From 48cd71b7078a28b0f37cfcb7974bc952189749c3 Mon Sep 17 00:00:00 2001
From: Lars Ruthotto <lruthotto@eos.ubc.ca>
Date: Wed, 19 Jun 2013 12:14:56 -0700
Subject: [PATCH] GaussNewton example for Rosenbrock function ( to be
 generalized!!)

---
 code/GaussNewton.py | 85 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 code/GaussNewton.py

diff --git a/code/GaussNewton.py b/code/GaussNewton.py
new file mode 100644
index 00000000..997ffbb4
--- /dev/null
+++ b/code/GaussNewton.py
@@ -0,0 +1,85 @@
+import numpy as np
+from pylab import norm
+
+def GaussNewton(x0, maxIter=20, maxIterLS=10, LSreduction=1e-4, tolJ=1e-3, tolX=1e-3, tolG=1e-3, eps=1e-16, xStop=np.empty):
+    """
+        GaussNewton optimization for Rosenbrock function (has to be generalized)
+    """
+    # initial output
+    print "%s GaussNewton %s" % ('='*22,'='*22)
+    print "iter\tJc\t\tnorm(dJ)\tLS" 
+    print "%s" % '-'*57
+    
+    # evaluate stopping criteria
+    if xStop==np.empty:
+        xStop=x0
+    Jstop = Rosenbrock(xStop)
+    print "%3d\t%1.2e" % (-1, Jstop[0])
+
+    # initialize
+    xc = x0
+    STOP = np.zeros((5,1),dtype=bool)
+    iterLS=0; iter=0
+    
+    Jold = Jstop
+    xOld=xc
+    while 1:
+        # evaluate objective function
+        Jc,dJ,H = Rosenbrock(xc)
+        print "%3d\t%1.2e\t%1.2e\t%d" % (iter, Jc[0],norm(dJ),iterLS)
+        
+        # check stopping rules
+        STOP[0] = (iter>0) & (abs(Jc[0]-Jold[0]) <= tolJ*(1+abs(Jstop[0])))
+        STOP[1] = (iter>0) & (norm(xc-xOld)      <= tolX*(1+norm(x0)))
+        STOP[2] = norm(dJ)                       <= tolG*(1+abs(Jstop[0]))
+        STOP[3] = norm(dJ)                       <= 1e3*eps
+        STOP[4] = (iter >= maxIter)
+        if all(STOP[0:3]) | any(STOP[3:]): 
+            break
+        
+        # get search direction
+        dx = np.linalg.solve(H,-dJ)
+        
+        # Armijo linesearch
+        descent = np.dot(dJ.T,dx)
+        LS =0; t = 1; iterLS=1
+        while  (iterLS<maxIterLS):
+            xt = xc + t*dx
+            Jt = Rosenbrock(xt)
+            LS = Jt[0]<Jc[0]+t*LSreduction*descent
+            if LS:
+                break
+            iterLS = iterLS+1
+            t = .5*t
+            
+        # store old values
+        Jold = Jc; xOld = xc
+        # update 
+        xc = xt
+        iter = iter +1
+        
+    print "%s STOP! %s" % ('-'*25,'-'*25)
+    print "%d : |Jc-Jold|=%1.4e <= tolJ*(1+|Jstop|)=%1.4e"  % (STOP[0],abs(Jc[0]-Jold[0]),tolJ*(1+abs(Jstop[0])))
+    print "%d : |xc-xOld|=%1.4e <= tolX*(1+|x0|)   =%1.4e"  % (STOP[1],norm(xc-xOld),tolX*(1+norm(x0)))
+    print "%d : |dJ|     =%1.4e <= tolG*(1+|Jstop|)=%1.4e"  % (STOP[2],norm(dJ),tolG*(1+abs(Jstop[0])))
+    print "%d : |dJ|     =%1.4e <= 1e3*eps         =%1.4e"  % (STOP[3],norm(dJ),1e3*eps)
+    print "%d : iter     =%d\t\t <= maxIter         =%d"     % (STOP[4],iter,maxIter)
+    print "%s DONE! %s\n" % ('='*25,'='*25)
+    
+    return xc
+      
+def Rosenbrock(x):
+    """
+        Rosenbrock function for testing GaussNewton scheme
+    """
+    J   = 100*(x[1]-x[0]**2)**2+(1-x[0])**2
+    dJ  = np.array([-400*(x[1]*x[0]-x[0]**3)-2*(1-x[0]),200*(x[1]-x[0]**2)])
+    H = np.array([[-400*x[1]+1200*x[0]**2+2, -400*x[0]],[ -400*x[0], 200]],dtype=float);
+    
+    return J,dJ,H
+    
+if __name__ == '__main__':
+    x = np.array([[2.6],[3.7]])
+    xOpt = GaussNewton(x,maxIter=20)
+    print "xOpt=[%f,%f]" % (xOpt[0],xOpt[1])
+   
\ No newline at end of file