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 ])