def milpTransfer(originProb):
newProb = NLP(originProb.f, originProb.x0)
originProb.fill(newProb)
newProb.discreteVars = originProb.discreteVars
def err(s): # to prevent text output
raise OpenOptException(s)
newProb.err = err
for fn in ['df', 'd2f', 'c', 'dc', 'h', 'dh']:
if hasattr(originProb, fn) and getattr(originProb.userProvided, fn) or originProb.isFDmodel:
setattr(newProb, fn, getattr(originProb, fn))
newProb.plot = 0
newProb.iprint = -1
newProb.nlpSolver = originProb.nlpSolver
return newProb
def milpTransfer(originProb):
newProb = NLP(originProb.f, originProb.x0)
originProb.inspire(newProb)
newProb.discreteVars = originProb.discreteVars
def err(s): # to prevent text output
raise OpenOptException(s)
newProb.err = err
for fn in ['df', 'd2f', 'c', 'dc', 'h', 'dh']:
if hasattr(originProb, fn) and getattr(originProb.userProvided,
fn) or originProb.isFDmodel:
setattr(newProb, fn, getattr(originProb, fn))
newProb.plot = 0
newProb.iprint = -1
newProb.nlpSolver = originProb.nlpSolver
return newProb
# p.maxfun=100
# see also: help(NLP) -> maxTime, maxCPUTime, ftol and xtol
# that are connected to / used in lincher and some other solvers
# optional: check of user-supplied derivatives
#p.checkdf()
#p.checkdc()
#p.checkdh()
# last but not least:
# please don't forget,
# Python indexing starts from ZERO!!
p.plot = 0
p.iprint = 1
#p.df_iter = 50
p.maxTime = 4000
print 'solving'
r = p.solve('algencan')
print 'done'
pout = r.xf
print 'solution:', pout
print len(pout)
P_up, P_down = transform_p(pout, Mx, Mz, M)
P = P_up - P_down
if 0:
chi = chisq(p,
def fit_node(self,index):
qnode=self.qlist[index]
print qnode.q
th=qnode.th_condensed['a3']
counts=qnode.th_condensed['counts']
counts_err=qnode.th_condensed['counts_err']
print qnode.th_condensed['counts'].std()
print qnode.th_condensed['counts'].mean()
maxval=qnode.th_condensed['counts'].max()
minval=qnode.th_condensed['counts'].min()
diff=qnode.th_condensed['counts'].max()-qnode.th_condensed['counts'].min()\
-qnode.th_condensed['counts'].mean()
sig=qnode.th_condensed['counts'].std()
if diff-2*sig>0:
#the difference between the high and low point and
#the mean is greater than 3 sigma so we have a signal
p0=findpeak(th,counts,1)
print 'p0',p0
#Area center width Bak
center=p0[0]
width=p0[1]
sigma=width/2/N.sqrt(2*N.log(2))
Imax=maxval-minval
area=Imax*(N.sqrt(2*pi)*sigma)
print 'Imax',Imax
pin=[area,center,width,0]
if 1:
p = NLP(chisq, pin, maxIter = 1e3, maxFunEvals = 1e5)
#p.lb=lowerm
#p.ub=upperm
p.args.f=(th,counts,counts_err)
p.plot = 0
p.iprint = 1
p.contol = 1e-5#3 # required constraints tolerance, default for NLP is 1e-6
# for ALGENCAN solver gradtol is the only one stop criterium connected to openopt
# (except maxfun, maxiter)
# Note that in ALGENCAN gradtol means norm of projected gradient of the Augmented Lagrangian
# so it should be something like 1e-3...1e-5
p.gradtol = 1e-5#5 # gradient stop criterium (default for NLP is 1e-6)
#print 'maxiter', p.maxiter
#print 'maxfun', p.maxfun
p.maxIter=50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
#r=p.solve('scipy_cobyla')
#r=p.solve('scipy_lbfgsb')
#r = p.solve('algencan')
print 'ralg'
r = p.solve('ralg')
print 'done'
pfit=r.xf
print 'pfit openopt',pfit
print 'r dict', r.__dict__
if 0:
print 'curvefit'
print sys.executable
pfit,popt=curve_fit(gauss2, th, counts, p0=pfit, sigma=counts_err)
print 'p,popt', pfit,popt
perror=N.sqrt(N.diag(popt))
print 'perror',perror
chisqr=chisq(pfit,th,counts,counts_err)
dof=len(th)-len(pfit)
print 'chisq',chisqr
if 0:
oparam=scipy.odr.Model(gauss)
mydatao=scipy.odr.RealData(th,counts,sx=None,sy=counts_err)
myodr = scipy.odr.ODR(mydatao, oparam, beta0=pfit)
myoutput=myodr.run()
myoutput.pprint()
pfit=myoutput.beta
if 1:
print 'mpfit'
p0=pfit
