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| 3 | <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> |
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| 5 | <title>spl_incr.pro (SAXO Documentation Assistant)</title> |
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| 44 | |
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| 45 | <table border="0" cellpadding="0" cellspacing="0" width="98%" bgcolor="#F0F0FF" valign="bottom"> |
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| 46 | <tr> |
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| 47 | <td width="10%"> |
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| 48 | <a href="spl_fstdrv.html"><img src="./../prev.gif" border="0" alt="Previous"></a></td> |
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| 49 | <td width="80%" align="center" valign="center"> |
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| 50 | <font size=-1><i>SAXO Documentation Assistant</i>: <a href="./../home.html">Overview</a></font></td> |
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| 51 | <td width="10%" align="right"> |
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| 52 | <a href="spl_keep_mean.html"><img src="./../next.gif" border="0" alt="Next"></a></td> |
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| 53 | </tr> |
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| 54 | </table> |
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| 55 | |
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| 56 | |
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| 57 | <h1><font size="-2">Interpolation/</font></h1> |
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| 58 | <h2>spl_incr.pro</h2> |
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| 59 | |
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| 60 | <dl> |
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| 61 | </dl> |
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| 62 | |
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| 63 | |
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| 64 | Given the arrays X and Y, which tabulate a function (with the X[i] |
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| 65 | AND Y[i] in ascending order), and given an input value X2, the |
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| [242] | 66 | spl_incr function returns an interpolated value for the given values |
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| [163] | 67 | of X2. The interpolation method is based on cubic spline, corrected |
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| 68 | in a way that interpolated values are also monotonically increasing. |
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| 69 | |
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| 70 | |
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| 71 | |
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| 72 | <h2>Routine summary</h2> |
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| 73 | |
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| 74 | <dl> |
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| 75 | |
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| 76 | <dt><a href="#_pure_concave"><i>result = </i>pure_concave(<i>x1, x2, y1, y2, der2, x</i>)</a><dt> |
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| 77 | <dd><font size="-1"> </font></dd> |
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| 78 | |
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| 79 | <dt><a href="#_pure_convex"><i>result = </i>pure_convex(<i>x1, x2, y1, y2, der2, x</i>)</a><dt> |
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| [242] | 80 | <dd><font size="-1"> </font></dd> |
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| [163] | 81 | |
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| 82 | <dt><a href="#_spl_incr"><i>result = </i>spl_incr(<i>x, y, x2</i>, YP0=<i>YP0</i>, YPN_1=<i>YPN_1</i>)</a><dt> |
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| [242] | 83 | <dd><font size="-1"> </font></dd> |
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| [163] | 84 | |
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| 85 | </dl> |
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| 86 | |
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| 87 | <p> </p> |
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| 88 | |
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| 89 | |
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| 90 | |
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| 91 | <a name="#_pure_concave"></a> |
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| 92 | |
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| 93 | <h2>pure_concave </h2> |
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| 94 | |
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| 95 | <p><font face="Courier"><i>result = </i>pure_concave(<i><a href="#_pure_concave_keyword_x1">x1</a>, <a href="#_pure_concave_keyword_x2">x2</a>, <a href="#_pure_concave_keyword_y1">y1</a>, <a href="#_pure_concave_keyword_y2">y2</a>, <a href="#_pure_concave_keyword_der2">der2</a>, <a href="#_pure_concave_keyword_x">x</a></i>)</font></p> |
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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 | <h3>Return value</h3> |
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| [242] | 101 | y2: f(x2) = y2. Double precision array |
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| [163] | 102 | |
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| 103 | |
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| 104 | |
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| 105 | <h3>Parameters</h3> |
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| 106 | |
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| 107 | |
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| 108 | <a name="#_pure_concave_keyword_x1"></a> |
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| 109 | <h4>x1 |
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| 110 | <font size="-1" color="#006633">in</font> |
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| 111 | |
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| 112 | |
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| 113 | <font size="-1" color="#006633">required</font> |
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| 114 | |
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| 115 | |
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| 116 | |
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| 117 | |
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| 118 | </h4> |
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| 119 | |
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| 120 | |
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| [242] | 121 | An n-elements (at least 2) input vector that specifies the tabulate points in |
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| [163] | 122 | a strict ascending order. |
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| 123 | |
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| 124 | |
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| 125 | |
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| 126 | <a name="#_pure_concave_keyword_x2"></a> |
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| 127 | <h4>x2 |
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| 128 | <font size="-1" color="#006633">in</font> |
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| 129 | |
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| 130 | |
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| 131 | <font size="-1" color="#006633">required</font> |
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| 132 | |
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| 133 | |
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| 134 | |
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| 135 | |
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| 136 | </h4> |
