DTPLQT(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 DTPLQT(3) — NAME 🌸

Bestie, this is the manual page for DTPLQT(3), and the file it lives in is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtplqt.f

🚀 SYNOPSIS 🚀

🧚 Functions/Subroutines 🧚

subroutine DTPLQT (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
    DTPLQT

💖 Function/Subroutine Documentation 💖

🫶 subroutine DTPLQT 🫶

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

🎯 Purpose 🎯

Okay so DTPLQT 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. Slay. 💅

🧾 Parameters 🧾

  • M — M is INTEGER. It’s the number of rows of the matrix B, and the order of the triangular matrix A. Constraint: M >= 0.
  • N — N is INTEGER. It’s the number of columns of the matrix B. Constraint: N >= 0.
  • L — L is INTEGER. It’s the number of rows of the lower trapezoidal part of B. Constraint: MIN(M,N) >= L >= 0. See Further Details.
  • MB — MB is INTEGER. The block size to be used in the blocked QR. Constraint: M >= MB >= 1.
  • A — A is DOUBLE PRECISION 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 — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N).
  • 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.
  • LDB — LDB is INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,M).
  • T — T is DOUBLE PRECISION array, dimension (LDT,N). The lower triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details.
  • LDT — LDT is INTEGER. The leading dimension of the array T. Constraint: LDT >= MB.
  • WORK — WORK is DOUBLE PRECISION array, dimension (MB*M).
  • 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 input matrix C is a M-by-(M+N) matrix 💫

             C = [ A ] [ B ]

where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on 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, a 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 dtplqt.f.

🧚 Author 🧚

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💅 That’s the tea, bestie: LAPACK Version 3.12.0, from /home/abui...IN/dtplqt.f(3). Periodt. 🫶✨
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