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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
}
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