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value']=p0[i]
fa = {'x':th, 'y':counts, 'err':counts_err}
#parinfo[1]['fixed']=1
#parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo,functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params=m.params
pfit=params
perror=m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr=chisq(pfit,th,counts,counts_err)
dof=m.dof
#Icalc=gauss(pfit,th)
#print 'mpfit chisqr', chisqr
if 0:
width_x=N.linspace(p0[0]-p0[1],p0[0]+p0[1],100)
width_y=N.ones(width_x.shape)*(maxval-minval)/2
pos_y=N.linspace(minval,maxval,100)
pos_x=N.ones(pos_y.shape)*p0[0]
if 1:
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(width_x,width_y)
pylab.plot(pos_x,pos_y)
pylab.plot(th,Icalc)
pylab.show()
else:
#fix center
#fix width
print 'no peak'
#Area center width Bak
area=0
center=th[len(th)/2]
width=(th.max()-th.min())/5.0 #rather arbitrary, but we don't know if it's the first....
Bak=qnode.th_condensed['counts'].mean()
p0=N.array([area,center,width,Bak],dtype='float64') #initial conditions
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value']=p0[i]
fa = {'x':th, 'y':counts, 'err':counts_err}
parinfo[1]['fixed']=1
parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo,functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params=m.params
pfit=params
perror=m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr=chisq(pfit,th,counts,counts_err)
dof=m.dof
Icalc=gauss(pfit,th)
#print 'perror',perror
if 0:
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(th,Icalc)
pylab.show()
print 'final answer'
print 'perror', 'perror'
#If the fit is unweighted (i.e. no errors were given, or the weights
# were uniformly set to unity), then .perror will probably not represent
#the true parameter uncertainties.
# *If* you can assume that the true reduced chi-squared value is unity --
# meaning that the fit is implicitly assumed to be of good quality --
# then the estimated parameter uncertainties can be computed by scaling
# .perror by the measured chi-squared value.
# dof = len(x) - len(mpfit.params) # deg of freedom
# # scaled uncertainties
# pcerror = mpfit.perror * sqrt(mpfit.fnorm / dof)
print 'params', pfit
print 'chisqr', chisqr #note that chisqr already is scaled by dof
pcerror=perror*N.sqrt(m.fnorm / m.dof)#chisqr
print 'pcerror', pcerror
self.qlist[index].th_integrated_intensity=N.abs(pfit[0])
self.qlist[index].th_integrated_intensity_err=N.abs(pcerror[0])
Icalc=gauss(pfit,th)
print 'perror',perror
if 0:
pylab.figure()
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(th,Icalc)
qstr=str(qnode.q['h_center'])+','+str(qnode.q['k_center'])+','+str(qnode.q['l_center'])
pylab.title(qstr)
#pylab.show()
return
upperm=N.ones(len(p0))
if 1:
p = NLP(Entropy, p0, maxIter = 1e3, maxFunEvals = 1e5)
if 0:
p = NLP(chisq, p0, maxIter = 1e3, maxFunEvals = 1e5)
if 0:
p = NLP(max_wrap, p0, maxIter = 1e3, maxFunEvals = 1e5)
if 0:
p.lb=lowerm
p.ub=upperm
p.args.f=(h,k,l,fq,fqerr,x,z,cosmat_list,coslist,flist)
p.plot = 0
p.iprint = 1
p.contol = 1e-5#3 # required constraints tolerance, default for NLP is 1e-6
# for ALGENCAN solver gradtol is the only one stop criterium connected to openopt
# (except maxfun, maxiter)
# Note that in ALGENCAN gradtol means norm of projected gradient of the Augmented Lagrangian
# so it should be something like 1e-3...1e-5
p.gradtol = 1e-5#5 # gradient stop criterium (default for NLP is 1e-6)
#print 'maxiter', p.maxiter
#print 'maxfun', p.maxfun
p.maxIter=50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
h_args=(h,k,l,fq,fqerr,x,z,cosmat_list,coslist,flist)
# see also: help(NLP) -> maxTime, maxCPUTime, ftol and xtol
# that are connected to / used in lincher and some other solvers
# optional: check of user-supplied derivatives
p.checkdf()
p.checkdc()
p.checkdh()
