def PlotWss(self, meshid, imagpath):
'''
This method plots Wss signal and returns peak wss.
'''
try:
import matplotlib
matplotlib.use('Agg') #switch to matplotlib.use('WXAgg') if you want to show and not save velocity profile.
from matplotlib.pyplot import plot, xlabel, ylabel, title, legend, savefig, close, ylim
except:
sys.exit("PlotWss method requires matplotlib package (http://matplotlib.sourceforge.net.\n")
tplot = linspace(0, self.tPeriod, len(self.Tauplot))
plot(tplot, self.Tauplot,'g-',linewidth = 3, label = 'WSS')
minY = 0
for w in self.Tauplot:
if w < minY:
minY = w
if minY != 0:
plot(tplot, zeros(len(self.Tauplot)),':',linewidth = 1)
ylim(ymin=minY)
xlabel('Time ($s$)')
ylabel('Wall shear stress ($dyne/cm^2$)')
title ('Wss'+' peak:'+str(round(max(self.Tauplot),1))+' mean:'+str(round(mean(self.Tauplot),1))+' min:'+str(round(min(self.Tauplot),1)))
legend()
savefig(imagpath+str(meshid)+'_'+str(self.Name)+'_wss.png')
print "Wss, MeshId", meshid, self.Name, "=", str(round(max(self.Tauplot),1)), "$dyne/cm^2$"
close()
return (round(max(self.Tauplot),1))
def test_smoothing_spline():
x = linspace(0, 2 * pi + pi / 4, 20)
y = sin(x) # + np.random.randn(x.size)
pp = SmoothSpline(x, y, p=1)
x1 = linspace(-1, 2 * pi + pi / 4 + 1, 20)
y1 = pp(x1)
pp1 = pp.derivative()
pp0 = pp1.integrate()
dy1 = pp1(x1)
y01 = pp0(x1)
#dy = y-y1
import matplotlib.pyplot as plb
plb.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
plb.show()
pass
def calculateTs_Kolmogorov_BVP(alpha, beta, tauchar = 1.0, xth= 1.0, xmin = -1.0):
D = beta*beta /2.
def dS(S,x):
return -( (alpha-x/tauchar)/D ) * S -1.0/D;
S_0 = .0;
xs = linspace(xmin, xth, 1000); dx = (xs[1]-xs[0])
Ss = odeint(dS, S_0, xs);
if max(Ss) > .0:
raise RuntimeError('Ss should be negative')
T1s = -cumsum(Ss[-1::-1]) * dx
T1s = T1s[-1::-1]
T1_interpolant = interp1d(xs, T1s, bounds_error=False, fill_value = T1s[-1]);
def dS2(S,x):
T1 = T1_interpolant(x)
return -( (alpha-x/tauchar)/D ) * S -2.0*T1/D;
Ss = odeint(dS2, S_0, xs);
if max(Ss) > .0:
raise RuntimeError('Ss should be negative')
T2s = -cumsum(Ss[-1::-1]) * dx
T2s = T2s[-1::-1]
return xs, T1s, T2s
def GetTaoFromQ(self, el):
'''
Computing wall shear stress in terms of the flow rate,
using inverse womersley method of Cezeaux et al.1997
'''
self.radius = mean(el.Radius)
self.Res = el.R
self.length = el.Length
self.Name = el.Name
#WOMERSLEY NUMBER
self.alpha = self.radius * sqrt(
(2.0 * pi * self.density) / (self.tPeriod * self.viscosity))
#FOURIER SIGNAL
k = len(self.signal)
n = 0
while n < (self.nHarmonics):
An = 0
Bn = 0
for i in arange(k):
An += self.signal[i] * cos(
n * (2.0 * pi / self.tPeriod) * self.dt * self.nSteps[i])
Bn += self.signal[i] * sin(
n * (2.0 * pi / self.tPeriod) * self.dt * self.nSteps[i])
An = An * (2.0 / k)
Bn = Bn * (2.0 / k)
self.fourierModes.append(complex(An, Bn))
n += 1
self.Steps = linspace(0, self.tPeriod, self.samples)
self.WssSignal = []
self.Tauplot = []
for step in self.Steps:
self.tao = -self.fourierModes[0].real * 2.0
k = 1
while k < self.nHarmonics:
cI = complex(0., 1.)
cA = (self.alpha * pow((1.0 * k), 0.5)) * pow(cI, 1.5)
c1 = 2.0 * jn(1, cA)
c0 = cA * jn(0, cA)
cT = complex(0, -2.0 * pi * k * self.t / self.tPeriod)
'''tao computation'''
taoNum = self.alpha**2 * cI**3 * jn(1, cA)
taoDen = c0 - c1
taoFract = taoNum / taoDen
cTao = self.fourierModes[k] * exp(cT) * taoFract
self.tao += cTao.real
k += 1
self.tao *= -(self.viscosity / (self.radius**3 * pi))
self.Tauplot.append(self.tao * 10) #dynes/cm2
self.WssSignal.append(self.tao)
self.t += self.dtPlot
return self.WssSignal #Pascal
def GetTaoFromQ(self,el):
'''
Computing wall shear stress in terms of the flow rate,
using inverse womersley method of Cezeaux et al.1997
'''
self.radius = mean(el.Radius)
self.Res = el.R
self.length = el.Length
self.Name = el.Name
#WOMERSLEY NUMBER
self.alpha = self.radius * sqrt((2.0 *pi*self.density)/(self.tPeriod*self.viscosity))
#FOURIER SIGNAL
k = len(self.signal)
n = 0
while n < (self.nHarmonics):
An = 0
Bn = 0
for i in arange(k):
An += self.signal[i] * cos(n*(2.0*pi/self.tPeriod)*self.dt*self.nSteps[i])
Bn += self.signal[i] * sin(n*(2.0*pi/self.tPeriod)*self.dt*self.nSteps[i])
An = An * (2.0/k)
Bn = Bn * (2.0/k)
self.fourierModes.append(complex(An, Bn))
n+=1
self.Steps = linspace(0,self.tPeriod,self.samples)
self.WssSignal = []
self.Tauplot = []
for step in self.Steps:
self.tao = -self.fourierModes[0].real * 2.0
k=1
while k < self.nHarmonics:
cI = complex(0.,1.)
