def condtn_nm_plot(G, w_start=-2, w_end=2, axlim=None, points=1000):
"""
Plot of the condition number, the maximum over the minimum singular value
Parameters
----------
G : numpy matrix
Plant model.
Returns
-------
Plot : matplotlib figure
Note
----
A condition number over 10 may indicate sensitivity to uncertainty and
control problems
With a small condition number, Gamma =1, the system is insensitive to
input uncertainty, irrespective of controller (p248).
"""
s, w, axlim = df.frequency_plot_setup(axlim, w_start, w_end, points)
def cndtn_nm(G):
return utils.sigmas(G)[0]/utils.sigmas(G)[-1]
freqresp = [G(si) for si in s]
plt.loglog(w, [cndtn_nm(Gfr) for Gfr in freqresp], label='$\gamma (G)$')
plt.axis(axlim)
plt.ylabel('$\gamma (G)$')
plt.xlabel('Frequency [rad/unit time]')
plt.axhline(10., color='red', ls=':', label='"Large" $\gamma (G) = 10$')
plt.legend()
def plot_mpl_fig():
rootdir = '/Users/catherinefielder/Documents/Research_Halos/HaloDetail'
cs = []
pops = []
for subdir, dirs, files in os.walk(rootdir):
head,tail = os.path.split(subdir)
haloname = tail
for file in files:
if file.endswith('_columnsadded'):
values = ascii.read(os.path.join(subdir, file), format = 'commented_header') #Get full path and access file
host_c = values[1]['host_c']
cs = np.append(cs, host_c)
pop = len(values['mvir(10)'])
pops = np.append(pops, pop)
print pop
plt.loglog(host_c, pop, alpha=0.8,label = haloname)
print "%s done. On to the next." %haloname
#plt.xscale('log')
#plt.yscale('log')
plt.xlabel('Host Concentration')
plt.ylabel('Nsat')
plt.title('Abundance vs. Host Concentration', ha='center')
#plt.legend(loc='best')
spearman = scipy.stats.spearmanr(cs, pops)
print spearman
def plotPeriodogram(fvec, pvec, axes=None, thinning=None):
'''
**plotPeriodogram(fvec, pvec, axes=None, thinning=None)**
Function that plot a periodogram
Parameters
----------
**fvec** : vector containing the frequencies resulting from fftdem() \n
**pvec** : vector containing the power values resulting from fftdem() \n
**axes** : string indicating what type of axes to use. Possible options are: \n\t
- "loglog" \n\t
- "semilogx"\n\t
- "semilogy" \n\t
- None (default option)\n
**thinning** : parameter to thin the data o plot as vectors can be ver large. It will plot only the number of dots indicated by thinning '''
# Wvec=1/fvec
if thinning == None:
thinning = thinningCheckup(fvec)
plt.figure()
if axes == "loglog":
plt.loglog(fvec[range(0,fvec.size,thinning)],pvec[range(0,pvec.size,thinning)])
elif axes == "semilogx":
plt.semilogx(fvec[range(0,fvec.size,thinning)],pvec[range(0,pvec.size,thinning)])
elif axes == "semilogy":
plt.semilogy(fvec[range(0,fvec.size,thinning)],pvec[range(0,pvec.size,thinning)])
else:
plt.plot(fvec[range(0,fvec.size,thinning)],pvec[range(0,pvec.size,thinning)])
plt.title("Periodogram")
plt.ylabel("DFT mean square amplitude")
plt.xlabel("Frequency (1/m)")
plt.show()
def RGA_w(w_start, w_end, x, y):
""" w_start is the start of logspace
w_end is the ending of the logspace
x and y is refer to the indices of the RGA matrix that needs to be plotted
this is to calculate the RGA at different freqeuncies
this give more conclusive values of which pairing would give fast responses
under dynamic situations"""
w = np.logspace(w_start, w_end, 1000)
store = np.zeros([len(x), len(w)])
count = 0
for w_i in w:
A = G(w_i)
RGA_w = np.multiply(A, np.transpose(np.linalg.pinv(A)))
store[:, count] = RGA_w[x, y]
count = count + 1
for i in range(len(x)):
plt.loglog(w, store[i, :])
plt.title("RGA over Freq")
plt.xlabel("w")
plt.ylabel("|RGA values| gevin x ,y ")
plt.show()
def addPlot(title,lbl,ref=None):
inFile = file(title,'r')
entries=[]
for line in inFile:
if line=='\n' or line.startswith('Moments') or line.startswith('N,'):
continue
entries.append([])
vals=line.strip().split(',')
entries[-1].append(int(vals[0]))
entries[-1].append(float(vals[1]))
entries[-1].append(float(vals[2]))
entries=np.array(entries)
entries=entries[entries[:,0].argsort()]
if ref==None:
errs=np.zeros([len(entries)-1,3])
errs[:,0] = entries[:-1,0]
errs[:,1] = abs(entries[:-1,1]-entries[-1,1])/entries[-1,1]
errs[:,2] = abs(entries[:-1,2]-entries[-1,2])/entries[-1,2]
else:
errs=np.zeros([len(entries),3])
errs[:,0] = entries[:,0]
errs[:,1] = abs(entries[:,1]-ref[1])/ref[1]
errs[:,2] = abs(entries[:,2]-ref[2])/ref[2]
#for e in errs:
# print e
errs=errs[errs[:,0].argsort()]
# print '\n\n'
# for e in errs:
# print e
errs=zip(*errs)
plt.loglog(errs[0],errs[1],'-o',label=lbl)
def fit_and_plot(cand):
data = cand.profile
n = len(data)
xs = np.linspace(0.0, 1.0, n, endpoint=False)
G = gauss._compute_data(cand)
print "k: %g, log(k): %g" % (G.k, np.log10(G.k))
test_ks = np.logspace(np.log10(G.k)-2, np.log10(G.k)+1, 1e3)
#test_ks = np.exp(np.linspace(np.log(1e-1),np.log(1e3),1e3))
plt.figure(1)
resids = [gauss._rms_residual(k,data) for k in test_ks]
plt.loglog(test_ks,resids,color="green", label="_nolabel_")
#plt.axvline(true_k,color="red", label="true k")
best_k = test_ks[np.argmin(resids)]
plt.axvline(best_k,color="green", label="best k")
plt.axvline(G.k,color="cyan", label="k from fit")
plt.ylabel("RMS of residuals")
plt.xlabel("Value of k used (i.e. held fixed) when fitting")
plt.legend(loc="best")
plt.figure(2)
mue, ae, be = gauss._fit_all_but_k(best_k, data)
#plt.plot(xs, true_prof, color="red", label="true")
plt.plot(xs, data, color="black", label="data")
plt.plot(xs, (ae*utils.vonmises_histogram(best_k,mue,n)+be), color="green", label="exhaustive best fit")
plt.plot(xs, G.histogram(n), color="cyan", label="best fit")
plt.legend(loc="best")
plt.show()
def __call__(self,u,v,w,bx,by,bz):
q = 4
d = (self.sim.zmx, self.sim.ymx, self.sim.xmx)
vspec = spec(u,v,w,dims=d)
bspec = spec(bx,by,bz,dims=d)
plt.subplot(221)
plt.plot(vspec)
plt.semilogy()
plt.title('v-spec')
plt.axis("tight")
plt.ylim([1e-12,1e-2])
plt.subplot(222)
plt.plot(vspec)
plt.loglog()
plt.title('v-spec')
plt.axis("tight")
plt.ylim([1e-12,1e-2])
plt.subplot(223)
plt.plot(bspec)
plt.semilogy()
plt.title('b-spec')
plt.axis("tight")
plt.ylim([1e-12,1e-2])
plt.subplot(224)
plt.plot(bspec)
plt.loglog()
plt.title('b-spec')
plt.axis("tight")
plt.ylim([1e-12,1e-2])
def disk_spec(file):
#Construct table
table=construct_table('tmpd')
disk_params=get_params(file)
specs=params_to_spec(disk_params, table)
r=disk_params[:, 0:2]
Teff=disk_params[:, 2]
#Finding the total flux
totf=sum_spec(r, specs, Teff)
totf1=totf[1]
totf2=totf[0]
#max1=np.max(totf1[1])
#max2=np.max(totf2[1])
#peak=np.max(max1, max2)
plt.loglog()
#plt.figsize(20, 8)
plt.xlabel("nu [hz]")
plt.ylabel("nu L_nu [ergs/s]")
plt.axis([10.**14, 2*10.**18, 10.**38, 10.**44])
plt.plot(totf1[0], totf1[0]*totf1[1])
plt.plot(totf2[0], totf2[0]*totf2[1])
plt.show()
def plotBode2(zpk, n=200, f_range=None, f_logspace=True):
"""
Bode plot of ZerosAndPoles object using matplotlib
"""
(f, y) = zpk.frequencyResponse(n=n, f_range=f_range, f_logspace=f_logspace)
y_A = numpy.abs(y)
y_phi = Misc.to_deg(Misc.continuousAngle(y))
plt.figure()
plt.subplot(211)
if f_logspace:
plt.loglog(f, y_A)
else:
plt.plot(f, y_A)
plt.grid(True, which="both")
plt.ylabel("Amplitude")
plt.subplot(212)
if f_logspace:
plt.semilogx(f, y_phi)
else:
plt.plot(f, y_A)
plt.grid(True, which="both")
plt.xlabel("Frequency [Hz]")
plt.ylabel("Phase [deg]")
plt.show()
def plot_area_vs_energy(self, filename=None, show_save_energy=True):
"""
Plot effective area vs. energy.
