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</o:shapelayout></xml><![endif]--></head><body bgcolor=white lang=FR link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=EN-US style='color:#1F497D'>Hi Adrien,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'>I forgot this basic … thanks<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'>I’ve another naïve question concerning eigen values calculation :<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'>D2 is a symmetrical 3x3 matrix while D1 not ; as expected, D1 gives 3 eigen values with (by convention) eigen_D1(1) > eigen_D1(2) > eigen_D1(3) … but this is not the case with the symmetrical matrix (under scilab5.3.3) -> the max value is on eigen_D2(<b>3</b>) … any reason ?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>D1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>[</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>0</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>]</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>D2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>[</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>]</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>eigen_D1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#32B9B9'>spec</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>D1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:windowtext'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:10.5pt;font-family:Monospaced;color:black'>eigen_D2</span><span style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span style='font-size:10.5pt;font-family:Monospaced;color:windowtext'> </span><span style='font-size:10.5pt;font-family:Monospaced;color:#32B9B9'>spec</span><span style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span style='font-size:10.5pt;font-family:Monospaced;color:black'>D2</span><span style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span style='font-size:10.5pt;font-family:Monospaced;color:windowtext'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'>Paul<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'>De :</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'> users-bounces@lists.scilab.org [mailto:users-bounces@lists.scilab.org] <b>De la part de</b> Adrien Vogt-Schilb<br><b>Envoyé :</b> mercredi 26 septembre 2012 22:32<br><b>À :</b> International users mailing list for Scilab.<br><b>Objet :</b> Re: [Scilab-users] funny result for tensor norm calculation<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>On 26/09/2012 19:42, Paul Carrico wrote:<o:p></o:p></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p class=MsoNormal><span lang=EN-US>Dear All,</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US>A funny result for calculating the norm of a tensor … for ounce a “traditional” method (that probably uses vectorization in back stage) is faster than the norm function …</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US>Paul</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#32B9B9'>mode</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>0</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>A</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>[</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>2</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>3</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>4</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>5</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>6</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>7</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>8</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>9</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>]</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1000</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>B</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i,j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>*</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j;</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><o:p></o:p></p><p class=MsoNormal><i><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#01A801'>// Scilab function</span></i><o:p></o:p></p><p class=MsoNormal><u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#AE5CB0'>tic</span></u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>()</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>;</span><o:p></o:p></p><p class=MsoNormal><u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#AE5CB0'>norm</span></u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>B</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>t1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#AE5CB0'>toc</span></u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>()</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><o:p></o:p></p><p class=MsoNormal><i><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#01A801'>// "traditional" method</span></i><o:p></o:p></p><p class=MsoNormal><i><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#01A801'>// norm = sqrt(trace(A_transp * A))</span></i><o:p></o:p></p><p class=MsoNormal><u><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#AE5CB0'>tic</span></u><o:p></o:p></p><p class=MsoNormal><span style='font-size:10.5pt;font-family:Monospaced;color:black'>norm_</span><span style='font-size:10.5pt;font-family:Monospaced'> </span><span style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span style='font-size:10.5pt;font-family:Monospaced'> </span><span style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><u><span style='font-size:10.5pt;font-family:Monospaced;color:#AE5CB0'>trace</span></u><span style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span style='font-size:10.5pt;font-family:Monospaced;color:black'>B</span><span style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>'*</span><span style='font-size:10.5pt;font-family:Monospaced;color:black'>B</span><span style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>))</span><span style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>**</span><span style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>0.5</span><o:p></o:p></p><p class=MsoNormal><span style='font-size:10.5pt;font-family:Monospaced;color:black'>t2</span><span style='font-size:10.5pt;font-family:Monospaced'> </span><span style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span style='font-size:10.5pt;font-family:Monospaced'> </span><u><span style='font-size:10.5pt;font-family:Monospaced;color:#AE5CB0'>toc</span></u><span style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>()</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US> </span><o:p></o:p></p></blockquote><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'>Hi<br>Yep, same result for me, the handmade computation is 4 times faster. Maybe norm i written assuming B is a complex hypermatrix or something.<br><br>But the real improvement would be to use a "vectorized" code to generate B, try this:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'><br>tic<br>n</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1000</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>B</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i,j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>*</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j;</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>toc<br><br><br>tic<br>BB=(1:n)'*(1:n);<br>toc<br><br>the second method is several hundred times faster than the first.<br><br><br>Note that the first method uses loops when matrix computations are able to do the job, and, worst, B is not initialized.<br><br>This means that every while, scilab will notice that B is larger than expected, and will ask for a new, larger place in memory to store B, will copy the existing B from the old place to the new one, only to find out later that B is actually even bigger.<br>I do not know how exactly this is implemented, but this can happen basically for each new value of i, so 1000 time.<br><br>The take away message is: when having to building a matrix with a loop, "initailize" your matrix:<br><br></span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>tic<br>n</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1000</span><span lang=EN-US style='font-size:12.0pt;font-family:"Times New Roman","serif"'> </span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>Bad</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i,j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>*</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j;</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>bad=toc()<br><br><br></span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>tic<br>Good = zeros(n,n);<br>n</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1000</span><span lang=EN-US style='font-size:12.0pt;font-family:"Times New Roman","serif"'> </span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>for</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:rosybrown'>1</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#FFAA00'>:</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>n</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>Good</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>(</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i,j</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#4A55DB'>)</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>=</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>i</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#5C5C5C'>*</span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:black'>j;</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced'> </span><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><o:p></o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:Monospaced;color:#A020F0'>end</span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>good=toc()<br><br>bad/good<br><br>//(in my PC this is already 3x faster)<br><br>tic<br>best=(1:n)'*(1:n);<br>best=toc()<br><br>bad/best<o:p></o:p></span></p></div></body></html>