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import numpy as onp
from scipy.signal import lfilter

import jax
import jax.numpy as jnp

def discount_lfilter(rewards, discount):
  return lfilter(b=[1], a=[1, -discount], x=rewards[::-1])[::-1]

def discount_correlate(rewards, discount):

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import numpy as onp


def forest_management(forest_stages=3, r1=4, r2=2, p=0.1):
    """Forest management example from the MDPToolbox package.

    Chadès, I., Chapron, G., Cros, M.‐J., Garcia, F. and Sabbadin, R. 2014.
    MDPtoolbox: a multi‐platform toolbox to solve stochastic dynamic programming problems.
    Ecography 37: 916–920 (ver. 0).

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from jax import jvp, grad

def f(x,y):
  return x + y**2

def freeze(f, argnum, val):
  def _f(arg):
    args = [val, arg] if argnum == 0 else [arg, val]
    return f(*args)
  return _f

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def dadashi_fig2d():
    """ Figure 2 d) of
    ''The Value Function Polytope in Reinforcement Learning''
    by Dadashi et al. (2019) https://arxiv.org/abs/1901.11524
    Returns:
        tuple (P, R, gamma) where the first element is a tensor of shape
        (A x S x S), the second element 'R' has shape (S x A) and the
        last element is the scalar (float) discount factor.
    """
    P = np.array([[[0.7, 0.3], [0.2, 0.8]],

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import autograd.numpy as np
from scipy.signal import lfilter
from autograd.extend import primitive, defvjp

@primitive
def accumulate_discounted(rewards, discount=1.):
    """Behaves like `accumulate` but where each array element gets discounted.
    Args:
      rewards (np.ndarray): 1D array of rewards
      discount (float): Scalar discount factor

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import jax
import jax.numpy as np
from jax import grad, jit
from jax.scipy.special import logsumexp


def dadashi_fig2d():
    """ Figure 2 d) of
    ''The Value Function Polytope in Reinforcement Learning''
    by Dadashi et al. (2019) https://arxiv.org/abs/1901.11524

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def induced_chain(transition, policy):
    """Marginalize the choice of actions under the given policy
    Args:
        transition (numpy.ndarray): Transition kernel as a (A x S x S) tensor
        policy (numpy.ndarray): Policy as a (S x A) matrix
    Returns:
        numpy.ndarray: Marginalized transition matrix as a (S x S) matrix,
        where the first dimension denote "source" states and the second is for
        "destination" states. From i to j.
    """

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 texexpand thesis.tex | grep -E '(\b.+) \1\b'

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ssh -ND 1080 user@hostname
google-chrome --proxy-server="socks5://localhost:1080"

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ffmpeg -f video4linux2 -thread_queue_size 512 -input_format mjpeg -video_size hd720 -i /dev/video0 \
-f alsa -thread_queue_size 512 -i hw:1,0,0 \
-acodec mp3 -async 1 -vcodec libx264 -preset veryfast output.mp4 \
-acodec mp3 -ar 44100 -vcodec libx264 -preset ultrafast -maxrate 1984k -bufsize 3968k -g 60 -f flv rtmp://x.rtmp.youtube.com/live2/yourid