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81 | <h1 class="directory"><a href="directory-overview.html?format=raw">ToBeReviewed/STATISTICS/</a></h1> |
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82 | <h2 class="pro_file">c_timecorrelate.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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97 | |
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98 | <div id="routine_summary"> |
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99 | <h2>Routine summary</h2> |
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100 | |
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101 | <dl> |
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102 | |
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103 | <dt><p><a href="#_TimeCross_Cov"><span class="result">result = </span>TimeCross_Cov(<span class="result">Xd, Yd, M, nT, Ndim</span>, Double=<span class="result">Double</span>, ZERO2NAN=<span class="result">ZERO2NAN</span>)</a></p><dt> |
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104 | <dd> NAME: C_TIMECORRELATE PURPOSE: This function computes the "time cross correlation" Pxy(L) or the "time cross covariance" between 2 arrays (this is some kind of c_correlate but for multidimenstionals arrays) as a function of the lag (L).</dd> |
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105 | |
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106 | <dt><p><a href="#_C_Timecorrelate"><span class="result">result = </span>C_Timecorrelate(<span class="result">X, Y, Lag</span>, Covariance=<span class="result">Covariance</span>, Double=<span class="result">Double</span>)</a></p><dt> |
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107 | <dd></dd> |
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108 | |
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109 | </dl> |
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110 | </div> |
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111 | |
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112 | |
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113 | <div id="routine_details"> |
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114 | |
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115 | |
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116 | <div class="routine_details" id="_TimeCross_Cov"> |
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117 | |
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118 | <h2><a class="top" href="#container">top</a>TimeCross_Cov </h2> |
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119 | |
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120 | <p class="header"> |
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121 | <span class="result">result = </span>TimeCross_Cov(<span class="result"><a href="#_TimeCross_Cov_param_Xd">Xd</a>, <a href="#_TimeCross_Cov_param_Yd">Yd</a>, <a href="#_TimeCross_Cov_param_M">M</a>, <a href="#_TimeCross_Cov_param_nT">nT</a>, <a href="#_TimeCross_Cov_param_Ndim">Ndim</a></span>, <a href="#_TimeCross_Cov_keyword_Double">Double</a>=<span class="result">Double</span>, <a href="#_TimeCross_Cov_keyword_ZERO2NAN">ZERO2NAN</a>=<span class="result">ZERO2NAN</span>)</p> |
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122 | |
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123 | <div class="comments"> |
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124 | NAME: |
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125 | C_TIMECORRELATE |
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126 | |
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127 | PURPOSE: |
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128 | This function computes the "time cross correlation" Pxy(L) or |
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129 | the "time cross covariance" between 2 arrays (this is some |
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130 | kind of c_correlate but for multidimenstionals arrays) as a |
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131 | function of the lag (L). |
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132 | |
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133 | CATEGORY: |
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134 | Statistics. |
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135 | |
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136 | CALLING SEQUENCE: |
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137 | Result = c_timecorrelate(X, Y, Lag) |
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138 | |
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139 | INPUTS: |
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140 | X: an Array which last dimension is the time dimension of |
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141 | size n, float or double. |
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142 | |
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143 | Y: an Array which last dimension is the time dimension of |
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144 | size n, float or double. |
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145 | |
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146 | LAG: A scalar or n-element vector, in the interval [-(n-2), (n-2)], |
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147 | of type integer that specifies the absolute distance(s) between |
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148 | indexed elements of X. |
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149 | |
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150 | KEYWORD PARAMETERS: |
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151 | COVARIANCE: If set to a non-zero value, the sample cross |
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152 | covariance is computed. |
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153 | |
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154 | DOUBLE: If set to a non-zero value, computations are done in |
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155 | double precision arithmetic. |
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156 | |
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157 | EXAMPLE |
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158 | Define two n-element sample populations. |
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159 | x = [3.73, 3.67, 3.77, 3.83, 4.67, 5.87, 6.70, 6.97, 6.40, 5.57] |
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160 | y = [2.31, 2.76, 3.02, 3.13, 3.72, 3.88, 3.97, 4.39, 4.34, 3.95] |
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161 | |
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162 | Compute the cross correlation of X and Y for LAG = -5, 0, 1, 5, 6, 7 |
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163 | lag = [-5, 0, 1, 5, 6, 7] |
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164 | result = c_timecorrelate(x, y, lag) |
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165 | |
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166 | The result should be: |
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167 | [-0.428246, 0.914755, 0.674547, -0.405140, -0.403100, -0.339685] |
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168 | |
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169 | PROCEDURE: |
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170 | |
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171 | |
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172 | FOR L>=0 |
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173 | |
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174 | n-L-1 |
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175 | sigma (X[k]-Xmean)(Y[k+L]-Ymean) |
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176 | k=0 |
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177 | correlation(X,Y,L)=------------------------------------------------------ |
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178 | n-1 n-1 |
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179 | sqrt( (sigma (X[k]-Xmean)^2)*(sigma (Y[k]-Ymean)^2)) |
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180 | k=0 k=0 |
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181 | |
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182 | |
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183 | |
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184 | n-L-1 |
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185 | sigma (X[k]-Xmean)(Y[k+L]-Ymean) |
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186 | k=0 |
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187 | covariance(X,Y,L)=------------------------------------------------------ |
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188 | n |
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189 | |
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190 | FOR L<0 |
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191 | |
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192 | |
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193 | n-L-1 |
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194 | sigma (X[k+L]-Xmean)(Y[k]-Ymean) |
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195 | k=0 |
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196 | correlation(X,Y,L)=------------------------------------------------------ |
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197 | n-1 n-1 |
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198 | sqrt( (sigma (X[k]-Xmean)^2)*(sigma (Y[k]-Ymean)^2)) |
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199 | k=0 k=0 |
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200 | |
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201 | |
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202 | |
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203 | n-L-1 |
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204 | sigma (X[k+L]-Xmean)(Y[k]-Ymean) |
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205 | k=0 |
