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<div class="title">TestIterTrack.cpp</div> </div>
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<a href="_test_iter_track_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* This file is part of Cloudy and is copyright (C)1978-2013 by Gary J. Ferland and</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * others. For conditions of distribution and use see copyright notice in license.txt */</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="preprocessor">#include <UnitTest++.h></span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="preprocessor">#include "<a class="code" href="cddefines_8h.html">cddefines.h</a>"</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="preprocessor">#include "<a class="code" href="iter__track_8h.html">iter_track.h</a>"</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> </div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="keyword">namespace </span>{</div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  <span class="comment">// test a function that would have gone into a limit cycle</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  TEST(IterTrackBasicFloat)</div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  {</div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  <a class="code" href="classiter__track__basic.html">iter_track_basic<sys_float></a> track;</div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>  <a class="code" href="cddefines_8h.html#a007d32812a920211b9fb1570666ee235">sys_float</a> x = 1.f;</div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  <a class="code" href="cddefines_8h.html#a007d32812a920211b9fb1570666ee235">sys_float</a> xnew = 2.f;</div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>  <span class="keywordflow">while</span>( abs(x-xnew) > 2.f*FLT_EPSILON*abs(x) )</div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  {</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  x = xnew;</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  <span class="comment">// derivative at root is -1</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  xnew = track.<a class="code" href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">next_val</a>( x, 2.f/x );</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  }</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( xnew, (<a class="code" href="cddefines_8h.html#a007d32812a920211b9fb1570666ee235">sys_float</a>)sqrt(2.) ) );</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="comment">// now clear the tracker and try again</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  track.<a class="code" href="classiter__track__basic.html#a2e161fba018e0ccfbd22ad9282a500a7">clear</a>();</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  x = 1.f;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  xnew = 2.f;</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keywordflow">while</span>( abs(x-xnew) > 2.f*FLT_EPSILON*abs(x) )</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  x = xnew;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="comment">// derivative at root is -1</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  xnew = track.<a class="code" href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">next_val</a>( x, 3.f/x );</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  }</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( xnew, (<a class="code" href="cddefines_8h.html#a007d32812a920211b9fb1570666ee235">sys_float</a>)sqrt(3.) ) );</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  }</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="comment">// now test the same for doubles</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  TEST(IterTrackBasicDouble)</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <a class="code" href="classiter__track__basic.html">iter_track_basic<double></a> track;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordtype">double</span> x = 1.;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordtype">double</span> xnew = 2.;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">while</span>( abs(x-xnew) > 2.*DBL_EPSILON*abs(x) )</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  x = xnew;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="comment">// derivative at root is -1</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  xnew = track.<a class="code" href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">next_val</a>( x, 2./x );</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( xnew, sqrt(2.) ) );</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  }</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// test a function that would have diverged</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  TEST(IterTrackBasicUnstable)</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <a class="code" href="classiter__track__basic.html">iter_track_basic<double></a> track;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordtype">double</span> x = 1.;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">double</span> xnew = 2.;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">while</span>( abs(x-xnew) > 2.