# This program is public domain
# Author: Paul Kienzle
"""
Fitting parameter objects.
Parameters are a big part of the interface between the model and the fitting
engine. By saving and retrieving values and ranges from the parameter, the
fitting engine does not need to be aware of the structure of the model.
Users can also perform calculations with parameters, tying together different
parts of the model, or different models.
"""
#__all__ = [ 'Parameter']
import operator
import sys
from six.moves import reduce
import warnings
from copy import copy
import math
from functools import wraps
import numpy as np
from numpy import inf, isinf, isfinite
from . import bounds as mbounds
# TODO: avoid evaluation of subexpressions if parameters do not change.
# This is especially important if the subexpression invokes an expensive
# calculation via a parameterized function. This will require a restructuring
# of the parameter claas. The park-1.3 solution is viable: given a parameter
# set, figure out which order the expressions need to be evaluated by
# building up a dependency graph. With a little care, we can check which
# parameters have actually changed since the last calculation update, and
# restrict the dependency graph to just them.
# TODO: support full aliasing, so that floating point model attributes can
# be aliased to a parameter. The same technique as subexpressions applies:
# when the parameter is changed, the model will be updated and will need
# to be re-evaluated.
# TODO: maybe move this to util?
[docs]
def to_dict(p):
if hasattr(p, 'to_dict'):
return p.to_dict()
elif isinstance(p, (tuple, list)):
return [to_dict(v) for v in p]
elif isinstance(p, dict):
return {k: to_dict(v) for k, v in p.items()}
elif isinstance(p, (bool, str, float, int, type(None))):
return p
elif isinstance(p, np.ndarray):
# TODO: what about inf, nan and object arrays?
return p.tolist()
elif False and callable(p):
# TODO: consider including functions and arbitrary values
import base64
import dill
encoding = base64.encodebytes(dill.dumps(p)).decode('ascii')
return {'type': 'dill', 'value': str(p), 'encoding': encoding}
## To recovert the function
# if allow_unsafe_code:
# encoding = item['encoding']
# p = dill.loads(base64.decodebytes(encoding).encode('ascii'))
else:
#print(f"converting type {type(p)} to str")
return str(p)
[docs]
class BaseParameter(object):
"""
Root of the parameter class, defining arithmetic on parameters
"""
# Parameters are fixed unless told otherwise
fixed = True
fittable = False
discrete = False
_bounds = mbounds.Unbounded()
name = None
value = None # value is an attribute of the derived class
# Parameters may be dependent on other parameters, and the
# fit engine will need to access them.
[docs]
def parameters(self):
return [self]
[docs]
def pmp(self, plus, minus=None, limits=None):
"""
Allow the parameter to vary as value +/- percent.
pmp(*percent*) -> [value*(1-percent/100), value*(1+percent/100)]
pmp(*plus*, *minus*) -> [value*(1+minus/100), value*(1+plus/100)]
In the *plus/minus* form, one of the numbers should be plus and the
other minus, but it doesn't matter which.
If *limits* are provided, bound the end points of the range to lie
within the limits.
The resulting range is converted to "nice" numbers.
"""
bounds = mbounds.pmp(self.value, plus, minus, limits=limits)
self.bounds = mbounds.Bounded(*bounds)
return self
[docs]
def pm(self, plus, minus=None, limits=None):
"""
Allow the parameter to vary as value +/- delta.
pm(*delta*) -> [value-delta, value+delta]
pm(*plus*, *minus*) -> [value+minus, value+plus]
In the *plus/minus* form, one of the numbers should be plus and the
other minus, but it doesn't matter which.
If *limits* are provided, bound the end points of the range to lie
within the limits.
The resulting range is converted to "nice" numbers.
"""
bounds = mbounds.pm(self.value, plus, minus, limits=limits)
self.bounds = mbounds.Bounded(*bounds)
return self
[docs]
def dev(self, std, mean=None, limits=None, sigma=None, mu=None):
"""
Allow the parameter to vary according to a normal distribution, with
deviations from the mean added to the overall cost function for the
model.
