|
| 1 | +import math |
| 2 | + |
| 3 | +class Var: |
| 4 | + def __init__(self, val, deriv=1.0): |
| 5 | + self.val = val |
| 6 | + self.deriv = deriv |
| 7 | + |
| 8 | + def __add__(self, other): |
| 9 | + if isinstance(other, Var): |
| 10 | + val = self.val + other.val |
| 11 | + deriv = self.deriv + other.deriv |
| 12 | + else: |
| 13 | + val = self.val + other |
| 14 | + deriv = self.deriv |
| 15 | + return Var(val, deriv) |
| 16 | + |
| 17 | + def __radd__(self, other): |
| 18 | + return self + other |
| 19 | + |
| 20 | + def __sub__(self, other): |
| 21 | + if isinstance(other, Var): |
| 22 | + val = self.val - other.val |
| 23 | + deriv = self.deriv - other.deriv |
| 24 | + else: |
| 25 | + val = self.val - other |
| 26 | + deriv = self.deriv |
| 27 | + return Var(val, deriv) |
| 28 | + |
| 29 | + def __rsub__(self, other): |
| 30 | + val = other - self.val |
| 31 | + deriv = - self.deriv |
| 32 | + return Var(val, deriv) |
| 33 | + |
| 34 | + def __mul__(self, other): |
| 35 | + if isinstance(other, Var): |
| 36 | + val = self.val * other.val |
| 37 | + deriv = self.val * other.deriv + self.deriv * other.val |
| 38 | + else: |
| 39 | + val = self.val * other |
| 40 | + deriv = self.deriv * other |
| 41 | + return Var(val, deriv) |
| 42 | + |
| 43 | + def __rmul__(self, other): |
| 44 | + return self * other |
| 45 | + |
| 46 | + def __truediv__(self, other): |
| 47 | + if isinstance(other, Var): |
| 48 | + val = self.val / other.val |
| 49 | + deriv = (self.deriv * other.val - self.val * other.deriv)/other.val**2 |
| 50 | + else: |
| 51 | + val = self.val / other |
| 52 | + deriv = self.deriv / other |
| 53 | + return Var(val, deriv) |
| 54 | + |
| 55 | + def __rtruediv__(self, other): |
| 56 | + val = other / self.val |
| 57 | + deriv = other * 1/self.val**2 |
| 58 | + return Var(val, deriv) |
| 59 | + |
| 60 | + def __repr__(self): |
| 61 | + return "value: {}\t deriv: {}".format(self.val, self.deriv) |
| 62 | + |
| 63 | + |
| 64 | +def exp(f: Var): |
| 65 | + return Var(math.exp(f.val), math.exp(f.val) * f.deriv) |
| 66 | + |
| 67 | + |
| 68 | +fx = lambda x: exp(x*x - x)/x |
| 69 | + |
| 70 | +df = fx(Var(2.0)) |
| 71 | +print(df) |
| 72 | + |
| 73 | +# value: 3.694528049465325 deriv: 9.236320123663312 |
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