*DBL_EPSILON*abs(x) )</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  x = xnew;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// derivative at root is -5</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  xnew = track.<a class="code" href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">next_val</a>( x, 1./x - 2.*x );</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// possible solutions are +/-sqrt(1/3), either one may be found</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( abs(xnew), 1./sqrt(3.) ) );</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  }</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// test a function that would have converged anyway</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  TEST(IterTrackBasicStableNeg)</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <a class="code" href="classiter__track__basic.html">iter_track_basic<double></a> track;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordtype">double</span> x = 1.;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordtype">double</span> xnew = 2.;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// this would have diverged without iter_tracking</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordflow">while</span>( abs(x-xnew) > 2.*DBL_EPSILON*abs(x) )</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  x = xnew;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// derivative at root is -1/3</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  xnew = track.<a class="code" href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">next_val</a>( x, 1./x + x/3. );</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( xnew, sqrt(1.5) ) );</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  TEST(IterTrackBasicStablePos)</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  {</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <a class="code" href="classiter__track__basic.html">iter_track_basic<double></a> track;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">double</span> x = 1.;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">double</span> xnew = 2.;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">// this would have diverged without iter_tracking</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">while</span>( abs(x-xnew) > 2.*DBL_EPSILON*abs(x) )</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  {</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  x = xnew;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// derivative at root is 1/3</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  xnew = track.<a class="code" href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">next_val</a>( x, 1./x + 2.*x/3. );</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  }</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( xnew, sqrt(3.) ) );</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">double</span> testfun(<span class="keywordtype">double</span> x)</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">return</span> sin(x)-0.5;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  TEST(IterTrack)</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  {</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordtype">double</span> <a class="code" href="atmdat__3body_8cpp.html#a984eb8f4ba5548d469ca2bdb3b3a9efc">x1</a>, fx1, <a class="code" href="atmdat__3body_8cpp.html#a4e6fc9d0607252ddfb72801404159738">x2</a>, fx2, x3, fx3;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <a class="code" href="classiter__track.html">iter_track</a> track;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  x1 = 0.;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  fx1 = testfun(x1);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  x3 = 1.5;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  fx3 = testfun(x3);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordtype">double</span> tol = 1.e-12;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  track.<a class="code" href="classiter__track.html#ad57705543eafcb5cfcccc94b72113354">set_tol</a>(tol);</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  CHECK_EQUAL( 0, track.<a class="code" href="classiter__track.html#a76e2ef3c1d024d9be97cb00392c78a39">init_bracket</a>(x1,fx1,x3,fx3) );</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( track.<a class="code" href="classiter__track.html#a12465bdea19b67dfa0d547a6c65feafb">bracket_width</a>(), abs(x3-x1) ) );</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  CHECK( !track.<a class="code" href="classiter__track.html#a76baca6c8fdbb1d8146692b638c9dbcb">lgConverged</a>() );</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  x2 = 0.5*(x1+x3);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  fx2 = testfun(x2);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  track.