Matlab 梯度下降法线性拟合：自变量r与因变量z的完整程序

%7B%22title%22%3A%22Matlab%20%E6%A2%AF%E5%BA%A6%E4%B8%8B%E9%99%8D%E6%B3%95%E7%BA%BF%E6%80%A7%E6%8C%AF%E5%90%88%EF%BC%9A%E8%87%AA%E5%8F%98%E9%87%8Fr%E5%92%8C%E5%9B%A0%E5%8F%98%E9%87%8Fz%E7%9A%84%E5%AE%8C%E6%95%B4%E7%A8%8B%E5%BA%8F%22%2C%22description%22%3A%22%E6%96%87%E7%AB%A0%E6%8F%90%E4%BE%9B%E4%BA%86%E4%B8%80%E4%B8%AA%E5%AE%8C%E6%95%B4%E7%9A%84%20Matlab%20%E7%A8%8B%E5%BA%8F%EF%BC%8C%E4%BD%BF%E7%94%A8%E6%A2%AF%E5%BA%A6%E4%B8%8B%E9%99%8D%E6%B3%95%E5%AF%B9%E8%87%E5%8F%98%E9%87%8F%20r%20%E5%92%8C%E5%9B%A0%E5%8F%98%E9%87%8F%20z%20%E8%BF%9B%E8%A1%8C%E7%BA%BF%E6%80%A7%E6%8C%AF%E5%90%88%E3%80%82%E8%AF%A5%E7%A8%8B%E5%BA%8F%E5%8C%85%E6%8B%AC%E6%95%B0%E6%8D%AE%E7%94%9F%E6%88%90%E3%80%81%E6%A8%A1%E5%9E%8B%E5%8F%82%E6%95%B0%E5%88%9D%E5%A7%8B%E5%8C%96%E3%80%81%E8%BF%87%E6%AD%A5%E4%BC%98%E5%8C%96%E5%92%8C%E7%B4%A0%E6%9E%9C%E5%8F%AF%E8%A7%86%E5%8C%96%E3%80%82%22%2C%22keywords%22%3A%22Matlab%2C%20%E6%A2%AF%E5%BA%A6%E4%B8%8B%E9%99%8D%E6%B3%95%2C%20%E7%BA%BF%E6%80%A7%E6%8C%AF%E5%90%88%2C%20%E8%87%E5%8F%98%E9%87%8F%2C%20%E5%9B%A0%E5%8F%98%E9%87%8F%2C%20%E7%A8%8B%E5%BA%8F%2C%20%E4%BB%A3%E7%A0%81%2C%20%E7%AE%97%E6%B3%95%2C%20%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%2C%20%E6%95%B0%E6%8D%AE%E5%88%86%E6%9E%90%22%2C%22content%22%3A%22%25%20%E7%94%9F%E6%88%90%E6%A0%87%E6%9C%AC%E6%95%B0%E6%8D%AE%0A%25n%20%3D%20100%3B%20%25%20%E6%A0%87%E6%9C%AC%E6%95%B0%E9%87%8F%0A%0A%25r%20%3D%20linspace(0%2C%2010%2C%20n)%27%3B%20%25%20%E8%87%E5%8F%98%E9%87%8Fr%EF%BC%8C%E8%8C%82%E5%9B%B4%E4%BB%8E0%E5%88%B010%0A%25z%20%3D%203%20*%20r%20%2B%202%20%2B%20randn(n%2C%201)%3B%20%25%20%E5%9B%A0%E5%8F%98%E9%87%8Fz%EF%BC%8C%E6%9C%8D%E5%90%8C%E7%BA%BF%E6%80%A7%E5%85%B3%E7%B3%BBz%20%3D%203r%20%2B%202%EF%BC%8C%E5%8A%A0%E5%85%A5%E5%9C%B0%E5%90%B9%E5%A4%9A%E5%B0%BC%E5%88%86%E5%B8%83%E7%9A%84%E5%9C%B0%E5%90%B9%0A%0A%25%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A8%A1%E5%9E%8B%E5%8F%82%E6%95%B0%0A%25theta%20%3D%20%5