# last but not least:
# please don't forget,
# Python indexing starts from ZERO!!
p.plot = 0
p.iprint = 0
p.df_iter = 4
p.maxTime = 4000
p.debug=1
#r = p.solve('algencan')
r = p.solve('ralg')
#r = p.solve('lincher')
"""
typical output:
OpenOpt checks user-supplied gradient df (size: (50,))
according to:
prob.diffInt = 1e-07
prob.check.maxViolation = 1e-05
max(abs(df_user - df_numerical)) = 2.50111104094e-06
def test(complexity=0, **kwargs):
n = 15 * (complexity+1)
x0 = 15*cos(arange(n)) + 8
f = lambda x: ((x-15)**2).sum()
df = lambda x: 2*(x-15)
c = lambda x: [2* x[0] **4-32, x[1]**2+x[2]**2 - 8]
# dc(x)/dx: non-lin ineq constraints gradients (optional):
def dc(x):
r = zeros((len(c(x0)), n))
r[0,0] = 2 * 4 * x[0]**3
r[1,1] = 2 * x[1]
r[1,2] = 2 * x[2]
return r
hp = 2
h1 = lambda x: (x[-1]-13)**hp
h2 = lambda x: (x[-2]-17)**hp
h = lambda x:[h1(x), h2(x)]
# dh(x)/dx: non-lin eq constraints gradients (optional):
def dh(x):
r = zeros((2, n))
r[0, -1] = hp*(x[-1]-13)**(hp-1)
r[1, -2] = hp*(x[-2]-17)**(hp-1)
return r
lb = -8*ones(n)
ub = 15*ones(n)+8*cos(arange(n))
ind = 3
A = zeros((2, n))
A[0, ind:ind+2] = 1
A[1, ind+2:ind+4] = 1
b = [15, 8]
Aeq = zeros(n)
Aeq[ind+4:ind+8] = 1
beq = 45
########################################################
colors = ['b', 'k', 'y', 'g', 'r']
#solvers = ['ipopt', 'ralg','scipy_cobyla']
solvers = ['ralg','scipy_slsqp', 'ipopt']
solvers = [ 'ralg', 'scipy_slsqp']
solvers = [ 'ralg']
solvers = [ 'r2']
solvers = [ 'ralg', 'scipy_slsqp']
########################################################
for i, solver in enumerate(solvers):
p = NLP(f, x0, df=df, c=c, h=h, dc=dc, dh=dh, lb=lb, ub=ub, A=A, b=b, Aeq=Aeq, beq=beq, maxIter = 1e4, \
show = solver==solvers[-1], color=colors[i], **kwargs )
if not kwargs.has_key('iprint'): p.iprint = -1
# p.checkdf()
# p.checkdc()
# p.checkdh()
r = p.solve(solver)
if r.istop>0: return True, r, p
else: return False, r, p
def fitpeak(x,y,yerr):
maxval=x.max()
minval=x.min()
diff=y.max()-y.min()-y.mean()
sig=y.std()
print 'diff',diff,'std',sig
if diff-1*sig>0:
#the difference between the high and low point and
#the mean is greater than 3 sigma so we have a signal
p0=findpeak(x,y,2)
print 'p0',p0
#Area center width Bak area2 center2 width2
center1=p0[0]
width1=p0[1]
center2=p0[2]
width2=p0[3]
sigma=width/2/N.sqrt(2*N.log(2))
ymax=maxval-minval
area=ymax*(N.sqrt(2*pi)*sigma)
print 'ymax',ymax
pin=[area,center1,width1,0,area,center2,width2]
if 1:
p = NLP(chisq, pin, maxIter = 1e3, maxFunEvals = 1e5)
#p.lb=lowerm
#p.ub=upperm
p.args.f=(x,y,yerr)
p.plot = 0
p.iprint = 1
p.contol = 1e-5#3 # required constraints tolerance, default for NLP is 1e-6
# for ALGENCAN solver gradtol is the only one stop criterium connected to openopt
# (except maxfun, maxiter)
# Note that in ALGENCAN gradtol means norm of projected gradient of the Augmented Lagrangian
# so it should be something like 1e-3...1e-5
p.gradtol = 1e-5#5 # gradient stop criterium (default for NLP is 1e-6)
#print 'maxiter', p.maxiter
#print 'maxfun', p.maxfun
p.maxIter=50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
#r=p.solve('scipy_cobyla')
#r=p.solve('scipy_lbfgsb')
#r = p.solve('algencan')
print 'ralg'
r = p.solve('ralg')
print 'done'
pfit=r.xf
print 'pfit openopt',pfit
print 'r dict', r.__dict__
if 1:
print 'mpfit'
p0=pfit
