计算sigmoid函数

Question

I am learning about machine learning from coursera. I am trying to calculate the sigmoid function and i have the below code:

function g = sigmoid(z)
%SIGMOID Compute sigmoid functoon
%   J = SIGMOID(z) computes the sigmoid of z.

% You need to return the following variables correctly 

g = zeros(size(z));

% ====================== YOUR CODE HERE ======================

% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
%               vector or scalar).



g = (1 + exp(-1 * z)) .^ -1;
 g = 1/(1+ (1/exp(z)))


% my question is why the first g calculation works for matrix(say 100*2) however the second only works for (100*1) as both are trying to do the same this.


% =============================================================

end

Answer 1

Sigmoid function g(z)=1/(1+e^(-z))

in octave it looks like

g = 1./(1 + exp(-z));

Answer 2

Correct answer

rt=-z;  %changing sign of z
rt=rt';  %transposing matrix

g=1./(1+e.^(rt));   %you need to use dot(.) while dividing and also while finding power to apply those operation for every element in the matrix.

Answer for your question

1.g = (1 + exp(-1 * z)) .^ -1;
2.g = 1/(1+ (1/exp(z)))           

you have missed dot operator(.) in second function for division and first function for exp() .

Answer 3

What you may want to try is to leverage the element operations (more info from Octave official documentation here ).

Note that with the element operations:

When you have two matrices of the same size, you can perform element by element operations on them

So as defined g and z are of the same size, the code below should return the Sigmoid function.

g = (g.+1)./(1 + e.^-z);

So essentially, it does 2 simple things. First, it turns the zeros matrix or scalar into one with ones "1". Then it divides each element with (1 + e ^z ) for each corresponding element.

Answer 4

.^ works for each element in the matrix. / does not. ./ might (though you might need to make some of the 1's matrices of 1's)

Answer 5

您需要使用 for 循环将 sigmoid 函数应用于向量或矩阵的每个元素。

Answer 6

In the latter case, you are trying to multiply (inverse of division) a multidimensional matrix with 1 which is literally a one-by-one matrix. So it will result in a 'Matrix dimensions must agree' error for a matrix having more than one column.

Answer 7

function g = sigmoid(z)
%SIGMOID Compute sigmoid function
%   g = SIGMOID(z) computes the sigmoid of z.

% You need to return the following variables correctly 
g = zeros(length(z),1);

for  i = 1:100,
  g(i) = 1/(1 + exp(-z(i)));

end

Answer 8

Following is the implementation in Octave:

Please add following code in file name sigmoid.m

function g = sigmoid(z)
g = 1 ./ (1+((e).^(-z)));
end

Following is Vector example from above implementation:

>> A = [1;2;3]
A =

   1
   2
   3

>> sigmoid(A)
ans =

   0.73106
   0.88080
   0.95257

Following is Scalar example from above implementation:

>> sigmoid(0)
ans =  0.50000

Answer 9

Well, you can make it like this:

g = ones(size(z)) ./ (ones(size(z)) + exp(-1 * z));

Turn 1 into a array with the dimension of z/g, then compute the sigmoid.