import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp

col = ['orange', 'purple', 'deepskyblue', 'mediumseagreen']

X = np.arange(-5, 10, 0.01)

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## PDF                                                                          
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plt.clf()
plt.figure(figsize=(4,3.2))
plt.axes([0.17,0.13,0.79,0.8])
plt.hold(True)

Q = []
for k,(mu,df) in enumerate([(0.,1.),(0.,4.),(2.,1.),(2.,4.)]):
    Y = df/2*np.log(df) + sp.gammaln(df+1) - df*np.log(2) - mu**2/2
    Y -= (df/2)*np.log(df+X**2)
    Y -= sp.gammaln(df/2)

    A = sp.hyp1f1(df/2+1, 1.5, mu**2*X**2/(2*(df+X**2)))
    B = sp.hyp1f1((df+1)/2, 0.5, mu**2*X**2/(2*(df+X**2)))

    C = np.sqrt(2)*mu*X*A
    C /= df+X**2
    C /= np.exp(sp.gammaln((df+1)/2))

    D = B/np.sqrt(df+X**2)
    D /= np.exp(sp.gammaln(df/2+1))

    Y += np.log(C+D)

    a = plt.plot(X, np.exp(Y), '-', color=col[k], lw=2)
    Q.append(a)

plt.xlabel("x")
plt.ylabel("P(x)")
bx = plt.legend(Q, (r"$\mu=0,\,\nu=1$", r"$\mu=0,\,\nu=4$",\
                    r"$\mu=2,\,\nu=1$", r"$\mu=2,\,\nu=4$"),\
                numpoints=1, handlelen=0.05, handletextpad=0.4,\
                loc="upper right")
bx.draw_frame(False)
plt.xlim(-5,10)

plt.savefig("nc_student_t_pdf.pdf")
plt.savefig("nc_student_t_pdf.svg")