github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/native/dlapll.go (about)

     1  // Copyright ©2017 The gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package native
     6  
     7  import "github.com/gonum/blas/blas64"
     8  
     9  // Dlapll returns the smallest singular value of the n×2 matrix A = [ x y ].
    10  // The function first computes the QR factorization of A = Q*R, and then computes
    11  // the SVD of the 2-by-2 upper triangular matrix r.
    12  //
    13  // The contents of x and y are overwritten during the call.
    14  //
    15  // Dlapll is an internal routine. It is exported for testing purposes.
    16  func (impl Implementation) Dlapll(n int, x []float64, incX int, y []float64, incY int) float64 {
    17  	checkVector(n, x, incX)
    18  	checkVector(n, y, incY)
    19  
    20  	if n <= 1 {
    21  		return 0
    22  	}
    23  
    24  	// Compute the QR factorization of the N-by-2 matrix [ X Y ].
    25  	a00, tau := impl.Dlarfg(n, x[0], x[incX:], incX)
    26  	x[0] = 1
    27  
    28  	bi := blas64.Implementation()
    29  	c := -tau * bi.Ddot(n, x, incX, y, incY)
    30  	bi.Daxpy(n, c, x, incX, y, incY)
    31  	a11, _ := impl.Dlarfg(n-1, y[incY], y[2*incY:], incY)
    32  
    33  	// Compute the SVD of 2-by-2 upper triangular matrix.
    34  	ssmin, _ := impl.Dlas2(a00, y[0], a11)
    35  	return ssmin
    36  }