def checkLambda(jtj, lMat, r2Mat, a, b):
lambdas = scipy.arange(-1., 1., 0.001)
residuals = [
l * l * jtj[a, a] + (1. - l * l) * jtj[b, b] +
2. * l * scipy.sqrt(1. - l * l) * jtj[a, b] for l in lambdas
]
Plotting.plot(lambdas, residuals)
Plotting.plot([lMat[a, b]], [r2Mat[a, b]], 'o')
Plotting.title(str(a) + ', ' + str(b))
return
def plotLevels(levels, offset=0):
xs = [offset + 0.6, offset + 1.4]
for lvl in levels:
Plotting.semilogy(xs, [lvl, lvl], 'k')
return
def plot_variances_subplot(chemnames, logprior):
times, bestfit, var = variances(chemnames, logprior)
nallplots = len(chemnames)
# 9 at a time
nfigs = nallplots / 9 # integer division -- no fractional part
for figno in range(1, nfigs + 1):
Plotting.figure()
for i in range(0, 9):
Plotting.subplot(3, 3, i + 1)
chemind = i + (figno - 1) * 9
Plotting.plot(times, bestfit[chemnames[chemind]])
Plotting.hold(True)
Plotting.plot(
times, bestfit[chemnames[chemind]] +
scipy.sqrt(var[chemnames[chemind]]), 'r-')
Plotting.plot(
times, bestfit[chemnames[chemind]] -
scipy.sqrt(var[chemnames[chemind]]), 'r-')
yt = Plotting.yticks()
Plotting.axis([0, 100.0, yt[0], yt[-1]])
Plotting.title(chemnames[chemind])
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
xt = Plotting.xticks()
Plotting.xticks([xt[0], xt[-1]])
Plotting.savefig('./figs/variance_wt_' + i.__str__() + '.ps')
Plotting.show()
def plot_variance_newpoint(chemnames,
sensvect_design,
logprior=1.0e20,
return_data=True):
"""
chemnames: list of chemical names
sensvect_design: a sensivity vector of a quantity that is
measurable
This will plot the old and new variances of the chemicals in
chemnames, given a new measurement that has sensitivity vector
sensvect_design
"""
times, bestfit, var = variances(chemnames, logprior)
times, varchange = variance_change(chemnames, sensvect_design, logprior)
for key in bestfit.keys():
Plotting.figure()
Plotting.plot(times, bestfit[key])
Plotting.hold(True)
Plotting.plot(times, bestfit[key] + scipy.sqrt(var[key]), 'r-')
Plotting.plot(times, bestfit[key] - scipy.sqrt(var[key]), 'r-')
Plotting.plot(times,
bestfit[key] + scipy.sqrt(var[key] + varchange[key]),
'k--')
Plotting.plot(times,
bestfit[key] - scipy.sqrt(var[key] + varchange[key]),
'k--')
Plotting.title(key, fontsize=14)
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
Plotting.axis([0.0, 40.0, -.01, 1.2e4])
Plotting.show()
if return_data:
newvar = {}
for ky in var.keys():
newvar[ky] = var[key] + varchange[key]
return times, bestfit, newvar
def plot_variance_newweights(weights,
chemnames,
sensarray_design,
logprior=1.0e20,
scale=1.0,
return_data=True):
"""
weights : a proposed set of weights for each of the row vectors in
sensarray_design
chemnames : a list of chemicals for which we will plot the variance
logprior : as before
This will plot the old and new variances on chemnames, similar to
above.
NOTE: the weights that are passed in do not necessarily have to sum to
one. e.g. if the weights are normalized such that max(weights) = 1, then
by scaling all the weights by 1/sigma, you are then assuming that
the most accurate measurement has an error of size sigma. sigma for
example could be 20% of the maximum value of a trajectory.