If *mean* is None, then it defaults to the current parameter value.
If *limits* are provide, then use a truncated normal distribution.
Note: *sigma* and *mu* have been replaced by *std* and *mean*, but
are left in for backward compatibility.
"""
if sigma is not None or mu is not None:
# CRUFT: remove sigma and mu parameters
warnings.warn(DeprecationWarning("use std,mean instead of mu,sigma in Parameter.dev"))
if sigma is not None:
std = sigma
if mu is not None:
mean = mu
if mean is None:
mean = self.value # Note: value is an attribute of the derived class
if limits is None:
self.bounds = mbounds.Normal(mean, std)
else:
self.bounds = mbounds.BoundedNormal(mean, std, limits)
return self
[docs]
def pdf(self, dist):
"""
Allow the parameter to vary according to any continuous scipy.stats
distribution.
"""
self.bounds = mbounds.Distribution(dist)
return self
[docs]
def range(self, low, high):
"""
Allow the parameter to vary within the given range.
"""
self.bounds = mbounds.init_bounds((low, high))
return self
[docs]
def soft_range(self, low, high, std):
"""
Allow the parameter to vary within the given range, or with Gaussian
probability, stray from the range.
"""
self.bounds = mbounds.SoftBounded(low, high, std)
return self
@property
def bounds(self):
"""Fit bounds"""
# print "getting bounds for",self,self._bounds
return self._bounds
@bounds.setter
def bounds(self, b):
# print "setting bounds for",self
if self.fittable:
self.fixed = (b is None)
self._bounds = b
# Functional form of parameter value access
def __call__(self):
return self.value
# Parameter algebra: express relationships between parameters
def __gt__(self, other):
return Constraint(self, other, "GT", ">")
def __ge__(self, other):
return Constraint(self, other, "GE", ">=")
def __le__(self, other):
return Constraint(self, other, "LE", "<=")
def __lt__(self, other):
return Constraint(self, other, "LT", "<")
# def __eq__(self, other):
# return ConstraintEQ(self, other)
# def __ne__(self, other):
# return ConstraintNE(self, other)
def __add__(self, other):
return Operator(self, other, "add", "+")
def __sub__(self, other):
return Operator(self, other, "sub", "-")
def __mul__(self, other):
return Operator(self, other, "mul", "*")
def __div__(self, other):
return Operator(self, other, "truediv", "/")
def __pow__(self, other):
return Operator(self, other, "pow", "**")
def __radd__(self, other):
return Operator(other, self, "add", "+")
def __rsub__(self, other):
return Operator(other, self, "sub", "-")
def __rmul__(self, other):
return Operator(other, self, "mul", "*")
def __rdiv__(self, other):
return Operator(other, self, "truediv", "/")
def __rpow__(self, other):
return Operator(other, self, "pow", "**")
def __abs__(self):
return _abs(self)
def __neg__(self):
return self * -1
def __pos__(self):
return self
def __float__(self):
return float(self.value)
__truediv__ = __div__
__rtruediv__ = __rdiv__
[docs]
def nllf(self):
"""
Return -log(P) for the current parameter value.
"""
return self.bounds.nllf(self.value)
[docs]
def residual(self):
"""
Return the z score equivalent for the current parameter value.
That is, the given the value of the parameter in the underlying
distribution, find the equivalent value in the standard normal.
For a gaussian, this is the z score, in which you subtract the
mean and divide by the standard deviation to get the number of
sigmas away from the mean. For other distributions, you need to
compute the cdf of value in the parameter distribution and invert
it using the ppf from the standard normal distribution.
"""
return self.bounds.residual(self.value)
[docs]
def valid(self):
"""
Return true if the parameter is within the valid range.
