matlab求解多项式系数,matlab如何提取多项式的系数???
下面提供比贴在17楼更高效的
多项式系数提取函数。
最大不同就是新版本不再使用变量temp
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function [c,t]= poly_coeffs_new(fcn,var)
% 输入：
% fcn 为待确定系数值多项式的符号表达式
% var 为多项式的主变量，如果是单变量可省略之。
% 输出：
% c 为多项式系数向量，输出变量为两个时(即[c,t])，c向量分量从左到右所对应的变量幂次由高到低。
% 输出变量(只有c或没有时)， c向量分量从左到右所对应的变量幂次由低到高。
% t 与系数向量相对应项的变量向量，即 fcn=c*conj(t)'
var0=findsym(fcn);
if nargin<2;
var=var0;
lvar=length(var0);
else
if ismember(abs(char(var)),abs(char(var0)))
lvar=1; %%% 'var' is included in 'fcn'
else
lvar=0; %%% 'var' is not included in 'fcn'
end
end
switch lvar
case 0
c=fcn;
t=sym(1);
case 1
[c0,t0]=coeffs(fcn,var);
pwr=log2(subs(t0,2));
m=pwr(1);
c=sym(zeros(1,m+1));
if nargout==2
c(m+1-pwr)=c0;
t=sym(char(var)).^(m:-1:0); %%% If t=var.^(m:-1:0), it does not work.
else
c(pwr+1)=c0;
end
otherwise
error('Specify var please.');
end
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下面是新旧版本运行时间比较实验。
每次测试实验分别重复执行多项式系数提取函数100次。
test 比较新旧版本执行效率的测试函数，在附件中。
新版本可节省近一半的运行时间。
>> syms x y
>> f3 =x^5 + 2*x^3*y^4 + x*y^2 + 4
f3 =
x^5 + 2*x^3*y^4 + x*y^2 + 4
[c1,c2,t1,t2] = test(f3,x)
Elapsed time is 10.1461 seconds for poly_coeffs_new.
Elapsed time is 17.7343 seconds for poly_coeffs_new.
c1 =
[ 1, 0, 2*y^4, 0, y^2, 4]
c2 =
[ 1, 0, 2*y^4, 0, y^2, 4]
t1 =
[ x^5, x^4, x^3, x^2, x, 1]
t2 =
[ x^5, x^4, x^3, x^2, x, 1]
>> [c1,c2,t1,t2] = test(f3,x)
Elapsed time is 9.4647 seconds for poly_coeffs_new.
Elapsed time is 16.0407 seconds for poly_coeffs_new.
c1 =
[ 1, 0, 2*y^4, 0, y^2, 4]
c2 =
[ 1, 0, 2*y^4, 0, y^2, 4]
t1 =
[ x^5, x^4, x^3, x^2, x, 1]
t2 =
[ x^5, x^4, x^3, x^2, x, 1]
>> [c1,c2,t1,t2] = test(f3,x)
Elapsed time is 9.5414 seconds for poly_coeffs_new.
Elapsed time is 16.252 seconds for poly_coeffs (old version).
c1 =
[ 1, 0, 2*y^4, 0, y^2, 4]
c2 =
[ 1, 0, 2*y^4, 0, y^2, 4]
t1 =
[ x^5, x^4, x^3, x^2, x, 1]
t2 =
[ x^5, x^4, x^3, x^2, x, 1]
>> [c1,c2,t1,t2] = test(f3,x)
>> [c1,c2,t1,t2] = test(f3,y)
Elapsed time is 8.0488 seconds for poly_coeffs_new.
Elapsed time is 13.8489 seconds for poly_coeffs (old version).
c1 =
[ 2*x^3, 0, x, 0, x^5 + 4]
c2 =
[ 2*x^3, 0, x, 0, x^5 + 4]
t1 =
[ y^4, y^3, y^2, y, 1]
t2 =
[ y^4, y^3, y^2, y, 1]
>> [c1,c2] = test(f3,y)
Elapsed time is 6.2817 seconds for poly_coeffs_new.
Elapsed time is 12.4151 seconds for poly_coeffs (old version).
c1 =
[ x^5 + 4, 0, x, 0, 2*x^3]
c2 =
[ x^5 + 4, 0, x, 0, 2*x^3]
>> [c1,c2] = test(f3,x)
Elapsed time is 7.6425 seconds for poly_coeffs_new.
Elapsed time is 14.7012 seconds for poly_coeffs (old version).
c1 =
[ 4, y^2, 0, 2*y^4, 0, 1]
c2 =
[ 4, y^2, 0, 2*y^4, 0, 1]
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附件：1.新版本m文件
2.比较新旧版本执行效率的测试函数之m文件