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| 137 | |
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| 138 | |
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| 139 | The input values for which the interpolated values are |
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| 140 | desired. Its values must be strictly monotonically increasing. |
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| 141 | |
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| 142 | |
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| 143 | |
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| 144 | <a name="#_pure_concave_keyword_y1"></a> |
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| 145 | <h4>y1 |
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| 146 | <font size="-1" color="#006633">in</font> |
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| 147 | |
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| 148 | |
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| 149 | <font size="-1" color="#006633">required</font> |
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| 150 | |
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| 151 | |
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| 152 | |
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| 153 | |
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| 154 | </h4> |
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| 155 | |
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| 156 | |
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| [242] | 157 | f(x) = y. An n-elements input vector that specifies the values |
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| [163] | 158 | of the tabulated function F(Xi) corresponding to Xi. As f is |
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| 159 | supposed to be monotonically increasing, y values must be |
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| 160 | monotonically increasing. y can have equal consecutive values. |
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| 161 | |
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| 162 | |
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| 163 | |
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| 164 | <a name="#_pure_concave_keyword_y2"></a> |
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| 165 | <h4>y2 |
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| 166 | |
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| 167 | |
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| 168 | |
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| 169 | |
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| 170 | |
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| 171 | |
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| 172 | |
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| 173 | |
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| 174 | </h4> |
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| 175 | |
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| 176 | |
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| 177 | |
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| 178 | |
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| 179 | <a name="#_pure_concave_keyword_der2"></a> |
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| 180 | <h4>der2 |
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| 181 | |
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| 182 | |
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| 183 | |
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| 184 | |
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| 185 | |
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| 186 | |
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| 187 | |
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| 188 | |
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| 189 | </h4> |
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| 190 | |
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| 191 | |
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| 192 | |
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| 193 | |
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| 194 | |
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| 195 | <a name="#_pure_concave_keyword_x"></a> |
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| 196 | <h4>x |
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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 | |
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| 203 | |
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| 204 | |
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| 205 | </h4> |
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| 206 | |
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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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| [234] | 214 | <h3>Examples</h3><pre> |
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| [163] | 215 | |
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| [402] | 216 | IDL> n = 100L |
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| 217 | IDL> x = (dindgen(n))^2 |
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| 218 | IDL> y = abs(randomn(0, n)) |
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| 219 | IDL> y[n/2:n/2+1] = 0. |
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| 220 | IDL> y[n-n/3] = 0. |
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| 221 | IDL> y[n-n/6:n-n/6+5] = 0. |
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| 222 | IDL> y = total(y, /cumulative, /double) |
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| 223 | IDL> x2 = dindgen((n-1)^2) |
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| 224 | IDL> n2 = n_elements(x2) |
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| 225 | IDL> print, min(y[1:n-1]-y[0:n-2]) LT 0 |
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| 226 | IDL> y2 = spl_incr( x, y, x2) |
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| 227 | IDL> splot, x, y, xstyle = 1, ystyle = 1, ysurx=.25, petit = [1, 2, 1], /land |
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| 228 | IDL> oplot, x2, y2, color = 100 |
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| 229 | IDL> c = y2[1:n2-1] - y2[0:n2-2] |
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| 230 | IDL> print, min(c) LT 0 |
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| 231 | IDL> print, min(c, max = ma), ma |
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| 232 | IDL> splot,c,xstyle=1,ystyle=1, yrange=[-.01,.05], ysurx=.25, petit = [1, 2, 2], /noerase |
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| 233 | IDL> oplot,[0, n_elements(c)], [0, 0], linestyle = 1 |
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| 234 | |
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| [234] | 235 | </pre><h3>Version history</h3> |
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| [163] | 236 | |
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| [234] | 237 | <h4>Version</h4> |
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| [402] | 238 | $Id: spl_incr.pro 371 2008-08-07 09:32:02Z pinsard $ |
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| [163] | 239 | |
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| 240 | <h4>History</h4> |
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| 241 | Sebastien Masson (smasson@lodyc.jussieu.fr): May-Dec 2005 |
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| 242 | |
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| 243 | |
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| 244 | |
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| 245 | <h3>Known issues</h3> |
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| 246 | |
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| 247 | |
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| 248 | |
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| 249 | <h4>Restrictions</h4> |
