reconnect moved files to git repo

venv/lib/python3.11/site-packages/statsmodels/sandbox/regression/sympy_diff.py

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+"""
+Created on Sat Mar 13 07:56:22 2010
+
+Author: josef-pktd
+"""
+import sympy as sy
+
+
+def pdf(x, mu, sigma):
+    """Return the probability density function as an expression in x"""
+    #x = sy.sympify(x)
+    return 1/(sigma*sy.sqrt(2*sy.pi)) * sy.exp(-(x-mu)**2 / (2*sigma**2))
+
+def cdf(x, mu, sigma):
+    """Return the cumulative density function as an expression in x"""
+    #x = sy.sympify(x)
+    return (1+sy.erf((x-mu)/(sigma*sy.sqrt(2))))/2
+
+
+mu = sy.Symbol('mu')
+sigma = sy.Symbol('sigma')
+sigma2 = sy.Symbol('sigma2')
+x = sy.Symbol('x')
+y = sy.Symbol('y')
+df = sy.Symbol('df')
+s = sy.Symbol('s')
+
+dldxnorm = sy.log(pdf(x, mu,sigma)).diff(x)
+print(sy.simplify(dldxnorm))
+print(sy.diff(sy.log(sy.gamma((s+1)/2)),s))
+
+print(sy.diff((df+1)/2. * sy.log(1+df/(df-2)), df))
+
+#standard t distribution, not verified
+tllf1 = sy.log(sy.gamma((df+1)/2.)) - sy.log(sy.gamma(df/2.)) - 0.5*sy.log((df)*sy.pi)
+tllf2 = (df+1.)/2. * sy.log(1. + (y-mu)**2/(df)/sigma2) + 0.5 * sy.log(sigma2)
+tllf2std = (df+1.)/2. * sy.log(1. + y**2/df) + 0.5
+tllf = tllf1 - tllf2
+print(tllf1.diff(df))
+print(tllf2.diff(y))
+dlddf = (tllf1-tllf2).diff(df)
+print(dlddf)
+print(sy.cse(dlddf))
+print('\n derivative of loglike of t distribution wrt df')
+for k,v in sy.cse(dlddf)[0]:
+    print(k, '=', v)
+
+print(sy.cse(dlddf)[1][0])
+
+print('\nstandard t distribution, dll_df, dll_dy')
+tllfstd = tllf1 - tllf2std
+print(tllfstd.diff(df))
+print(tllfstd.diff(y))
+
+print('\n')
+
+print(dlddf.subs(dict(y=1,mu=1,sigma2=1.5,df=10.0001)))
+print(dlddf.subs(dict(y=1,mu=1,sigma2=1.5,df=10.0001)).evalf())
+# Note: derivatives of nested function does not work in sympy
+#       at least not higher order derivatives (second or larger)
+#       looks like print(failure