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<html xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <!--This HTML is auto-generated from an M-file.To make changes, update the M-file and republish this document. --> <title>polyfitn_demo</title> <meta name="generator" content="MATLAB 7.0.1"> <meta name="date" content="2006-08-08"> <meta name="m-file" content="polyfitn_demo"><style>body { background-color: white; margin:10px;}h1 { color: #990000; font-size: x-large;}h2 { color: #990000; font-size: medium;}p.footer { text-align: right; font-size: xx-small; font-weight: lighter; font-style: italic; color: gray;}pre.codeinput { margin-left: 30px;}span.keyword {color: #0000FF}span.comment {color: #228B22}span.string {color: #A020F0}span.untermstring {color: #B20000}span.syscmd {color: #B28C00}pre.showbuttons { margin-left: 30px; border: solid black 2px; padding: 4px; background: #EBEFF3;}pre.codeoutput { color: gray; font-style: italic;}pre.error { color: red;}/* Make the text shrink to fit narrow windows, but not stretch too far in wide windows. On Gecko-based browsers, the shrink-to-fit doesn't work. */ p,h1,h2,div { /* for MATLAB's browser */ width: 600px; /* for Mozilla, but the "width" tag overrides it anyway */ max-width: 600px; /* for IE */ width:expression(document.body.clientWidth > 620 ? "600px": "auto" );} </style></head> <body> <h2>Contents</h2> <div> <ul> <li><a href="#2">Fit a 1-d model to cos(x). We only need the even order terms.</a></li> <li><a href="#3">A surface model in 2-d, with all terms up to third order.</a></li> <li><a href="#4">A linear model, but with no constant term, in 2-d</a></li> <li><a href="#5">A model with various exponents, not all positive integers.</a></li> </ul> </div><pre class="codeinput"><span class="comment">% Author: John D'Errico</span><span class="comment">% Release: 2.0</span><span class="comment">% Release date: 8/8/06</span><span class="comment">% What follows are example usages of polyfitn, polyvaln, poly2sympoly, polyn2sym</span></pre><h2>Fit a 1-d model to cos(x). We only need the even order terms.<a name="2"></a></h2><pre class="codeinput">x = -2:.1:2;y = cos(x);p = polyfitn(x,y,<span class="string">'constant x^2 x^4 x^6'</span>)<span class="keyword">if</span> exist(<span class="string">'sympoly'</span>) == 2 <span class="comment">% Conversion to a sympoly. If nothing else, its a nice way to display the model.</span> polyn2sympoly(p)<span class="keyword">end</span><span class="keyword">if</span> exist(<span class="string">'sym'</span>) == 2 <span class="comment">% Conversion to a symbolic form. Its also nice.</span> polyn2sym(p)<span class="keyword">end</span><span class="comment">% Evaluate the regression model at some set of points</span>polyvaln(p,[0 .5 1])</pre><pre class="codeoutput">p = ModelTerms: [4x1 double] Coefficients: [0.99996 -0.49968 0.041242 -0.0012079] ParameterVar: [1.2876e-10 1.084e-09 4.6603e-10 1.3903e-11] ParameterStd: [1.1347e-05 3.2925e-05 2.1588e-05 3.7286e-06] R2: 1 RMSE: 3.1468e-05 VarNames: {'x'}A scalar sympoly object 0.99996 - 0.49968*x^2 + 0.041242*x^4 - 0.0012079*x^6ans = 0.99996 0.8776 0.54031</pre><h2>A surface model in 2-d, with all terms up to third order.<a name="3"></a></h2><pre class="codeinput"><span class="comment">% Use lots of data.