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value']=p0[i]
fa = {'x':x, 'y':y, 'err':yerr}
#parinfo[1]['fixed']=1
#parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo,functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params=m.params
pfit=params
perror=m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr=chisq(pfit,x,y,yerr)
dof=m.dof
#Icalc=gauss(pfit,th)
#print 'mpfit chisqr', chisqr
ycalc=gauss(pfit,x)
if 1:
width_x=N.linspace(p0[0]-p0[1],p0[0]+p0[1],100)
width_y=N.ones(width_x.shape)*(maxval-minval)/2
pos_y=N.linspace(minval,maxval,100)
pos_x=N.ones(pos_y.shape)*p0[0]
if 0:
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(width_x,width_y)
pylab.plot(pos_x,pos_y)
pylab.plot(x,ycalc)
pylab.show()
else:
#fix center
#fix width
print 'no peak'
#Area center width Bak
area=0
center=x[len(x)/2]
width=(x.max()-x.min())/5.0 #rather arbitrary, but we don't know if it's the first.... #better to use resolution
Bak=y.mean()
p0=N.array([area,center,width,Bak],dtype='float64') #initial conditions
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value']=p0[i]
fa = {'x':x, 'y':y, 'err':yerr}
parinfo[1]['fixed']=1
parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo,functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params=m.params
pfit=params
perror=m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr=chisq(pfit,x,y,yerr)
dof=m.dof
ycalc=gauss(pfit,x)
#print 'perror',perror
if 0:
pylab.errorbar(x,y,yerr,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(x,ycalc)
pylab.show()
print 'final answer'
print 'perror', 'perror'
#If the fit is unweighted (i.e. no errors were given, or the weights
# were uniformly set to unity), then .perror will probably not represent
#the true parameter uncertainties.
# *If* you can assume that the true reduced chi-squared value is unity --
# meaning that the fit is implicitly assumed to be of good quality --
# then the estimated parameter uncertainties can be computed by scaling
# .perror by the measured chi-squared value.
# dof = len(x) - len(mpfit.params) # deg of freedom
# # scaled uncertainties
# pcerror = mpfit.perror * sqrt(mpfit.fnorm / dof)
print 'params', pfit
print 'chisqr', chisqr #note that chisqr already is scaled by dof
pcerror=perror*N.sqrt(m.fnorm / m.dof)#chisqr
print 'pcerror', pcerror
integrated_intensity=N.abs(pfit[0])
integrated_intensity_err=N.abs(pcerror[0])
ycalc=gauss(pfit,x)
print 'perror',perror
if 1:
pylab.figure()
pylab.errorbar(x,y,yerr,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(x,ycalc)
#qstr=str(qnode.q['h_center'])+','+str(qnode.q['k_center'])+','+str(qnode.q['l_center'])
#pylab.title(qstr)
pylab.show()
return pfit,perror,pcerror,chisq
def fit_node(self,index):
qnode=self.qlist[index]
print qnode.q
th=qnode.th_condensed['a3']
counts=qnode.th_condensed['counts']
counts_err=qnode.th_condensed['counts_err']
print qnode.th_condensed['counts'].std()
print qnode.th_condensed['counts'].mean()
maxval=qnode.th_condensed['counts'].max()
minval=qnode.th_condensed['counts'].min()
diff=qnode.th_condensed['counts'].max()-qnode.th_condensed['counts'].min()\
-qnode.th_condensed['counts'].mean()
sig=qnode.th_condensed['counts'].std()
if diff-2*sig>0:
#the difference between the high and low point and
#the mean is greater than 3 sigma so we have a signal
p0=findpeak(th,counts,1)
