/home/abui.../sgeqrt2.f(3)

hey bestie 💖 welcome to the Library Functions Manual page for the LAPACK file at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeqrt2.f — she's giving QR factorization, she's giving compact WY, she's literally the moment. ✨

💖 NAME

the one and only: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeqrt2.f 🎀

✨ 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. 🦋

🎀 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. 💅

🫶 Purpose

okay so the literal code-comment tea is:

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

that's the whole serve. QR factorization of a real M-by-N matrix A, compact WY representation of Q, iconic behavior only. 👑

🌸 Parameters

M

M is INTEGER. The number of rows of the matrix A. M >= N. 💖

N

N is INTEGER. The number of columns of the matrix A. N >= 0. ✨

A

A is a 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 a 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. The vibe check is:

• = 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

okay so here's the visual tea ☕: 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. 💅

Definition at line 126 of file sgeqrt2.f.

💅 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie 🫶 the footer is serving LAPACK Version 3.12.0 and points back at /home/abui.../sgeqrt2.f(3) — no date in this footer, just the version and the vibe. no cap, she's generated and iconic. 💖✨