http://www.convexoptimization.com/wikimization/index.php?action=history&feed=atom&title=Memoryless_Weak_Nonlinearity_Composition 2026-05-25T04:15:32Z Revision history for this page on the wiki MediaWiki 1.11.0 http://www.convexoptimization.com/wikimization/index.php?title=Memoryless_Weak_Nonlinearity_Composition&diff=3314&oldid=prev 2024-12-03T05:10:06Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 05:10, 3 December 2024</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>% zeta : memoryless weak power series z(x), first-order leading: [zeta_1, zeta_2 ... zeta_Nt]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>% zeta : memoryless weak power series z(x), first-order leading: [zeta_1, zeta_2 ... zeta_Nt]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>% xi : memoryless weak power series y(z), first-order leading: [ xi_1, xi_2 ... xi_Nh]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>% xi : memoryless weak power series y(z), first-order leading: [ xi_1, xi_2 ... xi_Nh]</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>% Mapping coefficients constituting nonlinearity composition zeta &amp; xi are not commutative.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>% Mapping coefficients<ins style="color: red; font-weight: bold; text-decoration: none;">, </ins>constituting nonlinearity composition<ins style="color: red; font-weight: bold; text-decoration: none;">, </ins>zeta &amp; xi are not commutative.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>function y = composite2(zeta, xi, precision)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>function y = composite2(zeta, xi, precision)</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> if nargin &lt; 3, precision = 34; end</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> if nargin &lt; 3, precision = 34; end</div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Memoryless_Weak_Nonlinearity_Composition&diff=3313&oldid=prev 2024-12-03T00:59:16Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 00:59, 3 December 2024</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;pre&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;pre&gt;</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>% Compute y(z(x)) coefficients of x given mapping coefficients xi <del style="color: red; font-weight: bold; text-decoration: none;">and zeta</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>% Compute <ins style="color: red; font-weight: bold; text-decoration: none;">composition </ins>y(z(x)) coefficients of x given mapping coefficients <ins style="color: red; font-weight: bold; text-decoration: none;">zeta &amp; </ins>xi.</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>% <del style="color: red; font-weight: bold; text-decoration: none;">xi </del>: <del style="color: red; font-weight: bold; text-decoration: none;">polynomial y(</del>z), first order leading: [<del style="color: red; font-weight: bold; text-decoration: none;">xi_1</del>, <del style="color: red; font-weight: bold; text-decoration: none;"> xi_2, </del>...]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>% <ins style="color: red; font-weight: bold; text-decoration: none;">zeta </ins>: <ins style="color: red; font-weight: bold; text-decoration: none;">memoryless weak power series </ins>z<ins style="color: red; font-weight: bold; text-decoration: none;">(x</ins>), first<ins style="color: red; font-weight: bold; text-decoration: none;">-</ins>order leading: [<ins style="color: red; font-weight: bold; text-decoration: none;">zeta_1</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">zeta_2 </ins>... <ins style="color: red; font-weight: bold; text-decoration: none;">zeta_Nt</ins>]</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>% <del style="color: red; font-weight: bold; text-decoration: none;">zeta </del>: <del style="color: red; font-weight: bold; text-decoration: none;">polynomial z</del>(<del style="color: red; font-weight: bold; text-decoration: none;">x</del>), first order leading: [<del style="color: red; font-weight: bold; text-decoration: none;">zeta_1, zeta_2</del>, ...]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>% <ins style="color: red; font-weight: bold; text-decoration: none;">xi </ins>: <ins style="color: red; font-weight: bold; text-decoration: none;">memoryless weak power series y</ins>(<ins style="color: red; font-weight: bold; text-decoration: none;">z</ins>), first<ins style="color: red; font-weight: bold; text-decoration: none;">-</ins>order leading: [ <ins style="color: red; font-weight: bold; text-decoration: none;"> xi_1</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;"> xi_2 </ins>... <ins style="color: red; font-weight: bold; text-decoration: none;"> xi_Nh</ins>]</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">% Mapping coefficients constituting nonlinearity composition zeta &amp; xi are not commutative.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>function y = composite2(zeta, xi, precision)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>function y = composite2(zeta, xi, precision)</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> if nargin &lt; 3, precision = 34; end</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> if nargin &lt; 3, precision = 34; end</div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Memoryless_Weak_Nonlinearity_Composition&diff=3312&oldid=prev 2024-11-23T03:11:32Z

<p>New page: &lt;pre&gt; % Compute y(z(x)) coefficients of x given mapping coefficients xi and zeta. % xi : polynomial y(z), first order leading: [xi_1, xi_2, ...] % zeta : polynomial z(x), first order...</p> <p><b>New page</b></p><div>&lt;pre&gt;<br /> % Compute y(z(x)) coefficients of x given mapping coefficients xi and zeta.<br /> % xi : polynomial y(z), first order leading: [xi_1, xi_2, ...]<br /> % zeta : polynomial z(x), first order leading: [zeta_1, zeta_2, ...]<br /> function y = composite2(zeta, xi, precision)<br /> if nargin &lt; 3, precision = 34; end<br /> mp.Digits(precision); %Advanpix Multiprecision Toolbox<br /> zeta = zeta(:)'; <br /> xi = xi(:)';<br /> y = mp('0');<br /> z_power = mp('1'); <br /> for power = 1:numel(xi)<br /> z_power = conv(z_power, zeta); <br /> term = [zeros(1,power-1,'mp'), xi(power)*z_power];<br /> y = term + [y, zeros(1,numel(term)-numel(y),'mp')];<br /> end<br /> end<br /> &lt;/pre&gt;</div>

Ranjelin