"""
import matplotlib.pyplot as plt
energy_hi = self.energy_hi.value
effective_area = self.effective_area.value
plt.plot(energy_hi, effective_area)
if show_save_energy:
plt.vlines(self.energy_thresh_hi.value, 1E3, 1E7, 'k', linestyles='--')
plt.text(self.energy_thresh_hi.value - 1, 3E6,
'Safe energy threshold: {0:3.2f}'.format(
self.energy_thresh_hi),
ha='right')
plt.vlines(self.energy_thresh_lo.value, 1E3, 1E7, 'k', linestyles='--')
plt.text(self.energy_thresh_lo.value + 0.1, 3E3,
'Safe energy threshold: {0:3.2f}'.format(self.energy_thresh_lo))
plt.xlim(0.1, 100)
plt.ylim(1E3, 1E7)
plt.loglog()
plt.xlabel('Energy [TeV]')
plt.ylabel('Effective Area [m^2]')
if filename is not None:
plt.savefig(filename)
log.info('Wrote {0}'.format(filename))
def makegood(prereqs,func,r,size,grid,smallrexp,largerexp,plotting):
"""
prereqs - array containing model class instance as first element
func - function to be evaluated
r - independent variable array
size - size of generated independent variable array with format
[log10(max),log10(min),stepsize]
grid - choice of grid generator function
smallrexp - log slope at small r or large E
largerexp - log slope at large r or small E
plotting - if False, do not plot.
if not False, must be array with ['<xlabel>','<ylabel>']
Returns an interpolated object version of the function based
computed values.
"""
model = prereqs[0]
#generate independent array grid
rarray,rchange,rstart = grid([model],size[0],size[1],size[2])
#compute value of function for grid points
tab,problems = func(rarray,prereqs)
frac = float(len(problems))/float(len(tab))
#report the fraction of problem points to console and file
print 'fraction reporting a message: {0}'.format(frac)
model.statfile.write('\nmesg frac = {0}\n'.format(frac))
#check for problem points not caught in integration process
gcheck = goodcheck(tab)
#interpolate in log10 space
inter = interp1d(log10(rarray),log10(tab))
#generate array to further extremes using powerlaw behaviour
m = piecewise(r,inter,tab[0],tab[len(rarray)-1],rstart,rchange,smallrexp,largerexp)
#interpolate extended array in log10 space
inter2 = interp1d(log10(r),log10(m))
#save values used to interpolate to file (NOT in log10 space)
saver = column_stack((r,m))
funcname = str(func).split(' ')[1][4:]
pklwrite('{0}/{1}.pkl'.format(model.directory,funcname),saver)
#if plotting is possible and the array doesn't consist entirely of problems
#add plot to pdf and return interpolate functional form
if plotting != False and gcheck == True:
xaxis,yaxis = plotting
plt.figure()
plt.loglog(r[1:-1],m[1:-1],'c',linewidth = 5)
plt.loglog(rarray,tab,'.',color = 'DarkOrange')
plt.ylabel(r'{0}'.format(yaxis))
plt.xlabel('{0}'.format(xaxis))
plt.xlim(min(r[1:-1]),max(r[1:-1]))
plt.ylim(min(m[1:-1]),max(m[1:-1]))
plt.title(model.name)
model.pdfdump.savefig()
plt.close()
return inter2
#if plotting isn't possible but array doesn't consist entirely of problems
#return interpolated functional form
elif plotting == False and gcheck == True:
return inter2
#if computation failed, return 0
#this signals the rest of the program that computation failed here
elif gcheck == False:
return 0
def compareXS(isotope, type_xs='capture', dir='.'):
#Get fake XS from info given
El, A = isotope.split('-', 1)
#Find proper filename for fake XS
if type_xs=='scatter':
type_xs='elastic'
path=str(pinspec.getXSLibDirectory())+'/'+El+'-'+A+'-'+type_xs+'.txt'
#Read in array for fictitious XS at 300
EnT=numpy.array([])
barnsT=numpy.array([])
invEnT=numpy.array([])
with open(path) as resT:
#Parse out String containing Temperature
Junk, temp = resT.readline().split('=', 1)
for line in resT:
EnTt, barnsTt=line.split(',', 1)
EnTt=float(EnTt)
barnsTt=float(barnsTt)
invEnTt=1/EnTt
EnT=numpy.append(EnT,EnTt)
barnsT=numpy.append(barnsT,barnsTt)
invEnT=numpy.append(invEnT, invEnTt)
py_printf('INFO', 'Read in Doppler Broadened XS correctly')
#Read in array for ENDF7 XS at 300
npath=str(pinspec.getXSLibDirectory())+'/BackupXS/'+El+'-'+A+'-' + \
type_xs+'.txt'
EndfE300=numpy.array([])
barnsEndF300=numpy.array([])
invEndfE300=numpy.array([])
with open(npath) as Endf300:
#Parse out String containing Temperature
Junk, xssource = Endf300.readline().split(' ', 1)
xssource=xssource.strip()
for line in Endf300:
EndfE300temp, barnsEndF300temp=line.split(',', 1)
EndfE300temp=float(EndfE300temp)
barnsEndF300temp=float(barnsEndF300temp)
invEndfE300temp=1/EndfE300temp
EndfE300=numpy.append(EndfE300,EndfE300temp)
barnsEndF300=numpy.append(barnsEndF300,barnsEndF300temp)
invEndfE300=numpy.append(invEndfE300,invEndfE300temp)
log_printf(INFO,'Read in ENDF/B-VII XS correctly')
#Plot values on top of each other
fig=plt.figure()
plt.loglog(EnT,barnsT)
plt.loglog(EndfE300,barnsEndF300)
CXStype=type_xs.title()
plt.legend(['Doppler broadened '+El+'-'+A+' '+CXStype+' XS at temp=' + \
temp,xssource+' '+El+'-'+A+' '+CXStype+' XS at temp=300K'], \
loc='lower left',prop={'size':10})
plt.grid()
plt.title(CXStype+' Cross Section Comparison')
plt.xlabel('XS [barns]')
plt.ylabel('E [eV]')
plt.savefig(dir+'/'+CXStype+'_XS_Comparison.png')
def plotting(self, msdtype="ensemble", particlemsdtime=0,error=0, showlegend=None,scale="loglog"):
"""
:param error: Number of standard deviations from mean, which is shown in the figure
:return: A figure with plotting of the Ensemble MSD
"""
if msdtype=="ensemble":
msd,std=self.msd_ensemble()
if msdtype=="time":
msd,std=self.msd_time(particlemsdtime)
colors=['r','b','g','k','c','w','b','r','g','b','k','c','w','b','r','g','b','k','c','w','bo','ro','go','bo','ko','co','wo','bo']
#fig=plt.plot(range(msd_ensemble.size), msd_ensemble ,colors[2], label="ensemble msd")
if scale == "lin":
plt.plot(self.t*self.dt,self.msdanalyt(),":",color=colors[1], label="analytisch D=%f,particles=%d,length=%d,alpha=%f" %(self.D,self.particles,self.n,self.alpha))
if scale == "loglog":
plt.loglog(self.t*self.dt,self.msdanalyt(),":",color=colors[1], label="analytisch D=%f,particles=%d,length=%d,alpha=%f" %(self.D,self.particles,self.n,self.alpha))
fig=plt.errorbar(self.t*self.dt, msd, yerr=error*std,label="Spektrale Methode mit D=%f,particles=%d, length=%d ,alpha=%f, Std=%f" %(self.D,self.particles,self.n,self.alpha,error))
if showlegend is not None:
plt.legend(loc=2)
plt.xlabel('Steps', fontsize=14)
plt.ylabel('MSD', fontsize=14)
return fig
def plot_clustering_spectrum (graph, path):
"""Plot the clusttering spectrum of the graph and save the figure
at the given path. On X-axis we have degrees and on Y-axis we have
average clustering coefficients of the nodes that have that degree"""
node_to_degree = graph.degree()
node_to_clustering = nx.clustering(graph)
degree_to_clustering = {}
# calculate average clustering coefficients for nodes with certain degree
for node in node_to_degree:
deg = node_to_degree[node]
tmp = degree_to_clustering.get(deg, [])
tmp.append(node_to_clustering[node])
degree_to_clustering[deg] = tmp
for degree in degree_to_clustering:
tmp = degree_to_clustering[degree]
degree_to_clustering[degree] = float(sum(tmp)) / len(tmp)
x = sorted(degree_to_clustering.keys(), reverse = True)
y = [degree_to_clustering[i] for i in x]
plt.loglog(x, y, 'b-', marker = '.')
plt.title("Clustering Spectrum")
plt.ylabel("Average clustering coefficient")
plt.xlabel("Degree")
plt.axis('tight')
plt.savefig(path)
def plot_shortest_path_spectrum (graph, path, paths_data):
"""Plot distribution of shortest paths of the graph and save the figure
at the given path. On X-axis we have distance values and on Y-axis we
have percentage of node pairs that have that distance value"""
diameter = graph_diameter(paths_data)
pairs = graph.order() * (graph.order()-1) * 0.5
distances_count = [0 for i in xrange(diameter + 1)]
for i in xrange(8):
with open('%s_%d' % (paths_data, i), 'r') as in_file:
for line in in_file:
tokens = line.split()
distances_count[int(tokens[2])] += 1
for i in xrange(diameter + 1):
distances_count[i] *= (100.0 / pairs)
y = distances_count
plt.loglog(y, 'b-', marker = '.')
