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| 25 | <div id="navbar_title"> |
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| 26 | <h1>SAXO Documentation</h1> |
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| 32 | <table cellspacing="0"> |
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| 33 | <tr> |
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| 34 | |
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| 35 | <td><a href="./../overview.html" title="Overview of library">Overview</a></td> |
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| 36 | |
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| 37 | |
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| 38 | |
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| 39 | <td >Directory</td> |
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| 43 | <td><a href="./../idldoc-categories.html" title="Browse library by category">Categories</a></td> |
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| 44 | |
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| 47 | <td><a href="./../idldoc-index.html" title="Index of files, routines, and parameters">Index</a></td> |
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| 48 | |
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| 51 | <td><a href="./../search-page.html" title="Search library">Search</a></td> |
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| 54 | <td id="selected">File</td> |
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| 55 | |
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| 56 | |
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| 57 | <td><a href="../../../Interpolation//spl_incr.pro" title="Source code of a file">Source</a></td> |
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| 58 | |
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| 61 | <td><a href="./../idldoc-help.html" title="Help on IDLdoc">Help</a></td> |
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| 62 | |
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| 63 | |
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| 64 | <td >Etc</td> |
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| 65 | |
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| 66 | <td id="flexible">Developer documentation</td> |
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| 67 | </tr> |
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| 68 | </table> |
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| 69 | |
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| 70 | </div> |
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| 71 | |
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| 72 | <div id="secondary_navbar"> |
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| 73 | |
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| 74 | <a href="spl_fstdrv.html"><<prev file</a> | <a href="spl_keep_mean.html">next file >></a> <a href="spl_incr.html" target="_TOP">view single page</a> | <a href="./../index.html" target="_TOP">view frames</a> summary: fields | <a href="#routine_summary">routine</a> details: <a href="#routine_details">routine</a> |
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| 75 | |
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| 76 | </div> |
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| 77 | |
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| 78 | |
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| 79 | <div id="container"> |
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| 80 | |
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| 81 | <h1 class="directory"><a href="directory-overview.html">Interpolation/</a></h1> |
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| 82 | <h2 class="pro_file">spl_incr.pro</h2> |
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| 83 | |
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| 84 | <div id="file_attr"> |
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| 85 | <dl> |
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| 86 | </dl> |
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| 87 | </div> |
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| 88 | |
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| 89 | <div id="file_comments"> |
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| 90 | Given the arrays X and Y, which tabulate a function (with the X[i] |
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| 91 | AND Y[i] in ascending order), and given an input value X2, the |
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| 92 | spl_incr function returns an interpolated value for the given values |
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| 93 | of X2. The interpolation method is based on cubic spline, corrected |
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| 94 | in a way that interpolated values are also monotonically increasing. |
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| 95 | </div> |
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| 96 | |
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| 97 | |
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| 98 | |
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| 99 | |
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| 100 | |
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| 101 | |
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| 102 | |
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| 103 | |
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| 104 | <div id="routine_summary"> |
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| 105 | <h2>Routine summary</h2> |
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| 106 | |
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| 107 | <dl> |
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| 108 | |
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| 109 | <dt><p><a href="#_pure_concave"><span class="result">result = </span>pure_concave(<span class="result">x1, x2, y1, y2, der2, x</span>)</a></p><dt> |
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| 110 | <dd> </dd> |
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| 111 | |
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| 112 | <dt><p><a href="#_pure_convex"><span class="result">result = </span>pure_convex(<span class="result">x1, x2, y1, y2, der2, x</span>)</a></p><dt> |
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| 113 | <dd> </dd> |
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| 114 | |
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| 115 | <dt><p><a href="#_spl_incr"><span class="result">result = </span>spl_incr(<span class="result">x, y, x2</span>, YP0=<span class="result">YP0</span>, YPN_1=<span class="result">YPN_1</span>)</a></p><dt> |
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| 116 | <dd> </dd> |
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| 117 | |
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| 118 | </dl> |
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| 119 | </div> |
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| 120 | |
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| 121 | |
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| 122 | <div id="routine_details"> |
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| 123 | |
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| 124 | |
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| 125 | <div class="routine_details" id="_pure_concave"> |
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| 126 | |
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| 127 | <h2><a class="top" href="#container">top</a>pure_concave </h2> |
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| 128 | |