B0%3B%200%5D%3B%20%25%20%E5%8F%82%E6%95%B0%E5%90%91%E9%87%8F%EF%BC%8C%E5%8C%85%E6%8B%AC%E6%96%9C%E7%8E%87%E5%92%8C%E6%88%AA%E6%89%93%0A%25alpha%20%3D%200.01%3B%20%25%20%E5%AD%A6%E4%B9%A0%E7%8E%87%0A%25iterations%20%3D%201000%3B%20%25%20%E8%BF%87%E6%AD%A5%E6%AC%A1%E6%95%B0%0A%0A%25%20%E4%BD%BF%E7%94%A8%E6%A2%AF%E5%BA%A6%E4%B8%8B%E9%99%8D%E6%B3%95%E8%BF%9B%E8%A1%8C%E7%BA%BF%E6%80%A7%E6%8C%AF%E5%90%88%0A%25for%20iter%20%3D%201%3Aiterations%0A%25%20%20%20%20%25%20%E8BA%8F%E7%AE%97%E9%A2%84%E6%B8%AC%E5%80%BC%0A%25%20%20%20%20z_pred%20%3D%20theta(1)%20*%20r%20%2B%20theta(2)%3B%0A%0A%25%20%20%20%20%25%20%E8BA%8F%E7%AE%97%E9%89%84%E5%85%A5%0A%25%20%20%20%20error%20%3D%20z_pred%20-%20z%3B%0A%0A%25%20%20%20%20%25%20%E6%9B%B4%E6%96%B0%E5%8F%82%E6%95%B0%0A%25%20%20%20%20theta(1)%20%3D%20theta(1)%20-%20alpha%20*%20(1%2Fn)%20*%20sum(error%20.%20r)%3B%0A%25%20%20%20%20theta(2)%20%3D%20theta(2)%20-%20alpha%20%20(1%2Fn)%20*%20sum(error)%3B%0A%0A%25%20%20%20%20%25%20%E8BA%8F%E7%AE%97%E6%8D%9F%E5%A4%9A%E5%87%BD%E6%95%B0%EF%BC%88%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AE%EF%BC%89%0A%25%20%20%20%20loss%20%3D%20(1%2F(2n))%20%20sum(error.^2)%3B%0A%0A%25%20%20%20%20%25%20%E6%89%93%E5%8D%B0%E6%8D%9F%E5%A4%9A%E5%87%BD%E6%95%B0%E5%80%BC%0A%25%20%20%20%20fprintf('Iteration%20%d%2C%20Loss%20%3D%20%f '%2C%20iter%2C%20loss)%3B%0A%25end%0A%0A%25%20%E6%89%93%E5%8D%B0%E7%BB%88%E6%9E%81%E5%8F%82%E6%95%B0%E5%80%BC%0A%25fprintf('Final%20parameters%3A%20theta0%20%3D%20%f%2C%20theta1%20%3D%20%f '%2C%20theta(2)%2C%20theta(1)%3B%0A%0A%25%20%E7%BB%98%E5%88%B6%E6%8C%AF%E5%90%88%E7%B4%A0%E6%9E%9C%0A%25plot(r%2C%20z%2C%20'b.')%3B%20%25%20%E7%BB%98%E5%88%B6%E6%A0%87%E6%9C%AC%E6%95%B0%E6%8D%AE%E7%82%B9%0A%25hold%20on%3B%0A%25plot(r%2C%20theta(1)%20*%20r%20%2B%20theta(2)%2C%20'r-')%3B%20%25%20%E7%BB%98%E5%88%B6%E6%8C%AF%E5%90%88%E76F%E7%9B%B4%E7%BA%BF%0A%25legend('Sample%20Data'%2C%20'Fitted%20Line')%3B%0A%25xlabel('r')%3B%0A%25ylabel('z')%3B%0A