SRC/sgelqt.f(3)

💖 SRC/sgelqt.f(3) 💖

okay bestie, this page is SRC/sgelqt.f(3) from the Library Functions Manual — manual name folded in near the top, header line not copied, we are so efficient. 💅 This is the SGELQT subroutine tea, and it is literally giving blocked LQ factorization with the compact WY representation of Q. Let's go. ✨

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🌸 NAME 🌸

SRC/sgelqt.f — that's the name, bestie. Short, iconic, to the point. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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🧚 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 — the main character, no cap. 👑

🎯 Purpose:

SGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q. That's the whole purpose, and it ate. 💅

🧮 Parameters

M

M is INTEGER. It's the number of rows of the matrix A. Constraint: M >= 0. Respect the row count. 🫶

N

N is INTEGER. It's the number of columns of the matrix A. Constraint: N >= 0. Respect the column count too. 🌸

MB

MB is INTEGER. It's the block size to be used in the blocked QR. Constraint: MIN(M,N) >= MB >= 1. Yes, the original says blocked QR right there — we're not editing the lore. 🎀

A

A is a REAL array, dimension (LDA,N).

On entry, it's 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.

That's the glow-up, bestie. ✨

LDA

LDA is INTEGER. It's the leading dimension of the array A. Constraint: LDA >= max(1,M). Respect the leading dimension. 💜

T

T is a REAL array, dimension (LDT,MIN(M,N)).

The upper triangular block reflectors are stored in compact form as a sequence of upper triangular blocks. See below for further details. It's giving compact storage excellence. 🦋

LDT

LDT is INTEGER. It's the leading dimension of the array T. Constraint: LDT >= MB. 🎀

WORK

WORK is a REAL array, dimension (MB*N). It's the workspace, doing background vocals. 🎤

INFO

INFO is INTEGER. Exit status tea:

• = 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:

Here's the deep lore. 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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okay that's the whole page, bestie. Signing off from LAPACK Version 3.12.0 and this footer's own SRC/sgelqt.f(3) — the footer doesn't give a date line, so no fake date here, periodt. 💖✨🌈