some new features

.venv/lib/python3.12/site-packages/statsmodels/sandbox/mle.py

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+'''What's the origin of this file? It is not ours.
+Does not run because of missing mtx files, now included
+
+changes: JP corrections to imports so it runs, comment out print
+'''
+import numpy as np
+from numpy import dot,  outer, random
+from scipy import io, linalg, optimize
+from scipy.sparse import eye as speye
+import matplotlib.pyplot as plt
+
+def R(v):
+    rq = dot(v.T,A*v)/dot(v.T,B*v)
+    res = (A*v-rq*B*v)/linalg.norm(B*v)
+    data.append(linalg.norm(res))
+    return rq
+
+def Rp(v):
+    """ Gradient """
+    result = 2*(A*v-R(v)*B*v)/dot(v.T,B*v)
+    #print "Rp: ", result
+    return result
+
+def Rpp(v):
+    """ Hessian """
+    result = 2*(A-R(v)*B-outer(B*v,Rp(v))-outer(Rp(v),B*v))/dot(v.T,B*v)
+    #print "Rpp: ", result
+    return result
+
+
+A = io.mmread('nos4.mtx') # clustered eigenvalues
+#B = io.mmread('bcsstm02.mtx.gz')
+#A = io.mmread('bcsstk06.mtx.gz') # clustered eigenvalues
+#B = io.mmread('bcsstm06.mtx.gz')
+n = A.shape[0]
+B = speye(n,n)
+random.seed(1)
+v_0=random.rand(n)
+
+print("try fmin_bfgs")
+full_output = 1
+data=[]
+v,fopt, gopt, Hopt, func_calls, grad_calls, warnflag, allvecs = \
+        optimize.fmin_bfgs(R,v_0,fprime=Rp,full_output=full_output,retall=1)
+if warnflag == 0:
+    plt.semilogy(np.arange(0,len(data)),data)
+    print('Rayleigh quotient BFGS',R(v))
+
+
+print("fmin_bfgs OK")
+
+print("try fmin_ncg")
+
+#
+# WARNING: the program may hangs if fmin_ncg is used
+#
+data=[]
+v,fopt, fcalls, gcalls, hcalls, warnflag, allvecs = \
+        optimize.fmin_ncg(R,v_0,fprime=Rp,fhess=Rpp,full_output=full_output,retall=1)
+if warnflag==0:
+    plt.figure()
+    plt.semilogy(np.arange(0,len(data)),data)
+    print('Rayleigh quotient NCG',R(v))