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| 129 | <p class="header"> |
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| 130 | <span class="result">result = </span>pure_concave(<span class="result"><a href="#_pure_concave_param_x1">x1</a>, <a href="#_pure_concave_param_x2">x2</a>, <a href="#_pure_concave_param_y1">y1</a>, <a href="#_pure_concave_param_y2">y2</a>, <a href="#_pure_concave_param_der2">der2</a>, <a href="#_pure_concave_param_x">x</a></span>)</p> |
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| 131 | |
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| 132 | <div class="comments"> |
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| 133 | </div> |
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| 134 | |
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| 135 | <h3>Return value</h3><div class="preformat"> |
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| 136 | y2: f(x2) = y2. Double precision array |
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| 137 | </div> |
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| 138 | |
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| 139 | |
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| 140 | <h3>Parameters</h3> |
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| 141 | |
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| 142 | |
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| 143 | <h4 id="_pure_concave_param_x1">x1 |
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| 144 | <span class="attr">in</span> |
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| 145 | |
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| 146 | |
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| 147 | <span class="attr">required</span> |
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| 148 | |
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| 149 | |
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| 150 | |
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| 151 | |
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| 152 | </h4> |
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| 153 | |
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| 154 | <div class="comments"> |
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| 155 | An n-elements (at least 2) input vector that specifies the tabulate points in |
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| 156 | a strict ascending order. |
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| 157 | </div> |
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| 158 | |
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| 159 | <h4 id="_pure_concave_param_x2">x2 |
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| 160 | <span class="attr">in</span> |
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| 161 | |
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| 162 | |
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| 163 | <span class="attr">required</span> |
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| 164 | |
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| 165 | |
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| 166 | |
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| 167 | |
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| 168 | </h4> |
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| 169 | |
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| 170 | <div class="comments"> |
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| 171 | The input values for which the interpolated values are |
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| 172 | desired. Its values must be strictly monotonically increasing. |
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| 173 | </div> |
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| 174 | |
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| 175 | <h4 id="_pure_concave_param_y1">y1 |
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| 176 | <span class="attr">in</span> |
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| 177 | |
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| 178 | |
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| 179 | <span class="attr">required</span> |
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| 180 | |
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| 181 | |
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| 182 | |
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| 183 | |
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| 184 | </h4> |
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| 185 | |
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| 186 | <div class="comments"> |
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| 187 | f(x) = y. An n-elements input vector that specifies the values |
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| 188 | of the tabulated function F(Xi) corresponding to Xi. As f is |
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| 189 | supposed to be monotonically increasing, y values must be |
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| 190 | monotonically increasing. y can have equal consecutive values. |
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| 191 | </div> |
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| 192 | |
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| 193 | <h4 id="_pure_concave_param_y2">y2 |
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| 194 | |
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| 195 | |
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| 196 | |
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| 197 | |
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| 198 | |
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| 199 | |
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| 200 | |
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| 201 | |
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| 202 | </h4> |
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| 203 | |
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| 204 | <div class="comments"></div> |
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| 205 | |
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| 206 | <h4 id="_pure_concave_param_der2">der2 |
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| 207 | |
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| 208 | |
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| 209 | |
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| 210 | |
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| 211 | |
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| 212 | |
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| 213 | |
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| 214 | |
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| 215 | </h4> |
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| 216 | |
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| 217 | <div class="comments"> |
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| 218 | </div> |
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| 219 | |
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| 220 | <h4 id="_pure_concave_param_x">x |
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| 221 | |
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| 222 | |
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| 223 | |
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| 224 | |
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| 225 | |
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| 226 | |
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| 227 | |
