You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: dgelqf.go
    path of file: ./repos/hoverfly/vendor/gonum.org/v1/gonum/lapack/gonum
    
    the code of the file until where you have to start completion: // Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package gonum

import (
	"gonum.org/v1/gonum/blas"
	"gonum.org/v1/gonum/lapack"
)

// Dgelqf computes the LQ factorization of the m×n matrix A using a blocked
// algorithm. See the documentation for Dgelq2 for a description of the
// parameters at entry and exit.
//
// work is temporary storage, and lwork specifies the usable memory length.
// At minimum, lwork >= m, and this function will panic otherwise.
// Dgelqf is a blocked LQ factorization, but the block size is limited
// by the temporary space available. If lwork == -1, instead of performing Dgelqf,
// the optimal work length will be stored into work[0].
//
// tau must have length at least min(m
    
func (impl Implementation) Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
	switch {
	case m < 0:
		panic(mLT0)
	case n < 0:
		panic(nLT0)
	case lda < max(1, n):
		panic(badLdA)
	case lwork < max(1, m) && lwork != -1:
		panic(badLWork)
	case len(work) < max(1, lwork):
		panic(shortWork)
	}

	k := min(m, n)
	if k == 0 {
		work[0] = 1
		return
	}

	nb := impl.Ilaenv(1, "DGELQF", " ", m, n, -1, -1)
	if lwork == -1 {
		work[0] = float64(m * nb)
		return
	}

	if len(a) < (m-1)*lda+n {
		panic(shortA)
	}
	if len(tau) < k {
		panic(shortTau)
	}

	// Find the optimal blocking size based on the size of available memory
	// and optimal machine parameters.
	nbmin := 2
	var nx int
	iws := m
	if 1 < nb && nb < k {
		nx = max(0, impl.Ilaenv(3, "DGELQF", " ", m, n, -1, -1))
		if nx < k {
			iws = m * nb
			if lwork < iws {
				nb = lwork / m
				nbmin = max(2, impl.Ilaenv(2, "DGELQF", " ", m, n, -1, -1))
			}
		}
	}
	ldwork := nb
	// Computed blocked LQ factorization.
	var i int
	if nbmin <= nb && nb < k && nx < k {
		for i = 0; i < k-nx; i += nb {
			ib := min(k-i, nb)
			impl.Dgelq2(ib, n-i, a[i*lda+i:], lda, tau[i:], work)
			if i+ib < m {
				impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
					a[i*lda+i:], lda,
					tau[i:],
					work, ldwork)
				impl.Dlarfb(blas.Right, blas.NoTrans, lapack.Forward, lapack.RowWise,
					m-i-ib, n-i, ib,
					a[i*lda+i:], lda,
					work, ldwork,
					a[(i+ib)*lda+i:], lda,
					work[ib*ldwork:], ldwork)
			}
		}
	}
	// Perform unblocked LQ factorization on the remainder.
	if i < k {
		impl.Dgelq2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
	}
	work[0] = float64(iws)
}