def __init__(self, x, y, degree):
Identifier.__init__(self, x, y)
self.poly_fitter = PolyFitter(x, y, degree)
self.i_points = self.poly_fitter.get_inflec_points()
self.calculate_inflec_point(0)
class ITMIdentifier(Identifier):
'''
Identifies data with the inflectional tangent method.
'''
def __init__(self, x, y, degree):
Identifier.__init__(self, x, y)
self.poly_fitter = PolyFitter(x, y, degree)
self.i_points = self.poly_fitter.get_inflec_points()
self.calculate_inflec_point(0)
@property
def t_x(self):
'''
x-values of the tangent.
'''
return numpy.arange(self.death_time, self.end_time, 0.1)
@property
def t_y(self):
'''
y-values of the tangent.
'''
m = self.tangent_slope
b = self.tangent_offset
return m * self.t_x + b
@property
def tu(self):
return self.death_time
@property
def tg(self):
return self.end_time - self.death_time
def calculate_inflec_point(self, num):
'''
Calculates the point of inflection.
'''
# Each tuple in i_points contains the x and y-value
# plus the slope
x, y, m = self.i_points[num]
# tangential form: "mx + b = y"
b = y - m*x
self.death_time = -b/m
self.tangent_slope = m
self.tangent_offset = b
self.split_point = self._calculate_split_point(x)
i = numpy.nonzero(self.x > self.split_point)
x, y = self.x[i], self.y[i]
self.model_fitter = ModelFitter(x, y, modellib.exp_approach)
mf = self.model_fitter
self.height = mf.params['c']
self.end_time = (self.height - b) / m
def _calculate_split_point(self, begin):
'''
Calculate a useful point, where the tangent should stop
and the exponential function begin.
'''
delta = 0.1
x = self.poly_fitter.x
y = self.poly_fitter.get_values(1)
i = numpy.nonzero(x > begin)
x, y = x[i], y[i]
for x_val, y_val in izip(x, y):
if abs(y_val - self.tangent_slope) > delta:
return x_val
def show_solution(self):
m = self.tangent_slope
b = self.tangent_offset
print 'Tangent: {0}x + {1}'.format(m, b)
print 'Tu: {0}'.format(self.tu)
print 'Tg: {0}'.format(self.tg)
print 'Tu/Tg: {0}'.format(self.tu/self.tg)
print 'Tg/Tu: {0}'.format(self.tg/self.tu)
self.plot_solution()
def plot_solution(self):
c = self.height
plot(self.x, self.y, label='data')
plot([self.x[0], self.x[-1]], [c, c], '--', label='limit')
plot(self.t_x, self.t_y, label='tangent')
legend()
grid()
show()