cA = (self.alpha * pow((1.0*k),0.5)) * pow(cI,1.5)
c1 = 2.0 * jn(1, cA)
c0 = cA * jn(0, cA)
cT = complex(0, -2.0*pi*k*self.t/self.tPeriod)
'''tao computation'''
taoNum = self.alpha**2*cI**3*jn(1,cA)
taoDen = c0-c1
taoFract = taoNum/taoDen
cTao = self.fourierModes[k] * exp(cT) * taoFract
self.tao += cTao.real
k+=1
self.tao *= -(self.viscosity/(self.radius**3*pi))
self.Tauplot.append(self.tao*10) #dynes/cm2
self.WssSignal.append(self.tao)
self.t += self.dtPlot
return self.WssSignal #Pascal
def test_func():
from scipy import interpolate
import matplotlib.pyplot as plt
import matplotlib
matplotlib.interactive(False)
coef = np.array([[1, 1], [0, 1]]) # linear from 0 to 2
# coef = np.array([[1,1],[1,1],[0,2]]) # linear from 0 to 2
breaks = [0, 1, 2]
pp = PPform(coef, breaks, a=-100, b=100)
x = linspace(-1, 3, 20)
y = pp(x) # @UnusedVariable
x = linspace(0, 2 * pi + pi / 4, 20)
y = sin(x) + np.random.randn(x.size)
tck = interpolate.splrep(x, y, s=len(x)) # @UndefinedVariable
xnew = linspace(0, 2 * pi, 100)
ynew = interpolate.splev(xnew, tck, der=0) # @UndefinedVariable
tck0 = interpolate.splmake( # @UndefinedVariable
xnew, ynew, order=3, kind='smoothest', conds=None)
pp = interpolate.ppform.fromspline(*tck0) # @UndefinedVariable
plt.plot(x, y, "x", xnew, ynew, xnew, sin(xnew), x, y, "b", x, pp(x), 'g')
plt.legend(['Linear', 'Cubic Spline', 'True'])
plt.title('Cubic-spline interpolation')
plt.show()
t = np.arange(0, 1.1, .1)
x = np.sin(2 * np.pi * t)
y = np.cos(2 * np.pi * t)
_tck1, _u = interpolate.splprep([t, y], s=0) # @UndefinedVariable
tck2 = interpolate.splrep(t, y, s=len(t), task=0) # @UndefinedVariable
# interpolate.spl
tck = interpolate.splmake(t, y, order=3, kind='smoothest', conds=None) # @UndefinedVariable
self = interpolate.ppform.fromspline(*tck2) # @UndefinedVariable
plt.plot(t, self(t))
plt.show()
pass
def __getitem__(self,key):
if isinstance(key, str):
raise MAError, "Unavailable for masked array."
if type(key) is not tuple:
key = (key,)
objs = []
scalars = []
final_dtypedescr = None
for k in range(len(key)):
scalar = False
if type(key[k]) is slice:
step = key[k].step
start = key[k].start
stop = key[k].stop
if start is None:
start = 0
if step is None:
step = 1
if type(step) is type(1j):
size = int(abs(step))
newobj = function_base.linspace(start, stop, num=size)
else:
newobj = numeric.arange(start, stop, step)
elif type(key[k]) is str:
if (key[k] in 'rc'):
self.matrix = True
self.col = (key[k] == 'c')
continue
try:
self.axis = int(key[k])
continue
except (ValueError, TypeError):
raise ValueError, "Unknown special directive"
elif type(key[k]) in numeric.ScalarType:
newobj = asarray([key[k]])
scalars.append(k)
scalar = True
else:
newobj = key[k]
objs.append(newobj)
if isinstance(newobj, numeric.ndarray) and not scalar:
if final_dtypedescr is None:
final_dtypedescr = newobj.dtype
elif newobj.dtype > final_dtypedescr:
final_dtypedescr = newobj.dtype
if final_dtypedescr is not None:
for k in scalars:
objs[k] = objs[k].astype(final_dtypedescr)
res = concatenate(tuple(objs),axis=self.axis)
return self._retval(res)
def generate_poisson_tex(params):
seed = params.seed
# TODO: select seed
length = params.length
cell_size = params.cell_size
sigma = params.smoothing_sigma
intensity = params.intensity
buffer_len = int(ceil(length / cell_size))
cell_size = (1.0 * length) / buffer_len
buffer = zeros(shape=(buffer_len,))
def generate_inverted_colors_sequence(length):
colors = zeros(shape=(length,))
for i in range(length):
colors[i] = i % 2
return colors
def generate_random_colors_sequence(length):
return numpy.random.rand(length)
events = generate_poisson_events(intensity, length)
colors = generate_random_colors_sequence(len(events))
current_event = 0
for i in xrange(buffer_len):
current_time = i * cell_size
if current_event < len(events) - 1 and current_time > events[current_event]: # XXX
current_event += 1
buffer[i] = colors[current_event]
tail = 4 * sigma
gaussian_filter_len = int(ceil(tail / cell_size))
xcoord = linspace(-tail, tail, gaussian_filter_len)
gaussian_filter = numpy.exp(-xcoord ** 2 / (2 * sigma ** 2))
gaussian_filter = gaussian_filter / gaussian_filter.sum()
buffer = loop_convolve(buffer, gaussian_filter)
return Texture(buffer=buffer, cell_size=cell_size)
def PlotWss(self, meshid, imagpath):
'''
This method plots Wss signal and returns peak wss.
