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37 lines
1.1 KiB
Go
37 lines
1.1 KiB
Go
// Copyright ©2017 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import "gonum.org/v1/gonum/blas/blas64"
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// Dlapll returns the smallest singular value of the n×2 matrix A = [ x y ].
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// The function first computes the QR factorization of A = Q*R, and then computes
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// the SVD of the 2-by-2 upper triangular matrix r.
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//
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// The contents of x and y are overwritten during the call.
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//
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// Dlapll is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dlapll(n int, x []float64, incX int, y []float64, incY int) float64 {
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checkVector(n, x, incX)
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checkVector(n, y, incY)
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if n <= 1 {
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return 0
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}
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// Compute the QR factorization of the N-by-2 matrix [ X Y ].
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a00, tau := impl.Dlarfg(n, x[0], x[incX:], incX)
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x[0] = 1
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bi := blas64.Implementation()
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c := -tau * bi.Ddot(n, x, incX, y, incY)
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bi.Daxpy(n, c, x, incX, y, incY)
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a11, _ := impl.Dlarfg(n-1, y[incY], y[2*incY:], incY)
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// Compute the SVD of 2-by-2 upper triangular matrix.
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ssmin, _ := impl.Dlas2(a00, y[0], a11)
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return ssmin
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}
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