</span>n = 1000;x = rand(n,2);y = exp(sum(x,2)) + randn(n,1)/100;p = polyfitn(x,y,3)<span class="keyword">if</span> exist(<span class="string">'sympoly'</span>) == 2 polyn2sympoly(p)<span class="keyword">end</span><span class="keyword">if</span> exist(<span class="string">'sym'</span>) == 2 polyn2sym(p)<span class="keyword">end</span><span class="comment">% Evaluate on a grid and plot:</span>[xg,yg]=meshgrid(0:.05:1);zg = polyvaln(p,[xg(:),yg(:)]);surf(xg,yg,reshape(zg,size(xg)))hold <span class="string">on</span>plot3(x(:,1),x(:,2),y,<span class="string">'o'</span>)hold <span class="string">off</span></pre><pre class="codeoutput">p = ModelTerms: [10x2 double] Coefficients: [1x10 double] ParameterVar: [1x10 double] ParameterStd: [1x10 double] R2: 0.99992 RMSE: 0.011198 VarNames: {}A scalar sympoly object 0.50402*X1^3 + 1.3927*X1^2*X2 - 0.017552*X1^2 + 1.3798*X1*X2^2 + 0.081473*X1*X2 + 1.2726*X1 + 0.43959*X2^3 + 0.087656*X2^2 + 1.2254*X2 + 0.96196</pre><img vspace="5" hspace="5" src="polyfitn_demo_01.png"> <h2>A linear model, but with no constant term, in 2-d<a name="4"></a></h2><pre class="codeinput">uv = rand(100,2);w = sin(sum(uv,2));p = polyfitn(uv,w,<span class="string">'u, v'</span>);<span class="keyword">if</span> exist(<span class="string">'sympoly'</span>) == 2 polyn2sympoly(p)<span class="keyword">end</span><span class="keyword">if</span> exist(<span class="string">'sym'</span>) == 2 polyn2sym(p)<span class="keyword">end</span></pre><pre class="codeoutput">A scalar sympoly object 0.76416*u + 0.70472*v</pre><h2>A model with various exponents, not all positive integers.<a name="5"></a></h2><pre class="codeinput"><span class="comment">% Note: with only 1 variable, x & y may be row or column vectors.</span>x = 1:10;y = 3 + 2./x + sqrt(x) + randn(size(x))/100;p = polyfitn(x,y,<span class="string">'constant x^-1 x^0.5'</span>);<span class="keyword">if</span> exist(<span class="string">'sympoly'</span>) == 2 polyn2sympoly(p)<span class="keyword">end</span><span class="keyword">if</span> exist(<span class="string">'sym'</span>) == 2 polyn2sym(p)<span class="keyword">end</span>xi = 1:.1:10;yi = polyvaln(p,xi);plot(x,y,<span class="string">'ro'</span>,xi,yi,<span class="string">'b-'</span>)</pre><pre class="codeoutput">A scalar sympoly object 2.9805 + 2.0448*x^-1 + 1.0041*x^0.5</pre><img vspace="5" hspace="5" src="polyfitn_demo_02.png"> <p class="footer"><br> Published with MATLAB® 7.0.1<br></p> <!--##### SOURCE BEGIN #####% Author: John D'Errico% Release: 2.0% Release date: 8/8/06% What follows are example usages of polyfitn, polyvaln, poly2sympoly, polyn2sym%% Fit a 1-d model to cos(x). We only need the even order terms.x = -2:.1:2;y = cos(x);p = polyfitn(x,y,'constant x^2 x^4 x^6')if exist('sympoly') == 2 % Conversion to a sympoly. If nothing else, its a nice way to display the model. polyn2sympoly(p)endif exist('sym') == 2 % Conversion to a symbolic form. Its also nice. polyn2sym(p)end% Evaluate the regression model at some set of pointspolyvaln(p,[0 .5 1])%% A surface model in 2-d, with all terms up to third order.% Use lots of data.n = 1000;x = rand(n,2);y = exp(sum(x,2)) + randn(n,1)/100;p = polyfitn(x,y,3)if exist('sympoly') == 2 polyn2sympoly(p)endif exist('sym') == 2 polyn2sym(p)end% Evaluate on a grid and plot:[xg,yg]=meshgrid(0:.05:1);zg = polyvaln(p,[xg(:),yg(:)]);surf(xg,yg,reshape(zg,size(xg)))hold onplot3(x(:,1),x(:,2),y,'o')hold off%% A linear model, but with no constant term, in 2-duv = rand(100,2);w = sin(sum(uv,2));p = polyfitn(uv,w,'u, v');if exist('sympoly') == 2 polyn2sympoly(p)endif exist('sym') == 2 polyn2sym(p)end%% A model with various exponents, not all positive integers.% Note: with only 1 variable, x & y may be row or column vectors.x = 1:10;y = 3 + 2./x + sqrt(x) + randn(size(x))/100;p = polyfitn(x,y,'constant x^-1 x^0.5');if exist('sympoly') == 2 polyn2sympoly(p)endif exist('sym') == 2 polyn2sym(p)endxi = 1:.1:10;yi = polyvaln(p,xi);plot(x,y,'ro',xi,yi,'b-')##### SOURCE END #####--> </body></html>⌨️ 快捷键说明
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