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</o:shapelayout></xml><![endif]--></head><body lang=DE link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span lang=EN-GB>Thanks. While not giving me ONE number, the analysis shows that my random generated xyz positions are uncorrelated as they should. Can one estimate the error bars for the xy xz and yz correlations?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Now, I can use this approach for actual measurements in real objects</span><span lang=EN-GB style='font-family:"Times New Roman",serif'>…</span><span lang=EN-GB><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>Heinz<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>//START<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>function Y=corrmatrix(M)<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> C = cov(M); // covariance matrix<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> D = sqrt(diag(C)); // standard deviations<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> D = inv(diag(D));<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> Y = D*C*D; // correlation matrix<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>endfunction<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>n=10000;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>r=23;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>radius = r*grand(n,1,'def').^(1/3); <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>phi = 2*%pi*grand(n,1, 'def'); <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>costheta = 1 - 2*grand(n,1, 'def'); <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>radsintheta = radius.*sin(acos(costheta));<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>X = [radsintheta.*cos(phi),radsintheta.*sin(phi), radius.*costheta];<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>Y = corrmatrix(X)<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> 1. 0.0058073 0.0078778<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> 0.0058073 1. 0.0014375<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB> 0.0078778 0.0014375 1. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>//END<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US>From:</span></b><span lang=EN-US> users [mailto:users-bounces@lists.scilab.org] <b>On Behalf Of </b>Rafael Guerra<br><b>Sent:</b> 08 February 2018 18:55<br><b>To:</b> Users mailing list for Scilab <users@lists.scilab.org><br><b>Subject:</b> Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoPlainText><span lang=EN-US>Hi Heinz,<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US style='font-size:10.0pt'><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>Scilab computes the covariance matrix and from which the correlation matrix can be obtained using formula in <a href="https://en.wikipedia.org/wiki/Covariance_matrix">https://en.wikipedia.org/wiki/Covariance_matrix</a><o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US style='font-size:10.0pt'><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>Check implementation below:<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US style='font-size:10.0pt'><o:p> </o:p></span></p><p class=MsoNormal><i><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:#64AE64'>//START OF CODE</span></i><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p></o:p></span></p><p class=MsoNormal><i><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:#64AE64'>// <a href="https://en.wikipedia.org/wiki/Covariance_matrix">https://en.wikipedia.org/wiki/Covariance_matrix</a></span></i><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif;color:#B01813'>function</span><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'> <b><span style='color:#834310'>Y</span></b><span style='color:#5C5C5C'>=</span><u><span style='color:black'>corrmatrix</span></u><span style='color:#4A55DB'>(</span><b><span style='color:#834310'>M</span></b><span style='color:#4A55DB'>)</span><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'> <span style='color:black'>C</span> <span style='color:#5C5C5C'>=</span> <u><span style='color:#AE5CB0'>cov</span></u><span style='color:#4A55DB'>(</span><b><span style='color:#834310'>M</span></b><span style='color:#4A55DB'>)</span><span style='color:black'>;</span> <i><span style='color:#64AE64'>// covariance matrix</span></i><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'> <span style='color:black'>D</span> <span style='color:#5C5C5C'>=</span> <span style='color:#32B9B9'>sqrt</span><span style='color:#4A55DB'>(</span><span style='color:#32B9B9'>diag</span><span style='color:#4A55DB'>(</span><span style='color:black'>C</span><span style='color:#4A55DB'>))</span><span style='color:black'>;</span> <i><span style='color:#64AE64'>// standard deviations</span></i><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'> <span style='color:black'>D</span> <span style='color:#5C5C5C'>=</span> <span style='color:#32B9B9'>inv</span><span style='color:#4A55DB'>(</span><span style='color:#32B9B9'>diag</span><span style='color:#4A55DB'>(</span><span style='color:black'>D</span><span style='color:#4A55DB'>))</span><span style='color:black'>;</span><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'> <b><span style='color:#834310'>Y</span></b> <span style='color:#5C5C5C'>=</span> <span style='color:black'>D</span><span style='color:#5C5C5C'>*</span><span style='color:black'>C</span><span style='color:#5C5C5C'>*</span><span style='color:black'>D;</span> <i><span style='color:#64AE64'>// correlation matrix</span></i><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif;color:#B01813'>endfunction</span><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:black'>M</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:#32B9B9'>grand</span><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>9</span><span style='color:black'>,</span><span style='color:rosybrown'>3</span><span style='color:black'>,</span><span style='color:rosybrown'>"def"</span><span style='color:#4A55DB'>)</span><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:black'>M</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:black'>,</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:black'>M</span><span style='color:#4A55DB'>(</span><span style='color:#FFAA00'>:</span><span style='color:black'>,</span><span style='color:rosybrown'>1</span><span style='color:#4A55DB'>)</span><span style='color:#5C5C5C'>*</span><span style='color:rosybrown'>2</span><span style='color:black'>;</span><o:p></o:p></span></p><p class=MsoNormal><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:black'>Y</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <u><span style='color:black'>corrmatrix</span></u><span style='color:#4A55DB'>(</span><span style='color:black'>M</span><span style='color:#4A55DB'>)</span><span style='color:black'>;</span><o:p></o:p></span></p><p class=MsoNormal><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:#32B9B9'>disp</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB'>(</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:black'>M,</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:rosybrown'>"M"</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB'>)</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p></o:p></span></p><p class=MsoNormal><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:#32B9B9'>disp</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB'>(</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:black'>Y,</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:rosybrown'>"Y"</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB'>)</span><span lang=ES style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p></o:p></span></p><p class=MsoNormal><i><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif;color:#64AE64'>// END OF CODE</span></i><span lang=EN-US style='font-size:10.0pt;font-family:"Monospaced",serif'><o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US style='font-size:10.0pt'><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>Regards,<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US style='color:black'>Rafael<o:p></o:p></span></p></div></body></html>