"""
return not isinf(self.nllf())
def __str__(self):
name = self.name if self.name is not None else '?'
return name
def __repr__(self):
return "Parameter(%s)" % self
[docs]
def to_dict(self):
"""
Return a dict represention of the object.
"""
# When reconstructing a model from json we will need to tie parameters
# together that were tied before. This can be done by managing a
# cache of allocated parameters indexed by id, and pulling from that
# cache on recontruction if the id already exists, otherwise create
# a new entry. Conveniently, this will handle free variable references
# in parameter sets as well. Note that the entire parameter description
# will be repeated each time it occurs, but there should be few
# enough of these that it isn't a problem.
# TODO: use id that is stable from session to session.
# TODO: have mechanism for clearing cache between save/load.
return dict(
type=type(self).__name__,
id=id(self), # Warning: this will be different every session
name=self.name,
value=self.value,
fixed=self.fixed,
fittable=self.fittable,
bounds=to_dict(self._bounds),
)
[docs]
class Constant(BaseParameter):
"""
An unmodifiable value.
"""
fittable = False
fixed = True
@property
def value(self):
return self._value
def __init__(self, value, name=None):
self._value = value
self.name = name
# to_dict() can inherit from BaseParameter
[docs]
class Parameter(BaseParameter):
"""
A parameter is a symbolic value.
It can be fixed or it can vary within bounds.
p = Parameter(3).pmp(10) # 3 +/- 10%
p = Parameter(3).pmp(-5,10) # 3 in [2.85,3.3] rounded to 2 digits
p = Parameter(3).pm(2) # 3 +/- 2
p = Parameter(3).pm(-1,2) # 3 in [2,5]
p = Parameter(3).range(0,5) # 3 in [0,5]
It has hard limits on the possible values, and a range that should live
within those hard limits. The value should lie within the range for
it to be valid. Some algorithms may drive the value outside the range
in order to satisfy soft It has a value which should lie within the range.
Other properties can decorate the parameter, such as tip for tool tip
and units for units.
"""
fittable = True
[docs]
@classmethod
def default(cls, value, **kw):
"""
Create a new parameter with the *value* and *kw* attributes, or return
the existing parameter if *value* is already a parameter.
The attributes are the same as those for Parameter, or whatever
subclass *cls* of Parameter is being created.
"""
# Need to constrain the parameter to fit within fixed limits and
# to receive a name if a name has not already been provided.
if isinstance(value, BaseParameter):
return value
else:
return cls(value, **kw)
[docs]
def set(self, value):
"""
Set a new value for the parameter, ignoring the bounds.
"""
self.value = value
[docs]
def clip_set(self, value):
"""
Set a new value for the parameter, clipping it to the bounds.
"""
low, high = self.bounds.limits
self.value = min(max(value, low), high)
def __init__(self, value=None, bounds=None, fixed=None, name=None, **kw):
# UI nicities:
# 1. check if we are started with value=range or bounds=range; if we
# are given bounds, then assume this is a fitted parameter, otherwise
# the parameter defaults to fixed; if value is not set, use the
# midpoint of the range.
if bounds is None:
try:
lo, hi = value
warnings.warn(DeprecationWarning("parameters can no longer be initialized with a fit range"))
bounds = lo, hi
value = None
except TypeError:
pass
if fixed is None:
fixed = (bounds is None)
bounds = mbounds.init_bounds(bounds)
if value is None:
value = bounds.start_value()
# Store whatever values the user needs to associate with the parameter
# Models should set units and tool tips so the user interface has
# something to work with.
limits = kw.get('limits', (-inf, inf))
for k, v in kw.items():
setattr(self, k, v)
# Initialize bounds, with limits clipped to the hard limits for the
# parameter
def clip(x, a, b):
return min(max(x, a), b)
self.bounds = bounds
self.bounds.limits = (clip(self.bounds.limits[0], *limits),
clip(self.bounds.limits[1], *limits))
self.value = value
self.fixed = fixed
self.name = name
[docs]
def randomize(self, rng=None):
"""
Set a random value for the parameter.
