| import numpy as np |
| import scipy.signal |
|
|
|
|
| def discount(x, gamma): |
| """ |
| computes discounted sums along 0th dimension of x. |
| |
| inputs |
| ------ |
| x: ndarray |
| gamma: float |
| |
| outputs |
| ------- |
| y: ndarray with same shape as x, satisfying |
| |
| y[t] = x[t] + gamma*x[t+1] + gamma^2*x[t+2] + ... + gamma^k x[t+k], |
| where k = len(x) - t - 1 |
| |
| """ |
| assert x.ndim >= 1 |
| return scipy.signal.lfilter([1],[1,-gamma],x[::-1], axis=0)[::-1] |
|
|
| def explained_variance(ypred,y): |
| """ |
| Computes fraction of variance that ypred explains about y. |
| Returns 1 - Var[y-ypred] / Var[y] |
| |
| interpretation: |
| ev=0 => might as well have predicted zero |
| ev=1 => perfect prediction |
| ev<0 => worse than just predicting zero |
| |
| """ |
| assert y.ndim == 1 and ypred.ndim == 1 |
| vary = np.var(y) |
| return np.nan if vary==0 else 1 - np.var(y-ypred)/vary |
|
|
| def explained_variance_2d(ypred, y): |
| assert y.ndim == 2 and ypred.ndim == 2 |
| vary = np.var(y, axis=0) |
| out = 1 - np.var(y-ypred)/vary |
| out[vary < 1e-10] = 0 |
| return out |
|
|
| def ncc(ypred, y): |
| return np.corrcoef(ypred, y)[1,0] |
|
|
| def flatten_arrays(arrs): |
| return np.concatenate([arr.flat for arr in arrs]) |
|
|
| def unflatten_vector(vec, shapes): |
| i=0 |
| arrs = [] |
| for shape in shapes: |
| size = np.prod(shape) |
| arr = vec[i:i+size].reshape(shape) |
| arrs.append(arr) |
| i += size |
| return arrs |
|
|
| def discount_with_boundaries(X, New, gamma): |
| """ |
| X: 2d array of floats, time x features |
| New: 2d array of bools, indicating when a new episode has started |
| """ |
| Y = np.zeros_like(X) |
| T = X.shape[0] |
| Y[T-1] = X[T-1] |
| for t in range(T-2, -1, -1): |
| Y[t] = X[t] + gamma * Y[t+1] * (1 - New[t+1]) |
| return Y |
|
|
| def test_discount_with_boundaries(): |
| gamma=0.9 |
| x = np.array([1.0, 2.0, 3.0, 4.0], 'float32') |
| starts = [1.0, 0.0, 0.0, 1.0] |
| y = discount_with_boundaries(x, starts, gamma) |
| assert np.allclose(y, [ |
| 1 + gamma * 2 + gamma**2 * 3, |
| 2 + gamma * 3, |
| 3, |
| 4 |
| ]) |
|
|