'''
try:
import matplotlib
matplotlib.use(
'Agg'
) #switch to matplotlib.use('WXAgg') if you want to show and not save velocity profile.
from matplotlib.pyplot import plot, xlabel, ylabel, title, legend, savefig, close, ylim
except:
sys.exit(
"PlotWss method requires matplotlib package (http://matplotlib.sourceforge.net.\n"
)
tplot = linspace(0, self.tPeriod, len(self.Tauplot))
plot(tplot, self.Tauplot, 'g-', linewidth=3, label='WSS')
minY = 0
for w in self.Tauplot:
if w < minY:
minY = w
if minY != 0:
plot(tplot, zeros(len(self.Tauplot)), ':', linewidth=1)
ylim(ymin=minY)
xlabel('Time ($s$)')
ylabel('Wall shear stress ($dyne/cm^2$)')
title('Wss' + ' peak:' + str(round(max(self.Tauplot), 1)) + ' mean:' +
str(round(mean(self.Tauplot), 1)) + ' min:' +
str(round(min(self.Tauplot), 1)))
legend()
savefig(imagpath + str(meshid) + '_' + str(self.Name) + '_wss.png')
print "Wss, MeshId", meshid, self.Name, "=", str(
round(max(self.Tauplot), 1)), "$dyne/cm^2$"
close()
return (round(max(self.Tauplot), 1))
def Adapt(self, day):
"""This method will apply adaptation law for specified elements."""
if day>0:
if day == 1:
for el in self.solutions[day-1].NetworkMesh.Elements:
if el.Type == "WavePropagation":
kd1 = el.Radius[0]
kd2 = el.Radius[len(el.Radius)-1]
el.dayRadius[day-1]=[kd1,kd2]
for el in self.solutions[day-1].NetworkMesh.Elements:
el.Initialized = False
preRun = False
for elem in self.solutions[day-1].NetworkMesh.Elements:
if elem.Type == "Anastomosis":
proximalArtery = elem.Proximal
distalArtery = elem.Distal
proximalVein = elem.Vein
#No adaptation in case of upper arm anastomosis and diabetic patient
if self.simulationContext.Context["diab"] == 1 and self.simulationContext.Context["ftype"] > 2:
print "Diabetic patient, no arterial adaptation"
for ent, elList in self.solutions[day-1].NetworkMesh.Entities.iteritems():
if ent.Id == "axillarian" or ent.Id == "brachial" or ent.Id == "radial" or ent.Id == "ulnar" or ent.Id == "cephalic_vein" or ent.Id == "cubiti_vein" or ent.Id == "basilic_vein" or ent.Id == "subclavian_vein":
for el in elList:
kd1_n = el.Radius[0]
kd2_n = el.Radius[len(el.Radius)-1]
el.dayRadius[day]=[kd1_n,kd2_n]
if ent.Id == "cephalic_vein" or ent.Id == "cubiti_vein" or ent.Id == "basilic_vein" or ent.Id == "subclavian_vein":
for el in elList:
taoRef = self.refValues[el.Name]
taoPeaks = self.solutions[day-1].GetWssPeak(el)
tao0 = taoPeaks[0]
tao1 = taoPeaks[1]
tao = linspace(tao0,tao1,len(el.Radius))
deltaTao = tao-taoRef
k = (1.0+(deltaTao*self.Coeff))
if el == proximalVein:
#linear adaptation on anastomosis of 20%
k2 = 45./44.
if day > 10:
k2 = 1.
x = linspace(0,len(el.Radius),len(el.Radius))
taoProxV = (tao0-tao1)*((x/len(el.Radius))**2-(2.0*(x/len(el.Radius))))+tao0 #y = (k1-k2)(x^2-2x)+k1 (quadratic decreasing wss)
tao = taoProxV
deltaTaoProxV = taoProxV-taoRef
k = (1.0+(deltaTaoProxV*self.Coeff))
kProxV = (k-k2)*((x/len(el.Radius))**2)+k2 #y = (k2-k1)x^2+k1 (quadratic increasing radius)
k=kProxV
if min(tao) > taoRef:
el.Radius*=k
kd1_n = el.Radius[0]
kd2_n = el.Radius[len(el.Radius)-1]
el.dayRadius[day]=[kd1_n,kd2_n]
else:
for ent, elList in self.solutions[day-1].NetworkMesh.Entities.iteritems():
if ent.Id == "axillarian" or ent.Id == "brachial" or ent.Id == "radial" or ent.Id == "ulnar" or ent.Id == "cephalic_vein" or ent.Id == "cubiti_vein" or ent.Id == "basilic_vein" or ent.Id == "subclavian_vein":
for el in elList:
taoRef = self.refValues[el.Name]
taoPeaks = self.solutions[day-1].GetWssPeak(el)
tao0 = taoPeaks[0]
tao1 = taoPeaks[1]
tao = linspace(tao0,tao1,len(el.Radius))
deltaTao = tao-taoRef
k = (1.0+(deltaTao*self.Coeff))
if el == proximalArtery:
x = linspace(0,len(el.Radius),len(el.Radius))
taoProxA = (tao1-tao0)*((x/len(el.Radius))**2)+tao0 #y = (k2-k1)x^2+k1 (quadratic increasing wss)
tao=taoProxA
deltaTaoProxA = taoProxA-taoRef
k = (1.0+(deltaTaoProxA*self.Coeff))
kProxA = (k-1.)*((x/len(el.Radius))**2-(2.0*(x/len(el.Radius))))+k #y = (k1-k2)(x^2-2x)+k1 (quadratic decreasing radius)
k=kProxA
if el == distalArtery:
x = linspace(0,len(el.Radius),len(el.Radius))
taoDistA = (tao0-tao1)*((x/len(el.Radius))**2-(2.0*(x/len(el.Radius))))+tao0 #y = (k1-k2)(x^2-2x)+k1 (quadratic decreasing wss)
tao = taoDistA
deltaTaoDistA = taoDistA-taoRef
k = (1.0+(deltaTaoDistA*self.Coeff))
kDistA = (k-1.)*((x/len(el.Radius))**2)+1. #y = (k2-k1)x^2+k1 (quadratic increasing radius)
k=kDistA
if el == proximalVein:
#linear adaptation on anastomosis of 20%
k2 = 1.02
#k2 = 45./44.
if day > 10:
k2 = 1.
