/home/abui.../dtplqt2.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 DTPLQT2 🌸

ok so this is a manpage from LAPACK, bestie — the Library Functions Manual situation — and we're talking about /home/abui.../dtplqt2.f(3). buckle up, it's a Fortran girlie and she's iconic 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtplqt2.f

like, that's the whole path, that's her address, no cap 🏠

🎀 SYNOPSIS 🎀

Functions/Subroutines

  • subroutine DTPLQT2 (m, n, l, a, lda, b, ldb, t, ldt, info) — DTPLQT2 computes a LQ factorization of a real or complex triangular-pentagonal "matrix", which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

(i'm not gonna lie the original strings those words together with zero spaces, but you get the vibe ✨)

💖 Function/Subroutine Documentation 💖

subroutine DTPLQT2 (integer m, integer n, integer l, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( ldb, *
    ) b, integer ldb, double precision, dimension( ldt, * ) t, integer ldt,
    integer info)

so DTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. that's the whole personality 🫶

🌈 Purpose 🌈

!> !> DTPLQT2 computes a LQ a 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. !>

(yes the source really does say "a factorization", we are respecting her choices 🙈)

🍓 Parameters 🍓

  • M — !> !> M is INTEGER !> The total number of rows of the matrix B. !> M >= 0. !> — like, the row count of B, and it's gotta be zero or more, periodt 💯
  • N — !> !> N is INTEGER !> The number of columns of the matrix B, and the order of !> the triangular matrix A. !> N >= 0. !> — columns of B and the order of A, she's doing double duty, main character energy 👑
  • L — !> !> L is INTEGER !> The number of rows of the lower trapezoidal part of B. !> MIN(M,N) >= L >= 0. See Further Details. !> — the row count of B's lower trapezoidal part, and MIN(M,N) >= L >= 0, and yes go read Further Details, i'm serious 📖
  • A — !> !> A is DOUBLE PRECISION array, dimension (LDA,M) !> On entry, the lower triangular M-by-M matrix A. !> On exit, the elements on and below the diagonal of the array !> contain the lower triangular matrix L. !> — comes in as the lower triangular M-by-M matrix A, leaves with the lower triangular matrix L living on and below the diagonal. glow-up fr ✨
  • LDA — !> !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> — leading dimension of A, gotta be LDA >= max(1,M) 🫡
  • B — !> !> B is DOUBLE PRECISION 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. !> — enters as the pentagonal M-by-N matrix B, first N-L columns rectangular, last L columns lower trapezoidal; exits holding the pentagonal matrix V. again: Further Details, bestie 💀
  • LDB — !> !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,M). !> — leading dimension of B, LDB >= max(1,M) 💜
  • T — !> !> T is DOUBLE PRECISION array, dimension (LDT,M) !> The N-by-N upper triangular factor T of the block reflector. !> See Further Details. !> — the N-by-N upper triangular factor T of the block reflector. Further Details. you know the drill 🎀
  • LDT — !> !> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,M) !> — leading dimension of T, LDT >= max(1,M) (no period on that one, she's quirky like that) 🙈
  • INFO — !> !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> — = 0 means we ate and left no crumbs 🍽️; < 0 means if INFO = -i, the i-th argument had an illegal value, and someone's getting read 💀

👑 Author 👑

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

the whole squad showed up, we love a collab 🌈

🧚 Further Details 🧚

ok this is the part where it gets math. stay with me 💖

The input matrix C is a M-by-(M+N) matrix

         C = [ A ][ B ]

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

         B = [ B1 ][ B2 ]
             [ B1 ]  <-     M-by-(N-L) rectangular
             [ B2 ]  <-     M-by-L lower 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 M-by-M
             [ B ]  <- M-by-N pentagonal

so that W can be represented as

         W = [ I ][ V ]
             [ I ]  <- identity, M-by-M
             [ 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,

         W = [ 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 (M+N)-by-(M+N) block reflector H is then given by

         H = I - W**T * T * W

where W^H is the conjugate transpose of W and T is the upper triangular factor of the block reflector.

ngl that last line is giving "the source says W^H but the formula says W**T" and we are simply not going to fight her about it 😭 the manpage said what it said

⭐ Definition ⭐

Definition at line 176 of file dtplqt2.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

(i didn't write this, a robot did, and honestly? she understood the assignment 🤖✨)

LAPACK · Version 3.12.0 · /home/abui.../dtplqt2.f(3) — that's a wrap bestie, go factor something LQ-shaped, ily, bye 🫶💖🎀

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