"""
self.value = self.bounds.random(rng if rng is not None else mbounds.RNG)
[docs]
def feasible(self):
"""
Value is within the limits defined by the model
"""
return self.bounds.limits[0] <= self.value <= self.bounds.limits[1]
# to_dict() can inherit from BaseParameter
[docs]
class Reference(Parameter):
"""
Create an adaptor so that a model attribute can be treated as if it
were a parameter. This allows only direct access, wherein the
storage for the parameter value is provided by the underlying model.
Indirect access, wherein the storage is provided by the parameter, cannot
be supported since the parameter has no way to detect that the model
is asking for the value of the attribute. This means that model
attributes cannot be assigned to parameter expressions without some
trigger to update the values of the attributes in the model.
"""
def __init__(self, obj, attr, **kw):
self.obj = obj
self.attr = attr
kw.setdefault('name', ".".join([obj.__class__.__name__, attr]))
Parameter.__init__(self, **kw)
@property
def value(self):
return getattr(self.obj, self.attr)
@value.setter
def value(self, value):
setattr(self.obj, self.attr, value)
[docs]
def to_dict(self):
ret = Parameter.to_dict(self)
ret["attr"] = self.attr
# TODO: another impossibility---an arbitrary python object
# Clearly we need a (safe??) json pickler to handle the full
# complexity of an arbitrary model.
ret["obj"] = to_dict(self.obj)
return ret
[docs]
class ParameterSet(object):
"""
A parameter that depends on the model.
"""
def __init__(self, reference, names=None):
"""
Create a parameter set, with one parameter for each model name.
*names* is the list of model names.
*reference* is the underlying :class:`parameter.Parameter` that will
be set when the model is selected.
*parameters* will be created, with one parameter per model.
"""
self.names = names
self.reference = reference
# TODO: explain better why parameters are using np.array
# Force numpy semantics on slice operations by using an array
# of objects rather than a list of objects
self.parameters = np.array([copy(reference) for _ in names])
# print self.reference, self.parameters
for p, n in zip(self.parameters, names):
p.name = " ".join((n, p.name))
# Reference is no longer directly fittable
self.reference.fittable = False
[docs]
def to_dict(self):
return {
"type": "ParameterSet",
"names": self.names,
"reference": to_dict(self.reference),
# Note: parameters are stored in a numpy array
"parameters": to_dict(self.parameters.tolist()),
}
# Make the parameter set act like a list
def __getitem__(self, i):
"""
Return the underlying parameter for the model index. Index can
either be an integer or a model name. It can also be a slice,
in which case a new parameter set is returned.
"""
# Try looking up the free variable by model name rather than model
# index. If this fails, assume index is a model index.
try:
i = self.names.index(i)
except ValueError:
pass
if isinstance(i, slice):
obj = copy(self)
obj.names = self.names[i]
obj.reference = self.reference
obj.parameters = self.parameters[i]
return obj
return self.parameters[i]
def __setitem__(self, i, v):
"""
Set the underlying parameter for the model index. Index can
either be an integer or a model name. It can also be a slice,
in which case all underlying parameters are set, either to the
same value if *v* is a single parameter, otherwise *v* must have
the same length as the slice.
"""
try:
i = self.names.index(i)
except ValueError:
pass
self.parameters[i] = v
def __iter__(self):
return iter(self.parameters)
def __len__(self):
return len(self.parameters)
[docs]
def set_model(self, index):
"""
Set the underlying model parameter to the value of the nth model.
"""
self.reference.value = self.parameters[index].value
[docs]
def get_model(self, index):
"""
Get the reference and underlying model parameter for the nth model.
"""
return (id(self.reference), self.parameters[index])
@property
def values(self):
return [p.value for p in self.parameters]
@values.setter
def values(self, values):
for p, v in zip(self.parameters, values):
p.value = v
[docs]
def range(self, *args, **kw):
"""
Like :meth:`Parameter.range`, but applied to all models.
