/home/abui.../sgeqrt3.f(3)

💖 NAME 💖

okay bestie, you're on the sgeqrt3.f(3) page from the Library Functions Manual — and the source file is this exact path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeqrt3.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

• recursive subroutine SGEQRT3 (m, n, a, lda, t, ldt, info) — SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. periodt.

🫶 Function/Subroutine Documentation 🫶

🦋 recursive subroutine SGEQRT3

recursive subroutine SGEQRT3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

and the description is literally: SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. iconic.

Purpose:

okay so the purpose is this: SGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. 💅

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. (The synopsis one-liner says general real or complex — keep both deets in your notes, bestie.)

🎀 Parameters 🎀

M

M is INTEGER. It's the number of rows of the matrix A. M >= N — yes, that inequality is a hard requirement, bestie. 💀

N

N is INTEGER. It's the number of columns of the matrix A. N >= 0. ✨

A

A is REAL array, dimension (LDA,N). On entry, 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. 👑

LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). 🫶

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. See below for further details. ✨

LDT

LDT is INTEGER. The leading dimension of the array T. LDT >= max(1,N). 🫶

INFO

INFO is INTEGER.

• = 0: successful exit. 🎉
• < 0: if INFO = -i, the i-th argument had an illegal value. 😭

🌈 Author 🌈

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

🦋 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.

For details of the algorithm, see Elmroth and Gustavson (cited above). 🫶

Definition at line 131 of file sgeqrt3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page! 💅 Footer sign-off deets: LAPACK Version 3.12.0, page path /home/abui.../sgeqrt3.f(3), and no date is listed in that footer — so I'm not inventing one. Stay slay, and may your arguments never be illegal. 🫶💖