/
dgelq2.go
44 lines (41 loc) · 1.39 KB
/
dgelq2.go
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// 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 native
import "github.com/gonum/blas"
// Dgelq2 computes the LQ factorization of the m×n matrix a.
//
// During Dgelq2, a is modified to contain the information to construct Q and L.
// The lower triangle of a contains the matrix L. The upper triangular elements
// (not including the diagonal) contain the elementary reflectors. Tau is modified
// to contain the reflector scales. Tau must have length of at least k = min(m,n)
// and this function will panic otherwise.
//
// See Dgeqr2 for a description of the elementary reflectors and orthonormal
// matrix Q. Q is constructed as a product of these elementary reflectors,
// Q = H_k ... H_2*H_1.
//
// Work is temporary storage of length at least m and this function will panic otherwise.
func (impl Implementation) Dgelq2(m, n int, a []float64, lda int, tau, work []float64) {
checkMatrix(m, n, a, lda)
k := min(m, n)
if len(tau) < k {
panic(badTau)
}
if len(work) < m {
panic(badWork)
}
for i := 0; i < k; i++ {
a[i*lda+i], tau[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
if i < m-1 {
aii := a[i*lda+i]
a[i*lda+i] = 1
impl.Dlarf(blas.Right, m-i-1, n-i,
a[i*lda+i:], 1,
tau[i],
a[(i+1)*lda+i:], lda,
work)
a[i*lda+i] = aii
}
}
}