x = linspace(0,len(el.Radius),len(el.Radius))
taoProxV = (tao0-tao1)*((x/len(el.Radius))**2-(2.0*(x/len(el.Radius))))+tao0 #y = (k1-k2)(x^2-2x)+k1 (quadratic decreasing wss)
tao = taoProxV
deltaTaoProxV = taoProxV-taoRef
k = (1.0+(deltaTaoProxV*self.Coeff))
kProxV = (k-k2)*((x/len(el.Radius))**2)+k2 #y = (k2-k1)x^2+k1 (quadratic increasing radius)
print "PROXV K" , kProxV
k=kProxV
if min(tao) > taoRef:
el.Radius*=k
kd1_n = el.Radius[0]
kd2_n = el.Radius[len(el.Radius)-1]
el.dayRadius[day]=[kd1_n,kd2_n]
if day == 0:
preRun = True
if day == -1:
preRun = False
return preRun
# tck = interpolate.splrep(x4, y4, s=smoothing)
# x4_new = num_base.linspace(0.01, 100, 100)
# y4_new = interpolate.splev(x4_new, tck, der=0)
# obtain exponential function through lease square fit
def erfc(p, x, y):
return y-(p[0]*np.exp(p[1]*x)+p[2])
def f(x, p):
return p[0]*np.exp(p[1]*x)+p[2]
p0 = [1, -1, 1]
plsq=optimize.leastsq(erfc, p0, args=(x1, y1))
x1_new = num_base.linspace(0.01, 100, 800)
y1_new = f(x1_new, plsq[0])
plsq=optimize.leastsq(erfc, p0, args=(x2, y2))
x2_new = num_base.linspace(0.01, 100, 800)
y2_new = f(x2_new, plsq[0])
plsq=optimize.leastsq(erfc, p0, args=(x3, y3))
x3_new = num_base.linspace(0.01, 100, 800)
y3_new = f(x3_new, plsq[0])
plsq=optimize.leastsq(erfc, p0, args=(x4, y4))
x4_new = num_base.linspace(0.01, 100, 800)
y4_new = f(x4_new, plsq[0])
# plot ECR with reduced range
def analyze_olfaction_covariance(covariance, receptors):
''' Covariance: n x n covariance matrix.
Positions: list of n positions '''
positions = [pose.get_2d_position() for pose, sens in receptors] #@UnusedVariable
positions = array(positions).transpose().squeeze()
require_shape(square_shape(), covariance)
n = covariance.shape[0]
require_shape((2, n), positions)
distances = create_distance_matrix(positions)
correlation = cov2corr(covariance)
flat_distances = distances.reshape(n * n)
flat_correlation = correlation.reshape(n * n)
# let's fit a polynomial
deg = 4
poly = polyfit(flat_distances, flat_correlation, deg=deg)
knots = linspace(min(flat_distances), max(flat_distances), 2000)
poly_int = polyval(poly, knots)
poly_fder = polyder(poly)
fder = polyval(poly_fder, distances)
Ttheta = create_olfaction_Ttheta(positions, fder)
Tx, Ty = create_olfaction_Txy(positions, fder, distances)
report = Node('olfaction-theory')
report.data('flat_distances', flat_distances)
report.data('flat_correlation', flat_correlation)
with report.data_file('dist_vs_corr', 'image/png') as filename:
pylab.figure()
pylab.plot(flat_distances, flat_correlation, '.')
pylab.plot(knots, poly_int, 'r-')
pylab.xlabel('distance')
pylab.ylabel('correlation')
pylab.title('Correlation vs distance')
pylab.legend(['data', 'interpolation deg = %s' % deg])
pylab.savefig(filename)
pylab.close()
with report.data('fder', fder).data_file('fder', 'image/png') as filename:
pylab.figure()
pylab.plot(knots, polyval(poly_fder, knots), 'r-')
pylab.title('f der')
pylab.savefig(filename)
pylab.close()
report.data('distances', distances)
report.data('correlation', correlation)
report.data('covariance', covariance)
report.data('f', polyval(poly, distances))
f = report.figure(id='cor-vs-distnace', caption='Estimated kernels',
shape=(3, 3))
f.sub('dist_vs_corr')
f.sub('fder')
f.sub('f', display='scale')
f.sub('distances', display='scale')
f.sub('correlation', display='posneg')
f.sub('covariance', display='posneg')
T = numpy.zeros(shape=(3, Tx.shape[0], Tx.shape[1]))
T[0, :, :] = Tx
T[1, :, :] = Ty
T[2, :, :] = Ttheta
T_report = create_report_figure_tensors(T, report_id='tensors',
caption="Predicted learned tensors")
report.add_child(T_report)
return report
if (os.path.isfile(ecr_name)):
# DEBUG
#print ecr_name
# DEBUG
plt.clf()
new_smoothing = 0
while new_smoothing >= 0:
smoothing = new_smoothing
x, y = io.loadtxt(ecr_name, usecols=[0,1], unpack=True)
# DEBUG
print "Current smoothing factor = %f" % (smoothing)
tck = interpolate.splrep(x, y, s=smoothing)
x_new = num_base.linspace(0.01, max(x), 100)
y_new = interpolate.splev(x_new, tck, der=0)
plt.plot(x, y, 'o', x_new, y_new, '-')
plt.show()
tmp = raw_input("Input new smoothing factor (press ENTER when done): ")
if (tmp == ""):
break
else:
new_smoothing = float(tmp)
else:
continue
# obtain 1-d spline representation of data
#tck = interpolate.splrep(x, y, s=smoothing)
def GetVelFromQ(self, el):
'''
Computing velocity profile in terms of the flow rate,
using inverse womersley method of Cezeaux et al.1997
'''
self.radius = mean(el.Radius)
self.Res = el.R
self.length = el.Length
self.Name = el.Name
Flow = mean(self.signal)
#WOMERSLEY NUMBER
self.alpha = self.radius * sqrt(
(2.0 * pi * self.density) / (self.tPeriod * self.viscosity))
self.Wom = self.alpha
self.Re = (2.0 * Flow * self.SimulationContext.Context['blood_density']
) / (pi * self.radius *
self.SimulationContext.Context['dynamic_viscosity'])
#FOURIER SIGNAL
k = len(self.signal)
n = 0
while n < (self.nHarmonics):
An = 0
Bn = 0
for i in arange(k):
An += self.signal[i] * cos(
n * (2.0 * pi / self.tPeriod) * self.dt * self.nSteps[i])
Bn += self.signal[i] * sin(
n * (2.0 * pi / self.tPeriod) * self.dt * self.nSteps[i])
An = An * (2.0 / k)
Bn = Bn * (2.0 / k)
self.fourierModes.append(complex(An, Bn))
n += 1
self.fourierModes[
0] *= 0.5 #mean Flow, as expected. It's defined into xml input file.
