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<TITLE> 多项式契合及函数计算 </TITLE>
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<H1>7.3.3 多项式契合及函数计算</H1>
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和<FONT FACE="Times New Roman"> </FONT><FONT COLOR=#FF0000 FACE="Times New Roman">polyfit</FONT><FONT FACE="Times New Roman"></FONT>有关的另一个函数是用来做多项式函数计算<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">polyval</FONT>，由<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">polyfit</FONT><FONT FACE="Times New Roman">
</FONT>算出多项式的各个系数
<FONT FACE="Times New Roman">(<IMG SRC="img00016-2.gif" tppabs="http://166.111.167.223/computer/cai/matlabjc/img7/img00016.gif">)</FONT>后，即可以<FONT FACE="Times New Roman"> </FONT><FONT COLOR=#FF0000 FACE="Times New Roman">polyval</FONT><FONT FACE="Times New Roman">
</FONT>计算多项式的函数值。它的语法为<FONT COLOR=#FF0000 FACE="Times New Roman">polyval(coef,x)</FONT>，其中<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">coef</FONT><FONT FACE="Times New Roman">
</FONT>是多项式的各个系数所构成的阵列，<FONT COLOR=#FF0000 FACE="Times New Roman">x</FONT>则是要计算多项式值的<TT><FONT FACE="Courier New">x</FONT></TT>阵列。举一例说明
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> x=[0 1 2 3
4 5];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> y=[0 20 60
68 77 110];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> coef=polyfit(x,y,1);
% </FONT><FONT COLOR=#FF0000>计算线性回归的各项系数</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> ybest=polyval(coef,x);
% </FONT><FONT COLOR=#FF0000>直接以</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">polyval</FONT><FONT COLOR=#FF0000>计算多项式的数值
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这个函数<FONT FACE="Times New Roman"> </FONT><FONT COLOR=#FF0000 FACE="Times New Roman">polyval</FONT>真是大大的好用，如果没有它的话，那我们要计算多项式的函数值还要费一番功夫。假设已有五阶的
多项式回归，要计算对应的多项式值，则须以下的步骤
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> coef=polyfit(x,y,5);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a0=coef(1);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a1=coef(2);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a2=coef(3);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a3=coef(4);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a4=coef(5);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a5=coef(6);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> f=a0 + a1*x
+ a2*x.^2 + a3*x.^3 + a4*x.^4 + a5*x.^5;<BR>
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我们接著示范从二阶到九阶的多项式回归的程式
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> x=[0 1 2 3
4 5];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> y=[0 20 60
68 77 110];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> newx=0:0.05:5;
% </FONT><FONT COLOR=#FF0000>以新阵列形成更小增量以利回归计算及绘图</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> for n=2:9</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> f(:,n)=polyval(polyfit(x,y,n),newx)';</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> plot(newx,f(:,n),x,y,'o')</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> title(['Poly.
regression, deg=',int2str(n)])</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> xlabel('Time'),
ylabel('Temp'), grid</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> pause
% </FONT><FONT COLOR=#FF0000>每次要暂停看清楚图再执行下一步骤</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> end<BR>
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在上述的<FONT FACE="Times New Roman"> </FONT><FONT COLOR=#FF0000 FACE="Times New Roman">title</FONT>指令中我们示范了如何将一变数输入（<FONT COLOR=#FF0000 FACE="Times New Roman">n</FONT>代表多项式的阶数），是利用<FONT COLOR=#FF0000 FACE="Times New Roman">int2str</FONT>这个指令，它是用来
将一整数<FONT FACE="Times New Roman">(integer) </FONT>转换成为一个字串<FONT FACE="Times New Roman">
(string)</FONT>，因为在<FONT COLOR=#FF0000 FACE="Times New Roman">title</FONT>中只能以字串出现。此外在<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">title</FONT>指令中尚须以<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">[ ]</FONT><FONT FACE="Times New Roman">
</FONT>将所有
叙述包括在内。类似的指令尚有<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">num2str</FONT><FONT FACE="Times New Roman">
</FONT>它是用来将实数转换成一字串。有关这几个新介绍的详细说明，请参
考<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">title</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">int2str</FONT><TT><FONT FACE="Courier New">,
</FONT></TT><FONT COLOR=#FF0000 FACE="Times New Roman">num2str</FONT><FONT FACE="Times New Roman">
</FONT>的线上说明。
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