plt.title("Shortest Paths Spectrum")
plt.ylabel("Percent of pairs")
plt.xlabel("Distance")
plt.axis('tight')
plt.savefig(path)
def plot_closeness_dist (graph, path):
"""Plot distribution of closeness centrality of the graph and save the figure
at the given path. On X-axis we have closeness centrality values and on
Y-axis we have percentage of the nodes that have that closeness value"""
N = float(graph.order())
node_to_closeness = nx.closeness_centrality(graph)
closeness_to_percent = {}
# calculate percentages of nodes with certain closeness value
for node in node_to_closeness:
closeness_to_percent[node_to_closeness[node]] = 1 + \
closeness_to_percent.get(node_to_closeness[node], 0)
for c in closeness_to_percent:
closeness_to_percent[c] = closeness_to_percent[c] / N * 100
x = sorted(closeness_to_percent.keys(), reverse = True)
y = [closeness_to_percent[i] for i in x]
plt.loglog(x, y, 'b-', marker = '.')
plt.title("Closeness Centrality Distribution")
plt.ylabel("Percentage")
plt.xlabel("Closeness value")
plt.axis('tight')
plt.savefig(path)
def plot_betweenness_dist (graph, path):
"""Plot distribution of betweenness centrality of the graph and save the figure
at the given path. On X-axis we have betweenness centrality values and on
Y-axis we have percentage of the nodes that have that betweenness value.
k is the number of samples for estimating the betweenness centrality."""
N = float(graph.order())
node_to_betweenness = nx.betweenness_centrality(graph)
betweenness_to_percent = {}
# calculate percentages of nodes with certain betweeness value
for node in node_to_betweenness:
betweenness_to_percent[node_to_betweenness[node]] = 1 + \
betweenness_to_percent.get(node_to_betweenness[node], 0)
for c in betweenness_to_percent:
betweenness_to_percent[c] = betweenness_to_percent[c] / N * 100
x = sorted(betweenness_to_percent.keys(), reverse = True)
y = [betweenness_to_percent[i] for i in x]
plt.loglog(x, y, 'b-', marker = '.')
plt.title("Betweenness Centrality Distribution")
plt.ylabel("Percentage")
plt.xlabel("Betweenness value")
plt.axis('tight')
plt.savefig(path)
def plot(dic):
items = dic.items()
items.sort()
x = [item[0] for item in items]
y = [item[1] for item in items]
pyplot.loglog(x, y, 'ro', color='blue')
pyplot.show()
def main(N, m, M, ximf):
numpy.random.seed(31415)
x_label = "M$_\odot$"
y_label = "N"
fig, ax = figure_frame(x_label, y_label, xsize=12, ysize=8)
cols = get_distinct(2)
masses = new_salpeter_mass_distribution(N, m, M, ximf)
masses = new_salpeter_mass_distribution(N, m, M, ximf)
lm = math.log10(0.5*m.value_in(units.MSun))
lM = math.log10(1.5*M.value_in(units.MSun))
bins = 10**numpy.linspace(lm, lM, 51)
Nbin, bin_edges= numpy.histogram(masses.value_in(units.MSun), bins=bins)
bin_sizes = bin_edges[1:] - bin_edges[:-1]
y = Nbin / bin_sizes
x = (bin_edges[1:] + bin_edges[:-1]) / 2.0
for i in range(len(y)):
y[i] = max(y[i], 1.e-10)
pyplot.scatter(x, y, s=100, c=cols[0], lw=0)
c = ((M.value_in(units.MSun)**(ximf+1)) - (m.value_in(units.MSun)**(ximf+1))) / (ximf+1)
pyplot.plot(x, N/ c * (x**ximf), c=cols[1])
pyplot.loglog()
pyplot.xlabel('$M [M_\odot]$')
pyplot.ylabel('N')
#pyplot.xlim(-3, 3)
# pyplot.show()
pyplot.savefig("salpeter")
def hurst_curv_exponent(xy,verbose=False):
"""computes the Hurst coefficient which qualify how the trajectory is persistent in time
it is related to the fractal dimension of the trajectory, here the denominator is the curvilinear distance
"""
#compute all distances
d = squareform(pdist(xy, 'euclidean'))
#max number of successive positions
N = 10
data = npy.zeros((N,2))
for k in range(N):
kd = npy.diag(d,k+1)
c_length = k+1
data[k,:] = (c_length,npy.mean(kd))
#linear fit in log-log
x = npy.log(data[:,0])
y = npy.log(data[:,1])
A = npy.vstack([x, npy.ones(len(x))]).T
m, c = npy.linalg.lstsq(A, y)[0]
if verbose:
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, aspect='equal')
plt.loglog(data[:,0],data[:,1])
plt.legend()
plt.show()
return m
def plot():
hmasses = []
lmasses = []
hvels = []
lvels = []
rootdir = 'C:\Users\Cat\Documents\Research_Halos\HaloDetail'
for subdir, dirs, files in os.walk(rootdir):
head,tail = os.path.split(subdir)
haloname = tail
for file in files:
if file.endswith('.list'):
hostvalues = ascii.read(os.path.join(subdir, file), format = 'commented_header')
highmass=max(hostvalues['mvir(10)'])
hi = np.where(highmass>=1.0e+12) #Index of host with highmass
low = np.where(highmass<1.0e+12)
hi_id = hostvalues[hi]['id(1)'] #Id of the highmass host
low_id = hostvalues[low]['id(1)']
whhi = np.where(hostvalues['pid(5)']==hi_id) #Indices of subhalos corresponding to the highmass host
whlow = np.where(hostvalues['pid(5)']==low_id)
hmass = hostvalues[whhi]['mvir(10)']
print len(hmass)
lmass = hostvalues[whlow]['mvir(10)']
print len(lmass)
hvel = hostvalues[whhi]['vmax(16)']
lvel = hostvalues[whlow]['vmax(16)']
hmasses = np.append(hmasses, hmass)
lmasses = np.append(lmasses, lmass)
hvels = np.append(hvels, hvel)
lvels = np.append(lvels, lvel)
print "%s done. On to the next." %haloname
plt.loglog(hmasses, hvels, lmasses, lvels, alpha=0.8)
def GpPlot(row, col, figNum):
n = 4
GpsAdd = np.zeros((n**3,1000), dtype=complex)
GpsMult = np.zeros((n**3,1000), dtype=complex)
w = np.logspace(-3,1,1000)
for i in range(1000):
GpsAdd[:,i], GpsMult[:,i] = Gp(w[i]*1j, row, col, n)
plt.figure(figNum)
# plt.clf()
plt.subplot(211)
for i in range(n**3):
plt.loglog(w, GpsAdd[i,],'-', color = ([row*0.3, col*0.3, 1]), alpha=0.2)
plt.grid(True)
plt.ylabel('|Additive Uncertainty|')
plt.xlabel('Frequency [rad/s)]')
plt.subplot(212)
for i in range(n**3):
plt.loglog(w, GpsMult[i,],'-', color = ([row*0.3, col*0.3, 1]), alpha=0.2)
plt.grid(True)
plt.ylabel('|Multiplicative Uncertainty|')
plt.xlabel('Frequency [rad/s)]')
fig = plt.gcf()
BG = fig.patch
BG.set_facecolor('white')
fig.subplots_adjust(bottom=0.2)
fig.subplots_adjust(top=0.9)
fig.subplots_adjust(left=0.2)
fig.subplots_adjust(right=0.9)
def Total_mass_plot(rbin, mTbin):
plt.loglog( rbin, mTbin)
#plt.axhline(chosen_ratio_number*particleMass, color = 'g')
plt.ylim(1e32, 1e37)
plt.xlim(3e-3, 3e0)
plt.ylabel(r'$M$ $({\rm g})$', fontsize=25)
plt.xlabel(r'$r$ $({\rm pc})$', fontsize=25)
def plot_powerlaw_fit(xdata, ydata, amp, index, yerr=None, fignum=None):
'''
Plot a powerlaw with some associated datapoints
'''
plt.figure(fignum)
plt.subplot(2, 1, 1)
plt.plot(xdata, utils_math.powerlaw(xdata, amp, index)) # Fit
if yerr is None:
plt.plot(xdata, ydata, 'k.') # Data
else:
plt.errorbar(xdata, ydata, yerr=yerr, fmt='k.')
plt.title('Best Fit Power Law')
plt.xlabel('X')
plt.ylabel('Y')
plt.xlim((xdata.min()*0.9, xdata.max()*1.1))
plt.subplot(2, 1, 2)
plt.loglog(xdata, utils_math.powerlaw(xdata, amp, index))
if yerr is None:
plt.plot(xdata, ydata, 'k.') # Data
else:
plt.errorbar(xdata, ydata, yerr=yerr, fmt='k.')
