def calculate_rsquared(data,poisson,popt):
if len(data)==0: return 0.0
ydata = data[:,1]
yfit = prony(data[:,0],*popt)
if poisson!=0.5:
ydata = np.hstack((ydata,data[:,2]))
yfit = np.hstack((yfit, prony(data[:,0],*popt)))
return CF.rsquared(ydata,yfit)
def calculate_rsquared(data, model, popt, t):
if len(data) == 0: return 0.0
for char in t:
if not char in data: continue
ydata = data[char][:, 1]
yfit = MU.get_function(model, char)(data[char][:, 0], *popt)
if 'yfits' in locals():
ydatas = np.hstack((ydatas, ydata))
yfits = np.hstack((yfits, yfit))
else:
ydatas = ydata
yfits = yfit
return CF.rsquared(ydatas, yfits)
def calc_fit(OF,cmd,expdata,init_nc,interpBOOL,optfunc,*popt):
fig,axis = pyplot.subplots(1,1)
popt_display = np.abs(list(popt))
popt_display[0] = calc_nc(popt[0],init_nc)
print '\n********************************************************************'
print '** Testing with parameters: ',popt_display
print '********************************************************************'
# Get the simulation results.
if not hasattr(calc_fit, "iter"): calc_fit.iter=0
simdata = optfunc((calc_fit.iter,)+popt)
if len(simdata)==0:
print '\n********************************************************************'
print ' Abaqus failed, we return an average error of 1000.0'
print '********************************************************************'
calc_fit.iter = calc_fit.iter + 1
pyplot.close()
return 1000.0
# Loop over multiple simulation results, if necessary.
NP = 50
errs = dict()
cm = pyplot.get_cmap('jet')
colors = [cm(float(i)/(2*len(simdata))) for i in range(2*len(simdata))]
cidx = 0
for T,sdata in simdata.iteritems():
if T in expdata: edata=expdata[T]
elif T.endswith('--strain'):
if 'strain' in expdata: edata=expdata['strain']
else: continue
else: U.print_error('Failed to find comparison data for '+T,True)
# Plot the simulation data.
axis.plot(1000.0*sdata[:,0],sdata[:,1],'o-',color=colors[cidx],label='Sim '+T)
# Interpolate the simulation results to remove zigzags and evenly space the points.
# This is important because otherwise we may weight solutions very heavily at one point
# in one solution, and completely differently in another.
u,idx = np.unique(sdata[:,0],return_index=True)
try:
if interpBOOL:
sim_smooth = np.zeros((NP,2))
sim_smooth[:,0] = np.linspace(min(sdata[idx,0]),max(sdata[idx,0]),NP)
# xvals = 1.0 - (np.logspace(0,np.log10(NP+1.0),NP,endpoint=True)-1.0)/(NP+1.0)
# sim_smooth[:,0] = min(sdata[idx,0]) + (max(sdata[idx,0])-min(sdata[idx,0]))*xvals
else:
sim_smooth = np.zeros(edata.shape)
sim_smooth[:,0] = edata[:,0]
dataF = interp.UnivariateSpline(sdata[idx,0],sdata[idx,1],k=3,s=0)
sim_smooth[:,1] = dataF(sim_smooth[:,0])
# Remove any extrapolations, replace with the max calculated value.
sim_smooth[sim_smooth[:,0]>max(sdata[:,0]),1] = max(sdata[:,1])
axis.plot(1000.0*sim_smooth[:,0],sim_smooth[:,1],'.--',color=colors[cidx],label='Sim '+T+' (Smoothed)')
except:
print '** Failed to smooth simulation data. Proceding with untouched data.'
sim_smooth = 1.0*sdata[idx,:]
interpBOOL = True
# Interpolate the experimental results to find comparable data.
axis.plot(1000.0*edata[:,0],edata[:,1],'-',color=colors[cidx+1],label='Exp '+T)
if interpBOOL:
try:
dataF = interp.UnivariateSpline(edata[:,0], edata[:,1],k=3,s=0)
exp_smooth = np.zeros(sim_smooth.shape)
exp_smooth[:,0] = sim_smooth[:,0]
exp_smooth[:,1] = dataF(exp_smooth[:,0])
except:
U.print_error('Failed to fit a spline to experimental data, consider using the '
'--no_interpolate option or adding more datapoints.',True)
else: exp_smooth = 1.0*edata
axis.plot(1000.0*exp_smooth[:,0],exp_smooth[:,1],'.--',color=colors[cidx+1],label='Exp '+T+' (Smoothed)')
# Make the comparison.
# Try to handle a case where Abaqus failed early, but we have partial results.
if max(sdata[:,0])<0.666*max(edata[:,0]):
errs[T] = 1000.0 - 1000.0*max(sdata[:,0])/max(edata[:,0])
print '\n********************************************************************'
print ' Abaqus only reached',max(sdata[:,0]),' (out of '+str(max(edata[:,0]))+')!'
