Also known as Logistic Function. 1 f(x) = ------- 1 + e⁻ˣ The sigmoid function approaches a value of 1 as its input 'x' becomes increasing positive. Opposite for negative values. Reference: https://en.wikipedia.org/wiki/Sigmoid_function @p
(z: float | np.ndarray)
| 29 | |
| 30 | |
| 31 | def sigmoid_function(z: float | np.ndarray) -> float | np.ndarray: |
| 32 | """ |
| 33 | Also known as Logistic Function. |
| 34 | |
| 35 | 1 |
| 36 | f(x) = ------- |
| 37 | 1 + e⁻ˣ |
| 38 | |
| 39 | The sigmoid function approaches a value of 1 as its input 'x' becomes |
| 40 | increasing positive. Opposite for negative values. |
| 41 | |
| 42 | Reference: https://en.wikipedia.org/wiki/Sigmoid_function |
| 43 | |
| 44 | @param z: input to the function |
| 45 | @returns: returns value in the range 0 to 1 |
| 46 | |
| 47 | Examples: |
| 48 | >>> float(sigmoid_function(4)) |
| 49 | 0.9820137900379085 |
| 50 | >>> sigmoid_function(np.array([-3, 3])) |
| 51 | array([0.04742587, 0.95257413]) |
| 52 | >>> sigmoid_function(np.array([-3, 3, 1])) |
| 53 | array([0.04742587, 0.95257413, 0.73105858]) |
| 54 | >>> sigmoid_function(np.array([-0.01, -2, -1.9])) |
| 55 | array([0.49750002, 0.11920292, 0.13010847]) |
| 56 | >>> sigmoid_function(np.array([-1.3, 5.3, 12])) |
| 57 | array([0.21416502, 0.9950332 , 0.99999386]) |
| 58 | >>> sigmoid_function(np.array([0.01, 0.02, 4.1])) |
| 59 | array([0.50249998, 0.50499983, 0.9836975 ]) |
| 60 | >>> sigmoid_function(np.array([0.8])) |
| 61 | array([0.68997448]) |
| 62 | """ |
| 63 | return 1 / (1 + np.exp(-z)) |
| 64 | |
| 65 | |
| 66 | def cost_function(h: np.ndarray, y: np.ndarray) -> float: |
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