plt.xlabel('X (log scale)')
plt.ylabel('Y (log scale)')
plt.xlim((xdata.min()*0.9, xdata.max()*1.1))
def total_mass_plot(rbin, mTbin):
pl.clf()
pl.loglog( rbin, mTbin)
pl.ylim(1e32, 1e37)
pl.xlim(1e-3, 3e0)
pl.ylabel('Total Mass ($g$)')
pl.xlabel('Radius ($pc$)')
def Magnetic_vs_radius(rbin, Btotbin):
plt.loglog( rbin, Btotbin*Btotbin/(8.*np.pi), 'b', label='$B_{tot}^2 / 8 \pi$', lw = 2)
plt.legend(loc=0, fontsize=22, frameon=False)
# plt.ylim(1e-1, 3e0)
# plt.xlim(3e-3, 3e0)
plt.ylabel(' $B$ $({\\rm gauss })$', fontsize=25)
plt.xlabel('$r$ $(\\rm pc)$', fontsize=25)
def main():
citation_graph = load_graph(CITATION_URL)
print compute_in_degrees(citation_graph)
start_time = timeit.default_timer()
dist = in_degree_distribution(citation_graph)
print 'dist =', dist
total = sum(dist.itervalues())
normalized = {key: float(value)/total for key, value in dist.items()}
print(timeit.default_timer() - start_time)
x = normalized.keys()
y = normalized.values()
print len(y)
plt.loglog(x, y, 'ro')
plt.yscale('log')
plt.xscale('log')
plt.minorticks_off()
plt.xlabel('In-degree distribution')
plt.ylabel('Normalized In-degree distribution')
plt.title('Graph of Citations')
plt.grid(True)
plt.savefig('citations-q1.png')
plt.show()
def plot_resolution_cddf(snap=3, maxfac=1.):
"""Plot the effect of changing resolution on the CDDF."""
base_large = myname.get_name(7, box=25)
base_small = myname.get_name(7, box=7.5)
ahalo_large = CIVPlottingSpectra(snap, base_large, None, None, savefile="rand_civ_spectra.hdf5", spec_res=5.,load_halo=True)
ahalo_small = CIVPlottingSpectra(snap, base_small, None, None, savefile="rand_civ_spectra.hdf5", spec_res=5.,load_halo=True)
maxmass = np.max(ahalo_small.sub_mass)/maxfac
print("Max mass=",maxmass/1e10," was ",np.max(ahalo_large.sub_mass)/1e10)
print("Small box has ",np.size(np.where(ahalo_small.sub_mass > maxmass))," larger halos")
print("Larger box has ",np.size(np.where(ahalo_large.sub_mass > maxmass))," larger halos")
ahalo_large.get_col_density("C",4)
ahalo_small.get_col_density("C",4)
(halos_large,_) = ahalo_large.find_nearest_halo("C",4, thresh=50)
(halos_small,_) = ahalo_small.find_nearest_halo("C",4, thresh=50)
ind_large = np.where((ahalo_large.sub_mass[halos_large] < maxmass)*(halos_large > 0))
ind_small = np.where((ahalo_small.sub_mass[halos_small] < maxmass)*(halos_small > 0))
print("Now ",np.size(ind_large),np.size(ind_small)," spectra")
#Editing the private data like this is perilous
ahalo_large.colden[("C",4)] = ahalo_large.colden[("C",4)][ind_large]
ahalo_small.colden[("C",4)] = ahalo_small.colden[("C",4)][ind_small]
(NHI_large, cddf_large) = ahalo_large.column_density_function("C", 4, minN=11.5,maxN=16.5, line=False, close=50.)
plt.loglog(NHI_large,cddf_large,color="blue", label="25 Mpc Box", ls="-")
(NHI_small, cddf_small) = ahalo_small.column_density_function("C", 4, minN=11.5,maxN=16.5, line=False, close=50.)
plt.loglog(NHI_small,cddf_small,color="red", label="7.5 Mpc Box", ls="--")
ax=plt.gca()
ax.set_xlabel(r"$N_\mathrm{CIV} (\mathrm{cm}^{-2})$")
ax.set_ylabel(r"$f(N) (\mathrm{cm}^2)$")
plt.xlim(10**12, 10**15)
plt.legend(loc=0)
ax=plt.gca()
ax.set_xlabel(r"$N_\mathrm{CIV} (\mathrm{cm}^{-2})$")
ax.set_ylabel(r"$f(N) (\mathrm{cm}^2)$")
def plot_P(self, kmin, kmax, step, units_k = 'default', units_P = 'default'):
stepsize = (kmax - kmin) / float(step)
x = [kmin + float(i) * stepsize for i in range(0, step)]
y1 = [self.P_delta(k, units_k, units_P) for k in x]
plot1 = plt.loglog(x, y1, basex = 10, basey = 10, label = r'P(k)')
if units_k == 'default':
plt.xlabel(r'$k$ $(h \, Mpc^{-1})$')
elif units_k == 'mpc-1' or units_k == 'Mpc-1':
plt.xlabel(r'$k$ $(Mpc^{-1})$')
if units_P == 'default':
plt.ylabel(r'$P(k)$ $(h^{-3} Mpc^3)$')
elif units_P == 'mpc3' or units_P == 'Mpc3':
plt.ylabel(r'$P(k)$ $(Mpc^3)$')
if units_k == 'default' and units_P == 'default':
xcomp, ycomp = np.loadtxt('compare.dat', unpack = True)
plot2 = plt.loglog(xcomp, ycomp, basex = 10, basey = 10, label = r'P(k) from iCosmo')
xcomp2, ycomp2 = np.loadtxt('test_matterpower.dat', unpack = True)
plot3 = plt.loglog(xcomp2, ycomp2, basex = 10, basey = 10, label = r'P(k) from CAMB')
plt.legend(loc = 'upper right')
plt.title(r'Matter Power Spectrum' )
plt.grid(True)
plt.xlim([10**(-3), 10])
plt.ylim([1, 100000])
plt.savefig('powerspectrum.png')
plt.show()
def calc_degree_sequence(g, dest_file):
"""
calc_degree_sequence(g)
Calculate & plot the degree sequence of the graph g & writes data to the created data output file
:param g: graph as source
:return: --
"""
func_intro = "\n\nDegree Sequence ... "
logging.info(cs_ref, func_intro)
print func_intro
with open(dest_file, "a") as dat_file:
dat_file.write(func_intro)
degree_sequence = sorted(nx.degree(g).values(), reverse=True)
with open(dest_file, "a") as dat_file:
dat_file.write("\n\tDegree Sequence = \t" + str(degree_sequence))
plt.loglog(degree_sequence, 'g-', marker='o')
plt.title("Degree Rank/Sequence" +src_file)
plt.ylabel("degree")
plt.xlabel("rank")
gcc = sorted(nx.connected_component_subgraphs(g), key=len, reverse=True)[0]
pos = nx.spring_layout(gcc)
plt.axes([0.45, 0.45, 0.45, 0.45])
plt.axis('off')
nx.draw_networkx_nodes(gcc, pos, node_size=10)
nx.draw_networkx_nodes(gcc, pos, alpha=0.4)
plt.figure(1)
plt.savefig("plots/cs1_degree_histogram.png")
plt.show()
timer.add_callback(close_ventana)
#ejemplo 5, custom plots with logs
''' legend(), axis(), xlabel(), ylabel() y savefig()'''
#es una opcion, la otra es logaritmicamente espaciada
#x=np.linspace(0,10,20)
x = np.logspace(-1, 1, 40) #0.1, 10, 40
y1 = x**2.0
y2 = x**1.5
'''
con las dos plots seguidas, las imprime ambas
'''
plt.loglog(x,
y1,
"bo-",
linewidth=2,
markersize=12,
label='$\sum_{i=0}^\infty x_i$')
plt.loglog(x, y2, "gs-", linewidth=2, markersize=12, label="second verde")
'''Ajusto los ejes con
plt.axis([xmin, xmax, ymin, ymax]) '''
'''Puedo usar latex adentro!!! :D'''
plt.xlabel(r"$\frac{x}{y}$")
plt.ylabel("$y$")
plt.title(r'$\alpha > \beta$', fontsize=16, color='r')
'''mostramos lo que hay en label, con loc="parametro" le decimos donde queremos que este las
lineas de cada funcion y1 o y2 correspondientes'''
plt.legend(loc="upper left")
#ejepmlo 2
#x=np.logspace(0,1,10)
y_init = [0, 0] # initial conditions
list_dic = integrate()
list_theta = list_dic['theta'] # dump psi values here
list_d_theta = list_dic['d_theta'] # dump dpsi values here
t = list_dic['xi'] # create array of values. Equidistant integration steps.
plt.xlim([0.1, 20])
plt.ylim([0.001, 1.0])
plt.plot(t, np.exp(list_theta), 'o', t,
np.power(1 + np.power(t / 2.88, 2), -1.47))
plt.loglog(t, np.exp(list_theta), 'o', t,
np.power(1 + np.power(t / 2.88, 2), -1.47))
for i in range(0, len(t) - 190000):
print(t[i], np.exp(list_theta[i]))
#
# # plt.plot(x,y1,'o', x_new, y1_new)
# plt.show()
# list_for_fit_theta =[]
# list_for_fit_d_theta =[]
#
# for i in range(0,len(t)):
#
# list_for_fit_theta.append((t[i], np.exp(psi[i])))
# list_for_fit_d_theta.append((t[i], dpsi[i]))
#
def guo(halo_catalog,
clear=False,
compare=True,
baryfrac=False,
filename=False,
**kwargs):
'''Stellar Mass vs. Halo Mass
Takes a halo catalogue and plots the member stellar masses as a
function of halo mass.
