gradient descent implementation

octave:

function parameters = gd(input, output, theta, step, eps)
% function that implement gradient descent algorithm
col = length(output);
do
  % j = 1 / 2 / col * sum((theta' * input - output) .^ 2);
  % 上行注释计算costfunction
  update = 1 / col * input * (theta' * input - output)';
  theta = theta - step * update;
until max(abs(update)) <= eps
parameters = theta;

值得一提的是，由于线性代数拙计，这里的更新规则我推了好久。。。

c:

void gd(trainingset *t, hypothesis *h, double step, double eps) {
    double * temp = MA(double, t->features + 1); //给偏导数向量申请空间
    double sum = 0;
    double sum_temp = 0;
    do {
        for (int i = 0; i < t->features + 1; i++) {
            sum = 0;
            for (int j = 0; j < t->count; j++) {
                sum_temp = 0;
                for (int k = 0; k < t->features + 1; k++) {
                    //计算h(x)
                    sum_temp += h->p[k] * t->p[j*(t->features + 2) + k];
                }
                //h(x)-y
                sum_temp -= t->p[j*(t->features + 2) + t->features + 1];
                //(h(x)-y)*xj
                sum_temp *= t->p[j*(t->features + 2) + i];
                //从1-m对上式求和
                sum += sum_temp;
            }
            sum /= t->count; //求和之后除样本总数
            sum *= step;     //乘学习速率
            temp[i] = sum;   //将偏导数项赋值给偏导数向量，计算完成之后一起更新
        }
        for (int i = 0; i < t->features + 1; i++) {
            h->p[i] -= temp[i]; //更新参数Theta
        }
    } while (!is_converge(temp, t->features + 1, eps)); //判断是否收敛
    free(temp);
}