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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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# null.py

import numpy as np
from scipy.linalg import qr

def qr_null(A, tol=None):
    Q, R, P = qr(A.T, mode='full', pivoting=True)
    tol = np.max(A) * np.finfo(R.dtype).eps if tol is None else tol
    rnk = min(A.shape) - np.abs(np.diag(R))[::-1].searchsorted(tol)
    return Q[:, rnk:].conj()

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import numpy as np
import bottleneck as bn

def top_n_indexes(arr, n):
    idx = bn.argpartsort(arr, arr.size-n, axis=None)[-n:]
    width = arr.shape[1]
    return [divmod(i, width) for i in idx]


np.random.seed(47)

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#Create bitbucket branch

##Create local branch

$ git checkout -b sync
Switched to a new branch 'sync'
$ git branch
  master
* sync

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require 'torch'
require 'cutorch'
require 'nn'
require 'cunn'
require 'cudnn'

local N = 32
local cin = 64
local cout = 64
local height = 256

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require 'nn'
require 'cutorch'
require 'cunn'

--[[
-- A simple benchmark comparing fully-connected net times on CPU and GPU.
--
-- Note that we don't count time it takes to transfer data to the GPU.
--]]