Usage:
>>> import pynbody.plot as pp
>>> h = s.halos()
>>> pp.guo(h,marker='+',markerfacecolor='k')
**Options:**
*compare* (True): Should comparison line be plotted?
If compare = 'guo', Guo+ (2010) plotted instead of Behroozi+ (2013)
*baryfrac* (False): Should line be drawn for cosmic baryon fraction?
*filename* (None): name of file to which to save output
'''
# if 'marker' not in kwargs :
# kwargs['marker']='o'
starmasshalos = []
totmasshalos = []
halo_catalog._halos[1]['mass'].convert_units('Msol')
for i in np.arange(len(halo_catalog._halos)) + 1:
halo = halo_catalog[i]
halostarmass = np.sum(halo.star['mass'])
if halostarmass:
starmasshalos.append(halostarmass)
totmasshalos.append(np.sum(halo['mass']))
if clear:
plt.clf()
plt.loglog(totmasshalos, starmasshalos, 'o', **kwargs)
plt.xlabel('Total Halo Mass')
plt.ylabel('Halo Stellar Mass')
if compare:
xmasses = np.logspace(np.log10(min(totmasshalos)),
1 + np.log10(max(totmasshalos)), 20)
if compare == 'guo':
# from Sawala et al (2011) + Guo et al (2009)
ystarmasses = xmasses * 0.129 * ((xmasses / 2.5e11)**-0.926 +
(xmasses / 2.5e11)**0.261)**-2.44
else:
ystarmasses, errors = behroozi(
xmasses, halo_catalog._halos[1].properties['z'])
plt.fill_between(xmasses,
np.array(ystarmasses) / np.array(errors),
y2=np.array(ystarmasses) * np.array(errors),
facecolor='#BBBBBB',
color='#BBBBBB')
plt.loglog(xmasses, ystarmasses, label='Behroozi et al (2013)')
if baryfrac:
xmasses = np.logspace(np.log10(min(totmasshalos)),
1 + np.log10(max(totmasshalos)), 20)
ystarmasses = xmasses * 0.04 / 0.24
plt.loglog(xmasses,
ystarmasses,
linestyle='dotted',
label='f_b = 0.16')
plt.axis([
0.8 * min(totmasshalos), 1.2 * max(totmasshalos),
0.8 * min(starmasshalos), 1.2 * max(starmasshalos)
])
if (filename):
logger.info("Saving %s", filename)
plt.savefig(filename)
color='C0') #, normed=True)
# plt.axis([1e-2, 73, 0, 11])
plt.axis([1e-2, 73, 0, 220])
plt.gca().set_xscale('log')
plt.gca().set_xticklabels([])
plt.gca().set_yticklabels([])
plt.title('{} GHz'.format(band_labels[band]))
if jband == 0:
plt.ylabel('$1/f$ knees of\nnoise stares')
# ax = plt.subplot(2,3,4)
plt.subplot2grid((4, 3), (1, 0), colspan=1, rowspan=3)
asd_diff = np.array(d["AverageASDDiff"]['90.0_w204'])
asd_sum = np.array(d["AverageASDSum"]['90.0_w204'])
plt.loglog(freq[freq < f_hi], asd_diff[freq < f_hi] / np.sqrt(2.))
plt.loglog(freq[freq < f_hi], asd_sum[freq < f_hi] / np.sqrt(2.))
print(np.mean(asd_diff[(freq > 1) & (freq < 5)]) / np.sqrt(2.))
plt.grid()
plt.axis([1e-2, 73, 200, 50000])
plt.ylabel('NET [$\mu$K $\sqrt{s}$]')
# plt.subplot(2,3,5)
plt.subplot2grid((4, 3), (1, 1), colspan=1, rowspan=3)
asd_diff = np.array(d["AverageASDDiff"]['150.0_w204'])
asd_sum = np.array(d["AverageASDSum"]['150.0_w204'])
plt.loglog(freq[freq < f_hi], asd_diff[freq < f_hi] / np.sqrt(2.))
plt.loglog(freq[freq < f_hi], asd_sum[freq < f_hi] / np.sqrt(2.))
print(np.mean(asd_diff[(freq > 1) & (freq < 5)]) / np.sqrt(2.))
plt.grid()
plt.axis([1e-2, 73, 200, 50000])
#model lomb
model_periods,model_mag,model_ph,model_fr,model_fi = modules.take_lomb(model_time,model_var,ofac,1./24)
obs_time = np.array(obs_time)
obs_var = np.array(obs_var)
#set plotting area & background to white
fig=plt.figure(figsize=(20,12))
fig.patch.set_facecolor('white')
ax = fig.add_subplot(1,1,1)
obs_periods,obs_mag, obs_breakpoint = modules.find_breakpoint(obs_periods,obs_mag)
model_periods,model_mag, model_breakpoint = modules.find_breakpoint(model_periods,model_mag)
plt.loglog(obs_periods,obs_mag, color='black', label = 'Obs.')
plt.axvline(x=obs_breakpoint, color = 'blue', linestyle = '--')
plt.loglog(model_periods,model_mag, color='red', label = 'GEOS %s'%(model_version))
plt.axvline(x=model_breakpoint, color = 'green', linestyle = '--')
def form2(x, pos):
""" This function returns a string with 3 decimal places, given the input x"""
return '%.2f' % x
def form5(x, pos):
""" This function returns a string with 3 decimal places, given the input x"""
return '%.5f' % x
xformatter = FuncFormatter(form2)
yformatter = FuncFormatter(form5)
model = lstm_for_dynamics(cf_trunc, deployment_mode)
output_state_lstm, state_tracker_lstm = evaluate_rom_deployment_lstm(
model, cf_trunc, tsteps)
np.save('Burgulence_LSTM_Coefficients.npy', state_tracker_lstm)
#Visualization - Spectra
u_true = sm_mean + (np.matmul(phi_trunc, perfect_output))[:]
u_gp = sm_mean + (np.matmul(phi_trunc, output_state_gp))[:]
u_lstm = sm_mean + (np.matmul(phi_trunc, output_state_lstm[:, 0]))[:]
plt.figure()
kx_plot = np.array([float(i) for i in list(range(0, nx // 2))])
espec1 = spectra_calculation(u_true)
espec2 = spectra_calculation(u_gp)
espec3 = spectra_calculation(u_lstm)
plt.loglog(kx_plot, espec1, label='Truth')
plt.loglog(kx_plot, espec2, label='GP')
plt.loglog(kx_plot, espec3, label='LSTM')
plt.legend()
plt.show()
# Spectra residuals
plt.figure()
kx_plot = np.array([float(i) for i in list(range(0, nx // 2))])
plt.loglog(kx_plot, np.abs(espec2 - espec1), label='GP-Residual')
plt.loglog(kx_plot, np.abs(espec3 - espec1), label='LSTM-Residual')
plt.legend()
plt.show()
plt.figure()
plt.plot(x[:], u_true[:], label='Truth')
tSeq_11, xSeq_11, ySeq_11, zSeq_11, uSeq_11, coors_11 = getData_sowfa(
ppDir, 'prbg11', ((0, 0, 0), 30.0), 'U', 0)
ky_seq_11, psdy_seq_11 = PSD_ky_sowfa(tSeq_11, ySeq_11, xSeq_11, 1, 5, uSeq_11,
2000 // 5)
tSeq_12, xSeq_12, ySeq_12, zSeq_12, uSeq_12, coors_12 = getData_sowfa(
ppDir, 'prbg12', ((0, 0, 0), 30.0), 'U', 0)
ky_seq_12, psdy_seq_12 = PSD_ky_sowfa(tSeq_12, ySeq_12, xSeq_12, 1, 5, uSeq_12,
2000 // 5)
""" check PSD_kx """
fig, ax = plt.subplots(figsize=(6, 4))
dn = 1
plt.loglog(kx_seq_3[0::dn],
psdx_seq_3[0::dn],
label='cell',
linewidth=1.0,
linestyle='-',
color='r')
plt.loglog(kx_seq_7[0::dn],
psdx_seq_7[0::dn],
label='cellPoint',
linewidth=1.0,
linestyle='-',
color='b')
plt.loglog(kx_seq_8[0::dn],
psdx_seq_8[0::dn],
label='cellPointFace',
linewidth=1.0,
linestyle='-',
color='g')
plt.loglog(kx_seq_9[0::dn],
def plot_dQ_Q(Q: pd.Series):
dQ = dQdt(Q)
plt.loglog(Q[dQ < 0], -dQ[dQ < 0], '.')