<a class="code" href="classiter__track.html#a1c097b55c70c05003e236ce92da28475">add</a>( x2, fx2 );</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordtype">double</span> xnew = track.<a class="code" href="classiter__track.html#a9fe6cf52181e46286474f92d721b6974">next_val</a>(0.01);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  CHECK( <a class="code" href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a>( abs(xnew/x2-1.), 0.01, 1.e-12 ) );</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> navg = 5;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  vector<double> xvals( navg ); <span class="comment">// keep track of the last navg x-values</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">for</span>( <span class="keywordtype">int</span> i=0; i < 100 && !track.<a class="code" href="classiter__track.html#a76baca6c8fdbb1d8146692b638c9dbcb">lgConverged</a>(); ++i )</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  {</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  x2 = track.<a class="code" href="classiter__track.html#a9fe6cf52181e46286474f92d721b6974">next_val</a>();</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  fx2 = testfun(x2);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  track.<a class="code" href="classiter__track.html#a1c097b55c70c05003e236ce92da28475">add</a>( x2, fx2 );</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// use xvals as circular buffer</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  xvals[i%navg] = <a class="code" href="atmdat__3body_8cpp.html#a4e6fc9d0607252ddfb72801404159738">x2</a>;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  }</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  CHECK( track.<a class="code" href="classiter__track.html#a76baca6c8fdbb1d8146692b638c9dbcb">lgConverged</a>() );</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">double</span> exact_root = asin(0.5);</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  CHECK( <a class="code" href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a>( track.<a class="code" href="classiter__track.html#a01633647a86d90043ee4086563e0b9cd">root</a>(), exact_root, tol ) );</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordtype">double</span> sigma;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordtype">double</span> val = track.<a class="code" href="classiter__track.html#a964220611f0672492eea9f291e459942">deriv</a>( navg, sigma );</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordtype">double</span> delta_lo = *min_element( xvals.begin(), xvals.end() ) - exact_root;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordtype">double</span> delta_hi = *max_element( xvals.begin(), xvals.end() ) - exact_root;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  CHECK( delta_lo < 0. );</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  CHECK( delta_hi > 0. );</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// the exact derivative at the root is sqrt(3)/2 = 0.8660254...</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// the exact 2nd derivative at the root is -1/2</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">double</span> err_lo = -0.5*delta_lo;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordtype">double</span> err_hi = -0.5*delta_hi;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  CHECK( <a class="code" href="cddefines_8h.html#aaccfed6289da64cc231821e5a58e02dd">fp_bound</a>( sqrt(3.)/2.+err_hi, val, sqrt(3.)/2.+err_lo ) );</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// the tangent at the exact root is given by asin(0.5) + sqrt(3)/2*(x-x0)</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">// if we subtract that from the Taylor expansion of testfun we get:</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="comment">// residual = -1/4*(x-x0)^2 + O((x-x0)^3), hence sigma should be less</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// than the maximum absolute value of -1/4*(x-x0)^2 (the actual fit</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// should run slightly closer to the maximum deviant value than the tangent).</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  CHECK( sigma < <a class="code" href="cddefines_8h.html#abeecded55c36d9bbddf7109747eacf8e">max</a>( <a class="code" href="cddefines_8h.html#a34a972cf4be2379a5ee363b82d623b3a">pow2</a>(err_lo), <a class="code" href="cddefines_8h.html#a34a972cf4be2379a5ee363b82d623b3a">pow2</a>(err_hi) ) );</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// ask for more points than are available to see if that is handled correctly</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  val = track.<a class="code" href="classiter__track.html#a964220611f0672492eea9f291e459942">deriv</a>( 200 );</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordtype">double</span> val2 = track.