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| 228 | |
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| 229 | </h4> |
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| 230 | |
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| 231 | <div class="comments"> |
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| 232 | </div> |
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| 233 | |
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| 234 | |
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| 235 | |
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| 236 | |
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| 237 | |
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| 238 | |
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| 239 | <h3>Examples</h3><div class="preformat"> |
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| 240 | |
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| 241 | IDL> n = 100L |
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| 242 | IDL> x = (dindgen(n))^2 |
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| 243 | IDL> y = abs(randomn(0, n)) |
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| 244 | IDL> y[n/2:n/2+1] = 0. |
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| 245 | IDL> y[n-n/3] = 0. |
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| 246 | IDL> y[n-n/6:n-n/6+5] = 0. |
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| 247 | IDL> y = total(y, /cumulative, /double) |
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| 248 | IDL> x2 = dindgen((n-1)^2) |
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| 249 | IDL> n2 = n_elements(x2) |
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| 250 | IDL> print, min(y[1:n-1]-y[0:n-2]) LT 0 |
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| 251 | IDL> y2 = spl_incr( x, y, x2) |
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| 252 | IDL> splot, x, y, xstyle = 1, ystyle = 1, ysurx=.25, petit = [1, 2, 1], /land |
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| 253 | IDL> oplot, x2, y2, color = 100 |
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| 254 | IDL> c = y2[1:n2-1] - y2[0:n2-2] |
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| 255 | IDL> print, min(c) LT 0 |
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| 256 | IDL> print, min(c, max = ma), ma |
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| 257 | IDL> splot,c,xstyle=1,ystyle=1, yrange=[-.01,.05], ysurx=.25, petit = [1, 2, 2], /noerase |
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| 258 | IDL> oplot,[0, n_elements(c)], [0, 0], linestyle = 1 |
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| 259 | </div> |
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| 260 | <h3>Version history</h3> |
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| 261 | |
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| 262 | <h4>Version</h4><div class="preformat"> |
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| 263 | $Id: spl_incr.pro 371 2008-08-07 09:32:02Z pinsard $ |
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| 264 | </div> |
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| 265 | <h4>History</h4><div class="preformat"> |
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| 266 | Sebastien Masson (smasson@lodyc.jussieu.fr): May-Dec 2005 |
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| 267 | </div> |
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| 268 | |
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| 269 | |
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| 270 | <h3>Known issues</h3> |
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| 271 | |
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| 272 | |
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| 273 | |
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| 274 | <h4>Restrictions</h4><div class="preformat"> |
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| 275 | It might be possible that y2[i+1]-y2[i] has very small negative |
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| 276 | values (amplitude smaller than 1.e-6)... |
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| 277 | </div> |
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| 278 | |
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| 279 | |
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| 280 | |
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| 281 | |
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| 282 | |
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| 283 | |
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| 284 | |
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| 285 | |
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| 286 | |
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| 287 | <h3>Statistics</h3> |
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| 288 | <table class="statistics"> |
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| 289 | <tr><td>McCabe cyclic</td><td> 1</td></tr> |
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| 290 | <tr><td>McCabe essential</td><td> 1</td></tr> |
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| 291 | <tr><td>McCabe modular design</td><td> 1</td></tr> |
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| 292 | </table> |
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| 293 | |
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| 294 | |
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| 295 | </div> |
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| 296 | |
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| 297 | |
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| 298 | <div class="routine_details" id="_pure_convex"> |
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| 299 | |
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| 300 | <h2><a class="top" href="#container">top</a>pure_convex </h2> |
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| 301 | |
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| 302 | <p class="header"> |
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| 303 | <span class="result">result = </span>pure_convex(<span class="result"><a href="#_pure_convex_param_x1">x1</a>, <a href="#_pure_convex_param_x2">x2</a>, <a href="#_pure_convex_param_y1">y1</a>, <a href="#_pure_convex_param_y2">y2</a>, <a href="#_pure_convex_param_der2">der2</a>, <a href="#_pure_convex_param_x">x</a></span>)</p> |
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| 304 | |
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| 305 | <div class="comments"> |
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| 306 | </div> |
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| 307 | |
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| 308 | |
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| 309 | |
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| 310 | |
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| 311 | <h3>Parameters</h3> |
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| 312 | |
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| 313 | |
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| 314 | <h4 id="_pure_convex_param_x1">x1 |
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| 315 | <span class="attr">in</span> |
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| 316 | |
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| 317 | |
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| 318 | <span class="attr">required</span> |
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| 319 | |
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| 320 | |
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| 321 | |
