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 // 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 { switch { case n < 0: panic(nLT0) case incX <= 0: panic(badIncX) case incY <= 0: panic(badIncY) } // Quick return if possible. if n == 0 { return 0 } switch { case len(x) < 1+(n-1)*incX: panic(shortX) case len(y) < 1+(n-1)*incY: panic(shortY) } // Quick return if possible. 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 }