"""
times, bestfit, var = variances(chemnames, logprior)
times, varchange = var_change_weighted(weights, chemnames,
sensarray_design, logprior)
for key in bestfit.keys():
Plotting.figure()
Plotting.plot(times, scale * bestfit[key])
Plotting.hold(True)
Plotting.plot(times,
scale * bestfit[key] + scale * scipy.sqrt(var[key]),
'r-')
Plotting.plot(times,
scale * bestfit[key] - scale * scipy.sqrt(var[key]),
'r-')
Plotting.plot(
times, scale * bestfit[key] +
scale * scipy.sqrt(var[key] + varchange[key]), 'k--')
Plotting.plot(
times, scale * bestfit[key] -
scale * scipy.sqrt(var[key] + varchange[key]), 'k--')
Plotting.title(key, fontsize=14)
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
Plotting.axis([0.0, 40.0, -.01, 1.2e4])
Plotting.show()
if return_data:
newvar = {}
for ky in var.keys():
newvar[ky] = var[key] + varchange[key]
return times, bestfit, newvar
def plot_variances(chemnames, logprior, scale=1.0, return_var=False):
"""
chemnames: list of chemical names
logprior: prior on params. logprior = log(1000.0) means parameters
allowed to fluctuate by a factor of 1000 """
times, bestfit, var = variances(chemnames, logprior)
for key in bestfit.keys():
Plotting.figure()
Plotting.plot(times, bestfit[key] / scale)
Plotting.hold(True)
Plotting.plot(times,
bestfit[key] / scale + scipy.sqrt(var[key]) / scale,
'r--')
Plotting.plot(times,
bestfit[key] / scale - scipy.sqrt(var[key]) / scale,
'r--')
Plotting.title(key, fontsize=16)
Plotting.xlabel('time (minutes)', fontsize=16)
Plotting.ylabel('number of molecules', fontsize=16)
xtics = Plotting.gca().get_xticklabels()
ytics = Plotting.gca().get_yticklabels()
Plotting.setp(xtics, size=16)
Plotting.setp(ytics, size=16)
#Plotting.axis([0.0,40.0,-.01,1.2e4])
Plotting.show()
if return_var:
return times, bestfit, var
def plot_variances_log_chems(chemnames, logprior):
"""
chemnames: list of chemical names
logprior: prior on params
Plots the standard deviation of the chemicals when the variance
is computed using logs of the chemical trajectories. This
makes sure the final plots do not have best_fit+-stddev that
do not become negative """
times, bestfit, var = variances_log_chems(chemnames, logprior)
for key in bestfit.keys():
Plotting.figure()
Plotting.plot(times, bestfit[key])
Plotting.hold(True)
Plotting.plot(times, bestfit[key] * scipy.exp(scipy.sqrt(var[key])),
'r-')
Plotting.plot(times, bestfit[key] * scipy.exp(-scipy.sqrt(var[key])),
'r-')
Plotting.title(key, fontsize=14)
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
#Plotting.axis([0.0,40.0,-.01,1.2e4])
Plotting.show()
def plot_variances_subplot(chemnames,logprior) :
times, bestfit, var = variances(chemnames,logprior)
nallplots = len(chemnames)
# 9 at a time
nfigs = nallplots/9 # integer division -- no fractional part
for figno in range(1,nfigs+1) :
Plotting.figure()
for i in range(0,9) :
Plotting.subplot(3,3,i+1)
chemind = i+(figno-1)*9
Plotting.plot(times,bestfit[chemnames[chemind]])
Plotting.hold(True)
Plotting.plot(times,bestfit[chemnames[chemind]]
+ scipy.sqrt(var[chemnames[chemind]]),'r-')
Plotting.plot(times,bestfit[chemnames[chemind]]
- scipy.sqrt(var[chemnames[chemind]]),'r-')
yt = Plotting.yticks()
Plotting.axis([0,100.0,yt[0],yt[-1]])
Plotting.title(chemnames[chemind])
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
xt = Plotting.xticks()
Plotting.xticks([xt[0],xt[-1]])
Plotting.savefig('./figs/variance_wt_'+i.__str__()+'.ps')
Plotting.show()
def plot_variance_newweights(weights,chemnames,sensarray_design,logprior=1.0e20,scale=1.0,return_data = True) :
"""
weights : a proposed set of weights for each of the row vectors in
sensarray_design
chemnames : a list of chemicals for which we will plot the variance
logprior : as before
This will plot the old and new variances on chemnames, similar to
above.
NOTE: the weights that are passed in do not necessarily have to sum to
one. e.g. if the weights are normalized such that max(weights) = 1, then
by scaling all the weights by 1/sigma, you are then assuming that
the most accurate measurement has an error of size sigma. sigma for
example could be 20% of the maximum value of a trajectory.
