github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/native/dlasq3.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 native
     6  
     7  import "math"
     8  
     9  // Dlasq3 checks for deflation, computes a shift (tau) and calls dqds.
    10  // In case of failure it changes shifts, and tries again until output
    11  // is positive.
    12  //
    13  // Dlasq3 is an internal routine. It is exported for testing purposes.
    14  func (impl Implementation) Dlasq3(i0, n0 int, z []float64, pp int, dmin, sigma, desig, qmax float64, nFail, iter, nDiv int, ttype int, dmin1, dmin2, dn, dn1, dn2, g, tau float64) (
    15  	i0Out, n0Out, ppOut int, dminOut, sigmaOut, desigOut, qmaxOut float64, nFailOut, iterOut, nDivOut, ttypeOut int, dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut float64) {
    16  	const cbias = 1.5
    17  
    18  	n0in := n0
    19  	eps := dlamchP
    20  	tol := eps * 100
    21  	tol2 := tol * tol
    22  	var nn int
    23  	var t float64
    24  	for {
    25  		if n0 < i0 {
    26  			return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
    27  		}
    28  		if n0 == i0 {
    29  			z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
    30  			n0--
    31  			continue
    32  		}
    33  		nn = 4*(n0+1) + pp - 1
    34  		if n0 != i0+1 {
    35  			// Check whether e[n0-1] is negligible, 1 eigenvalue.
    36  			if z[nn-5] > tol2*(sigma+z[nn-3]) && z[nn-2*pp-4] > tol2*z[nn-7] {
    37  				// Check whether e[n0-2] is negligible, 2 eigenvalues.
    38  				if z[nn-9] > tol2*sigma && z[nn-2*pp-8] > tol2*z[nn-11] {
    39  					break
    40  				}
    41  			} else {
    42  				z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
    43  				n0--
    44  				continue
    45  			}
    46  		}
    47  		if z[nn-3] > z[nn-7] {
    48  			z[nn-3], z[nn-7] = z[nn-7], z[nn-3]
    49  		}
    50  		t = 0.5 * (z[nn-7] - z[nn-3] + z[nn-5])
    51  		if z[nn-5] > z[nn-3]*tol2 && t != 0 {
    52  			s := z[nn-3] * (z[nn-5] / t)
    53  			if s <= t {
    54  				s = z[nn-3] * (z[nn-5] / (t * (1 + math.Sqrt(1+s/t))))
    55  			} else {
    56  				s = z[nn-3] * (z[nn-5] / (t + math.Sqrt(t)*math.Sqrt(t+s)))
    57  			}
    58  			t = z[nn-7] + (s + z[nn-5])
    59  			z[nn-3] *= z[nn-7] / t
    60  			z[nn-7] = t
    61  		}
    62  		z[4*(n0+1)-8] = z[nn-7] + sigma
    63  		z[4*(n0+1)-4] = z[nn-3] + sigma
    64  		n0 -= 2
    65  	}
    66  	if pp == 2 {
    67  		pp = 0
    68  	}
    69  
    70  	// Reverse the qd-array, if warranted.
    71  	if dmin <= 0 || n0 < n0in {
    72  		if cbias*z[4*(i0+1)+pp-4] < z[4*(n0+1)+pp-4] {
    73  			ipn4Out := 4 * (i0 + n0 + 2)
    74  			for j4loop := 4 * (i0 + 1); j4loop <= 2*((i0+1)+(n0+1)-1); j4loop += 4 {
    75  				ipn4 := ipn4Out - 1
    76  				j4 := j4loop - 1
    77  
    78  				z[j4-3], z[ipn4-j4-4] = z[ipn4-j4-4], z[j4-3]
    79  				z[j4-2], z[ipn4-j4-3] = z[ipn4-j4-3], z[j4-2]
    80  				z[j4-1], z[ipn4-j4-6] = z[ipn4-j4-6], z[j4-1]
    81  				z[j4], z[ipn4-j4-5] = z[ipn4-j4-5], z[j4]
    82  			}
    83  			if n0-i0 <= 4 {
    84  				z[4*(n0+1)+pp-2] = z[4*(i0+1)+pp-2]
    85  				z[4*(n0+1)-pp-1] = z[4*(i0+1)-pp-1]
    86  			}
    87  			dmin2 = math.Min(dmin2, z[4*(i0+1)-pp-2])
    88  			z[4*(n0+1)+pp-2] = math.Min(math.Min(z[4*(n0+1)+pp-2], z[4*(i0+1)+pp-2]), z[4*(i0+1)+pp+2])
    89  			z[4*(n0+1)-pp-1] = math.Min(math.Min(z[4*(n0+1)-pp-1], z[4*(i0+1)-pp-1]), z[4*(i0+1)-pp+3])
    90  			qmax = math.Max(math.Max(qmax, z[4*(i0+1)+pp-4]), z[4*(i0+1)+pp])
    91  			dmin = math.Copysign(0, -1) // Fortran code has -zero, but -0 in go is 0
    92  		}
    93  	}
    94  
    95  	// Choose a shift.
    96  	tau, ttype, g = impl.Dlasq4(i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
    97  
    98  	// Call dqds until dmin > 0.
    99  loop:
   100  	for {
   101  		i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq5(i0, n0, z, pp, tau, sigma)
   102  
   103  		nDiv += n0 - i0 + 2
   104  		iter++
   105  		switch {
   106  		case dmin >= 0 && dmin1 >= 0:
   107  			// Success.
   108  			goto done
   109  
   110  		case dmin < 0 && dmin1 > 0 && z[4*n0-pp-1] < tol*(sigma+dn1) && math.Abs(dn) < tol*sigma:
   111  			// Convergence hidden by negative dn.
   112  			z[4*n0-pp+1] = 0
   113  			dmin = 0
   114  			goto done
   115  
   116  		case dmin < 0:
   117  			// Tau too big. Select new Tau and try again.
   118  			nFail++
   119  			if ttype < -22 {
   120  				// Failed twice. Play it safe.
   121  				tau = 0
   122  			} else if dmin1 > 0 {
   123  				// Late failure. Gives excellent shift.
   124  				tau = (tau + dmin) * (1 - 2*eps)
   125  				ttype -= 11
   126  			} else {
   127  				// Early failure. Divide by 4.
   128  				tau = tau / 4
   129  				ttype -= 12
   130  			}
   131  
   132  		case math.IsNaN(dmin):
   133  			if tau == 0 {
   134  				break loop
   135  			}
   136  			tau = 0
   137  
   138  		default:
   139  			// Possible underflow. Play it safe.
   140  			break loop
   141  		}
   142  	}
   143  
   144  	// Risk of underflow.
   145  	dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq6(i0, n0, z, pp)
   146  	nDiv += n0 - i0 + 2
   147  	iter++
   148  	tau = 0
   149  
   150  done:
   151  	if tau < sigma {
   152  		desig += tau
   153  		t = sigma + desig
   154  		desig -= t - sigma
   155  	} else {
   156  		t = sigma + tau
   157  		desig += sigma - (t - tau)
   158  	}
   159  	sigma = t
   160  	return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
   161  }