argument had an illegal value. Not me crying over a negative info code. 😭

🌈 Author 🌈

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

The whole academic dream team wrote this. Icons only. 🫶

⭐ Further Details ⭐

!> !> The matrix V stores the elementary reflectors H(i) in the i-th column !> below the diagonal. For example, if M=5 and N=3, the matrix V is !> !> V = ( 1 ) !> ( v1 1 ) !> ( v1 v2 1 ) !> ( v1 v2 v3 ) !> ( v1 v2 v3 ) !> !> where the vi's represent the vectors which define H(i), which are returned !> in the matrix A. The 1's along the diagonal of V are not stored in A. The !> block reflector H is then given by !> !> H = I - V * T * V**T !> !> where V**T is the transpose of V. !>

So like, V stores the elementary reflectors H(i) in the i-th column below the diagonal. If M=5 and N=3, the matrix V looks exactly like that little triangle above — the vis are the vectors defining H(i), returned in A. The 1s along the diagonal of V are NOT stored in A (they're implied, lowkey iconic), and the block reflector H is literally H = I - V * T * V**T, where V**T is the transpose of V. Not me doing matrix math in my head, it's giving genius fr fr. 🔥

📁 Definition location 📁

Definition at line 126 of file sgeqrt2.f. You can literally go find it. Iykyk. 💜

🧚 Author (meta) 🧚

Generated automatically by Doxygen for LAPACK from the source code. The robots did this one, bestie — we just made it cute. 🤖✨

LAPACK — Version 3.12.0 — SRC/sgeqrt2.f(3) 🎀

That's the whole page, bestie! Go forth and factorize your QR like the linear algebra icon you are. No cap, you're gonna eat this up. 💖💅🦋🌸

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