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| 250 | It might be possible that y2[i+1]-y2[i] has very small negative |
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| 251 | values (amplitude smaller than 1.e-6)... |
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| 252 | |
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| 253 | |
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| 254 | |
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| 255 | |
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| 256 | |
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| 257 | |
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| 258 | |
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| 259 | |
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| 260 | |
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| 261 | |
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| 262 | <font size="-3"><p> </p></font> |
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| 263 | <hr size="1" color="#CCCCCC"/> |
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| 264 | |
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| 265 | <a name="#_pure_convex"></a> |
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| 266 | |
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| 267 | <h2>pure_convex </h2> |
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| 268 | |
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| 269 | <p><font face="Courier"><i>result = </i>pure_convex(<i><a href="#_pure_convex_keyword_x1">x1</a>, <a href="#_pure_convex_keyword_x2">x2</a>, <a href="#_pure_convex_keyword_y1">y1</a>, <a href="#_pure_convex_keyword_y2">y2</a>, <a href="#_pure_convex_keyword_der2">der2</a>, <a href="#_pure_convex_keyword_x">x</a></i>)</font></p> |
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| 270 | |
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| 271 | |
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| 272 | |
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| [242] | 273 | |
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| [163] | 274 | |
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| 275 | |
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| 276 | |
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| 277 | <h3>Parameters</h3> |
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| 278 | |
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| 279 | |
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| 280 | <a name="#_pure_convex_keyword_x1"></a> |
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| 281 | <h4>x1 |
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| 282 | <font size="-1" color="#006633">in</font> |
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| 283 | |
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| 284 | |
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| 285 | <font size="-1" color="#006633">required</font> |
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| 286 | |
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| 287 | |
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| 288 | |
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| 289 | |
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| 290 | </h4> |
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| 291 | |
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| 292 | |
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| [242] | 293 | An n-elements (at least 2) input vector that specifies the tabulate points in |
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| [163] | 294 | a strict ascending order. |
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| 295 | |
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| 296 | |
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| 297 | |
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| 298 | <a name="#_pure_convex_keyword_x2"></a> |
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| 299 | <h4>x2 |
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| 300 | <font size="-1" color="#006633">in</font> |
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| 301 | |
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| 302 | |
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| 303 | <font size="-1" color="#006633">required</font> |
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| 304 | |
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| 305 | |
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| 306 | |
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| 307 | |
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| 308 | </h4> |
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| 309 | |
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| 310 | |
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| 311 | The input values for which the interpolated values are |
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| 312 | desired. Its values must be strictly monotonically increasing. |
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| 313 | |
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| 314 | |
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| 315 | |
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| 316 | <a name="#_pure_convex_keyword_y1"></a> |
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| 317 | <h4>y1 |
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| 318 | <font size="-1" color="#006633">in</font> |
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| 319 | |
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| 320 | |
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| 321 | <font size="-1" color="#006633">required</font> |
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| 322 | |
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| 323 | |
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| 324 | |
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| 325 | |
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| 326 | </h4> |
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| 327 | |
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| 328 | |
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| [242] | 329 | f(x) = y. An n-elements input vector that specifies the values |
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| [163] | 330 | of the tabulated function F(Xi) corresponding to Xi. As f is |
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| 331 | supposed to be monotonically increasing, y values must be |
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| 332 | monotonically increasing. y can have equal consecutive values. |
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| 333 | |
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| 334 | |
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| 335 | |
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| 336 | <a name="#_pure_convex_keyword_y2"></a> |
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| 337 | <h4>y2 |
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| 338 | |
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| 339 | |
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| 340 | |
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| 341 | |
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| 342 | |
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| 343 | |
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| 344 | |
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| 345 | |
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| 346 | </h4> |
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| 347 | |
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| 348 | |
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| 349 | |
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| 350 | |
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| 351 | <a name="#_pure_convex_keyword_der2"></a> |
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| 352 | <h4>der2 |
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| 353 | |
