SRC/dgeqrt.f(3)

🌸 NAME 🌸

SRC/dgeqrt.f — that’s the name, bestie, and honestly she’s giving mysterious minimal icon energy 💅

Welcome to SRC/dgeqrt.f(3), living in the Library Functions Manual, where the main character is the DGEQRT subroutine ✨

🎀 SYNOPSIS 🎀

🦋 Functions/Subroutines 🦋

• subroutine dgeqrt (m, n, nb, a, lda, t, ldt, work, info) — DGEQRT

💖 Function/Subroutine Documentation 💖

subroutine dgeqrt (integer m, integer n, integer nb, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( ldt, *
    ) t, integer ldt, double precision, dimension( * ) work, integer info)

DGEQRT

✨ Purpose ✨

Okay so DGEQRT computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q. Periodt. 🔥

🌈 Parameters 🌈

🍓 M

M is INTEGER, and it’s literally the number of rows of matrix A. Constraint: M >= 0.

🍓 N

N is INTEGER, bestie — the number of columns of matrix A. Constraint: N >= 0.

🍓 NB

NB is INTEGER: the block size used in the blocked QR. Constraint: MIN(M,N) >= NB >= 1.

🍓 A

A is a DOUBLE PRECISION array, dimension (LDA,N).

On entry, it’s the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

🍓 LDA

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

🍓 T

T is a DOUBLE PRECISION 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 👀

🍓 LDT

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

🍓 WORK

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

🍓 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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is

             V = (  1       )
                 ( v1  1    )
                 ( v1 v2  1 )
                 ( v1 v2 v3 )
                 ( v1 v2 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/NB), where each block is of order NB except for the last block, which is of order IB = K - (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-K matrix T as

             T = (T1 T2 ... TB).

Definition at line 140 of file dgeqrt.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole page — peace out from LAPACK, Version 3.12.0, on SRC/dgeqrt.f(3) 🦋💅✨