<a class="code" href="classiter__track.html#a964220611f0672492eea9f291e459942">deriv</a>();</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( val, val2 ) );</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  val = track.<a class="code" href="classiter__track.html#a964220611f0672492eea9f291e459942">deriv</a>( 200, sigma );</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordtype">double</span> sigma2;</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  val = track.<a class="code" href="classiter__track.html#a964220611f0672492eea9f291e459942">deriv</a>( sigma2 );</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( sigma, sigma2 ) );</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// now do the same thing for the zero_fit() methods...</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  val = track.<a class="code" href="classiter__track.html#adcd60ada03588cf5d0cc30b22cdc5ae4">zero_fit</a>( navg, sigma );</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// the exact root is asin(0.5) = 0.52359877...</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  CHECK( <a class="code" href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a>( exact_root, val, 2.*sigma ) );</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  val = track.<a class="code" href="classiter__track.html#adcd60ada03588cf5d0cc30b22cdc5ae4">zero_fit</a>( 200 );</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  val2 = track.<a class="code" href="classiter__track.html#adcd60ada03588cf5d0cc30b22cdc5ae4">zero_fit</a>();</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( val, val2 ) );</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  val = track.<a class="code" href="classiter__track.html#adcd60ada03588cf5d0cc30b22cdc5ae4">zero_fit</a>( 200, sigma );</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  val = track.<a class="code" href="classiter__track.html#adcd60ada03588cf5d0cc30b22cdc5ae4">zero_fit</a>( sigma2 );</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  CHECK( <a class="code" href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a>( sigma, sigma2 ) );</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  }</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> </div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// this is the short version of the above...</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  TEST(AmsterdamMethod)</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordtype">double</span> <a class="code" href="atmdat__3body_8cpp.html#a984eb8f4ba5548d469ca2bdb3b3a9efc">x1</a>, fx1, <a class="code" href="atmdat__3body_8cpp.html#a4e6fc9d0607252ddfb72801404159738">x2</a>, fx2;</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  x1 = 0.;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  fx1 = testfun(x1);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  x2 = 1.5;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  fx2 = testfun(x2);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordtype">double</span> tol = 1.e-12;</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordtype">int</span> err = -1;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordtype">double</span> x = <a class="code" href="iter__track_8cpp.html#ad6a73cba3857b5828ef8f7762778b98e">Amsterdam_Method</a>( testfun, x1, fx1, x2, fx2, tol, 1000, err );</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  CHECK_EQUAL( 0, err );</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  CHECK( <a class="code" href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a>( x, asin(0.5), tol ) );</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  }</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="comment">// now test some unstable functions</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordtype">double</span> testfun2(<span class="keywordtype">double</span> x)</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">return</span> exp(x)-3.;</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="comment">// the derivative at the root is 3</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  TEST(AmsterdamMethod2)</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  {</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordtype">double</span> <a class="code" href="atmdat__3body_8cpp.html#a984eb8f4ba5548d469ca2bdb3b3a9efc">x1</a>, fx1, <a class="code" href="atmdat__3body_8cpp.html#a4e6fc9d0607252ddfb72801404159738">x2</a>, fx2;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  x1 = 0.;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  fx1 = testfun2(x1);</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  x2 = 3.;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  fx2 = testfun2(x2);</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordtype">double</span> tol = 1.e-12;</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordtype">int</span> err = -1;</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordtype">double</span> x = <a class="code" href="iter__track_8cpp.html#ad6a73cba3857b5828ef8f7762778b98e">Amsterdam_Method</a>( testfun2, x1, fx1, x2, fx2, tol, 1000, err );</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  CHECK_EQUAL( 0, err );</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  CHECK( <a class="code" href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a>( x, log(3.), tol ) );</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  }</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordtype">double</span> testfun3(<span class="keywordtype">double</span> x)</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  {</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">return</span> 1./x - 2.