"""
for p in self.parameters:
p.range(*args, **kw)
[docs]
def pm(self, *args, **kw):
"""
Like :meth:`Parameter.pm`, but applied to all models.
"""
for p in self.parameters:
p.pm(*args, **kw)
[docs]
def pmp(self, *args, **kw):
"""
Like :meth:`Parameter.pmp`, but applied to all models.
"""
for p in self.parameters:
p.pmp(*args, **kw)
[docs]
class FreeVariables(object):
"""
A collection of parameter sets for a group of models.
*names* is the set of model names.
The parameters themselves are specified as key=value pairs, with key
being the attribute name which is used to retrieve the parameter set
and value being a :class:`Parameter` containing the parameter that is
shared between the models.
In order to evaluate the log likelihood of all models simultaneously,
the fitting program will need to call set_model with the model index
for each model in turn in order to substitute the values from the free
variables into the model. This allows us to share a common sample
across multiple data sets, with each dataset having its own values for
some of the sample parameters. The alternative is to copy the entire
sample structure, sharing references to common parameters and creating
new parameters for each model for the free parameters. Setting up
these copies was inconvenient.
"""
def __init__(self, names=None, **kw):
if names is None:
raise TypeError("FreeVariables needs name=[model1, model2, ...]")
self.names = names
# Create slots to hold the free variables
self._parametersets = dict((k, ParameterSet(v, names=names))
for k, v in kw.items())
# Shouldn't need explicit __getstate__/__setstate__ but mpi4py pickle
# chokes without it.
def __getstate__(self):
return self.__dict__
def __setstate__(self, state):
self.__dict__ = state
def __getattr__(self, k):
"""
Return the parameter set for the given free parameter.
"""
try:
return self._parametersets[k]
except KeyError:
raise AttributeError('FreeVariables has no attribute %r' % k)
[docs]
def parameters(self):
"""
Return the set of free variables for all the models.
"""
return dict((k, v.parameters) for k, v in self._parametersets.items())
[docs]
def to_dict(self):
return {
'type': type(self).__name__,
'names': self.names,
'parameters': to_dict(self._parametersets)
}
[docs]
def set_model(self, i):
"""
Set the reference parameters for model *i*.
"""
for p in self._parametersets.values():
p.set_model(i)
[docs]
def get_model(self, i):
"""
Get the parameters for model *i* as {reference: substitution}
"""
return dict(p.get_model(i) for p in self._parametersets.values())
# Current implementation computes values on the fly, so you only
# need to plug the values into the parameters and the parameters
# are automatically updated.
#
# This will not work well for wrapped models. In those cases you
# want to do a number of optimizations, such as only updating the
#
# ==== Comparison operators ===
COMPARISONS = [
('GT', '>'),
('GE', '>='),
('LE', '<='),
('LT', '<'),
('EQ', '=='),
('NE', '!=')
]
[docs]
class Constraint(object):
def __init__(self, a, b, op_name, op_str=""):
import operator
self.a, self.b = a, b
self.op_name = op_name
self.op = getattr(operator, op_name.lower())
self.op_str = op_str
def __bool__(self):
return self.op(float(self.a), float(self.b))
__nonzero__ = __bool__
def __str__(self):
return "(%s %s %s)" %(self.a, self.op_str, self.b)
# ==== Arithmetic operators ===
ALLOWED_OPERATORS = ["add","sub","mul","truediv","floordiv","pow"]
[docs]
class Operator(BaseParameter):
"""
Parameter operator
"""
def __init__(self, a, b, op_name, op_str):
import operator
if not op_name.lower() in ALLOWED_OPERATORS:
raise ValueError("Operator name %s is not in allowed operators: %s" % (op_name, str(ALLOWED_OPERATORS)))
self.a, self.b = a,b
self.op_name = op_name
self.op = getattr(operator, op_name.lower())
self.op_str = op_str
pars = []
if isinstance(a,BaseParameter): pars += a.parameters()
if isinstance(b,BaseParameter): pars += b.parameters()
self._parameters = pars
self.name = str(self)
[docs]
def parameters(self):
return self._parameters
[docs]
def to_dict(self):
return dict(
type="Operator",
op_name=self.op_name,
op_str=self.op_str,
left=to_dict(self.a),
right=to_dict(self.b),
)
@property
def value(self):
return self.op(float(self.a), float(self.b))
@property
def dvalue(self):
return float(self.a)
def __str__(self):
return "(%s %s %s)" % (self.a,self.op_str, self.b)
[docs]
def substitute(a):
"""
Return structure a with values substituted for all parameters.
