import numpy as np
import matplotlib.pyplot as plt
import tensorflow.compat.v2 as tf
tf.enable_v2_behavior()

import tensorflow_probability as tfp
tfd = tfp.distributions
tfb = tfp.bijectors

class GaussianCopulaTriL(tfd.TransformedDistribution):
  """Takes a location, and lower triangular matrix for the Cholesky factor."""
  def __init__(self, loc, scale_tril):
    super(GaussianCopulaTriL, self).__init__(
        distribution=tfd.MultivariateNormalTriL(
            loc=loc,
            scale_tril=scale_tril),
        bijector=tfb.NormalCDF(),
        validate_args=False,
        name="GaussianCopulaTriLUniform")


# Plot an example of this.
unit_interval = np.linspace(0.01, 0.99, num=200, dtype=np.float32)
x_grid, y_grid = np.meshgrid(unit_interval, unit_interval)
coordinates = np.concatenate(
    [x_grid[..., np.newaxis],
     y_grid[..., np.newaxis]], axis=-1)

pdf = GaussianCopulaTriL(
    loc=[0., 0.],
    scale_tril=[[1., 0.8], [0., 0.6]],
).prob(coordinates)

# Plot its density.

plt.contour(x_grid, y_grid, pdf, 100, cmap=plt.cm.jet);

a = 2.0
b = 2.0
gloc = 0.
gscale = 1.

x = tfd.Kumaraswamy(a, b)
y = tfd.Gumbel(loc=gloc, scale=gscale)

# Plot the distributions, assuming independence
x_axis_interval = np.linspace(0.01, 0.99, num=200, dtype=np.float32)
y_axis_interval = np.linspace(-2., 3., num=200, dtype=np.float32)
x_grid, y_grid = np.meshgrid(x_axis_interval, y_axis_interval)

pdf = x.prob(x_grid) * y.prob(y_grid)

# Plot its density

plt.contour(x_grid, y_grid, pdf, 100, cmap=plt.cm.jet);

class WarpedGaussianCopula(tfd.TransformedDistribution):
  """Application of a Gaussian Copula on a list of target marginals.

  This implements an application of a Gaussian Copula. Given [x_0, ... x_n]
  which are distributed marginally (with CDF) [F_0, ... F_n],
  `GaussianCopula` represents an application of the Copula, such that the
  resulting multivariate distribution has the above specified marginals.

  The marginals are specified by `marginal_bijectors`: These are
  bijectors whose `inverse` encodes the CDF and `forward` the inverse CDF.

  block_sizes is a 1-D Tensor to determine splits for `marginal_bijectors`
  length should be same as length of `marginal_bijectors`.
  See tfb.Blockwise for details
  """
  def __init__(self, loc, scale_tril, marginal_bijectors, block_sizes=None):
    super(WarpedGaussianCopula, self).__init__(
        distribution=GaussianCopulaTriL(loc=loc, scale_tril=scale_tril),
        bijector=tfb.Blockwise(bijectors=marginal_bijectors,
                               block_sizes=block_sizes),
        validate_args=False,
        name="GaussianCopula")

# Create our coordinates:
coordinates = np.concatenate(
    [x_grid[..., np.newaxis], y_grid[..., np.newaxis]], -1)


def create_gaussian_copula(correlation):
  # Use Gaussian Copula to add dependence.
  return WarpedGaussianCopula(
      loc=[0.,  0.],
      scale_tril=[[1., 0.], [correlation, tf.sqrt(1. - correlation ** 2)]],
      # These encode the marginals we want. In this case we want X_0 has
      # Kumaraswamy marginal, and X_1 has Gumbel marginal.

      marginal_bijectors=[
          tfb.Invert(tfb.KumaraswamyCDF(a, b)),
          tfb.Invert(tfb.GumbelCDF(loc=0., scale=1.))])


# Note that the zero case will correspond to independent marginals!
correlations = [0., -0.8, 0.8]
copulas = []
probs = []
for correlation in correlations:
  copula = create_gaussian_copula(correlation)
  copulas.append(copula)
  probs.append(copula.prob(coordinates))


# Plot it's density

for correlation, copula_prob in zip(correlations, probs):
  plt.figure()
  plt.contour(x_grid, y_grid, copula_prob, 100, cmap=plt.cm.jet)
  plt.title('Correlation {}'.format(correlation))

def kumaraswamy_pdf(x):
    return tfd.Kumaraswamy(a, b).prob(np.float32(x))

def gumbel_pdf(x):
    return tfd.Gumbel(gloc, gscale).prob(np.float32(x))


copula_samples = []
for copula in copulas:
  copula_samples.append(copula.sample(10000))

plot_rows = len(correlations)
plot_cols = 2  # for 2  densities [kumarswamy, gumbel]
fig, axes = plt.subplots(plot_rows, plot_cols, sharex='col', figsize=(18,12))

# Let's marginalize out on each, and plot the samples.

for i, (correlation, copula_sample) in enumerate(zip(correlations, copula_samples)):
  k = copula_sample[..., 0].numpy()
  g = copula_sample[..., 1].numpy()


  _, bins, _ = axes[i, 0].hist(k, bins=100, density=True)
  axes[i, 0].plot(bins, kumaraswamy_pdf(bins), 'r--')
  axes[i, 0].set_title('Kumaraswamy from Copula with correlation {}'.format(correlation))

  _, bins, _ = axes[i, 1].hist(g, bins=100, density=True)
  axes[i, 1].plot(bins, gumbel_pdf(bins), 'r--')
  axes[i, 1].set_title('Gumbel from Copula with correlation {}'.format(correlation))