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359 lines (245 loc) · 7.85 KB
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#!/usr/bin/python
###############
# implicitFilter.py
#
# Copyright David Baddeley, 2012
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
################
import numpy as np
from scipy import linalg
def impfilt(fcn, x0, args, maxIters=200, initStepSize=.01, minStepSize=.0005, maxFevals = 200):
nIters = 0
nFeval = 0
stepsize = initStepSize
x0 = np.array(x0, 'f')
nDim = len(x0)
fval = fcn(x0, *args)
#print fval
nFeval += 1
#xts = []
while nIters < maxIters and nFeval < maxFevals and stepsize > minStepSize:
nIters += 1
changed = False
#print stepsize
for i in range(nDim):
#print i
dx = stepsize
xCand = x0.copy()
xCand[i] = x0[i] + dx
fCand = fcn(xCand, *args)
#print xCand, fCand
nFeval += 1
if not fCand < fval: #try the other direction
dx = -dx
xCand[i] = x0[i] + dx
fCand = fcn(xCand, *args)
nFeval += 1
while fCand < fval and nFeval < maxFevals:
#search along this line, with this step size
changed = True
dx *= 2
x0[:] = xCand[:]
fval = fCand
#xts.append(x0.copy())
xCand[i] = x0[i] + dx
fCand = fcn(xCand, *args)
#print xCand,fCand
nFeval += 1
if not changed:
stepsize *=.5
print('Optimisation terminated:')
print(('nIterations: %d' % nIters))
print(('nFevals: %d' % nFeval))
return x0 #, xts
def impfilt2(fcn, x0, args, maxIters=200, initStepSize=.01, minStepSize=.0005, maxFevals = 200):
nIters = 0
nFeval = 0
stepsize = initStepSize
x0 = np.array(x0, 'f')
nDim = len(x0)
fval = fcn(x0, *args)
#print fval
nFeval += 1
xv = np.zeros(3)
fv = np.zeros(3)
ons = np.ones(3)
#xts = []
changed = True
while nIters < maxIters and nFeval < maxFevals and stepsize > minStepSize and changed:
nIters += 1
changed = False
maxChange = 0
#print stepsize
for i in range(nDim):
#print i
dx = stepsize
xCand = x0.copy()
xCand[i] = x0[i] + dx
xv[0] = x0[i]
fv[0] = fval
xv[1] = xCand[i]
fCand = fcn(xCand, *args)
fv[1] = fCand
#print xCand, fCand
nFeval += 1
dfdx = (fCand - fval)/dx
if fCand < fval: #may as well already update
x0[:] = xCand[:]
fval = fCand
changed = True
#try to overshoot
dx = -np.sign(dfdx)*2*dx
#print i, xv[0], xv[1], dfdx, dx
xCand[i] = x0[i] + dx
fCand = fcn(xCand, *args)
nFeval += 1
while fCand < fval and nFeval < maxFevals:
#search along this line, with this step size
#print 's'
changed = True
dx *= 2
xv[0] = x0[i]
fv[0] = fval
x0[:] = xCand[:]
fval = fCand
xv[1] = x0[i]
fv[1] = fval
#xts.append(x0.copy())
xCand[i] = x0[i] + dx
fCand = fcn(xCand, *args)
#print xCand,fCand
nFeval += 1
#now fit a parabola
xv[2] = xCand[i]
fv[2] = fCand
#print np.vstack([xv**2, xv, ons])
A, B, C = linalg.solve(np.hstack([(xv**2)[:, None], xv[:, None], ons[:, None]]), fv)
#should be minimum
xn = -B/(2*A)
#try and see if this is better
xCand[i] = xn
fCand = fcn(xCand, *args)
nFeval += 1
#print xv[0],fval, xn, fCand
if fCand < fval:
#print 'Accepting quad est.'
x0[:] = xCand[:]
fval = fCand
changed = True
maxChange = max(maxChange, abs(x0[i] - xv[0]))
#print maxChange
#if not changed:
stepsize *=.1
print('Optimisation terminated:')
print(('nIterations: %d' % nIters))
print(('nFevals: %d' % nFeval))
return x0 #, xts
def impfilt3(fcn, x0, args, maxIters=200, initStepSize=.01, minStepSize=.0005, maxFevals = 200):
nIters = 0
nFeval = 0
stepsize = initStepSize
x0 = np.array(x0, 'f')
nDim = len(x0)
fval = fcn(x0, *args)
#print fval
nFeval += 1
tv = np.zeros(3)
fv = np.zeros(3)
ons = np.ones(3)
dfdx = np.zeros(2)
#xts = []
changed = True
while nIters < maxIters and nFeval < maxFevals and stepsize > minStepSize and changed:
nIters += 1
changed = False
maxChange = 0
#print stepsize
#find gradient
for i in range(nDim):
dx = stepsize
xCand = x0.copy()
xCand[i] = x0[i] + dx
fCand = fcn(xCand, *args)
nFeval += 1
dfdx[i] = (fCand - fval)/dx
if fCand < fval: #may as well already update
x0[:] = xCand[:]
fval = fCand
changed = True
dfdx_hat = dfdx/linalg.norm(dfdx)
x_0 = x0.copy()
B = -linalg.norm(dfdx)
C = fval
#t = 0
#print linalg.norm(dfdx), linalg.norm(dfdx_hat)
#print dfdx_hat, dfdx
#try to overshoot
dxv = -dfdx_hat*2*dx
t = 2*dx
#print i, xv[0], xv[1], dfdx, dx
fPred = fval + t*B
xCand = x0 + dxv
fCand = fcn(xCand, *args)
nFeval += 1
print((x0, xCand, fPred, fCand))
while fCand < fval and nFeval < maxFevals:
#search along this line, with this step size
#print 's'
changed = True
#print B
B = (fval-fCand)/t
#print B
x0[:] = xCand[:]
fval = fCand
C = fval
dxv *= 2
t = 2*dx
#xts.append(x0.copy())
xCand = x0 + dxv
fCand = fcn(xCand, *args)
fPred = fval + t*B
#print xCand,fCand
nFeval += 1
# #now fit a parabola
# xv[2] = xCand[i]
# fv[2] = fCand
#
# #print np.vstack([xv**2, xv, ons])
# A, B, C = linalg.solve(np.hstack([(xv**2)[:, None], xv[:, None], ons[:, None]]), fv)
#print t
A = (-C - B*t)/t**2
print((A, B, C))
#should be minimum
tn = -B/(2*A)
#try and see if this is better
xCand = x0 + tn*dfdx_hat
fCand = fcn(xCand, *args)
nFeval += 1
print(('q\t', tn, x0, xCand, fval, fCand))
if fCand < fval:
print('Accepting quad est.')
x0[:] = xCand[:]
fval = fCand
changed = True
#maxChange = max(maxChange, abs(x0[i] - xv[0]))
#print maxChange
#if not changed:
stepsize *=.1
print('Optimisation terminated:')
print(('nIterations: %d' % nIters))
print(('nFevals: %d' % nFeval))
return x0 #, xts