The function traverses lists, tuples and dicts recursively. Things
which are not parameters are returned directly.
"""
if isinstance(a, BaseParameter):
return float(a.value)
elif isinstance(a, tuple):
return tuple(substitute(v) for v in a)
elif isinstance(a, list):
return [substitute(v) for v in a]
elif isinstance(a, dict):
return dict((k, substitute(v)) for k, v in a.items())
elif isinstance(a, np.ndarray):
return np.array([substitute(v) for v in a])
else:
return a
[docs]
class Function(BaseParameter):
"""
Delayed function evaluator.
f.value evaluates the function with the values of the
parameter arguments at the time f.value is referenced rather
than when the function was invoked.
"""
__slots__ = ['op', 'args', 'kw']
def __init__(self, op, *args, **kw):
self.name = kw.pop('name', None)
self.op, self.args, self.kw = op, args, kw
self._parameters = self._find_parameters()
def _find_parameters(self):
# Figure out which arguments to the function are parameters
#deps = [p for p in self.args if isinstance(p,BaseParameter)]
args = [arg for arg in self.args if isinstance(arg, BaseParameter)]
kw = dict((name, arg) for name, arg in self.kw.items()
if isinstance(arg, BaseParameter))
deps = flatten((args, kw))
# Find out which other parameters these parameters depend on.
res = []
for p in deps:
res.extend(p.parameters())
return res
[docs]
def parameters(self):
return self._parameters
def _value(self):
# Expand args and kw, replacing instances of parameters
# with their values
return self.op(*substitute(self.args), **substitute(self.kw))
value = property(_value)
[docs]
def to_dict(self):
return {
"type": "Function",
"name": self.name,
# TODO: function not stored properly in json
"op": to_dict(self.op),
"args": to_dict(self.args),
"kw": to_dict(self.kw),
}
def __getstate__(self):
return self.name, self.op, self.args, self.kw
def __setstate__(self, state):
self.name, self.op, self.args, self.kw = state
self._parameters = self._find_parameters()
def __str__(self):
if self.name is not None:
name = self.name
else:
args = [str(v) for v in self.args]
kw = [str(k) + "=" + str(v) for k, v in self.kw.items()]
name = self.op.__name__ + "(" + ", ".join(args + kw) + ")"
return name
#return "%s:%g" % (name, self.value)
[docs]
def function(op):
"""
Convert a function into a delayed evaluator.
The value of the function is computed from the values of the parameters
at the time that the function value is requested rather than when the
function is created.
"""
# Note: @functools.wraps(op) does not work with numpy ufuncs
# Note: @decorator does not work with builtins like abs
def function_generator(*args, **kw):
return Function(op, *args, **kw)
function_generator.__name__ = op.__name__
function_generator.__doc__ = op.__doc__
return function_generator
_abs = function(abs)
