SGELQT(3)

💅 SGELQT(3) — bestie's LAPACK era ✨

Okay so this is the manual page for SGELQT(3) from the Library Functions Manual, and the source file it's repping is /home/abui...RC/sgelqt.f(3). Manual name folded in near the top like a little bow 🎀. It's giving blocked LQ factorization, it's giving compact WY representation, and we're keeping every parameter, constraint, and block-reflector detail exactly as the source says. No cap. 💖

🌸 NAME

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

✨ SYNOPSIS

Functions/Subroutines

subroutine SGELQT (m, n, mb, a, lda, t, ldt, work, info)
    SGELQT

💜 Function/Subroutine Documentation

subroutine SGELQT (integer m, integer n, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)
    SGELQT

🎯 Purpose

The Purpose text says, and I quote:

DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q.

Yes bestie, the page is SGELQT and that line says DGELQT — we are not touching it, we're just delivering it exactly. 💀

🧚 Parameters

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. 💖
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. 💖
• MB — MB is INTEGER. The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. 🎀
• A — A is REAL array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are the rows of V. 🌸
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). 🦋
• T — T is REAL array, dimension (LDT,MIN(M,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details. ⭐
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= MB. 🔥
• WORK — WORK is REAL array, dimension (MB*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 row above the diagonal. For example, if M=5 and N=3, the matrix V is:

V = (  1  v1 v1 v1 v1 )
    (     1  v2 v2 v2 )
    (         1 v3 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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, an upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as:

T = (T1 T2 ... TB).

Definition at line 123 of file sgelqt.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, your LAPACK bestie 💖 — footer info: LAPACK Version 3.12.0 · /home/abui...RC/sgelqt.f(3) · no date printed on this page, bestie, so no made-up date 🫶✨