print 'p0',p0
#Area center width Bak
center=p0[0]
width=p0[1]
sigma=width/2/N.sqrt(2*N.log(2))
Imax=maxval-minval
area=Imax*(N.sqrt(2*pi)*sigma)
print 'Imax',Imax
pin=[area,center,width,0]
if 1:
p = NLP(chisq, pin, maxIter = 1e3, maxFunEvals = 1e5)
#p.lb=lowerm
#p.ub=upperm
p.args.f=(th,counts,counts_err)
p.plot = 0
p.iprint = 1
p.contol = 1e-5#3 # required constraints tolerance, default for NLP is 1e-6
# for ALGENCAN solver gradtol is the only one stop criterium connected to openopt
# (except maxfun, maxiter)
# Note that in ALGENCAN gradtol means norm of projected gradient of the Augmented Lagrangian
# so it should be something like 1e-3...1e-5
p.gradtol = 1e-5#5 # gradient stop criterium (default for NLP is 1e-6)
#print 'maxiter', p.maxiter
#print 'maxfun', p.maxfun
p.maxIter=50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
#r=p.solve('scipy_cobyla')
#r=p.solve('scipy_lbfgsb')
#r = p.solve('algencan')
print 'ralg'
r = p.solve('ralg')
print 'done'
pfit=r.xf
print 'pfit openopt',pfit
print 'r dict', r.__dict__
if 0:
print 'curvefit'
print sys.executable
pfit,popt=curve_fit(gauss2, th, counts, p0=pfit, sigma=counts_err)
print 'p,popt', pfit,popt
perror=N.sqrt(N.diag(popt))
print 'perror',perror
chisqr=chisq(pfit,th,counts,counts_err)
dof=len(th)-len(pfit)
print 'chisq',chisqr
if 0:
oparam=scipy.odr.Model(gauss)
mydatao=scipy.odr.RealData(th,counts,sx=None,sy=counts_err)
myodr = scipy.odr.ODR(mydatao, oparam, beta0=pfit)
myoutput=myodr.run()
myoutput.pprint()
pfit=myoutput.beta
if 1:
print 'mpfit'
p0=pfit
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value']=p0[i]
fa = {'x':th, 'y':counts, 'err':counts_err}
#parinfo[1]['fixed']=1
#parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo,functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params=m.params
pfit=params
perror=m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr=chisq(pfit,th,counts,counts_err)
dof=m.dof
#Icalc=gauss(pfit,th)
#print 'mpfit chisqr', chisqr
if 0:
width_x=N.linspace(p0[0]-p0[1],p0[0]+p0[1],100)
width_y=N.ones(width_x.shape)*(maxval-minval)/2
pos_y=N.linspace(minval,maxval,100)
pos_x=N.ones(pos_y.shape)*p0[0]
if 1:
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(width_x,width_y)
pylab.plot(pos_x,pos_y)
pylab.plot(th,Icalc)
pylab.show()
else:
#fix center
#fix width
print 'no peak'
#Area center width Bak
area=0
center=th[len(th)/2]
width=(th.max()-th.min())/5.0 #rather arbitrary, but we don't know if it's the first....
Bak=qnode.th_condensed['counts'].mean()
p0=N.array([area,center,width,Bak],dtype='float64') #initial conditions
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value']=p0[i]
fa = {'x':th, 'y':counts, 'err':counts_err}
parinfo[1]['fixed']=1
parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo,functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params=m.params
pfit=params
perror=m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr=chisq(pfit,th,counts,counts_err)
dof=m.dof
Icalc=gauss(pfit,th)
#print 'perror',perror
if 0:
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(th,Icalc)
pylab.show()
print 'final answer'
print 'perror', 'perror'
#If the fit is unweighted (i.e. no errors were given, or the weights
# were uniformly set to unity), then .perror will probably not represent
#the true parameter uncertainties.
