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标题:
ATLAB 脚本进行最小二乘法拟合
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作者:
2744557306
时间:
2023-12-31 16:12
标题:
ATLAB 脚本进行最小二乘法拟合
这是一个 MATLAB 脚本，用于进行最小二乘法拟合。脚本首先要求用户输入已知点的 x 和 y 坐标，然后输入拟合的多项式次数 n。脚本使用最小二乘法拟合数据，并绘制了原始数据点和拟合曲线的图表。以下是对代码的主要部分的解释：
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function fp = fitpt()
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% 最小二乘
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% 基取 {1, x, ...}
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% fitpt.m
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% 默认算例为课本：P65，例3.2
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% x = [0,1,2,3,4,5,6,7]
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% y = [3.95,6.82,9.78,12.91,15.74,19.26,21.73,24.07]
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% 结果：P(x) = 4.005 + 2.936x 平方误差=0.6162
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% MatLab函数：polyfit(x, y, n)
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s = input('<最小二乘>\n输入已知点的x坐标：（回车表示[0,1,2,3,4,5,6,7]）\n', 's');
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if isempty(s)
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s = '[0,1,2,3,4,5,6,7]';
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else
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if (s(1) ~= '[')
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s = strcat('[', s);
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s = strcat(s, ']');
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end
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end
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x = sym(s);
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s = input('输入已知点的y坐标：（回车表示[3.95,6.82,9.78,12.91,15.74,19.26,21.73,24.07]）\n', 's');
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if isempty(s)
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s = '[3.95,6.82,9.78,12.91,15.74,19.26,21.73,24.07]';
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else
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if (s(1) ~= '[')
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s = strcat('[', s);
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s = strcat(s, ']');
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end
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end
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y = sym(s);
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sz = size(x);
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sz = sz(2);
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n = input('输入多项式次数n：');
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if (n + 1 > sz)
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n = input('多项式次数需要小于已知点个数，请重新输入n：');
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end
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if (n + 1 > sz)
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error('多项式次数不能小于已知点个数！');
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end
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fp = s_fitpt_p(x, y, n);
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% 绘制原始数据点和拟合曲线
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plot(double(x), double(y), 'r*')
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hold on
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a = double(x(1));
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b = double(x(sz));
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x = a:abs(b - 1)/100:b;
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y = subs(fp, x);
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plot(x, y)
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function f = s_fitpt_p(x, y, n)
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% 用 n 次多项式实现的最小二乘法
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sz = size(x);
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sz = sz(2);
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A = zeros(sz, n + 1);
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v = vh(n);
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for i = 1:sz
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A(i,
= subs(v, double(x(i)));
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end
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f = linsolve(A' * A, A' * y');
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f = vpa(f, 4);
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f = v * f;
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function v = vh(n)
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% Create vector in horizontal style, such as
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% v = [1, x, x^2, ..., x^n]
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if (n < 0 || n > 9)
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error('Make sure ''n'' is in range of [0, 9]')
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end
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s = '';
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for i = 0:n
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s = strcat(s, ',x^');
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s = strcat(s, num2str(i));
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end
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s(1) = '[';
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sz = size(s);
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s(sz(2) + 1) = ']';
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v = simplify(sym(s));
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end
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这个脚本首先获取用户输入的已知点的 x 和 y 坐标，然后使用最小二乘法进行拟合。最后，脚本绘制了原始数据点和拟合曲线的图表。
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= subs(v, double(x(i)));/ o4 c4 ^3 s, h" s! a