| // Copyright ©2017 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/blas64" |
| |
| // Dlapll returns the smallest singular value of the n×2 matrix A = [ x y ]. |
| // The function first computes the QR factorization of A = Q*R, and then computes |
| // the SVD of the 2-by-2 upper triangular matrix r. |
| // |
| // The contents of x and y are overwritten during the call. |
| // |
| // Dlapll is an internal routine. It is exported for testing purposes. |
| func (impl Implementation) Dlapll(n int, x []float64, incX int, y []float64, incY int) float64 { |
| checkVector(n, x, incX) |
| checkVector(n, y, incY) |
| |
| if n <= 1 { |
| return 0 |
| } |
| |
| // Compute the QR factorization of the N-by-2 matrix [ X Y ]. |
| a00, tau := impl.Dlarfg(n, x[0], x[incX:], incX) |
| x[0] = 1 |
| |
| bi := blas64.Implementation() |
| c := -tau * bi.Ddot(n, x, incX, y, incY) |
| bi.Daxpy(n, c, x, incX, y, incY) |
| a11, _ := impl.Dlarfg(n-1, y[incY], y[2*incY:], incY) |
| |
| // Compute the SVD of 2-by-2 upper triangular matrix. |
| ssmin, _ := impl.Dlas2(a00, y[0], a11) |
| return ssmin |
| } |