# *If* you can assume that the true reduced chi-squared value is unity --
# meaning that the fit is implicitly assumed to be of good quality --
# then the estimated parameter uncertainties can be computed by scaling
# .perror by the measured chi-squared value.
# dof = len(x) - len(mpfit.params) # deg of freedom
# # scaled uncertainties
# pcerror = mpfit.perror * sqrt(mpfit.fnorm / dof)
print 'params', pfit
print 'chisqr', chisqr #note that chisqr already is scaled by dof
pcerror=perror*N.sqrt(m.fnorm / m.dof)#chisqr
print 'pcerror', pcerror
self.qlist[index].th_integrated_intensity=N.abs(pfit[0])
self.qlist[index].th_integrated_intensity_err=N.abs(pcerror[0])
Icalc=gauss(pfit,th)
print 'perror',perror
if 0:
pylab.figure()
pylab.errorbar(th,counts,counts_err,marker='s',linestyle='None',mfc='black',mec='black',ecolor='black')
pylab.plot(th,Icalc)
qstr=str(qnode.q['h_center'])+','+str(qnode.q['k_center'])+','+str(qnode.q['l_center'])
pylab.title(qstr)
#pylab.show()
return
def test(complexity=0, **kwargs):
n = 15 * (complexity + 1)
x0 = 15 * cos(arange(n)) + 8
f = lambda x: ((x - 15)**2).sum()
df = lambda x: 2 * (x - 15)
c = lambda x: [2 * x[0]**4 - 32, x[1]**2 + x[2]**2 - 8]
# dc(x)/dx: non-lin ineq constraints gradients (optional):
def dc(x):
r = zeros((len(c(x0)), n))
r[0, 0] = 2 * 4 * x[0]**3
r[1, 1] = 2 * x[1]
r[1, 2] = 2 * x[2]
return r
hp = 2
h1 = lambda x: (x[-1] - 13)**hp
h2 = lambda x: (x[-2] - 17)**hp
h = lambda x: [h1(x), h2(x)]
# dh(x)/dx: non-lin eq constraints gradients (optional):
def dh(x):
r = zeros((2, n))
r[0, -1] = hp * (x[-1] - 13)**(hp - 1)
r[1, -2] = hp * (x[-2] - 17)**(hp - 1)
return r
lb = -8 * ones(n)
ub = 15 * ones(n) + 8 * cos(arange(n))
ind = 3
A = zeros((2, n))
A[0, ind:ind + 2] = 1
A[1, ind + 2:ind + 4] = 1
b = [15, 8]
Aeq = zeros(n)
Aeq[ind + 4:ind + 8] = 1
beq = 45
########################################################
colors = ['b', 'k', 'y', 'g', 'r']
#solvers = ['ipopt', 'ralg','scipy_cobyla']
solvers = ['ralg', 'scipy_slsqp', 'ipopt']
solvers = ['ralg', 'scipy_slsqp']
solvers = ['ralg']
solvers = ['r2']
solvers = ['ralg', 'scipy_slsqp']
########################################################
for i, solver in enumerate(solvers):
p = NLP(f, x0, df=df, c=c, h=h, dc=dc, dh=dh, lb=lb, ub=ub, A=A, b=b, Aeq=Aeq, beq=beq, maxIter = 1e4, \
show = solver==solvers[-1], color=colors[i], **kwargs )
if not kwargs.has_key('iprint'): p.iprint = -1
# p.checkdf()
# p.checkdc()
# p.checkdh()
r = p.solve(solver)
if r.istop > 0: return True, r, p
else: return False, r, p
def fitpeak(x, y, yerr):
maxval = x.max()
minval = x.min()
diff = y.max() - y.min() - y.mean()
sig = y.std()
print 'diff', diff, 'std', sig
if diff - 1 * sig > 0:
#the difference between the high and low point and
#the mean is greater than 3 sigma so we have a signal
p0 = findpeak(x, y, 2)
print 'p0', p0
#Area center width Bak area2 center2 width2
center1 = p0[0]
width1 = p0[1]
center2 = p0[2]
width2 = p0[3]
sigma = width / 2 / N.sqrt(2 * N.log(2))
ymax = maxval - minval
area = ymax * (N.sqrt(2 * pi) * sigma)
print 'ymax', ymax
pin = [area, center1, width1, 0, area, center2, width2]
if 1:
p = NLP(chisq, pin, maxIter=1e3, maxFunEvals=1e5)
#p.lb=lowerm
#p.ub=upperm
p.args.f = (x, y, yerr)
p.plot = 0
p.iprint = 1
p.contol = 1e-5 #3 # required constraints tolerance, default for NLP is 1e-6
# for ALGENCAN solver gradtol is the only one stop criterium connected to openopt
# (except maxfun, maxiter)
# Note that in ALGENCAN gradtol means norm of projected gradient of the Augmented Lagrangian
# so it should be something like 1e-3...1e-5
p.gradtol = 1e-5 #5 # gradient stop criterium (default for NLP is 1e-6)
#print 'maxiter', p.maxiter
#print 'maxfun', p.maxfun
p.maxIter = 50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
#r=p.solve('scipy_cobyla')
#r=p.solve('scipy_lbfgsb')
#r = p.solve('algencan')
print 'ralg'
r = p.solve('ralg')
print 'done'
pfit = r.xf
print 'pfit openopt', pfit
print 'r dict', r.__dict__
if 1:
print 'mpfit'
p0 = pfit
parbase = {
'value': 0.,
'fixed': 0,
'limited': [0, 0],
'limits': [0., 0.]