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| 355 | |
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| 356 | |
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| 357 | |
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| 358 | |
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| 359 | |
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| 360 | |
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| 361 | </h4> |
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| 362 | |
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| 363 | |
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| [242] | 364 | |
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| [163] | 365 | |
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| 366 | |
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| 367 | <a name="#_pure_convex_keyword_x"></a> |
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| 368 | <h4>x |
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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 | |
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| 374 | |
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| 375 | |
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| 376 | |
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| 377 | </h4> |
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| 378 | |
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| 402 | |
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| 403 | |
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| 404 | |
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| 405 | |
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| 406 | |
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| 407 | <font size="-3"><p> </p></font> |
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| 408 | <hr size="1" color="#CCCCCC"/> |
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| 409 | |
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| 410 | <a name="#_spl_incr"></a> |
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| 411 | |
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| 412 | <h2>spl_incr </h2> |
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| 413 | |
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| 414 | <p><font face="Courier"><i>result = </i>spl_incr(<i><a href="#_spl_incr_keyword_x">x</a>, <a href="#_spl_incr_keyword_y">y</a>, <a href="#_spl_incr_keyword_x2">x2</a></i>, <a href="#_spl_incr_keyword_YP0">YP0</a>=<i>YP0</i>, <a href="#_spl_incr_keyword_YPN_1">YPN_1</a>=<i>YPN_1</i>)</font></p> |
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| 415 | |
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| 417 | |
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| [242] | 418 | |
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| [163] | 419 | |
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| 420 | |
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| 421 | |
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| 422 | <h3>Parameters</h3> |
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| 423 | |
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| 424 | |
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| 425 | <a name="#_spl_incr_keyword_x"></a> |
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| 426 | <h4>x |
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| 427 | |
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| 429 | |
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| 430 | |
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| 432 | |
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| 433 | |
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| 434 | |
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| 435 | </h4> |
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| 436 | |
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| 437 | |
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| 438 | |
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| 439 | |
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| 440 | <a name="#_spl_incr_keyword_y"></a> |
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| 441 | <h4>y |
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| 442 | |
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| 444 | |
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| 445 | |
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| 446 | |
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| 447 | |
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| 448 | |
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| 449 | |
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| 450 | </h4> |
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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 | <a name="#_spl_incr_keyword_x2"></a> |
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| 456 | <h4>x2 |
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| 457 | |
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| 458 | |
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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 | </h4> |
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| 466 | |
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| 467 | |
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| 468 | |
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| 469 | |
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| 470 | |
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| 471 | |
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| 472 | <h3>Keywords</h3> |
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| 473 | |
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| 474 | |
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| 475 | <a name="#_spl_incr_keyword_YP0"></a> |
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| 476 | <h4>YP0 |
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| 477 | |
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| 478 | |
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| 479 | |
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| 480 | |
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| 481 | |
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| 482 | |
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| 483 | |
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| 484 | |
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| 485 | </h4> |
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| 486 | |
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| [242] | 487 | |
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| 488 | The first derivative of the interpolating function at the |
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| [163] | 489 | point X0. If YP0 is omitted, the second derivative at the |
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| 490 | boundary is set to zero, resulting in a "natural spline." |
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| [242] | 491 | |
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| [163] | 492 | |
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| 493 | <a name="#_spl_incr_keyword_YPN_1"></a> |
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| 494 | <h4>YPN_1 |
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| 495 | |
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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 | |
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| 503 | </h4> |
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| 504 | |
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| [242] | 505 | |
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| 506 | The first derivative of the interpolating function at the |
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| [163] | 507 | point Xn-1. If YPN_1 is omitted, the second derivative at the |
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| 508 | boundary is set to zero, resulting in a "natural spline." |
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