TESTING/LIN/stplqt.f(3)

💖 TESTING/LIN/stplqt.f(3) 💖

hey bestie, welcome to TESTING/LIN/stplqt.f(3) — Library Functions Manual energy, LAPACK edition. This page is all about the stplqt subroutine, and yes, we're gonna read the whole thing. 💅

💖 NAME 💖

TESTING/LIN/stplqt.f — the LAPACK test-doc page for stplqt, in the Library Functions Manual. It's giving “subroutine documentation but make it iconic.” ✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine stplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info) — STPLQT

💅 Function/Subroutine Documentation 💅

Okay so here's the full signature, no cap:

subroutine stplqt (integer m, integer n, integer l, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)

STPLQT — main character routine, obviously. 👑

🌸 Purpose 🌸

STPLQT computes a blocked LQ factorization of a real matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q. That's the whole vibe. 🦋

🦋 Parameters 🦋

• M — INTEGER. The number of rows of the matrix B, and the order of the triangular matrix A. Constraint: M >= 0. 💖
• N — INTEGER. The number of columns of the matrix B. Constraint: N >= 0. ✨
• L — INTEGER. The number of rows of the lower trapezoidal part of B. Constraint: MIN(M,N) >= L >= 0. See Further Details. 🎀
• MB — INTEGER. The block size to be used in the blocked QR. Constraint: M >= MB >= 1. Yes, the page says QR right there — we're keeping QR. 🫶
• A — REAL array, dimension (LDA,N). On entry, the lower triangular N-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L. 🌸
• LDA — INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N). 💅
• B — REAL array, dimension (LDB,N). On entry, the pentagonal M-by-N matrix B. The first N-L columns are rectangular, and the last L columns are lower trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details. 🦋
• LDB — INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,M). ⭐
• T — REAL array, dimension (LDT,N). The lower triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details. 🔥
• LDT — INTEGER. The leading dimension of the array T. Constraint: LDT >= MB. 💜
• WORK — REAL array, dimension (MB*M). 🍓
• INFO — 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 🔥

Okay, this is the extra-detailed part, and it's lowkey the best part. The input matrix C is a M-by-(M+N) matrix:

               C = [ A ] [ B ]

where A is a lower triangular N-by-N matrix, and B is an M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on the left of a M-by-L upper trapezoidal matrix B2:

          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L upper trapezoidal.

The lower trapezoidal matrix B2 consists of the first L columns of a N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular. 💀

The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C:

            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular N-by-N
                   [ B ]  <- M-by-N pentagonal

so that W can be represented as:

            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, N-by-N
                   [ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which we call V above. Note that V has the same form as B; that is:

            [ V ] = [ V1 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal.

The rows of V represent the vectors which define the H(i)'s. 🌈

The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-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-N matrix T as:

               T = [T1 T2 ... TB].

Definition at line 187 of file stplqt.f. 📌

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 🧚

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That's the whole page, bestie. Signing off with the footer deets: LAPACK Version 3.12.0, page TESTING/LIN/stplqt.f(3). 💜✨