*x;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  }</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// the derivative at the root is -4</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  TEST(AmsterdamMethod3)</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  {</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordtype">double</span> <a class="code" href="atmdat__3body_8cpp.html#a984eb8f4ba5548d469ca2bdb3b3a9efc">x1</a>, fx1, <a class="code" href="atmdat__3body_8cpp.html#a4e6fc9d0607252ddfb72801404159738">x2</a>, fx2;</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  x1 = 0.1;</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  fx1 = testfun3(x1);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  x2 = 3.;</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  fx2 = testfun3(x2);</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordtype">double</span> tol = 1.e-12;</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordtype">int</span> err = -1;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordtype">double</span> x = <a class="code" href="iter__track_8cpp.html#ad6a73cba3857b5828ef8f7762778b98e">Amsterdam_Method</a>( testfun3, x1, fx1, x2, fx2, tol, 1000, err );</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  CHECK_EQUAL( 0, err );</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  CHECK( <a class="code" href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a>( x, sqrt(0.5), tol ) );</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> }</div>
<div class="ttc" id="atmdat__3body_8cpp_html_a4e6fc9d0607252ddfb72801404159738"><div class="ttname"><a href="atmdat__3body_8cpp.html#a4e6fc9d0607252ddfb72801404159738">x2</a></div><div class="ttdeci">static double x2[63]</div><div class="ttdef"><b>Definition:</b> <a href="atmdat__3body_8cpp_source.html#l00018">atmdat_3body.cpp:18</a></div></div>
<div class="ttc" id="classiter__track_html_a12465bdea19b67dfa0d547a6c65feafb"><div class="ttname"><a href="classiter__track.html#a12465bdea19b67dfa0d547a6c65feafb">iter_track::bracket_width</a></div><div class="ttdeci">double bracket_width() const </div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00085">iter_track.h:85</a></div></div>
<div class="ttc" id="atmdat__3body_8cpp_html_a984eb8f4ba5548d469ca2bdb3b3a9efc"><div class="ttname"><a href="atmdat__3body_8cpp.html#a984eb8f4ba5548d469ca2bdb3b3a9efc">x1</a></div><div class="ttdeci">static double x1[83]</div><div class="ttdef"><b>Definition:</b> <a href="atmdat__3body_8cpp_source.html#l00027">atmdat_3body.cpp:27</a></div></div>
<div class="ttc" id="classiter__track_html_a9fe6cf52181e46286474f92d721b6974"><div class="ttname"><a href="classiter__track.html#a9fe6cf52181e46286474f92d721b6974">iter_track::next_val</a></div><div class="ttdeci">double next_val()</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8cpp_source.html#l00018">iter_track.cpp:18</a></div></div>
<div class="ttc" id="classiter__track_html_a1c097b55c70c05003e236ce92da28475"><div class="ttname"><a href="classiter__track.html#a1c097b55c70c05003e236ce92da28475">iter_track::add</a></div><div class="ttdeci">void add(double x, double fx)</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00120">iter_track.h:120</a></div></div>
<div class="ttc" id="cddefines_8h_html_af82a96e48df6d99882899c45886541d8"><div class="ttname"><a href="cddefines_8h.html#af82a96e48df6d99882899c45886541d8">fp_equal_tol</a></div><div class="ttdeci">bool fp_equal_tol(sys_float x, sys_float y, sys_float tol)</div><div class="ttdef"><b>Definition:</b> <a href="cddefines_8h_source.html#l00858">cddefines.h:858</a></div></div>
<div class="ttc" id="iter__track_8cpp_html_ad6a73cba3857b5828ef8f7762778b98e"><div class="ttname"><a href="iter__track_8cpp.html#ad6a73cba3857b5828ef8f7762778b98e">Amsterdam_Method</a></div><div class="ttdeci">double Amsterdam_Method(double(*f)(double), double a, double fa, double c, double fc, double tol, int max_iter, int &err)</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8cpp_source.html#l00238">iter_track.cpp:238</a></div></div>
<div class="ttc" id="classiter__track__basic_html_a8ffc4d6573237e1fb99470f8a5d8e0b4"><div class="ttname"><a href="classiter__track__basic.html#a8ffc4d6573237e1fb99470f8a5d8e0b4">iter_track_basic::next_val</a></div><div class="ttdeci">T next_val(T current, T next_est)</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00241">iter_track.h:241</a></div></div>