"""
times,bestfit,var = variances(chemnames,logprior)
times,varchange = var_change_weighted(weights,chemnames,sensarray_design,logprior)
for key in bestfit.keys() :
Plotting.figure()
Plotting.plot(times,scale*bestfit[key])
Plotting.hold(True)
Plotting.plot(times,scale*bestfit[key] + scale*scipy.sqrt(var[key]),'r-')
Plotting.plot(times,scale*bestfit[key] - scale*scipy.sqrt(var[key]),'r-')
Plotting.plot(times,scale*bestfit[key] + scale*scipy.sqrt(var[key]+varchange[key]),'k--')
Plotting.plot(times,scale*bestfit[key] - scale*scipy.sqrt(var[key]+varchange[key]),'k--')
Plotting.title(key,fontsize=14)
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
Plotting.axis([0.0,40.0,-.01,1.2e4])
Plotting.show()
if return_data :
newvar = {}
for ky in var.keys() :
newvar[ky] = var[key] + varchange[key]
return times,bestfit,newvar
def plot_variance_newpoint(chemnames,sensvect_design,logprior=1.0e20,
return_data = True) :
"""
chemnames: list of chemical names
sensvect_design: a sensivity vector of a quantity that is
measurable
This will plot the old and new variances of the chemicals in
chemnames, given a new measurement that has sensitivity vector
sensvect_design
"""
times,bestfit,var = variances(chemnames,logprior)
times,varchange = variance_change(chemnames,sensvect_design,logprior)
for key in bestfit.keys() :
Plotting.figure()
Plotting.plot(times,bestfit[key])
Plotting.hold(True)
Plotting.plot(times,bestfit[key] + scipy.sqrt(var[key]),'r-')
Plotting.plot(times,bestfit[key] - scipy.sqrt(var[key]),'r-')
Plotting.plot(times,bestfit[key] + scipy.sqrt(var[key]+varchange[key]),'k--')
Plotting.plot(times,bestfit[key] - scipy.sqrt(var[key]+varchange[key]),'k--')
Plotting.title(key,fontsize=14)
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
Plotting.axis([0.0,40.0,-.01,1.2e4])
Plotting.show()
if return_data :
newvar = {}
for ky in var.keys() :
newvar[ky] = var[key] + varchange[key]
return times,bestfit,newvar
def plot_variances_log_chems(chemnames,logprior) :
"""
chemnames: list of chemical names
logprior: prior on params
Plots the standard deviation of the chemicals when the variance
is computed using logs of the chemical trajectories. This
makes sure the final plots do not have best_fit+-stddev that
do not become negative """
times, bestfit, var = variances_log_chems(chemnames,logprior)
for key in bestfit.keys() :
Plotting.figure()
Plotting.plot(times,bestfit[key])
Plotting.hold(True)
Plotting.plot(times,bestfit[key]*scipy.exp(scipy.sqrt(var[key])),'r-')
Plotting.plot(times,bestfit[key]*scipy.exp(-scipy.sqrt(var[key])),'r-')
Plotting.title(key,fontsize=14)
Plotting.xlabel('time')
Plotting.ylabel('arb. units')
#Plotting.axis([0.0,40.0,-.01,1.2e4])
Plotting.show()
def plot_variances(chemnames,logprior,scale=1.0,return_var = False) :
"""
chemnames: list of chemical names
logprior: prior on params. logprior = log(1000.0) means parameters
allowed to fluctuate by a factor of 1000 """
times, bestfit, var = variances(chemnames,logprior)
for key in bestfit.keys() :
Plotting.figure()
Plotting.plot(times,bestfit[key]/scale)
Plotting.hold(True)
Plotting.plot(times,bestfit[key]/scale + scipy.sqrt(var[key])/scale,'r--')
Plotting.plot(times,bestfit[key]/scale - scipy.sqrt(var[key])/scale,'r--')
Plotting.title(key,fontsize=16)
Plotting.xlabel('time (minutes)',fontsize=16)
Plotting.ylabel('number of molecules',fontsize=16)
xtics = Plotting.gca().get_xticklabels()
ytics = Plotting.gca().get_yticklabels()
Plotting.setp(xtics,size=16)
Plotting.setp(ytics,size=16)
#Plotting.axis([0.0,40.0,-.01,1.2e4])
Plotting.show()
if return_var :
return times, bestfit, var
