github.com/gopherd/gonum@v0.0.4/lapack/gonum/dlasq1.go (about)

     1  // Copyright ©2015 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 gonum
     6  
     7  import (
     8  	"math"
     9  
    10  	"github.com/gopherd/gonum/blas/blas64"
    11  	"github.com/gopherd/gonum/lapack"
    12  )
    13  
    14  // Dlasq1 computes the singular values of an n×n bidiagonal matrix with diagonal
    15  // d and off-diagonal e. On exit, d contains the singular values in decreasing
    16  // order, and e is overwritten. d must have length at least n, e must have
    17  // length at least n-1, and the input work must have length at least 4*n. Dlasq1
    18  // will panic if these conditions are not met.
    19  //
    20  // Dlasq1 is an internal routine. It is exported for testing purposes.
    21  func (impl Implementation) Dlasq1(n int, d, e, work []float64) (info int) {
    22  	if n < 0 {
    23  		panic(nLT0)
    24  	}
    25  
    26  	if n == 0 {
    27  		return info
    28  	}
    29  
    30  	switch {
    31  	case len(d) < n:
    32  		panic(shortD)
    33  	case len(e) < n-1:
    34  		panic(shortE)
    35  	case len(work) < 4*n:
    36  		panic(shortWork)
    37  	}
    38  
    39  	if n == 1 {
    40  		d[0] = math.Abs(d[0])
    41  		return info
    42  	}
    43  
    44  	if n == 2 {
    45  		d[1], d[0] = impl.Dlas2(d[0], e[0], d[1])
    46  		return info
    47  	}
    48  
    49  	// Estimate the largest singular value.
    50  	var sigmx float64
    51  	for i := 0; i < n-1; i++ {
    52  		d[i] = math.Abs(d[i])
    53  		sigmx = math.Max(sigmx, math.Abs(e[i]))
    54  	}
    55  	d[n-1] = math.Abs(d[n-1])
    56  	// Early return if sigmx is zero (matrix is already diagonal).
    57  	if sigmx == 0 {
    58  		impl.Dlasrt(lapack.SortDecreasing, n, d)
    59  		return info
    60  	}
    61  
    62  	for i := 0; i < n; i++ {
    63  		sigmx = math.Max(sigmx, d[i])
    64  	}
    65  
    66  	// Copy D and E into WORK (in the Z format) and scale (squaring the
    67  	// input data makes scaling by a power of the radix pointless).
    68  
    69  	eps := dlamchP
    70  	safmin := dlamchS
    71  	scale := math.Sqrt(eps / safmin)
    72  	bi := blas64.Implementation()
    73  	bi.Dcopy(n, d, 1, work, 2)
    74  	bi.Dcopy(n-1, e, 1, work[1:], 2)
    75  	impl.Dlascl(lapack.General, 0, 0, sigmx, scale, 2*n-1, 1, work, 1)
    76  
    77  	// Compute the q's and e's.
    78  	for i := 0; i < 2*n-1; i++ {
    79  		work[i] *= work[i]
    80  	}
    81  	work[2*n-1] = 0
    82  
    83  	info = impl.Dlasq2(n, work)
    84  	if info == 0 {
    85  		for i := 0; i < n; i++ {
    86  			d[i] = math.Sqrt(work[i])
    87  		}
    88  		impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
    89  	} else if info == 2 {
    90  		// Maximum number of iterations exceeded. Move data from work
    91  		// into D and E so the calling subroutine can try to finish.
    92  		for i := 0; i < n; i++ {
    93  			d[i] = math.Sqrt(work[2*i])
    94  			e[i] = math.Sqrt(work[2*i+1])
    95  		}
    96  		impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
    97  		impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, e, 1)
    98  	}
    99  	return info
   100  }