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Generalized Gauss Newton by using Lambda Functions

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This commit is contained in:
Lars Ruthotto
2013-06-19 12:39:00 -07:00
parent 48cd71b707
commit 70a143031b
1 changed files with 18 additions and 7 deletions
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code/GaussNewton.py
+18 -7
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@@ -1,9 +1,19 @@
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):
def GaussNewton(fctn, 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)
GaussNewton Optimization
Input:
------
fctn - objective Function (lambda function)
x0 - starting guess
Output:
-------
xOpt - numerical optimizer
"""
# initial output
print "%s GaussNewton %s" % ('='*22,'='*22)
@@ -13,7 +23,7 @@ def GaussNewton(x0, maxIter=20, maxIterLS=10, LSreduction=1e-4, tolJ=1e-3, tolX=
# evaluate stopping criteria
if xStop==np.empty:
xStop=x0
Jstop = Rosenbrock(xStop)
Jstop = fctn(xStop)
print "%3d\t%1.2e" % (-1, Jstop[0])
# initialize
@@ -25,7 +35,7 @@ def GaussNewton(x0, maxIter=20, maxIterLS=10, LSreduction=1e-4, tolJ=1e-3, tolX=
xOld=xc
while 1:
# evaluate objective function
Jc,dJ,H = Rosenbrock(xc)
Jc,dJ,H = fctn(xc)
print "%3d\t%1.2e\t%1.2e\t%d" % (iter, Jc[0],norm(dJ),iterLS)
# check stopping rules
@@ -45,7 +55,7 @@ def GaussNewton(x0, maxIter=20, maxIterLS=10, LSreduction=1e-4, tolJ=1e-3, tolX=
LS =0; t = 1; iterLS=1
while (iterLS<maxIterLS):
xt = xc + t*dx
Jt = Rosenbrock(xt)
Jt = fctn(xt)
LS = Jt[0]<Jc[0]+t*LSreduction*descent
if LS:
break
@@ -79,7 +89,8 @@ def Rosenbrock(x):
return J,dJ,H
if __name__ == '__main__':
x = np.array([[2.6],[3.7]])
xOpt = GaussNewton(x,maxIter=20)
x0 = np.array([[2.6],[3.7]])
fctn = lambda x:Rosenbrock(x)
xOpt = GaussNewton(fctn,x0,maxIter=20)
print "xOpt=[%f,%f]" % (xOpt[0],xOpt[1])