plt.xlabel('Discharge ($Q, mm day^{-1}$)')
plt.ylabel(r'$-\frac{dQ}{dt} mm day^{-1}$')
print numOfCh
if (count in countDict):
countDict[count] += 1
else:
countDict[count] = 1
countList.sort()
countList.reverse()
cumulativeCountDict = {} #ECCDF P[X > x]
bte = 0
bt = 0
for count in countList:
bte += countDict[count]
bt = bte - countDict[count]
cumulativeCountDict[count] = bt * 1.0 / numOfCh
#print cumulativeCountDict
input.close()
output.close()
import numpy as np
import matplotlib.pyplot as plt
import math
x = cumulativeCountDict.keys()
y = cumulativeCountDict.values()
plt.xlim([min(x), max(x)])
#plt.plot(x,y,'ro')
plt.loglog(x, y, 'ro')
plt.show()
ncfile.variables[tracer + 'Tend'][0, :, iz], [ny, nx])
dif = abs(var[1:ny - 1, 1:nx - 1] - sol[1:ny - 1, 1:nx - 1])
err = abs((var[1:ny - 1, 1:nx - 1] - sol[1:ny - \
1, 1:nx - 1]) / sol[1:ny - 1, 1:nx - 1])
difL2[i, j, k] = np.sqrt(np.mean(dif[:]**2))
errL2[i, j, k] = np.sqrt(np.mean(err[:]**2))
#errL2[i,j,k] = np.max(err[:])
ncfileIC.close()
ncfile.close()
for i in range(ntests):
test = tests[i]
plt.subplot(ntests, 3, 3 * i + 1)
for k in range(len(tracers)):
tracer = tracers[k]
plt.loglog(dx, difL2[i, :, k], '-x', label=tracer)
plt.ylabel('diff: rms(exact[:] - calc[:])')
plt.legend()
plt.grid()
plt.xlabel('cell width, km')
for i in range(ntests):
test = tests[i]
plt.subplot(ntests, 3, 3 * i + 2)
for k in range(len(tracers)):
tracer = tracers[k]
plt.loglog(dx, errL2[i, :, k], '-x', label=tracer)
plt.title('Error in Redi tendancy term, ' + test)
plt.ylabel('error: rms((exact[:] - calc[:])/exact[:])')
def fit_gm():
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import nnls
lnorm = 20
nwave = 800
# files = glob.glob('SED_J13/*RES')
# files = glob.glob('SED_C11/*RES')
# #files = glob.glob('SED_DL07/*RES')
#
# du = np.zeros((nwave, len(files)))
#
# for i, file in enumerate(files):
# dust = np.loadtxt(file, skiprows=8)
# w, f = dust[:,0], dust[:,1]
# print(file, len(w))
# plt.plot(w, f/np.interp(lnorm, w, f), label=file, alpha=0.5)
# du[:,i] = f/np.interp(lnorm, w, f)
# du_wave = w
# Magdis
mag = np.loadtxt('ms.txt')
mag_wave = mag[:, 0]
mag_flux = mag[:, 1:]
for i in range(10):
mag_flux[:, i] /= np.interp(lnorm, mag_wave, mag_flux[:, i])
#plt.plot(mag_wave, mag_flux[:,i], color='k', alpha=0.8)
### By hand, blackbodies following da Cunha + Magphys
from astropy.modeling.physical_models import BlackBody
import astropy.units as u
from astropy.constants import c
# Eazy for wavelength grid
ez = np.loadtxt('templates/fsps_full/fsps_QSF_12_v3_001.dat')
wave_grid = ez[:, 0] / 1.e4
nwave = len(wave_grid)
# PAH template. C11 dies down quickly
file = 'SED_C11/SED_C11_100.RES'
#file = 'SED_DL07/SED_DL07_100.RES'
dust = np.loadtxt(file, skiprows=8)
du_wave, du_pah = dust[:, 0], dust[:, 1]
comps = [np.interp(wave_grid, du_wave, du_pah)]
nu = (c / (wave_grid * u.um)).to(u.Hz)
# equilibrium components, da Cunha
# modified black-bodies, extra factor of 1 turns from Fnu to nu Fnu
# cold
for t in np.arange(20, 40):
comps.append(
BlackBody(temperature=t * u.K)(wave_grid * u.um) * nu**(1 + 2.0))
#warm
for t in np.arange(30, 80):
comps.append(
BlackBody(temperature=t * u.K)(wave_grid * u.um) * nu**(1 + 1.5))
# Hot
for t in [130, 250]:
comps.append(
BlackBody(temperature=t * u.K)(wave_grid * u.um) * nu**(1 + 1))
_A = np.array(comps).T
nc = _A.shape[1]
for i in range(nc):
_A[:, i] /= np.interp(lnorm, wave_grid, _A[:, i])
#######
mag_int = np.zeros((nwave, 10))
clip = (wave_grid > 4.) & (wave_grid < 5000)
models_flam = mag_int * 0.
for i in range(10):
mag_int[:, i] = np.interp(wave_grid, mag_wave, mag_flux[:, i])
_a = nnls(_A[clip, :], mag_int[clip, i])
model = _A.dot(_a[0])
norm = np.trapz(model / wave_grid, wave_grid)
pl = plt.plot(wave_grid, mag_int[:, i] / norm, linewidth=4, alpha=0.2)
plt.plot(wave_grid[clip],
mag_int[clip, i] / norm,
linewidth=4,
alpha=0.8,
color=pl[0].get_color())
plt.plot(wave_grid, model / norm, linewidth=3, color='w', alpha=0.8)
plt.plot(wave_grid,
model / norm,
linewidth=1,
color=pl[0].get_color(),
alpha=0.8)
mflam = model / wave_grid
mflam /= np.trapz(mflam, wave_grid)
models_flam[:, i] = mflam
fp = open(f'templates/magdis/magdis_{i+1:02d}.txt', 'w')
np.savetxt(
fp,
np.array([wave_grid * 1.e4, mflam]).T,
header=
'wave flam\n wave: A, flux: flam \nnormalized to unit energy',
fmt='%.5e')
fp.close()
# components
# plt.plot(wave_grid, (_A*_a[0]), linewidth=1, color='k', alpha=0.2)
plt.loglog()
plt.xlim(0.2, 5000)
plt.ylim(1.e-6, 10)
plt.grid()
plt.savefig('templates/magdis/magdis_fit.png')
n_runs = len(rho_err)
slope_1_ref = [2e-6 / 2**i
for i in range(n_runs)] # adjust initial error as necessary
slope_2_ref = [1e-7 / 4**i
for i in range(n_runs)] # adjust initial error as necessary
plt.figure(figsize=(8, 6))
plt.rc('text', usetex=True)
plt.rc('font', family='sans-serif')
ax = plt.subplot(1, 1, 1)
ax.get_yaxis().get_major_formatter().set_useOffset(False)
plt.xlabel("Mesh size, $h$")
plt.ylabel("Error, $\\|e\\|_1$")
plt.loglog(dx,
slope_1_ref,
linestyle='-',
marker='',
color='black',
label='$m=1$')
plt.loglog(dx,
slope_2_ref,
linestyle='-',
marker='',
color='gray',
label='$m=2$')
plt.loglog(dx,
rho_err,
linestyle='--',
marker='x',
color='indianred',
label='$\\|\\rho - \\rho_h\\|_1$')
plt.loglog(dx,
def prob4():
"""Compare the build and search speeds of the SinglyLinkedList, BST, and
AVL classes. For search times, use iterative_search(), BST.find(), and
AVL.find() to search for 5 random elements in each structure. Plot the
number of elements in the structure versus the build and search times.
Use log scales if appropriate.
"""
N = 11
# Initialize lists to hold results
lls_build, lls_search = [], []
bst_build, bst_search = [], []
avl_build, avl_search = [], []
with open("english.txt", 'r') as infile:
data = infile.readlines()
domain = 2**np.arange(3,N+1)
for n in domain:
# Initialize the data subset and the data structures.
subset = np.random.choice(data, size=n, replace=False)
bst = BST()
avl = AVL()
lls = SinglyLinkedList()
# Time the SinglyLinkedList build.
start = time()
for item in subset:
lls.append(item)
lls_build.append(time() - start)
# Time the BST build.
start = time()
for item in subset:
bst.insert(item)
bst_build.append(time() - start)
# Time the AVL Tree build.
start = time()
for item in subset:
avl.insert(item)
avl_build.append(time() - start)
random_subset = np.random.choice(subset, size=5, replace=False)
# Time the SinglyLinkedList search (using iterative_search()).
start = time()
for target in random_subset:
iterative_search(lls, target)
lls_search.append(time() - start)
# Time the BST search.
start = time()
for target in random_subset:
bst.find(target)
bst_search.append(time() - start)
# Time the AVL Tree search.
start = time()
for target in random_subset:
avl.find(target)
avl_search.append(time() - start)