}
parinfo = []
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value'] = p0[i]
fa = {'x': x, 'y': y, 'err': yerr}
#parinfo[1]['fixed']=1
#parinfo[2]['fixed']=1
m = mpfit(myfunct_res, p0, parinfo=parinfo, functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params = m.params
pfit = params
perror = m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr = chisq(pfit, x, y, yerr)
dof = m.dof
#Icalc=gauss(pfit,th)
#print 'mpfit chisqr', chisqr
ycalc = gauss(pfit, x)
if 1:
width_x = N.linspace(p0[0] - p0[1], p0[0] + p0[1], 100)
width_y = N.ones(width_x.shape) * (maxval - minval) / 2
pos_y = N.linspace(minval, maxval, 100)
pos_x = N.ones(pos_y.shape) * p0[0]
if 0:
pylab.errorbar(th,
counts,
counts_err,
marker='s',
linestyle='None',
mfc='black',
mec='black',
ecolor='black')
pylab.plot(width_x, width_y)
pylab.plot(pos_x, pos_y)
pylab.plot(x, ycalc)
pylab.show()
else:
#fix center
#fix width
print 'no peak'
#Area center width Bak
area = 0
center = x[len(x) / 2]
width = (
x.max() - x.min()
) / 5.0 #rather arbitrary, but we don't know if it's the first.... #better to use resolution
Bak = y.mean()
p0 = N.array([area, center, width, Bak],
dtype='float64') #initial conditions
parbase = {
'value': 0.,
'fixed': 0,
'limited': [0, 0],
'limits': [0., 0.]
}
parinfo = []
for i in range(len(p0)):
parinfo.append(copy.deepcopy(parbase))
for i in range(len(p0)):
parinfo[i]['value'] = p0[i]
fa = {'x': x, 'y': y, 'err': yerr}
parinfo[1]['fixed'] = 1
parinfo[2]['fixed'] = 1
m = mpfit(myfunct_res, p0, parinfo=parinfo, functkw=fa)
if (m.status <= 0):
print 'error message = ', m.errmsg
params = m.params
pfit = params
perror = m.perror
#chisqr=(myfunct_res(m.params, x=th, y=counts, err=counts_err)[1]**2).sum()
chisqr = chisq(pfit, x, y, yerr)
dof = m.dof
ycalc = gauss(pfit, x)
#print 'perror',perror
if 0:
pylab.errorbar(x,
y,
yerr,
marker='s',
linestyle='None',
mfc='black',
mec='black',
ecolor='black')
pylab.plot(x, ycalc)
pylab.show()
print 'final answer'
print 'perror', 'perror'
#If the fit is unweighted (i.e. no errors were given, or the weights
# were uniformly set to unity), then .perror will probably not represent
#the true parameter uncertainties.
# *If* you can assume that the true reduced chi-squared value is unity --
# meaning that the fit is implicitly assumed to be of good quality --
# then the estimated parameter uncertainties can be computed by scaling
# .perror by the measured chi-squared value.
# dof = len(x) - len(mpfit.params) # deg of freedom
# # scaled uncertainties
# pcerror = mpfit.perror * sqrt(mpfit.fnorm / dof)
print 'params', pfit
print 'chisqr', chisqr #note that chisqr already is scaled by dof
pcerror = perror * N.sqrt(m.fnorm / m.dof) #chisqr
print 'pcerror', pcerror
integrated_intensity = N.abs(pfit[0])
integrated_intensity_err = N.abs(pcerror[0])
ycalc = gauss(pfit, x)
print 'perror', perror
if 1:
pylab.figure()
pylab.errorbar(x,
y,
yerr,
marker='s',
linestyle='None',
mfc='black',
mec='black',
ecolor='black')
pylab.plot(x, ycalc)
#qstr=str(qnode.q['h_center'])+','+str(qnode.q['k_center'])+','+str(qnode.q['l_center'])
#pylab.title(qstr)
pylab.show()
return pfit, perror, pcerror, chisq
def run_optimization(self, plot=True, _only_check_gradients=False):
"""Start/run optimization procedure and the optimum unless.