<div class="ttc" id="classiter__track__basic_html"><div class="ttname"><a href="classiter__track__basic.html">iter_track_basic</a></div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00222">iter_track.h:222</a></div></div>
<div class="ttc" id="cddefines_8h_html_abf352ab93b9855e49d54873654b521e2"><div class="ttname"><a href="cddefines_8h.html#abf352ab93b9855e49d54873654b521e2">fp_equal</a></div><div class="ttdeci">bool fp_equal(sys_float x, sys_float y, int n=3)</div><div class="ttdef"><b>Definition:</b> <a href="cddefines_8h_source.html#l00816">cddefines.h:816</a></div></div>
<div class="ttc" id="classiter__track_html_a76e2ef3c1d024d9be97cb00392c78a39"><div class="ttname"><a href="classiter__track.html#a76e2ef3c1d024d9be97cb00392c78a39">iter_track::init_bracket</a></div><div class="ttdeci">int init_bracket(double x1, double fx1, double x2, double fx2)</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00104">iter_track.h:104</a></div></div>
<div class="ttc" id="classiter__track_html_a76baca6c8fdbb1d8146692b638c9dbcb"><div class="ttname"><a href="classiter__track.html#a76baca6c8fdbb1d8146692b638c9dbcb">iter_track::lgConverged</a></div><div class="ttdeci">bool lgConverged()</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00089">iter_track.h:89</a></div></div>
<div class="ttc" id="cddefines_8h_html_a007d32812a920211b9fb1570666ee235"><div class="ttname"><a href="cddefines_8h.html#a007d32812a920211b9fb1570666ee235">sys_float</a></div><div class="ttdeci">float sys_float</div><div class="ttdef"><b>Definition:</b> <a href="cddefines_8h_source.html#l00110">cddefines.h:110</a></div></div>
<div class="ttc" id="cddefines_8h_html_abeecded55c36d9bbddf7109747eacf8e"><div class="ttname"><a href="cddefines_8h.html#abeecded55c36d9bbddf7109747eacf8e">max</a></div><div class="ttdeci">long max(int a, long b)</div><div class="ttdef"><b>Definition:</b> <a href="cddefines_8h_source.html#l00779">cddefines.h:779</a></div></div>
<div class="ttc" id="cddefines_8h_html_aaccfed6289da64cc231821e5a58e02dd"><div class="ttname"><a href="cddefines_8h.html#aaccfed6289da64cc231821e5a58e02dd">fp_bound</a></div><div class="ttdeci">bool fp_bound(sys_float lo, sys_float x, sys_float hi, int n=3)</div><div class="ttdef"><b>Definition:</b> <a href="cddefines_8h_source.html#l00881">cddefines.h:881</a></div></div>
<div class="ttc" id="iter__track_8h_html"><div class="ttname"><a href="iter__track_8h.html">iter_track.h</a></div></div>
<div class="ttc" id="cddefines_8h_html"><div class="ttname"><a href="cddefines_8h.html">cddefines.h</a></div></div>
<div class="ttc" id="cddefines_8h_html_a34a972cf4be2379a5ee363b82d623b3a"><div class="ttname"><a href="cddefines_8h.html#a34a972cf4be2379a5ee363b82d623b3a">pow2</a></div><div class="ttdeci">T pow2(T a)</div><div class="ttdef"><b>Definition:</b> <a href="cddefines_8h_source.html#l00935">cddefines.h:935</a></div></div>
<div class="ttc" id="classiter__track_html_adcd60ada03588cf5d0cc30b22cdc5ae4"><div class="ttname"><a href="classiter__track.html#adcd60ada03588cf5d0cc30b22cdc5ae4">iter_track::zero_fit</a></div><div class="ttdeci">double zero_fit(int n, double &sigma) const </div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8cpp_source.html#l00164">iter_track.cpp:164</a></div></div>
<div class="ttc" id="classiter__track_html_a964220611f0672492eea9f291e459942"><div class="ttname"><a href="classiter__track.html#a964220611f0672492eea9f291e459942">iter_track::deriv</a></div><div class="ttdeci">double deriv(int n, double &sigma) const </div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8cpp_source.html#l00145">iter_track.cpp:145</a></div></div>
<div class="ttc" id="classiter__track_html"><div class="ttname"><a href="classiter__track.html">iter_track</a></div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00017">iter_track.h:17</a></div></div>
<div class="ttc" id="classiter__track__basic_html_a2e161fba018e0ccfbd22ad9282a500a7"><div class="ttname"><a href="classiter__track__basic.html#a2e161fba018e0ccfbd22ad9282a500a7">iter_track_basic::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00237">iter_track.h:237</a></div></div>
<div class="ttc" id="classiter__track_html_ad57705543eafcb5cfcccc94b72113354"><div class="ttname"><a href="classiter__track.html#ad57705543eafcb5cfcccc94b72113354">iter_track::set_tol</a></div><div class="ttdeci">void set_tol(double tol)</div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00081">iter_track.h:81</a></div></div>
<div class="ttc" id="classiter__track_html_a01633647a86d90043ee4086563e0b9cd"><div class="ttname"><a href="classiter__track.html#a01633647a86d90043ee4086563e0b9cd">iter_track::root</a></div><div class="ttdeci">double root() const </div><div class="ttdef"><b>Definition:</b> <a href="iter__track_8h_source.html#l00100">iter_track.h:100</a></div></div>
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