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</o:shapelayout></xml><![endif]--></head><body lang=DE link="#0563C1" vlink="#954F72"><div class=WordSection1><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><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></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>For random generated xyz positions, I get the matrix below and this looks fine with me:<o:p></o:p></span></p><table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=192 style='width:144.0pt;border-collapse:collapse'><tr style='height:36.75pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:36.75pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>1.000<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:36.75pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.009<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:36.75pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.003<o:p></o:p></span></p></td></tr><tr style='height:15.0pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.009<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>1.000<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.001<o:p></o:p></span></p></td></tr><tr style='height:15.0pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.003<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.001<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>1.000<o:p></o:p></span></p></td></tr><tr style='height:15.0pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p></td></tr></table><p class=MsoPlainText><span lang=EN-US> <o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>But this here is a manufactured object and every singly xyz-value is obtained from X-ray tomography<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><a href="https://www.dropbox.com/s/87osn38agn8jfzo/Measured%2016867%20data%20points%20in%203d.png?dl=0">https://www.dropbox.com/s/87osn38agn8jfzo/Measured%2016867%20data%20points%20in%203d.png?dl=0</a><o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>and looks much more regular than the Monte-Carlo. However, the correlation analysis suggested here, gives much the same numbers.<o:p></o:p></span></p><table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=192 style='width:144.0pt;border-collapse:collapse'><tr style='height:15.0pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>1.000<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.009<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>0.008<o:p></o:p></span></p></td></tr><tr style='height:15.0pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.009<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>1.000<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.001<o:p></o:p></span></p></td></tr><tr style='height:15.0pt'><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>0.008<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>-0.001<o:p></o:p></span></p></td><td width=64 nowrap valign=bottom style='width:48.0pt;padding:0cm 3.5pt 0cm 3.5pt;height:15.0pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:black'>1.000<o:p></o:p></span></p></td></tr></table><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>Perhaps, I have asked the wrong question: <o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US style='font-family:Wingdings'>à</span><span lang=EN-US>what I need is one single figures that summarizes the spatial correlation.<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>Heinz<o:p></o:p></span></p></div></body></html>