DTPQRT(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 NAME 🌸

okay so bestie, this page is literally just the file path, no cap:

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

like, that's the whole NAME section. iconic of it honestly 💅

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine DTPQRT (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info) — DTPQRT 🫶

💖 Function/Subroutine Documentation 💖

subroutine DTPQRT (integer m, integer n, integer l, integer nb, 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)

DTPQRT ✨ (yes the name again, she said it twice, main character energy)

🎯 Purpose

DTPQRT computes a blocked QR 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.

so basically: C is stitched together from A (triangular) + B (pentagonal), and DTPQRT does the blocked QR thing on it using the compact WY representation for Q. slay 💅

🧸 Parameters

M

M is INTEGER The number of rows of the matrix B. M >= 0.

N

N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.

L

L is INTEGER The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.

like, MIN(M,N) >= L >= 0 — remember that, there's a whole diagram down in Further Details 👀

NB

NB is INTEGER The block size to be used in the blocked QR. N >= NB >= 1.

the block size, bestie. N >= NB >= 1, no zero, no negative, we don't do that here 🙈

A

A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the upper triangular N-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the upper triangular matrix R.

she goes in as A, she comes out holding R — glow-up fr fr ⭐

LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

B

B is DOUBLE PRECISION array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B. The first M-L rows are rectangular, and the last L rows are upper trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details.

on entry: pentagonal B. on exit: V. same shape, new vibe 💫

LDB

LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).

T

T is DOUBLE PRECISION array, dimension (LDT,N) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details.

the block reflectors, all cute and compact 🎀

LDT

LDT is INTEGER The leading dimension of the array T. LDT >= NB.

WORK

WORK is DOUBLE PRECISION array, dimension (NB*N)

scratch space, dimension (NB*N), she works hard so you don't have to 💜

INFO

INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
  • = 0 — successful exit, we ate 🔥
  • < 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 (N+M)-by-N matrix text C = [ A ] [ B ]
where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N upper trapezoidal matrix B2:
            B = [ B1 ]  <- (M-L)-by-N rectangular
                [ B2 ]  <-     L-by-N upper trapezoidal.
The upper trapezoidal matrix B2 consists of the first L rows of a N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular M-by-N; if M=L=N, B is upper triangular.

okay so the little edge cases: L=0 makes B a rectangular M-by-N girly, and M=L=N makes B upper triangular. love that for her 🫶

The matrix W stores the elementary reflectors H(i) in the i-th column below the diagonal (of A) in the (N+M)-by-N input matrix C
            C = [ A ]  <- upper triangular N-by-N
                [ B ]  <- M-by-N pentagonal
so that W can be represented as
            W = [ 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 ] <- (M-L)-by-N rectangular
                [ V2 ] <-     L-by-N upper trapezoidal.
The columns of V represent the vectors which define the H(i)'s.

literally everything you need for W is chilling in B on exit, and we call it V up there. same shape as B. iykyk 💅

The number of blocks is B = ceiling(N/NB), where each block is of order NB except for the last block, which is of order IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-N matrix T as
            T = [T1 T2 ... TB].

block count is B = ceiling(N/NB), every block is order NB except the last one which is IB = N - (B-1)*NB. then you get T1, T2, ..., TB — NB-by-NB each (and IB-by-IB for that last one) — all packed into the NB-by-N matrix T as T = [T1 T2 ... TB]. ✨

Definition at line 187 of file dtpqrt.f. 📍

Author

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LAPACK — Version 3.12.0 🌈 and the date slot on this page is literally just the file path /home/abui...RC/dtpqrt.f(3), so that's your sign-off 🎀 bye bestie, go factor something 💖✨

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