self.Steps = linspace(0, self.tPeriod, self.samples)
self.VelRadius = {}
self.VelRadiusSteps = {}
self.VelocityPlot = {}
for step in self.Steps:
self.Velocity = {}
y = -1 # raggio da -1 a 1, 200 punti.
while y <= 1.:
self.VelRadius[y] = 2 * (1.0**2 - y**2) * self.fourierModes[0]
y += 0.01
k = 1
while k < self.nHarmonics:
cI = complex(0., 1.)
cA = (self.alpha * pow((1.0 * k), 0.5)) * pow(cI, 1.5)
c1 = 2.0 * jn(1, cA)
c0 = cA * jn(0, cA)
cT = complex(0, -2.0 * pi * k * self.t / self.tPeriod)
y = -1 #da -1 a 1 #y=0 #centerline
while y <= 1.0:
'''vel computation'''
c0_y = cA * jn(0, (cA * y))
vNum = c0 - c0_y
vDen = c0 - c1
vFract = vNum / vDen
cV = self.fourierModes[k] * exp(cT) * vFract
self.VelRadius[
y] += cV.real #valore di velocity riferito al raggio adimensionalizzato
self.Velocity[y] = self.VelRadius[y].real
y += 0.01
k += 1
unsortedRadii = []
for rad, vel in self.Velocity.iteritems():
unsortedRadii.append(rad)
radii = sorted(unsortedRadii)
self.VelPlot = []
for x in radii:
for rad, vel in self.Velocity.iteritems():
if x == rad:
self.VelPlot.append(vel * (100.0 /
(self.radius**2 * pi)))
self.VelocityPlot[step] = self.VelPlot
self.t += self.dtPlot
def ShowVelocityProfile(self, meshid):
'''
This method plots an animated representation of the velocity profile
evolving in time using wx python library.
'''
try:
import matplotlib
matplotlib.use('WXAgg')
from matplotlib.pyplot import xlabel, ylabel, title, close, figure, ylim, show
except:
sys.exit("VelocityProfile methods require matplotlib package (http://matplotlib.sourceforge.net.\n")
try:
from wx import GetApp,EVT_CLOSE, EVT_IDLE
except:
sys.exit("ShowVelocityProfile method requires wxpython package (http://www.wxpython.org).\n")
self.count = 0
orderingStep = []
for step, vel in self.VelocityPlot.iteritems():
orderingStep.append(step)
lenVel = len(vel)
if step == 0.0:
firstVel = vel
orderedStep = sorted(orderingStep)
orderedVel = []
for timeStep in orderedStep:
for step, vel in self.VelocityPlot.iteritems():
if timeStep == step:
orderedVel.append(vel)
orderedVel.reverse()
maxY = 0
minY = 0
for vY in orderedVel:
if max(vY) > maxY:
maxY = max(vY)
if min(vY) < minY:
minY = min(vY)
fig = figure()
ax = fig.add_subplot(111)
t = linspace(-1.0,1.0,lenVel)
line, = ax.plot(t, firstVel,'r-',linewidth = 3)
ylim(ymax=maxY)
ylim(ymin=minY)
xlabel('Fractional radius')
ylabel('Velocity profile ($cm/s$)')
title ('Mean radius($mm$)= '+str(round(self.radius*1e3,0))+' Reynolds N.= '+str(round(self.Re,0))+' Womersley N.= '+str(round(self.Wom,2)))
'''WX ANIMATION'''
def update_line(idleevent):
if orderedVel == []:
for timeStep in orderedStep:
for step, vel in self.VelocityPlot.iteritems():
if timeStep == step:
orderedVel.append(vel)
orderedVel.reverse()
self.count +=1
if self.count >=2:
self.count = 0
EVT_CLOSE(GetApp(), update_line)
close()
line.set_ydata(orderedVel.pop())
fig.canvas.draw_idle()
EVT_IDLE(GetApp(), update_line)
show()
def SaveVelocityProfile(self, meshid, daystr):
'''
This method plots velocity profile into png files and makes
an avi file from png set. Mencoder is required.
'''
try:
import matplotlib
matplotlib.use('Agg')
from matplotlib.pyplot import plot, xlabel, ylabel, title, savefig, ylim, axis, clf
except:
sys.exit("VelocityProfile methods require matplotlib package (http://matplotlib.sourceforge.net.\n")
#Create temporary image and videos directories'''
if not os.path.exists ('tmp/'):
os.mkdir('tmp/')
if not os.path.exists ('videos/'):
os.mkdir('videos/')
if not os.path.exists ('videos/%s' % daystr):
os.mkdir('videos/%s' % daystr)
not_found_msg = """
The mencoder command was not found;
mencoder is used by this script to make an avi file from a set of pngs.
It is typically not installed by default on linux distros because of
legal restrictions, but it is widely available.