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206 | covariance(X,Y,L)=------------------------------------------------------ |
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207 | n |
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208 | |
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209 | Where Xmean and Ymean are the time means of the sample populations |
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210 | x=(x[t=0],x[t=1],...,x[t=n-1]) and y=(y[t=0],y[t=1],...,y[t=n-1]), |
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211 | respectively. |
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212 | |
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213 | |
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214 | |
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215 | REFERENCE: |
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216 | INTRODUCTION TO STATISTICAL TIME SERIES |
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217 | Wayne A. Fuller |
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218 | ISBN 0-471-28715-6 |
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219 | |
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220 | MODIFICATION HISTORY:</div> |
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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 | <h3>Parameters</h3> |
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226 | |
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227 | |
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228 | <h4 id="_TimeCross_Cov_param_Xd">Xd |
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229 | |
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237 | </h4> |
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238 | |
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239 | <div class="comments"></div> |
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240 | |
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241 | <h4 id="_TimeCross_Cov_param_Yd">Yd |
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242 | |
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248 | |
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249 | |
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250 | </h4> |
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251 | |
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252 | <div class="comments"></div> |
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253 | |
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254 | <h4 id="_TimeCross_Cov_param_M">M |
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255 | |
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261 | |
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262 | |
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263 | </h4> |
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264 | |
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265 | <div class="comments"></div> |
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266 | |
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267 | <h4 id="_TimeCross_Cov_param_nT">nT |
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268 | |
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270 | |
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274 | |
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275 | |
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276 | </h4> |
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277 | |
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278 | <div class="comments"></div> |
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279 | |
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280 | <h4 id="_TimeCross_Cov_param_Ndim">Ndim |
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281 | |
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282 | |
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283 | |
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284 | |
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287 | |
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288 | |
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289 | </h4> |
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290 | |
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291 | <div class="comments"></div> |
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292 | |
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293 | |
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296 | |
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297 | |
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298 | <h3>Keywords</h3> |
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299 | |
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300 | <h4 id="_TimeCross_Cov_keyword_Double">Double |
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301 | |
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307 | |
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308 | |
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309 | </h4> |
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310 | |
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311 | <div class="comments"></div> |
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312 | |
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313 | <h4 id="_TimeCross_Cov_keyword_ZERO2NAN">ZERO2NAN |
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314 | |
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315 | |
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316 | |
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317 | |
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318 | |
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320 | |
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321 | |
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322 | </h4> |
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323 | |
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324 | <div class="comments"></div> |
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349 | |
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350 | |
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351 | </div> |
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352 | |
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353 | |
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354 | <div class="routine_details" id="_C_Timecorrelate"> |
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355 | |
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356 | <h2><a class="top" href="#container">top</a>C_Timecorrelate </h2> |
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357 | |
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358 | <p class="header"> |
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359 | <span class="result">result = </span>C_Timecorrelate(<span class="result"><a href="#_C_Timecorrelate_param_X">X</a>, <a href="#_C_Timecorrelate_param_Y">Y</a>, <a href="#_C_Timecorrelate_param_Lag">Lag</a></span>, <a href="#_C_Timecorrelate_keyword_Covariance">Covariance</a>=<span class="result">Covariance</span>, <a href="#_C_Timecorrelate_keyword_Double">Double</a>=<span class="result">Double</span>)</p> |
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360 | |
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361 | <div class="comments"></div> |
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362 | |
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363 | |
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364 | |
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365 | |
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366 | <h3>Parameters</h3> |
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367 | |
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368 | |
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369 | <h4 id="_C_Timecorrelate_param_X">X |
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370 | |
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376 | |
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377 | |
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378 | </h4> |
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379 | |
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380 | <div class="comments"></div> |
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381 | |
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382 | <h4 id="_C_Timecorrelate_param_Y">Y |
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383 | |
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384 | |
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386 | |
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389 | |
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390 | |
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391 | </h4> |
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392 | |
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393 | <div class="comments"></div> |
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394 | |
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395 | <h4 id="_C_Timecorrelate_param_Lag">Lag |
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396 | |
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397 | |
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404 | </h4> |
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406 | <div class="comments"></div> |
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411 | |
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412 | |
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413 | <h3>Keywords</h3> |
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414 | |
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415 | <h4 id="_C_Timecorrelate_keyword_Covariance">Covariance |
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424 | </h4> |
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425 | |
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426 | <div class="comments"></div> |
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427 | |
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428 | <h4 id="_C_Timecorrelate_keyword_Double">Double |
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