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"""
This example demonstrates the use of TAO for Python to solve an
unconstrained minimization problem on a single processor.
We minimize the extended Rosenbrock function::
sum_{i=0}^{n/2-1} ( alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2 )
"""
try: range = xrange
except NameError: pass
# the two lines below are only
# needed to build options database
# from command line arguments
import sys, petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
class AppCtx(object):
"""
Extended Rosenbrock function.
"""
def __init__(self, n=2, alpha=99.0):
self.size = int(n)
self.alpha = float(alpha)
def formObjective(self, tao, x):
#print 'AppCtx.formObjective()'
alpha = self.alpha
nn = self.size // 2
ff = 0.0
for i in range(nn):
t1 = x[2*i+1] - x[2*i] * x[2*i]
t2 = 1 - x[2*i];
ff += alpha*t1*t1 + t2*t2;
return ff
def formGradient(self, tao, x, G):
#print 'AppCtx.formGradient()'
alpha = self.alpha
nn = self.size // 2
G.zeroEntries()
for i in range(nn):
t1 = x[2*i+1] - x[2*i] * x[2*i]
t2 = 1 - x[2*i];
G[2*i] = -4*alpha*t1*x[2*i] - 2*t2;
G[2*i+1] = 2*alpha*t1;
def formObjGrad(self, tao, x, G):
#print 'AppCtx.formObjGrad()'
alpha = self.alpha
nn = self.size // 2
ff = 0.0
G.zeroEntries()
for i in range(nn):
t1 = x[2*i+1] - x[2*i] * x[2*i]
t2 = 1 - x[2*i];
ff += alpha*t1*t1 + t2*t2;
G[2*i] = -4*alpha*t1*x[2*i] - 2*t2;
G[2*i+1] = 2*alpha*t1;
return ff
def formHessian(self, tao, x, H, HP):
#print 'AppCtx.formHessian()'
alpha = self.alpha
nn = self.size // 2
idx = [0, 0]
v = [[0.0, 0.0],
[0.0, 0.0]]
H.zeroEntries()
for i in range(nn):
v[1][1] = 2*alpha
v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2
v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
idx[0] = 2*i
idx[1] = 2*i+1
H[idx,idx] = v
H.assemble()
# access PETSc options database
OptDB = PETSc.Options()
# create user application context
# and configure user parameters
user = AppCtx()
user.size = OptDB.getInt ( 'n', user.size)
user.alpha = OptDB.getReal('alpha', user.alpha)
# create solution vector
x = PETSc.Vec().create(PETSc.COMM_SELF)
x.setSizes(user.size)
x.setFromOptions()
# create Hessian matrix
H = PETSc.Mat().create(PETSc.COMM_SELF)
H.setSizes([user.size, user.size])
H.setFromOptions()
H.setOption(PETSc.Mat.Option.SYMMETRIC, True)
H.setUp()
# pass the following to command line:
# $ ... -methods nm,lmvm,nls,ntr,cg,blmvm,tron
# to try many methods
methods = OptDB.getString('methods', '')
methods = methods.split(',')
for meth in methods:
# create TAO Solver
tao = PETSc.TAO().create(PETSc.COMM_SELF)
if meth: tao.setType(meth)
tao.setFromOptions()
# solve the problem
tao.setObjectiveGradient(user.formObjGrad)
tao.setObjective(user.formObjective)
tao.setGradient(user.formGradient)
tao.setHessian(user.formHessian, H)
#app.getKSP().getPC().setFromOptions()
x.set(0) # zero initial guess
tao.setSolution(x)
tao.solve()
tao.destroy()
## # this is just for testing
## x = app.getSolution()
## G = app.getGradient()
## H, HP = app.getHessian()
## f = tao.computeObjective(x)
## tao.computeGradient(x, G)
## f = tao.computeObjectiveGradient(x, G)
## tao.computeHessian(x, H, HP)
|
