mirror of https://github.com/k3s-io/k3s
46 lines
1.5 KiB
Go
46 lines
1.5 KiB
Go
// Copyright ©2016 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"
|
||
|
||
// Dgeql2 computes the QL factorization of the m×n matrix A. That is, Dgeql2
|
||
// computes Q and L such that
|
||
// A = Q * L
|
||
// where Q is an m×m orthonormal matrix and L is a lower trapezoidal matrix.
|
||
//
|
||
// Q is represented as a product of elementary reflectors,
|
||
// Q = H_{k-1} * ... * H_1 * H_0
|
||
// where k = min(m,n) and each H_i has the form
|
||
// H_i = I - tau[i] * v_i * v_i^T
|
||
// Vector v_i has v[m-k+i+1:m] = 0, v[m-k+i] = 1, and v[:m-k+i+1] is stored on
|
||
// exit in A[0:m-k+i-1, n-k+i].
|
||
//
|
||
// tau must have length at least min(m,n), and Dgeql2 will panic otherwise.
|
||
//
|
||
// work is temporary memory storage and must have length at least n.
|
||
//
|
||
// Dgeql2 is an internal routine. It is exported for testing purposes.
|
||
func (impl Implementation) Dgeql2(m, n int, a []float64, lda int, tau, work []float64) {
|
||
checkMatrix(m, n, a, lda)
|
||
if len(tau) < min(m, n) {
|
||
panic(badTau)
|
||
}
|
||
if len(work) < n {
|
||
panic(badWork)
|
||
}
|
||
k := min(m, n)
|
||
var aii float64
|
||
for i := k - 1; i >= 0; i-- {
|
||
// Generate elementary reflector H_i to annihilate A[0:m-k+i-1, n-k+i].
|
||
aii, tau[i] = impl.Dlarfg(m-k+i+1, a[(m-k+i)*lda+n-k+i], a[n-k+i:], lda)
|
||
|
||
// Apply H_i to A[0:m-k+i, 0:n-k+i-1] from the left.
|
||
a[(m-k+i)*lda+n-k+i] = 1
|
||
impl.Dlarf(blas.Left, m-k+i+1, n-k+i, a[n-k+i:], lda, tau[i], a, lda, work)
|
||
a[(m-k+i)*lda+n-k+i] = aii
|
||
}
|
||
}
|