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| 322 | |
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| 323 | </h4> |
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| 324 | |
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| 325 | <div class="comments"> |
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| 326 | An n-elements (at least 2) input vector that specifies the tabulate points in |
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| 327 | a strict ascending order. |
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| 328 | </div> |
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| 329 | |
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| 330 | <h4 id="_pure_convex_param_x2">x2 |
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| 331 | <span class="attr">in</span> |
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| 332 | |
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| 333 | |
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| 334 | <span class="attr">required</span> |
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| 335 | |
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| 336 | |
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| 337 | |
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| 338 | |
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| 339 | </h4> |
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| 340 | |
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| 341 | <div class="comments"> |
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| 342 | The input values for which the interpolated values are |
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| 343 | desired. Its values must be strictly monotonically increasing. |
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| 344 | </div> |
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| 345 | |
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| 346 | <h4 id="_pure_convex_param_y1">y1 |
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| 347 | <span class="attr">in</span> |
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| 348 | |
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| 349 | |
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| 350 | <span class="attr">required</span> |
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| 351 | |
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| 352 | |
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| 353 | |
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| 354 | |
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| 355 | </h4> |
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| 356 | |
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| 357 | <div class="comments"> |
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| 358 | f(x) = y. An n-elements input vector that specifies the values |
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| 359 | of the tabulated function F(Xi) corresponding to Xi. As f is |
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| 360 | supposed to be monotonically increasing, y values must be |
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| 361 | monotonically increasing. y can have equal consecutive values. |
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| 362 | </div> |
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| 363 | |
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| 364 | <h4 id="_pure_convex_param_y2">y2 |
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| 365 | |
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| 366 | |
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| 367 | |
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| 368 | |
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| 369 | |
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| 370 | |
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| 371 | |
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| 372 | |
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| 373 | </h4> |
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| 374 | |
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| 375 | <div class="comments"></div> |
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| 376 | |
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| 377 | <h4 id="_pure_convex_param_der2">der2 |
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| 378 | |
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| 379 | |
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| 380 | |
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| 381 | |
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| 382 | |
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| 383 | |
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| 384 | |
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| 385 | |
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| 386 | </h4> |
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| 387 | |
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| 388 | <div class="comments"> |
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| 389 | </div> |
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| 390 | |
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| 391 | <h4 id="_pure_convex_param_x">x |
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| 392 | |
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| 393 | |
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| 394 | |
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| 395 | |
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| 396 | |
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| 397 | |
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| 398 | |
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| 399 | |
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| 400 | </h4> |
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| 401 | |
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| 402 | <div class="comments"> |
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| 403 | </div> |
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| 404 | |
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| 426 | |
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| 427 | |
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| 428 | |
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| 429 | |
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| 430 | |
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| 431 | <h3>Statistics</h3> |
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| 432 | <table class="statistics"> |
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| 433 | <tr><td>McCabe cyclic</td><td> 1</td></tr> |
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| 434 | <tr><td>McCabe essential</td><td> 1</td></tr> |
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| 435 | <tr><td>McCabe modular design</td><td> 1</td></tr> |
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| 436 | </table> |
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| 437 | |
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| 438 | |
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| 439 | </div> |
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| 440 | |
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| 441 | |
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| 442 | <div class="routine_details" id="_spl_incr"> |
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| 443 | |
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| 444 | <h2><a class="top" href="#container">top</a>spl_incr </h2> |
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| 445 | |
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| 446 | <p class="header"> |