print '********************************************************************'
else:
# For errors on max strain, no penalty for being too low.
if T.endswith('--strain'):
if max(exp_smooth[:,1])>=max(sim_smooth[:,1]): errs[T]=0.0
else: errs[T] = 1.0 - CH.rsquared(exp_smooth,sim_smooth)
else:
errs[T] = 1.0 - CH.rsquared(exp_smooth,sim_smooth)
cidx = cidx+2
# Record to file.
if calc_fit.iter==0:
OF.write('# Each row shows the iteration #, the '+str(len(popt))+' parameters,\n')
OF.write('# and then the '+str(len(errs.keys()))+' errors: '+str(errs.keys())+'\n')
record_string = str(calc_fit.iter)+','
for p in popt_display: record_string = record_string + str(p) + ','
for err in errs.values(): record_string = record_string + str(err) + ','
OF.write(record_string[:-1]+'\n')
# Plot settings.
if cmd=='act':
axis.set_xlabel('Internal Pressure (kPa)')
if len(simdata)>1: axis.set_ylabel('Displacement (mm) or Force (N)')
else:
if 'linU' in simdata or 'bndU' in simdata: axis.set_ylabel('Displacement (mm)')
elif 'linF' in simdata or 'bndF' in simdata: axis.set_ylabel('Force (N)')
axis.grid()
# Plot with the same axis every time.
if not hasattr(calc_fit, "xlim"):
calc_fit.xlim = axis.get_xlim()
calc_fit.ylim = axis.get_ylim()
axis.set_xlim(calc_fit.xlim)
axis.set_ylim(calc_fit.ylim)
axis.set_aspect(np.diff(calc_fit.xlim)/np.diff(calc_fit.ylim)) # Square axis.
err_str = ', '.join("{:}:{:g}".format(key,val) for (key,val) in errs.iteritems())
title = axis.set_title('\n'.join(textwrap.wrap(str(popt_display),100))+'\nitr='+str(calc_fit.iter)+'\nerrs=['+err_str+']\nerr_sum='+str(sum(errs.values())))
title.set_y(1.05)
fig.subplots_adjust(top=0.8)
L = axis.legend(loc='best',frameon=False,framealpha=0)
for legobj in L.legendHandles: legobj.set_linewidth(2.0)
pyplot.tight_layout()
pyplot.savefig('results--'+str(calc_fit.iter)+'.png')
pyplot.savefig('results--latest.png')
pyplot.close()
print '\n********************************************************************'
print ' Calculated sum-of-squares error:',errs,'=',sum(errs.values())
print '********************************************************************'
calc_fit.iter = calc_fit.iter + 1
return sum(errs.values())
def calc_fit(act,test,cmd,expdata,matdata,testfunc,*popt):
fig,ax = pyplot.subplots(1,2,figsize=(10,6))
print '\n********************************************************************'
print '** Testing with parameters: ',popt
print '********************************************************************'
# Get the simulation results.
if not hasattr(calc_fit, "iter"): calc_fit.iter=0
simdata = testfunc((calc_fit.iter,)+popt)
if len(simdata)==0:
print '\n********************************************************************'
print ' Abaqus failed, we return an average error of 1000.0'
print '********************************************************************'
calc_fit.iter = calc_fit.iter + 1
return 1000.0
# Loop over multiple simulation results, if necessary.
NP = 50
errs = dict()
cm = pyplot.get_cmap('jet')
colors = [cm(float(i)/(2*len(simdata))) for i in range(2*len(simdata))]
cidx = 0
for T,sdata in simdata.iteritems():
# Plot the simulation data.
ax[0].plot(1000.0*sdata[:,0],sdata[:,1],'o-',color=colors[cidx],label='Sim '+T)
# Interpolate the simulation results to remove zigzags and evenly space the points.
# This is important because otherwise we may weight solutions very heavily at one point
# in one solution, and completely differently in another.
u,idx = np.unique(sdata[:,0],return_index=True)
try:
sim_smooth = np.zeros((NP,2))
# sim_smooth[:,0] = np.linspace(min(sdata[idx,0]),max(sdata[idx,0]),NP)
xvals = 1.0 - (np.logspace(0,np.log10(NP+1.0),NP,endpoint=True)-1.0)/(NP+1.0)
sim_smooth[:,0] = min(sdata[idx,0]) + (max(sdata[idx,0])-min(sdata[idx,0]))*xvals
dataF = interp.UnivariateSpline(sdata[idx,0],sdata[idx,1],k=3,s=0)
sim_smooth[:,1] = dataF(sim_smooth[:,0])
ax[0].plot(1000.0*sim_smooth[:,0],sim_smooth[:,1],'.--',color=colors[cidx],label='Sim '+T+' (Smoothed)')
except:
print '** Failed to smooth simulation data. Proceding with untouched data.'