"""
try:
subprocess.check_call(['mencoder'])
except subprocess.CalledProcessError:
print "mencoder command was found"
pass # mencoder is found, but returns non-zero exit as expected
# This is a quick and dirty check; it leaves some spurious output
# for the user to puzzle over.
except OSError:
print not_found_msg
sys.exit("quitting\n")
self.count = 0
orderingStep = []
for step, vel in self.VelocityPlot.iteritems():
orderingStep.append(step)
lenStep = len(self.VelocityPlot)
lenVel = len(vel)
orderedStep = sorted(orderingStep)
orderedVel = []
for timeStep in orderedStep:
for step, vel in self.VelocityPlot.iteritems():
if timeStep == step:
orderedVel.append(vel)
maxY = 0
minY = 0
for vY in orderedVel:
if max(vY) > maxY:
maxY = max(vY)
if min(vY) < minY:
minY = min(vY)
x = linspace(-1.0,1.0,lenVel) # Values to be plotted on the x-axis.
ylim(ymax=maxY)
ylim(ymin=minY)
i = 0
print 'Computing Images for velocity profile...'
while i<lenStep:
plot(x,orderedVel[i],'r-',linewidth = 3)
axis((x[1],x[-1],minY,maxY))
xlabel('Fractional radius')
ylabel('Velocity profile ($cm/s$)')
title (str(self.Name)+' radius($mm$)= '+str(round(self.radius*1e3,1))+' Reynolds N.= '+str(round(self.Re,0))+' Womersley N.= '+str(round(self.Wom,2)))
filename = str('%04d' % i) + '.png'
savefig('tmp/'+filename, dpi=100)
clf()
i+=1
print 'Making movie from images..'
command = ('mencoder',
'mf://tmp/*.png',
'-mf',
'type=png:w=800:h=600:fps=25',
'-ovc',
'lavc',
'-lavcopts',
'vcodec=mpeg4',
'-oac',
'copy',
'-o',
'videos/%s%s.avi' % (daystr,self.Name))
print "\n\nabout to execute:\n%s\n\n" % ' '.join(command)
subprocess.check_call(command)
print "\n\n The movie was written"
# obtain exponential function through lease square fit
def erfc(p, x, y):
return y - (p[0] * np.exp(p[1] * x) + p[2])
def f(x, p):
return p[0] * np.exp(p[1] * x) + p[2]
p0 = [1, -1, 1]
plsq = optimize.leastsq(erfc, p0, args=(x1, y1))
x1_new = num_base.linspace(0.01, 100, 800)
y1_new = f(x1_new, plsq[0])
plsq = optimize.leastsq(erfc, p0, args=(x2, y2))
x2_new = num_base.linspace(0.01, 100, 800)
y2_new = f(x2_new, plsq[0])
plsq = optimize.leastsq(erfc, p0, args=(x3, y3))
x3_new = num_base.linspace(0.01, 100, 800)
y3_new = f(x3_new, plsq[0])
plsq = optimize.leastsq(erfc, p0, args=(x4, y4))
x4_new = num_base.linspace(0.01, 100, 800)
y4_new = f(x4_new, plsq[0])
# plot ECR with reduced range
def GetWssPeaks(self, el, flowsig):
'''
This method returns Wss peak along the element.
Wss in s=0 and s=1 is computed.
'''
r0 = el.Radius[0]
r1 = el.Radius[len(el.Radius) - 1]
r01Signal = []
for sig in flowsig:
r01Signal.append(sig)
self.nSteps = arange(0, len(r01Signal), 1)
self.dt = self.tPeriod / (len(self.nSteps) - 1)
self.dtPlot = self.tPeriod / self.samples
fourierModes = []
#Computing for s=0
r0WssSignal = []
#WOMERSLEY NUMBER
r0Alpha = r0 * sqrt(
(2.0 * pi * self.density) / (self.tPeriod * self.viscosity))
#Computing for s=1
r1WssSignal = []
#WOMERSLEY NUMBER
r1Alpha = r1 * sqrt(
(2.0 * pi * self.density) / (self.tPeriod * self.viscosity))
k01 = len(r01Signal)
n = 0
while n < (self.nHarmonics):
An = 0
Bn = 0
for i in arange(k01):
An += r01Signal[i] * cos(
n * (2.0 * pi / self.tPeriod) * self.dt * self.nSteps[i])
Bn += r01Signal[i] * sin(
n * (2.0 * pi / self.tPeriod) * self.dt * self.nSteps[i])
An = An * (2.0 / k01)
Bn = Bn * (2.0 / k01)
fourierModes.append(complex(An, Bn))
n += 1
self.Steps = linspace(0, self.tPeriod, self.samples)
for step in self.Steps:
tao0 = -fourierModes[0].real * 2.0
tao1 = -fourierModes[0].real * 2.0
k = 1
while k < self.nHarmonics:
cI = complex(0., 1.)
cA_0 = (r0Alpha * pow((1.0 * k), 0.5)) * pow(cI, 1.5)
c1_0 = 2.0 * jn(1, cA_0)
c0_0 = cA_0 * jn(0, cA_0)
cA_1 = (r1Alpha * pow((1.0 * k), 0.5)) * pow(cI, 1.5)
c1_1 = 2.0 * jn(1, cA_1)
c0_1 = cA_1 * jn(0, cA_1)
cT = complex(0, -2.0 * pi * k * self.t / self.tPeriod)
'''R0: Wall shear stress computation'''
taoNum_0 = r0Alpha**2 * cI**3 * jn(1, cA_0)
taoDen_0 = c0_0 - c1_0
taoFract_0 = taoNum_0 / taoDen_0
cTao_0 = fourierModes[k] * exp(cT) * taoFract_0
tao0 += cTao_0.real
'''R1: Wall shear stress computation'''
taoNum_1 = r1Alpha**2 * cI**3 * jn(1, cA_1)
taoDen_1 = c0_1 - c1_1
taoFract_1 = taoNum_1 / taoDen_1
cTao_1 = fourierModes[k] * exp(cT) * taoFract_1
tao1 += cTao_1.real
k += 1
tao0 *= -(self.viscosity / (r0**3 * pi))
r0WssSignal.append(tao0)
tao1 *= -(self.viscosity / (r1**3 * pi))
r1WssSignal.append(tao1)
self.t += self.dtPlot
r0Peak = max(r0WssSignal)
r1Peak = max(r1WssSignal)
return r0Peak, r1Peak
def GetVelFromQ(self,el):
'''
Computing velocity profile in terms of the flow rate,
using inverse womersley method of Cezeaux et al.1997
'''
self.radius = mean(el.Radius)
self.Res = el.R
self.length = el.Length
self.Name = el.Name
Flow = mean(self.signal)
#WOMERSLEY NUMBER
self.alpha = self.radius * sqrt((2.0 *pi*self.density)/(self.tPeriod*self.viscosity))
self.Wom = self.alpha
self.Re = (2.0*Flow*self.SimulationContext.Context['blood_density'])/(pi*self.radius*self.SimulationContext.Context['dynamic_viscosity'])
#FOURIER SIGNAL
k = len(self.signal)
n = 0
while n < (self.nHarmonics):
An = 0
Bn = 0
for i in arange(k):
An += self.signal[i] * cos(n*(2.0*pi/self.tPeriod)*self.dt*self.nSteps[i])
Bn += self.signal[i] * sin(n*(2.0*pi/self.tPeriod)*self.dt*self.nSteps[i])
An = An * (2.0/k)
Bn = Bn * (2.0/k)
self.fourierModes.append(complex(An, Bn))
n+=1
self.fourierModes[0] *= 0.5 #mean Flow, as expected. It's defined into xml input file.
