def fixNegsConstrainedOpt(self, to_minimize=norm_diff, badness=1e6):
"""Uses constrained minimization to find approx q matrix.
to_minimize: metric for comparing orig result and new result.
badness: scale factor for penalizing negative off-diagonal values.
"""
if not sum_neg_off_diags(self._data):
return self
q = ravel(without_diag(self._data))
p = expm(self._data)(t=1)
def err_f(q):
new_q = reshape(array(q), (4, 3))
new_q = with_diag(new_q, -sum(new_q, 1))
p_new = expm(new_q)(t=1)
result = to_minimize(ravel(p), ravel(p_new))
if q.min() < 0:
result += -q.min() * badness
return result
a = array(q)
xmin = fmin(func=err_f, x0=a, disp=0)
r = reshape(xmin, (4, 3))
new_q = with_diag(r, -sum(r, 1))
return self.__class__(new_q, self.Alphabet)
def _timeForSimilarity_naive(self, similarity, freqs=None):
"""Returns time exponent so that exp(q*time) diverges to right distance.
Takes symbol freqs into account if specified; otherwise assumes equal.
freqs: vector of frequencies, applied to each row successively.
WARNING: Factor of 5 slower than timeForSimilarity. Included for
testing that results are identical.
"""
q = self._data
if freqs is None:
def similarity_f(t):
return abs(average(diagonal(expm(q)(t)))-similarity)
else:
def similarity_f(t):
return abs(sum(diagonal(expm(q)(t)*freqs)) - similarity)
initial_guess = array([1.0])
result = fmin(similarity_f, initial_guess, disp=0)
#disp=0 turns off fmin messages
return result
def _timeForSimilarity_naive(self, similarity, freqs=None):
"""Returns time exponent so that exp(q*time) diverges to right distance.
Takes symbol freqs into account if specified; otherwise assumes equal.
freqs: vector of frequencies, applied to each row successively.
WARNING: Factor of 5 slower than timeForSimilarity. Included for
testing that results are identical.
"""
q = self._data
if freqs is None:
def similarity_f(t):
return abs(average(diagonal(expm(q)(t)))-similarity)
else:
def similarity_f(t):
return abs(sum(diagonal(expm(q)(t)*freqs)) - similarity)
initial_guess = array([1.0])
result = fmin(similarity_f, initial_guess, disp=0)
#disp=0 turns off fmin messages
return result
def fit_function(x_vals, y_vals, func, n_params, iterations=2):
""" Fit any function to any array of values of x and y.
:Parameters:
x_vals : array
Values for x to fit the function func.
y_vals : array
Values for y to fit the function func.
func : callable ``f(x, a)``
Objective function (model) to be fitted to the data. This function
should return either an array for models that are not a constant,
i.e. f(x)=exp(a[0]+x*a[1]), or a single value for models that are a
cosntant, i.e. f(x)=a[0]
n_params : int
Number of parameters to fit in func
iterations : int
Number of iterations to fit func
:Returns: param_guess
param_guess : array
Values for each of the arguments to fit func to x_vals and y_vals
:Notes:
Fit a function to a given array of values x and y using simplex to
minimize the error.
"""
# internal function to minimize the error
def f2min(a):
#sum square deviation
return ((func(x_vals, a) - y_vals)**2).sum()
param_guess = array(range(n_params))
for i in range(iterations):
xopt = fmin(f2min, param_guess, disp=0)
param_guess = xopt
return xopt
def fit_function(x_vals, y_vals, func, n_params, iterations=2):
""" Fit any function to any array of values of x and y.
:Parameters:
x_vals : array
Values for x to fit the function func.
y_vals : array
Values for y to fit the function func.
func : callable ``f(x, a)``
Objective function (model) to be fitted to the data. This function
should return either an array for models that are not a constant,
i.e. f(x)=exp(a[0]+x*a[1]), or a single value for models that are a
cosntant, i.e. f(x)=a[0]
n_params : int
Number of parameters to fit in func
iterations : int
Number of iterations to fit func
:Returns: param_guess
param_guess : array
Values for each of the arguments to fit func to x_vals and y_vals
:Notes:
Fit a function to a given array of values x and y using simplex to
minimize the error.
"""
# internal function to minimize the error
def f2min(a):
#sum square deviation
return ((func(x_vals, a) - y_vals)**2).sum()
param_guess = array(range(n_params))
for i in range(iterations):
xopt = fmin(f2min, param_guess, disp=0)
param_guess = xopt
return xopt
def fixNegsConstrainedOpt(self, to_minimize=norm_diff, badness=1e6):
"""Uses constrained minimization to find approx q matrix.
to_minimize: metric for comparing orig result and new result.
badness: scale factor for penalizing negative off-diagonal values.
"""
if not sum_neg_off_diags(self._data):
return self
q = ravel(without_diag(self._data))
p = expm(self._data)(t=1)
def err_f(q):
new_q = reshape(array(q), (4,3))
new_q = with_diag(new_q, -sum(new_q, 1))
p_new = expm(new_q)(t=1)
result = to_minimize(ravel(p), ravel(p_new))
if q.min() < 0:
result += -q.min() * badness
return result
a = array(q)
xmin = fmin(func=err_f, x0=a, disp=0)
r = reshape(xmin, (4,3))
new_q = with_diag(r, -sum(r, 1))
return self.__class__(new_q, self.Alphabet)
def _minimise(self, f, x, **kw):
return fmin(f, x, **kw)
def _minimise(self, f, x, **kw):
return fmin(f, x, **kw)
