function ff=f(net) %compute the output of hidden unit or output unit a=1.716; b=2/3; len=size(net,1); for numl=1:len ff(numl,:)=(2*a)/(1+exp(-b*net(numl,:)))-a; end

这段代码是一个常用的神经网络的激活函数，叫做 Sigmoid 函数，具体来说，它是一个双曲正切函数的变形，具有以下形式：

$$
f(x) = \frac{2}{1+e^{-bx}}-1.716
$$

其中，$b$ 为一个常数，可以控制函数的斜率，一般取值为 $2/3$。

这段代码的作用是计算神经网络中每个隐藏层或输出层的激活值，即输入到 Sigmoid 函数中的参数 $net$。对于每个输入，Sigmoid 函数会将其映射到 $[-1,1]$ 的范围内。这个过程也被称为“激活”。

值得注意的是，由于 Sigmoid 函数的取值范围不包括 $0$，因此该函数容易产生“梯度消失”问题，即当输入值过大或过小时，函数的导数会变得非常小。为了解决这个问题，后来出现了更加稳定的激活函数，如 ReLU、LeakyReLU 等。

相关问题

Please use C language and pointers to define a function to compute the integral of any unary function.

Here is an example implementation of a function to compute the integral of any unary function using C language and pointers:

#include <stdio.h>

double integral(double (*f)(double), double a, double b, int n) {
    double h = (b - a) / n;  // width of each subinterval
    double sum = 0.0;  // initialize the sum
    int i;
    for (i = 0; i < n; i++) {
        double x1 = a + i * h;
        double x2 = a + (i + 1) * h;
        double y1 = (*f)(x1);
        double y2 = (*f)(x2);
        double area = (y1 + y2) * h / 2.0;
        sum += area;
    }
    return sum;
}

// example usage
double square(double x) {
    return x * x;
}

int main() {
    double a = 0.0;
    double b = 1.0;
    int n = 1000;
    double result = integral(&square, a, b, n);
    printf("Integral of x^2 from %g to %g with %d subintervals: %g\n", a, b, n, result);
    return 0;
}

In this example, the `integral` function takes four arguments: a pointer to the unary function to integrate (`f`), the lower and upper bounds of integration (`a` and `b`, respectively), and the number of subintervals to use in the approximation (`n`). The function then computes the width of each subinterval (`h`), initializes the sum to 0, and iterates over the subintervals, computing the area under the curve for each and adding it to the sum. The final result is the sum of all the subinterval areas, which is returned by the function.

To demonstrate the usage of this function, the `square` function is defined as an example of a unary function to integrate, and is passed as a pointer to the `integral` function along with the bounds of integration and number of subintervals. The result is printed to the console.

Implement a function with Matlab to output the histogram values of a given grey level image. Display in the boxes the resulting histograms.

Sure, here's an implementation of a function in Matlab that takes a grey level image as input and outputs its histogram:

function [hist, edges] = grey_histogram(img)
% img: grey level image
% hist: histogram values
% edges: edges of histogram bins

% Compute histogram
[hist, edges] = histcounts(img, 256);

% Display histogram
figure;
bar(edges(1:end-1), hist);
xlabel('Grey Level');
ylabel('Frequency');
title('Grey Level Histogram');
end

To use this function, simply call it with your grey level image as input. For example:

img = imread('my_grey_image.jpg');
[hist, edges] = grey_histogram(img);

This will display a histogram of the grey levels in your image.