# Plot the data.
plt.subplot(121)
plt.title("Build Times")
plt.loglog(domain, lls_build, 'b.-', lw=2, ms=10, basex=2, basey=2,
label='Singly Linked List')
plt.loglog(domain, bst_build, 'g.-', lw=2, ms=10, basex=2, basey=2,
label='Binary Search Tree')
plt.loglog(domain, avl_build, 'r.-', lw=2, ms=10, basex=2, basey=2,
label='AVL Tree')
plt.xlabel("n")
plt.ylabel("Seconds")
plt.legend(loc='upper left')
plt.subplot(122)
plt.title("Search Times")
plt.loglog(domain, lls_search, 'b.-', lw=2, ms=10, basex=2, basey=2,
label='Singly Linked List')
plt.loglog(domain, bst_search, 'g.-', lw=2, ms=10, basex=2, basey=2,
label='Binary Search Tree')
plt.loglog(domain, avl_search, 'r.-', lw=2, ms=10, basex=2, basey=2,
label='AVL Tree')
plt.xlabel("n")
plt.legend(loc='upper left')
plt.suptitle("Problem 4 Solution")
plt.show()
"""compute for additive parametric uncertainty"""
"""The condition for robust stability is derived & gives: RS <==> K*S < 1/W_A
with Lp = Gp*K = k*(G + W_A*delta_I)"""
def W_A(Gn, G): # We take W_A = l_A , Additive error (l_A = G'- G)
return np.abs(Gn - G)
def S(G, K):
return 1/(1 + G*K)
w = np.logspace(-3, 1, 300)
s = 1j*w
plt.figure(0)
plt.loglog(w, l(Gnom(s), G(s)), 'r', label='Relative Error')
plt.loglog(w, np.abs(Wi(s)), 'k', label='$W_I$')
plt.title(r'Figure 7.12')
plt.xlabel(r'Frequency [rad/s]', fontsize=14)
plt.ylabel(r'Magnitude', fontsize=15)
plt.legend()
#Plotting with multiplicative uncertainty
plt.figure(1)
plt.loglog(w, np.abs(T(G(s), K(s, 1.13))), label='$T_1$ (not RS)')
plt.loglog(w, np.abs(T(G(s), K(s, 0.31))), label='$T_2$')
line = plt.loglog(w, 1/np.abs(Wi(s)), label='$1/W_I$')
plt.title(r'Figure 7.13')
plt.xlabel(r'Frequency [rad/s]', fontsize=14)
plt.ylabel(r'Magnitude', fontsize=15)
plt.legend()
T = 1
M = 50000
Xem = np.zeros((5, 1))
for p in range(1, 6):
Dt = 2**(p - 10)
L = float(T) / Dt
Xtemp = Xzero * np.ones((M, 1))
for j in range(1, int(L) + 1):
Winc = np.sqrt(Dt) * np.random.randn(M)
Xtemp += Dt * gamma * Xtemp + mu * np.multiply(Xtemp.T, Winc).T
Xem[p - 1] = np.mean(Xtemp, 0)
Xerr = np.abs(Xem - np.exp(gamma))
Dtvals = np.power(float(2), [x - 10 for x in range(1, 6)])
plt.loglog(Dtvals, Xerr, 'b*-')
plt.loglog(Dtvals, Dtvals, 'r--')
plt.axis([1e-3, 1e-1, 1e-4, 1])
plt.xlabel('$\Delta t$')
plt.ylabel('| $E(X(T))$ - Sample average of $X_L$ |')
plt.title('emweak.py', fontsize=16)
### Least squares fit of error = C * Dt^q ###
A = np.column_stack((np.ones((p, 1)), np.log(Dtvals)))
rhs = np.log(Xerr)
sol = np.linalg.lstsq(A, rhs)[0]
q = sol[1][0]
resid = np.linalg.norm(np.dot(A, sol) - rhs)
#print 'q = ', q
#print 'residual = ', resid
w = np.logspace(-3, 3, 1000)
dim = G(0).shape[0]
Sv_G = np.zeros((len(w), dim))
Sv_G_min = np.zeros((len(w), 1))
Sv_G_max = np.zeros((len(w), 1))
wB_index = 0
for i in range(len(w)):
_, Sv_G[i, :], _ = np.linalg.svd(G(1j * w[i]))
Sv_G_min[i] = np.min(Sv_G[i, :])
if w[i] > 0.05 and wB_index == 0:
wB_index = i
figure = plt.figure()
plt.hold
plt.loglog(w, Sv_G_min, label='$\sigma_{min}(G)$')
plt.loglog([w[wB_index], w[wB_index]], [plt.ylim()[0], plt.ylim()[1]], '--')
plt.legend()
plt.xlabel('Frequency [rad/s]')
plt.ylabel('Magnitude')
# Note that minimum singular value of G(iw) where w < wB* is located at steady state (w=0)
u, _, _ = np.linalg.svd(G(0))
# Most difficult output direction
u_min = u[:, 1]
# Unsure of how to form gd with given information, cannot determine gd = y/d
# TODO Complete section b
TDGC = (dm_mass_cands == 0) & (star_mass_cands > 5e-3)
rich = (dm_mass_cands / star_mass_cands >= 1) & (star_mass_cands < 0.1) & (
star_mass_cands > 5e-3) & (dm_mass_cands > 0)
poor = (dm_mass_cands / star_mass_cands < 1) & (star_mass_cands < 0.1) & (
star_mass_cands > 5e-3) & (dm_mass_cands > 0)
print('TDGCs: ', np.sum(TDGC), '\nDM-rich: ', np.sum(rich), '\nDM-poor: ',
np.sum(poor))
# In[13]:
base_path = './haslbauer_subhalomasstype'
pathlib.Path(base_path).mkdir(parents=True, exist_ok=True)
plt.loglog(hst_shmr[hst_shmr != 0], s[hst_shmr != 0], '.')
x = np.linspace(10**(-2), 10**4, 100)
plt.loglog(x, 2 * x, '--b', label='s/shmr = 2')
plt.loglog(x, 5 * x, '--k', label='s/shmr = 5')
plt.loglog(x, 10 * x, '--r', label='s/shmr = 10')
plt.loglog(x, 100 * x, '--g', label='s/shmr = 100')
plt.legend(fontsize='x-large')
plt.xlabel('host stellar half mass', fontsize=20)
plt.ylabel('Distance to host', fontsize=20)
plt.savefig(base_path + '/dist_crit.png')
# In[16]:
plt.hist2d(10 + np.log10(star_mass[dmc]),
with open('zipf.txt', 'r') as zipf_file:
zipf_wrank, zipf_normedcumsum = getFileCDF(zipf_file)
zipf_file.close()
print("zipf CDF calculation done")
with open('uniform.txt', 'r') as uniform_file:
uniform_wrank, uniform_normedcumsum = getFileCDF(uniform_file)
uniform_file.close()
print("uniform CDF calculation done")
#here i calculate the maximum point wise distance for both 2 generated corpuses
print("calculating the maximum point wise distance for zipf")
print("zipf max point= " +
str(max(list(map(operator.sub, normedcumsum,
zipf_normedcumsum))))) #0.411679964745
print("calculating the maximum point wise distance for uniform")
print("uniform max point= " +
str(max(list(map(operator.sub, normedcumsum,
uniform_normedcumsum))))) #0.436318188857
print("plotting now")
plt.title("Exercise 2")
plt.xlabel('Word Rrank')
plt.ylabel('CDF')
plt.loglog(list(range(len(wrank))), normedcumsum)
plt.loglog(list(range(len(zipf_wrank))), zipf_normedcumsum)
plt.loglog(list(range(len(uniform_wrank))), uniform_normedcumsum)
plt.show()
f[i] = peaks(x)
nfe += 1
# find m best parents, truncation selection
ix = np.argsort(f)[:m]
Q = P[ix, :] # parents
# keep track of best here
if f_best is None or f[ix[0]] < f_best:
f_best = f[ix[0]]
x_best = Q[0, :]
# then mutate: each parent generates l/m children (integer division)
child = 0
for x in Q:
for _ in range(int(l / m)):
P[child, :] = mutate(x, lb, ub, s) # new population members
child += 1
ft[seed, int(nfe / l) - 1] = f_best
# for each trial print the result (but the traces are saved in ft)
print(x_best)
print(f_best)
nfe = range(l, max_NFE + 1, l)
plt.loglog(nfe, ft.T, color='steelblue', linewidth=1)
plt.xlabel('NFE')
plt.ylabel('Objective Value')
plt.show()
with open("neko.txt.mecab") as f:
surface = []
for i, line in enumerate(f):
split_line = line.rstrip("\r\n").split("\t")
if len(split_line) > 1:
surface.append(split_line[0])
surfaces = []
surfaces = collections.Counter(surface)
fre = []
for v in surfaces.values():
fre.append(v)
fre = collections.Counter(surfaces)
fres = []
for value in fre.values():
fres.append(value)
fres = collections.Counter(fres)
f = zip(fres.values(), fres.keys())
f = sorted(f, reverse=True)
ka = [i[0] for i in f]
va = range(1, len(ka) + 1)
import matplotlib.pyplot as plt
plt.loglog(va, ka)
plt.show()
neg15_1_45nG_vecCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg15_1_45nG_vecCls.dat')[:,3]
neg10_1_45nG_vecCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg10_1_45nG_vecCls.dat')[:,3]
pos0_1_45nG_vecCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/pos0_1_45nG_vecCls.dat')[:,3]
pos10_1_45nG_vecCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/pos10_1_45nG_vecCls.dat')[:,3]
neg29_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg29_2_45nG_tensCls.dat')[:,3]
neg25_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg25_2_45nG_tensCls.dat')[:,3]
neg20_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg20_2_45nG_tensCls.dat')[:,3]
neg15_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg15_2_45nG_tensCls.dat')[:,3]
neg10_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/neg10_2_45nG_tensCls.dat')[:,3]
pos0_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/pos0_2_45nG_tensCls.dat')[:,3]