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| 447 | <span class="result">result = </span>spl_incr(<span class="result"><a href="#_spl_incr_param_x">x</a>, <a href="#_spl_incr_param_y">y</a>, <a href="#_spl_incr_param_x2">x2</a></span>, <a href="#_spl_incr_keyword_YP0">YP0</a>=<span class="result">YP0</span>, <a href="#_spl_incr_keyword_YPN_1">YPN_1</a>=<span class="result">YPN_1</span>)</p> |
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| 448 | |
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| 449 | <div class="comments"> |
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| 450 | </div> |
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| 451 | |
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| 452 | |
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| 453 | |
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| 454 | |
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| 455 | <h3>Parameters</h3> |
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| 456 | |
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| 457 | |
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| 458 | <h4 id="_spl_incr_param_x">x |
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| 459 | |
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| 460 | |
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| 461 | |
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| 462 | |
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| 463 | |
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| 464 | |
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| 465 | |
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| 466 | |
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| 467 | </h4> |
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| 468 | |
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| 469 | <div class="comments"></div> |
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| 470 | |
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| 471 | <h4 id="_spl_incr_param_y">y |
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| 472 | |
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| 473 | |
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| 474 | |
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| 475 | |
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| 476 | |
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| 477 | |
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| 478 | |
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| 479 | |
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| 480 | </h4> |
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| 481 | |
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| 482 | <div class="comments"></div> |
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| 483 | |
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| 484 | <h4 id="_spl_incr_param_x2">x2 |
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| 485 | |
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| 486 | |
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| 487 | |
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| 488 | |
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| 489 | |
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| 490 | |
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| 491 | |
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| 492 | |
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| 493 | </h4> |
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| 494 | |
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| 495 | <div class="comments"></div> |
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| 496 | |
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| 497 | |
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| 498 | |
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| 499 | |
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| 500 | |
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| 501 | |
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| 502 | <h3>Keywords</h3> |
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| 503 | |
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| 504 | <h4 id="_spl_incr_keyword_YP0">YP0 |
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| 505 | |
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| 506 | |
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| 507 | |
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| 512 | |
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| 513 | </h4> |
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| 514 | |
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| 515 | <div class="comments"> |
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| 516 | The first derivative of the interpolating function at the |
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| 517 | point X0. If YP0 is omitted, the second derivative at the |
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| 518 | boundary is set to zero, resulting in a "natural spline." |
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| 519 | </div> |
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| 520 | |
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| 521 | <h4 id="_spl_incr_keyword_YPN_1">YPN_1 |
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| 522 | |
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| 524 | |
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| 529 | |
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| 530 | </h4> |
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| 531 | |
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| 532 | <div class="comments"> |
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| 533 | The first derivative of the interpolating function at the |
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| 534 | point Xn-1. If YPN_1 is omitted, the second derivative at the |
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| 535 | boundary is set to zero, resulting in a "natural spline."</div> |
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| 559 | |
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| 560 | <h3>Statistics</h3> |
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| 561 | <table class="statistics"> |
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| 562 | <tr><td>McCabe cyclic</td><td> 46</td></tr> |
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| 563 | <tr><td>McCabe essential</td><td> 10</td></tr> |
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| 564 | <tr><td>McCabe modular design</td><td> 1</td></tr> |
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| 565 | </table> |
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| 566 | |
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| 567 | |
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| 568 | </div> |
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| 569 | |
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| 570 | </div> |
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| 571 | |
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| 572 | |
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| 573 | |
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| 574 | <div id="tagline">Produced by IDLdoc 2.0.</div> |
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| 575 | |
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| 576 | </div> |
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| 577 | |
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| 578 | </body> |
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| 579 | </html> |
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