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trunk/SRC/Documentation/idldoc_html_output/Interpolation/spl_incr.html
r89 r101 87 87 </div> 88 88 89 <div id="file_comments"></div> 89 <div id="file_comments"> 90 91 Given the arrays X and Y, which tabulate a function (with the X[i] 92 AND Y[i] in ascending order), and given an input value X2, the 93 SPL_INCR function returns an interpolated value for the given values 94 of X2. The interpolation method is based on cubic spline, corrected 95 in a way that interpolated values are also monotonically increasing. 96 </div> 90 97 91 98 … … 102 109 103 110 <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> 104 <dd> NAME:spl_incr PURPOSE: Given the arrays X and Y, which tabulate a function (with the X[i] AND Y[i] in ascending order), and given an input value X2, the SPL_INCR function returns an interpolated value for the given values of X2.</dd>111 <dd> </dd> 105 112 106 113 <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> … … 125 132 126 133 <div class="comments"> 127 NAME:spl_incr 128 129 PURPOSE: 130 131 Given the arrays X and Y, which tabulate a function (with the X[i] 132 AND Y[i] in ascending order), and given an input value X2, the 133 SPL_INCR function returns an interpolated value for the given values 134 of X2. The interpolation method is based on cubic spline, corrected 135 in a way that interpolated values are also monotonically increasing. 136 137 CATEGORY: 138 139 CALLING SEQUENCE: y2 = spl_incr(x, y, x2) 140 141 INPUTS: 142 143 x: An n-element (at least 2) input vector that specifies the 134 </div> 135 136 <h3>Return value</h3><div class="value"> 137 138 y2: f(x2) = y2. Double precision array 139 </div> 140 141 142 <h3>Parameters</h3> 143 144 145 <h4 id="_pure_concave_param_x1">x1 146 <span class="attr">in</span> 147 148 149 <span class="attr">required</span> 150 151 152 153 154 </h4> 155 156 <div class="comments"> An n-element (at least 2) input vector that specifies the 144 157 tabulate points in a strict ascending order. 145 146 y: f(x) = y. An n-element input vector that specifies the values 158 </div> 159 160 <h4 id="_pure_concave_param_x2">x2 161 <span class="attr">in</span> 162 163 164 <span class="attr">required</span> 165 166 167 168 169 </h4> 170 171 <div class="comments"> The input values for which the interpolated values are 172 desired. Its values must be strictly monotonically increasing. 173 174 175 176 </div> 177 178 <h4 id="_pure_concave_param_y1">y1 179 <span class="attr">in</span> 180 181 182 <span class="attr">required</span> 183 184 185 186 187 </h4> 188 189 <div class="comments"> f(x) = y. An n-element input vector that specifies the values 147 190 of the tabulated function F(Xi) corresponding to Xi. As f is 148 191 supposed to be monotonically increasing, y values must be 149 192 monotonically increasing. y can have equal consecutive values. 150 151 x2: The input values for which the interpolated values are 152 desired. Its values must be strictly monotonically increasing. 153 154 KEYWORD PARAMETERS: 155 156 YP0: The first derivative of the interpolating function at the 157 point X0. If YP0 is omitted, the second derivative at the 158 boundary is set to zero, resulting in a "natural spline." 159 160 YPN_1: The first derivative of the interpolating function at the 161 point Xn-1. If YPN_1 is omitted, the second derivative at the 162 boundary is set to zero, resulting in a "natural spline." 163 164 OUTPUTS: 165 166 y2: f(x2) = y2. Double precision array 167 168 COMMON BLOCKS: none 169 170 SIDE EFFECTS: ? 171 172 RESTRICTIONS: 173 It might be possible that y2[i+1]-y2[i] has very small negative 174 values (amplitude smaller than 1.e-6)... 175 176 EXAMPLE: 193 </div> 194 195 <h4 id="_pure_concave_param_y2">y2 196 197 198 199 200 201 202 203 204 </h4> 205 206 <div class="comments"></div> 207 208 <h4 id="_pure_concave_param_der2">der2 209 210 211 212 213 214 215 216 217 </h4> 218 219 <div class="comments"></div> 220 221 <h4 id="_pure_concave_param_x">x 222 223 224 225 226 227 228 229 230 </h4> 231 232 <div class="comments"></div> 233 234 235 236 237 238 239 <h3>Examples</h3><div class="value"> y2 = spl_incr(x, y, x2) 240 241 177 242 178 243 n = 100L … … 194 259 splot,c,xstyle=1,ystyle=1, yrange=[-.01,.05], ysurx=.25, petit = [1, 2, 2], /noerase 195 260 oplot,[0, n_elements(c)], [0, 0], linestyle = 1 196 197 MODIFICATION HISTORY:</div> 198 199 200 201 202 <h3>Parameters</h3> 203 204 205 <h4 id="_pure_concave_param_x1">x1 206 207 208 209 210 211 212 213 214 </h4> 215 216 <div class="comments"></div> 217 218 <h4 id="_pure_concave_param_x2">x2 219 220 221 222 223 224 225 226 227 </h4> 228 229 <div class="comments"></div> 230 231 <h4 id="_pure_concave_param_y1">y1 232 233 234 235 236 237 238 239 240 </h4> 241 242 <div class="comments"></div> 243 244 <h4 id="_pure_concave_param_y2">y2 245 246 247 248 249 250 251 252 253 </h4> 254 255 <div class="comments"></div> 256 257 <h4 id="_pure_concave_param_der2">der2 258 259 260 261 262 263 264 265 266 </h4> 267 268 <div class="comments"></div> 269 270 <h4 id="_pure_concave_param_x">x 271 272 273 274 275 276 277 278 279 </h4> 280 281 <div class="comments"></div> 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 261 </div> 262 <h3>Version history</h3> 263 264 265 <h4>History</h4><div class="value"> 266 Sebastien Masson (smasson@lodyc.jussieu.fr): May-Dec 2005</div> 267 268 269 <h3>Known issues</h3> 270 271 272 273 <h4>Restrictions</h4><div class="value"> 274 It might be possible that y2[i+1]-y2[i] has very small negative 275 values (amplitude smaller than 1.e-6)... 276 </div> 300 277 301 278 … … 508 485 </h4> 509 486 510 <div class="comments"></div> 487 <div class="comments"> The first derivative of the interpolating function at the 488 point X0. If YP0 is omitted, the second derivative at the 489 boundary is set to zero, resulting in a "natural spline."</div> 511 490 512 491 <h4 id="_spl_incr_keyword_YPN_1">YPN_1 … … 521 500 </h4> 522 501 523 <div class="comments"></div> 502 <div class="comments"> The first derivative of the interpolating function at the 503 point Xn-1. If YPN_1 is omitted, the second derivative at the 504 boundary is set to zero, resulting in a "natural spline." </div> 524 505 525 506
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