pos10_2_45nG_tensCls = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/pos10_2_45nG_tensCls.dat')[:,3]
ells = np.loadtxt('/home/student.unimelb.edu.au/brycem1/MagCAMB/bryce/research17/pos10_2_45nG_tensCls.dat')[:,0]
plt.loglog(ells,neg29_1_1nG_vecCls,label = r'$n_B = -2.9$')
plt.loglog(ells,neg25_1_1nG_vecCls,label = r'$n_B = -2.5$')
plt.loglog(ells,neg20_1_1nG_vecCls,label = r'$n_B = -2.0$')
plt.loglog(ells,neg15_1_1nG_vecCls,label = r'$n_B = -1.5$')
plt.loglog(ells,neg10_1_1nG_vecCls,label = r'$n_B = -1.0$')
plt.loglog(ells,pos0_1_1nG_vecCls,label = r'$n_B = 0.0$')
plt.loglog(ells,pos10_1_1nG_vecCls,label = r'$n_B = 1.0$')
plt.loglog(ells,neg29_1_45nG_vecCls,label = r'$n_B = -2.9$')
plt.loglog(ells,neg25_1_45nG_vecCls,label = r'$n_B = -2.5$')
plt.loglog(ells,neg20_1_45nG_vecCls,label = r'$n_B = -2.0$')
plt.loglog(ells,neg15_1_45nG_vecCls,label = r'$n_B = -1.5$')
plt.loglog(ells,neg10_1_45nG_vecCls,label = r'$n_B = -1.0$')
plt.loglog(ells,pos0_1_45nG_vecCls,label = r'$n_B = 0.0$')
plt.loglog(ells,pos10_1_45nG_vecCls,label = r'$n_B = 1.0$')
'C0o', # Input jitter
'C9o', # Output jitter
'C4o', # Scatter
'C2o', # Intensity
'C6o', # Frequency
'C7o', # Dark
'ko', # OMC Length
'C5o', # PUM DAC
'C8o', # Stray Fields
])
for label, ASD, style in zip(labels, ASDs, styles):
# ASD_logbinned = np.dot(logbin_matrix, ASD)
lin_log_ff, lin_log_ASD = linear_log_ASD(fflog, ff, ASD)
if label == 'Measured noise (O3)':
plt.loglog(lin_log_ff, lin_log_ASD, style, label=label, zorder=3)
else:
plt.loglog(lin_log_ff, lin_log_ASD, style, label=label)
#lin_log_ff_O1, lin_log_ASD_O1 = linear_log_ASD(fflog, ff_O1, arm_length*spectra['o1'][:,1])
#lin_log_ff_O2, lin_log_ASD_O2 = linear_log_ASD(fflog, ff_O2, arm_length*spectra['o2'][:,1])
#plt.loglog(lin_log_ff_O1, lin_log_ASD_O1, 'C1-', label='O1', alpha=0.5)
#plt.loglog(lin_log_ff_O2, lin_log_ASD_O2, 'C7-', label='O2', alpha=0.5)
plt.xlabel('Frequency [Hz]')
plt.ylabel(r'DARM [$\mathrm{m}/\sqrt{\mathrm{Hz}}$]')
plt.grid()
plt.grid(which='minor', ls='--', alpha=0.7)
plt.legend(ncol=2, markerscale=3, loc='upper right')
pows = np.logspace(2, 4, 300)
mass_mot_burton = mass_motor_electric(pows, method="burton")
mass_mot_hobbyking = mass_motor_electric(pows, method="hobbyking")
mass_mot_astroflight = mass_motor_electric(pows, method="astroflight")
import matplotlib.pyplot as plt
import matplotlib.style as style
import plotly.express as px
import plotly.graph_objects as go
import dash
import seaborn as sns
sns.set(font_scale=1)
plt.loglog(pows, np.array(mass_mot_burton), label="Burton Model")
plt.plot(pows, np.array(mass_mot_hobbyking), label="Hobbyking Model")
plt.plot(pows, np.array(mass_mot_astroflight), label="Astroflight Model")
plt.xlabel("Motor Power [W]")
plt.ylabel("Motor Mass [kg]")
plt.title("Motor Mass Models")
plt.tight_layout()
plt.legend()
plt.show()
print(
mass_wires(wire_length=1,
max_current=100,
allowable_voltage_drop=1,
material="aluminum"))
uu = Function(V, u)
err[xx - 1] = errornorm(ue,
Function(V, u),
norm_type="L2",
degree_rise=3,
mesh=mesh)
print err[xx - 1]
# uE = interpolate(ue,V)
# ue = uE.vector().array()
# u = u.vector().array()
# print scipy.linalg.norm(u-ue)
# # Plot solution
# plot(u)
# plot(interpolate(ue,V))
# interactive()
# print N,err
# print '\n\n'
# print (err[0:m-2]/err[1:m-1])
# print '\n\n'
if Saving == 'yes':
MO.SaveEpertaMatrix(AA.down_cast().mat(), "A2d")
else:
plt.loglog(N, err)
plt.title('Error plot for P2 elements - L2 convergence = %f' %
np.log2(np.average((err[0:m - 2] / err[1:m - 1]))))
plt.xlabel('N')
plt.ylabel('L2 error')
plt.show()
# =========================================================
# Plot
# =========================================================
plt.rcParams.update(conf.params)
plt.figure(figsize=(conf.width,3.5))
labels = [r'$e$ pair production', 'Bremsstrahlung', 'Photonuclear', 'Ionization', r'$\mu$ pair production']
colors = ['C0', 'C1', 'C2', 'C3', 'C4']
for dEdx, param, _label, color in zip(dEdx_photo, params, labels, colors):
plt.loglog(
energy,
dEdx,
linestyle='-',
label=_label,
c = color
)
plt.loglog(energy, energy * sigma_decay(energy, medium.mass_density), linestyle='-', label='Decay', c = 'C5')
plt.loglog(energy, dEdx_weak(energy), linestyle='-', label='Weak interaction', c = 'C6')
plt.xlabel(r'$E \,/\, \mathrm{MeV} $')
plt.ylabel(r'$\left\langle\frac{\mathrm{d}E}{\mathrm{d}X}\right\rangle \,\left/\, \left( \rm{MeV} \cdot \rm{g}^{-1} \rm{cm}^2 \right) \right. $')
plt.grid(conf.grid_conf)
plt.legend(loc='best')
plt.xlim(1e5, 1e12)
# Log the progress made
print('Objective value is %f at iteration %d' % (phi, i + 1))
# In[17]:
#NBVAL_IGNORE_OUTPUT
# Plot inverted velocity model
plot_velocity(model0)
# In[18]:
#NBVAL_SKIP
import matplotlib.pyplot as plt
# Plot objective function decrease
plt.figure()
plt.loglog(history)
plt.xlabel('Iteration number')
plt.ylabel('Misift value Phi')
plt.title('Convergence')
plt.show()
# ## References
#
# [1] _Virieux, J. and Operto, S.: An overview of full-waveform inversion in exploration geophysics, GEOPHYSICS, 74, WCC1–WCC26, doi:10.1190/1.3238367, http://library.seg.org/doi/abs/10.1190/1.3238367, 2009._
#
# [2] _Haber, E., Chung, M., and Herrmann, F. J.: An effective method for parameter estimation with PDE constraints with multiple right hand sides, SIAM Journal on Optimization, 22, http://dx.doi.org/10.1137/11081126X, 2012._
# <sup>This notebook is part of the tutorial "Optimised Symbolic Finite Difference Computation with Devito" presented at the Intel® HPC Developer Conference 2017.</sup>
for language in os.listdir(book_dir):
for author in os.listdir(book_dir + "/" + language):
for title in os.listdir(book_dir + "/" + language + "/" + author):
inputfile = book_dir + "/" + language + "/" + author + "/" + title
print(inputfile)
text = read_book(inputfile)
(num_unique, counts) = word_stats(count_words(text))
stats.loc[title_num] = language, author.capitalize(), title.replace(".txt", ""), sum(counts), num_unique
title_num += 1
stats.length
stats.unique
import matplotlib.pyplot as plt
plt.plot(stats.length, stats.unique, "bo")
plt.loglog(stats.length, stats.unique, "bo")
stats[stats.language == "English"]
stats[stats.language == "French"]
plt.figure(figsize = (10, 10))
subset = stats[stats.language == "English"]
plt.loglog(subset.length, subset.unique, "o", label = "English", color = "crimson")
subset = stats[stats.language == "French"]
plt.loglog(subset.length, subset.unique, "o", label = "French", color = "forestgreen")
subset = stats[stats.language == "German"]
plt.loglog(subset.length, subset.unique, "o", label = "German", color = "orange")
subset = stats[stats.language == "Portuguese"]
#qdata_bkd=[]
#Idata_bkd=[]
#for i in range(5,30):
# qdata_bkd.append(qdata[i])
# Idata_bkd.append(Idata[i])
#for i in range(200,300):
# qdata_bkd.append(qdata[i])
# Idata_bkd.append(Idata[i])
#qdata_bkd=np.array(qdata_bkd)
#Idata_bkd=np.array(Idata_bkd)
#-----------------------------------------------------------------------------------------------------
plt.figure(figsize=(7, 5), dpi=300)
#now graph the rest of the data
plt.loglog(qdata,
Idata,
'o',
color='k',
label='(5.0-2.0) (Mg$^{2+}$) diblock',
markersize=4) # this graphs the data
# identify the region to fit for leibler, ie, "just the hump"
qdata_leib = []
Isub_leib = []
for i in range(1, 70):
qdata_leib.append(qdata[i])
Isub_leib.append(Idata[i])
qdata_leib = np.array(qdata_leib)
Isub_leib = np.array(Isub_leib)
#print(len(qdata_leib),len(Isub_leib))
#------------------------------------------------------------
#identify the initial guesses for x0
x0 = [26, .18, .04, .0294, 2.79]
bds = ([0, 0.01, .001, .02,