helper update

content/GA_1_8/solution/helper.py

+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.cm as cm
+import pyvinecopulib as cop
+
+class Bivariate:
+    """Bivariate dependent distribution, design to function in the 
+    same way as an instance of the scipy.stats.rv_continuous class,
+    specifically, with methods: cdf, pdf, rvs.
+    """
+    
+    def __init__(self, X1, X2, rho):
+        """Constructor to initialize Bivariate object.
+        
+        Arguments:
+        ---
+        X1: scipy.stats.rv_continuous object. Marginal distribution
+        X2: scipy.stats.rv_continuous object. Marginal distribution
+        rho: float. Pearson correlation coefficient.
+        """
+        self.X1 = X1
+        self.X2 = X2
+        self.rho = rho
+        self.copula_uv = cop.Bicop(family=cop.BicopFamily.gaussian, parameters = [rho])
+        
+    def cdf(self, x):
+        """Compute cdf with array or list as argument: [x1, x2]."""
+        x1 = x[0]
+        x2 = x[1]
+        u = self.X1.cdf(x1)
+        v = self.X2.cdf(x2)
+        return self.copula_uv.cdf(np.array([[u, v]]))[0]
+
+    def pdf(self, x):
+        """Compute pdf with array or list as argument: [x1, x2]."""
+        x1 = x[0]
+        x2 = x[1]
+        u = self.X1.cdf(x1)
+        v = self.X2.cdf(x2)
+        return self.copula_uv.pdf(np.array([[u, v]]))[0]*self.X1.pdf(x1)*self.X2.pdf(x2)
+
+    def rvs(self, size=1):
+        """Create random sample with keyword argument size."""
+        sample = self.copula_uv.simulate(size)
+        sample_X1 = self.X1.ppf(sample[:,0])
+        sample_X2 = self.X2.ppf(sample[:,1])
+        return np.vstack([sample_X1.T, sample_X2.T]).T
+
+def plot_contour(bivar, xy_lim, data=None,
+                 case=None, region=None,
+                 nb_points=100):
+    """Contour plot of PDF in the bivariate plane (X,Y).
+    
+    bivar: bivariate distribution, defined by
+        scipy.stats.multivariate_normal.
+    xy_lim: list. 1x4 list of xlim and ylim (in order) for plot limits.
+        
+    Optional arguments:
+    
+    data: array. A 2xN array of points.
+    case: list. Typically a 1x2 list defining a key
+        calculation point; plots as a red dot(s)
+    region: array. A 2xN array of points that define the
+        boundary of a region that will be shaded in gray between
+        the boundary and the max y-axis value (ylim[1]).
+    nb_points: int. Size of the grid (default: 200).
+
+    returns: matplotlib.pyplot Figure and Axis objects. 
+    """
+    
+    f, ax = plt.subplots(1)
+
+    xlim = [xy_lim[0], xy_lim[1]]
+    ylim = [xy_lim[2], xy_lim[3]]
+
+    x = np.linspace(xlim[0], xlim[1], nb_points)
+    y = np.linspace(ylim[0], ylim[1], nb_points)
+    X,Y = np.meshgrid(x,y)
+    pdf = np.zeros(X.shape)
+    for i in range(X.shape[0]):
+            for j in range(X.shape[1]):
+                # if X[i,j]>0 and Y[i,j]>0:
+                pdf[i,j] = bivar.pdf([X[i,j], Y[i,j]])
+    
+    ax.contour(X, Y, pdf, levels=8, cmap=cm.Blues)
+    
+    if isinstance(data, np.ndarray):
+        if data.shape[1] == 2:
+             data = data.T
+        ax.scatter(data[0,:], data[1,:], s=10.0,
+                   facecolors='none', edgecolors='darkgray',
+                   label='Data')
+    
+    if isinstance(region, np.ndarray):
+        ax.plot(region[0,:], region[1,:],
+                label='Boundary', color='k')
+        ax.fill_between(region[0,:], region[1,:],
+                        ylim[1], label='Region', color='grey')
+    
+    if case:
+        ax.plot(case[0], case[1], 'ro',
+                label=' Case')
+    
+    ax.set_aspect("equal")
+    ax.set_xlim(xlim)
+    ax.set_ylim(ylim)
+    ax.set_xlabel(r"$X_1$", fontsize=14)
+    ax.set_ylabel(r"$X_2$", fontsize=14)
+    if isinstance(region, np.ndarray) or case:
+        ax.legend()
+    return f, ax 
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