self.Steps = linspace(0,self.tPeriod,self.samples)
self.VelRadius = {}
self.VelRadiusSteps = {}
self.VelocityPlot = {}
for step in self.Steps:
self.Velocity = {}
y = -1 # raggio da -1 a 1, 200 punti.
while y <=1.:
self.VelRadius[y] = 2*(1.0**2 - y**2)*self.fourierModes[0]
y+=0.01
k=1
while k < self.nHarmonics:
cI = complex(0.,1.)
cA = (self.alpha * pow((1.0*k),0.5)) * pow(cI,1.5)
c1 = 2.0 * jn(1, cA)
c0 = cA * jn(0, cA)
cT = complex(0, -2.0*pi*k*self.t/self.tPeriod)
y=-1 #da -1 a 1 #y=0 #centerline
while y<=1.0:
'''vel computation'''
c0_y = cA * jn(0, (cA*y))
vNum = c0-c0_y
vDen = c0-c1
vFract = vNum/vDen
cV = self.fourierModes[k] * exp(cT) * vFract
self.VelRadius[y] += cV.real #valore di velocity riferito al raggio adimensionalizzato
self.Velocity[y] = self.VelRadius[y].real
y+=0.01
k+=1
unsortedRadii = []
for rad, vel in self.Velocity.iteritems():
unsortedRadii.append(rad)
radii = sorted(unsortedRadii)
self.VelPlot = []
for x in radii:
for rad, vel in self.Velocity.iteritems():
if x == rad:
self.VelPlot.append(vel*(100.0/(self.radius**2*pi)))
self.VelocityPlot[step] = self.VelPlot
self.t += self.dtPlot
def ShowVelocityProfile(self, meshid):
'''
This method plots an animated representation of the velocity profile
evolving in time using wx python library.
'''
try:
import matplotlib
matplotlib.use('WXAgg')
from matplotlib.pyplot import xlabel, ylabel, title, close, figure, ylim, show
except:
sys.exit(
"VelocityProfile methods require matplotlib package (http://matplotlib.sourceforge.net.\n"
)
try:
from wx import GetApp, EVT_CLOSE, EVT_IDLE
except:
sys.exit(
"ShowVelocityProfile method requires wxpython package (http://www.wxpython.org).\n"
)
self.count = 0
orderingStep = []
for step, vel in self.VelocityPlot.iteritems():
orderingStep.append(step)
lenVel = len(vel)
if step == 0.0:
firstVel = vel
orderedStep = sorted(orderingStep)
orderedVel = []
for timeStep in orderedStep:
for step, vel in self.VelocityPlot.iteritems():
if timeStep == step:
orderedVel.append(vel)
orderedVel.reverse()
maxY = 0
minY = 0
for vY in orderedVel:
if max(vY) > maxY:
maxY = max(vY)
if min(vY) < minY:
minY = min(vY)
fig = figure()
ax = fig.add_subplot(111)
t = linspace(-1.0, 1.0, lenVel)
line, = ax.plot(t, firstVel, 'r-', linewidth=3)
ylim(ymax=maxY)
ylim(ymin=minY)
xlabel('Fractional radius')
ylabel('Velocity profile ($cm/s$)')
title('Mean radius($mm$)= ' + str(round(self.radius * 1e3, 0)) +
' Reynolds N.= ' + str(round(self.Re, 0)) + ' Womersley N.= ' +
str(round(self.Wom, 2)))
'''WX ANIMATION'''
def update_line(idleevent):
if orderedVel == []:
for timeStep in orderedStep:
for step, vel in self.VelocityPlot.iteritems():
if timeStep == step:
orderedVel.append(vel)
orderedVel.reverse()
self.count += 1
if self.count >= 2:
self.count = 0
EVT_CLOSE(GetApp(), update_line)
close()
line.set_ydata(orderedVel.pop())
fig.canvas.draw_idle()
EVT_IDLE(GetApp(), update_line)
show()
def SaveVelocityProfile(self, meshid, daystr):
'''
This method plots velocity profile into png files and makes
an avi file from png set. Mencoder is required.
'''
try:
import matplotlib
matplotlib.use('Agg')
from matplotlib.pyplot import plot, xlabel, ylabel, title, savefig, ylim, axis, clf
except:
sys.exit(
"VelocityProfile methods require matplotlib package (http://matplotlib.sourceforge.net.\n"
)
#Create temporary image and videos directories'''
if not os.path.exists('tmp/'):
os.mkdir('tmp/')
if not os.path.exists('videos/'):
os.mkdir('videos/')
if not os.path.exists('videos/%s' % daystr):
os.mkdir('videos/%s' % daystr)
not_found_msg = """
The mencoder command was not found;
mencoder is used by this script to make an avi file from a set of pngs.
It is typically not installed by default on linux distros because of
legal restrictions, but it is widely available.