Set the keyword parameter 'plot' to False (default=True) if plotting
should not be conducted.
"""
grid = self.get_grid()
model = self.get_model()
# Initial try
p0 = self.get_p0()
# Less than (-0.5 < u < 1)
# TODO: These are currently hard coded. They shouldn't be.
#NLT = len(grid) * len(model.u)
#Alt = N.zeros( (NLT, len(p0)) )
#Alt[:, (len(grid) - 1) * len(model.x):] = -N.eye(len(grid) *
# len(model.u))
#blt = -0.5*N.ones(NLT)
# TODO: These are currently hard coded. They shouldn't be.
#N_xvars = (len(grid) - 1) * len(model.x)
#N_uvars = len(grid) * len(model.u)
#N_vars = N_xvars + N_uvars
#Alt = -N.eye(N_vars)
#blt = N.zeros(N_vars)
#blt[0:N_xvars] = -N.ones(N_xvars)*0.001
#blt[N_xvars:] = -N.ones(N_uvars)*1;
# Get OpenOPT handler
p = NLP(
self.f,
p0,
maxIter=1e3,
maxFunEvals=1e3,
#A=Alt, # See TODO above
#b=blt, # See TODO above
df=self.df,
ftol=1e-4,
xtol=1e-4,
contol=1e-4)
if len(grid) > 1:
p.h = self.h
p.dh = self.dh
if plot:
p.plot = 1
p.iprint = 1
if _only_check_gradients:
# Check gradients against finite difference quotients
p.checkdf(maxViolation=0.05)
p.checkdh()
return None
#opt = p.solve('ralg') # does not work - serious convergence issues
opt = p.solve('scipy_slsqp')
if plot:
plot_control_solutions(model, grid, opt.xf)
return opt
def single_shooting(model, initial_u=0.4, plot=True):
"""Run single shooting of model model with a constant u.
The function returns the optimal u.
Notes:
* Currently written specifically for VDP.
* Currently only supports one input/control signal.
Parameters:
model -- the model which is to be simulated. Only models with one control
signal is supported.
Keyword parameters:
initial_u -- the initial input U_0 used to initialize the optimization
with.
"""
assert len(model.u) == 1, "More than one control signal is " \
"not supported as of today."
start_time = model.opt_interval_get_start_time()
end_time = model.opt_interval_get_final_time()
u = model.u
u0 = N.array([initial_u])
print "Initial u:", u
gradient = None
gradient_u = None
def f(cur_u):
"""The cost evaluation function."""
model.reset()
u[:] = cur_u
print "u is", u
big_gradient, last_y, gradparams, sens = _shoot(
model, start_time, end_time)
model.set_x_p(last_y, 0)
model.set_dx_p(model.dx, 0)
model.set_u_p(model.u, 0)
cost = model.opt_eval_J()
gradient_u = cur_u.copy()
gradient = big_gradient[gradparams['u_start']:gradparams['u_end']]
print "Cost:", cost
print "Grad:", gradient
return cost
def df(cur_u):
"""The gradient of the cost function.
NOT USED right now.
"""
model.reset()
u[:] = cur_u
print "u is", u
big_gradient, last_y, gradparams, sens = _shoot(
model, start_time, end_time)
model.set_x_p(last_y, 0)
model.set_dx_p(model.dx, 0)
model.set_u_p(model.u, 0)
cost = model.opt_eval_J()
gradient_u = cur_u.copy()
gradient = big_gradient[gradparams['u_start']:gradparams['u_end']]
print "Cost:", cost
print "Grad:", gradient
return gradient
p = NLP(f, u0, maxIter=1e3, maxFunEvals=1e2)
p.df = df
if plot:
p.plot = 1
else:
p.plot = 0
p.iprint = 1
u_opt = p.solve('scipy_slsqp')
return u_opt
def solve(self):
p=NLP(self.cost_function,self.initial_solution,Aeq=self.Aeq,beq=self.beq,A=self.A,b=self.b,lb=self.lb,ub=self.ub)
p.iprint = -1
r=p.solve('ralg')
return [r.xf,r.ff]