mirror of
https://github.com/gonum/gonum.git
synced 2025-10-05 23:26:52 +08:00
50 lines
1.6 KiB
Go
50 lines
1.6 KiB
Go
// 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.
|
||
//
|
||
// In an LQ factorization, L is a lower triangular m×n matrix, and Q is an n×n
|
||
// orthonormal matrix.
|
||
//
|
||
// a is modified to contain the information to construct L and Q.
|
||
// 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-1} * ... * H_1 * H_0.
|
||
//
|
||
// work is temporary storage of length at least m and this function will panic otherwise.
|
||
//
|
||
// Dgelq2 is an internal routine. It is exported for testing purposes.
|
||
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
|
||
}
|
||
}
|
||
}
|