"""
try:
subprocess.check_call(['mencoder'])
except subprocess.CalledProcessError:
print "mencoder command was found"
pass # mencoder is found, but returns non-zero exit as expected
# This is a quick and dirty check; it leaves some spurious output
# for the user to puzzle over.
except OSError:
print not_found_msg
sys.exit("quitting\n")
self.count = 0
orderingStep = []
for step, vel in self.VelocityPlot.iteritems():
orderingStep.append(step)
lenStep = len(self.VelocityPlot)
lenVel = len(vel)
orderedStep = sorted(orderingStep)
orderedVel = []
for timeStep in orderedStep:
for step, vel in self.VelocityPlot.iteritems():
if timeStep == step:
orderedVel.append(vel)
maxY = 0
minY = 0
for vY in orderedVel:
if max(vY) > maxY:
maxY = max(vY)
if min(vY) < minY:
minY = min(vY)
x = linspace(-1.0, 1.0, lenVel) # Values to be plotted on the x-axis.
ylim(ymax=maxY)
ylim(ymin=minY)
i = 0
print 'Computing Images for velocity profile...'
while i < lenStep:
plot(x, orderedVel[i], 'r-', linewidth=3)
axis((x[1], x[-1], minY, maxY))
xlabel('Fractional radius')
ylabel('Velocity profile ($cm/s$)')
title(
str(self.Name) + ' radius($mm$)= ' +
str(round(self.radius * 1e3, 1)) + ' Reynolds N.= ' +
str(round(self.Re, 0)) + ' Womersley N.= ' +
str(round(self.Wom, 2)))
filename = str('%04d' % i) + '.png'
savefig('tmp/' + filename, dpi=100)
clf()
i += 1
print 'Making movie from images..'
command = ('mencoder', 'mf://tmp/*.png', '-mf',
'type=png:w=800:h=600:fps=25', '-ovc', 'lavc', '-lavcopts',
'vcodec=mpeg4', '-oac', 'copy', '-o',
'videos/%s%s.avi' % (daystr, self.Name))
print "\n\nabout to execute:\n%s\n\n" % ' '.join(command)
subprocess.check_call(command)
print "\n\n The movie was written"
def GetWssPeaks(self,el, flowsig):
'''
This method returns Wss peak along the element.
Wss in s=0 and s=1 is computed.
'''
r0 = el.Radius[0]
r1 = el.Radius[len(el.Radius)-1]
r01Signal = []
for sig in flowsig:
r01Signal.append(sig)
self.nSteps = arange(0,len(r01Signal),1)
self.dt = self.tPeriod/(len(self.nSteps)-1)
self.dtPlot = self.tPeriod/self.samples
fourierModes = []
#Computing for s=0
r0WssSignal = []
#WOMERSLEY NUMBER
r0Alpha = r0 * sqrt((2.0 *pi*self.density)/(self.tPeriod*self.viscosity))
#Computing for s=1
r1WssSignal = []
#WOMERSLEY NUMBER
r1Alpha = r1 * sqrt((2.0 *pi*self.density)/(self.tPeriod*self.viscosity))
k01 = len(r01Signal)
n = 0
while n < (self.nHarmonics):
An = 0
Bn = 0
for i in arange(k01):
An += r01Signal[i] * cos(n*(2.0*pi/self.tPeriod)*self.dt*self.nSteps[i])
Bn += r01Signal[i] * sin(n*(2.0*pi/self.tPeriod)*self.dt*self.nSteps[i])
An = An * (2.0/k01)
Bn = Bn * (2.0/k01)
fourierModes.append(complex(An, Bn))
n+=1
self.Steps = linspace(0,self.tPeriod,self.samples)
for step in self.Steps:
tao0 = -fourierModes[0].real * 2.0
tao1 = -fourierModes[0].real * 2.0
k=1
while k < self.nHarmonics:
cI = complex(0.,1.)
cA_0 = (r0Alpha * pow((1.0*k),0.5)) * pow(cI,1.5)
c1_0 = 2.0 * jn(1, cA_0)
c0_0 = cA_0 * jn(0, cA_0)
cA_1 = (r1Alpha * pow((1.0*k),0.5)) * pow(cI,1.5)
c1_1 = 2.0 * jn(1, cA_1)
c0_1 = cA_1 * jn(0, cA_1)
cT = complex(0, -2.0*pi*k*self.t/self.tPeriod)
'''R0: Wall shear stress computation'''
taoNum_0 = r0Alpha**2*cI**3*jn(1,cA_0)
taoDen_0 = c0_0-c1_0
taoFract_0 = taoNum_0/taoDen_0
cTao_0 = fourierModes[k] * exp(cT) * taoFract_0
tao0 += cTao_0.real
'''R1: Wall shear stress computation'''
taoNum_1 = r1Alpha**2*cI**3*jn(1,cA_1)
taoDen_1 = c0_1-c1_1
taoFract_1 = taoNum_1/taoDen_1
cTao_1 = fourierModes[k] * exp(cT) * taoFract_1
tao1 += cTao_1.real
k+=1
tao0 *= -(self.viscosity/(r0**3*pi))
r0WssSignal.append(tao0)
tao1 *= -(self.viscosity/(r1**3*pi))
r1WssSignal.append(tao1)
self.t += self.dtPlot
r0Peak = max(r0WssSignal)
r1Peak = max(r1WssSignal)
return r0Peak,r1Peak
if (os.path.isfile(ecr_name)):
# DEBUG
#print ecr_name
# DEBUG
plt.clf()
new_smoothing = 0
while new_smoothing >= 0:
smoothing = new_smoothing
x, y = io.loadtxt(ecr_name, usecols=[0, 1], unpack=True)
# DEBUG
print "Current smoothing factor = %f" % (smoothing)
tck = interpolate.splrep(x, y, s=smoothing)
x_new = num_base.linspace(0.01, max(x), 100)
y_new = interpolate.splev(x_new, tck, der=0)
plt.plot(x, y, 'o', x_new, y_new, '-')
plt.show()
tmp = raw_input(
"Input new smoothing factor (press ENTER when done): ")
if (tmp == ""):
break
else:
new_smoothing = float(tmp)
else:
continue
# obtain 1-d spline representation of data
#tck = interpolate.splrep(x, y, s=smoothing)