sim_smooth = 1.0*sdata[idx,:]
# Interpolate the experimental results to find comparable data.
edata = expdata[T]
ax[0].plot(1000.0*edata[:,0],edata[:,1],'-',color=colors[cidx+1],label='Exp '+T)
dataF = interp.UnivariateSpline(edata[:,0], edata[:,1],k=3,s=0)
exp_smooth = np.zeros(sim_smooth.shape)
exp_smooth[:,0] = sim_smooth[:,0]
exp_smooth[:,1] = dataF(exp_smooth[:,0])
ax[0].plot(1000.0*exp_smooth[:,0],exp_smooth[:,1],'.--',color=colors[cidx+1],label='Exp '+T+' (Smoothed)')
# Make the comparison.
# Try to handle a case where Abaqus failed early, but we have partial results.
if max(sdata[:,0])<0.666*max(edata[:,0]):
errs[T] = 1000.0 - 1000.0*max(sdata[:,0])/max(edata[:,0])
print '\n********************************************************************'
print ' Abaqus only reached',max(sdata[:,0]),' (out of '+str(max(edata[:,0]))+')!'
print '********************************************************************'
else:
# errs[T] = np.linalg.norm((exp_smooth[:,1]-sim_smooth[:,1])/max(edata[:,1]))
errs[T] = 1.0 - CH.rsquared(exp_smooth,sim_smooth)
cidx = cidx+2
# Plot the model uniaxial, biaxial, and planar curves.
if cmd!='vis':
for t in 'ubp':
if not t in matdata: continue
dataF = interp.interp1d(matdata[t][:,0], matdata[t][:,1], kind='nearest', bounds_error=False, fill_value=0.0)
vals = np.zeros((NP,3))
vals[:,0] = np.linspace(min(matdata[t][:,0]),max(matdata[t][:,0]),NP)
vals[:,1] = dataF(vals[:,0])
vals[:,2] = MU.get_function(model,t)(vals[:,0],*popt) # splat operator.
# errs['mat_'+t] = np.linalg.norm((vals[:,1]-vals[:,2])/max(matdata[t][:,1]))
errs['mat_'+t] = 1.0 - CH.rsquared(vals[:,1],vals[:,2])
CHP.plot_data(ax[1],model,matdata,popt,[0,4],[0,.25])
ax[1].set_aspect(np.diff(ax[1].get_xlim())/np.diff(ax[1].get_ylim())) # Square axis.
# Plot settings.
if cmd=='mat':
ax[0].set_xlabel('Engineering Strain')
ax[0].set_ylabel(r'Nominal Stress $\left({}^N\!/{}_{mm^2}\right)$')
elif cmd=='act' or cmd=='vis':
ax[0].set_xlabel('Internal Pressure (kPa)')
if len(simdata)>1: ax[0].set_ylabel('Displacement (mm) or Force (N)')
else:
if 'linU' in simdata or 'bndU' in simdata: ax[0].set_ylabel('Displacement (mm)')
elif 'linF' in simdata or 'bndF' in simdata: ax[0].set_ylabel('Force (N)')
ax[0].grid()
# Plot with the same axis every time.
if not hasattr(calc_fit, "xlim"):
calc_fit.xlim = ax[0].get_xlim()
calc_fit.ylim = ax[0].get_ylim()
ax[0].set_xlim(calc_fit.xlim)
ax[0].set_ylim(calc_fit.ylim)
ax[0].set_aspect(np.diff(calc_fit.xlim)/np.diff(calc_fit.ylim)) # Square axis.
# ax[0].set_aspect(abs(xlim[1]-xlim[0])/abs(ylim[1]-ylim[0])) # Square axis.
pyplot.suptitle('\n'.join(textwrap.wrap(str(popt),100))+'\nitr='+str(calc_fit.iter)+'\nerrs='+str(errs)+'\nerr_sum='+str(sum(errs.values())))
L = ax[0].legend(loc='best',frameon=False,framealpha=0)
for legobj in L.legendHandles: legobj.set_linewidth(2.0)
pyplot.tight_layout()
pyplot.savefig('results--'+str(calc_fit.iter)+'.png')
pyplot.savefig('results--latest.png')
pyplot.close()
print '\n********************************************************************'
print ' Calculated sum-of-squares error:',errs,'=',sum(errs.values())
print '********************************************************************'
calc_fit.iter = calc_fit.iter + 1
return sum(errs.values())