# Numpy trick: math functions from numpy delegate to the math function of
# the class if that function exists as a class attribute.
BaseParameter.exp = function(math.exp)
BaseParameter.expm1 = function(math.expm1)
BaseParameter.log = function(math.log)
BaseParameter.log10 = function(math.log10)
BaseParameter.log1p = function(math.log1p)
BaseParameter.sqrt = function(math.sqrt)
BaseParameter.degrees = function(math.degrees)
BaseParameter.radians = function(math.radians)
BaseParameter.sin = function(math.sin)
BaseParameter.cos = function(math.cos)
BaseParameter.tan = function(math.tan)
BaseParameter.arcsin = function(math.asin)
BaseParameter.arccos = function(math.acos)
BaseParameter.arctan = function(math.atan)
BaseParameter.sinh = function(math.sinh)
BaseParameter.cosh = function(math.cosh)
BaseParameter.tanh = function(math.tanh)
BaseParameter.arcsinh = function(math.asinh)
BaseParameter.arccosh = function(math.acosh)
BaseParameter.arctanh = function(math.atanh)
BaseParameter.ceil = function(math.ceil)
BaseParameter.floor = function(math.floor)
BaseParameter.trunc = function(math.trunc)
[docs]
def boxed_function(f):
box = function(f)
@wraps(f)
def wrapped(*args, **kw):
if any(isinstance(v, BaseParameter) for v in args):
return box(*args, **kw)
else:
return f(*args, **kw)
return wrapped
# arctan2 is special since either argument can be a parameter
arctan2 = boxed_function(math.atan2)
# Trig functions defined in degrees rather than radians
[docs]
@boxed_function
def cosd(v):
"""Return the cosine of x (measured in in degrees)."""
return math.cos(math.radians(v))
[docs]
@boxed_function
def sind(v):
"""Return the sine of x (measured in in degrees)."""
return math.sin(math.radians(v))
[docs]
@boxed_function
def tand(v):
"""Return the tangent of x (measured in in degrees)."""
return math.tan(math.radians(v))
[docs]
@boxed_function
def acosd(v):
"""Return the arc cosine (measured in in degrees) of x."""
return math.degrees(math.acos(v))
arccosd = acosd
[docs]
@boxed_function
def asind(v):
"""Return the arc sine (measured in in degrees) of x."""
return math.degrees(math.asin(v))
arcsind = asind
[docs]
@boxed_function
def atand(v):
"""Return the arc tangent (measured in in degrees) of x."""
return math.degrees(math.atan(v))
arctand = atand
[docs]
@boxed_function
def atan2d(dy, dx):
"""Return the arc tangent (measured in in degrees) of y/x.
Unlike atan(y/x), the signs of both x and y are considered."""
return math.degrees(math.atan2(dy, dx))
arctan2d = atan2d
[docs]
def flatten(s):
if isinstance(s, (tuple, list, np.ndarray)):
return reduce(lambda a, b: a + flatten(b), s, [])
elif isinstance(s, set):
raise TypeError("parameter flattening cannot order sets")
elif isinstance(s, dict):
return reduce(lambda a, b: a + flatten(s[b]), sorted(s.keys()), [])
elif isinstance(s, BaseParameter):
return [s]
elif s is None:
return []
else:
raise TypeError("don't understand type %s for %r" % (type(s), s))
[docs]
def summarize(pars, sorted=False):
"""
Return a stylized list of parameter names and values with range bars
suitable for printing.
If sorted, then print the parameters sorted alphabetically by name.
"""
output = []
if sorted:
pars = sorted(pars, cmp=lambda x, y: cmp(x.name, y.name))
for p in pars:
if not isfinite(p.value):
bar = ["*invalid* "]
else:
position = int(p.bounds.get01(p.value) * 9.999999999)
bar = ['.'] * 10
if position < 0:
bar[0] = '<'
elif position > 9:
bar[9] = '>'
else:
bar[position] = '|'
output.append("%40s %s %10g in %s" %
(p.name, "".join(bar), p.value, p.bounds))
return "\n".join(output)
[docs]
def unique(s):
"""
Return the unique set of parameters
The ordering is stable. The same parameters/dependencies will always
return the same ordering, with the first occurrence first.
"""
# Walk structures such as dicts and lists
pars = flatten(s)
# print "====== flattened"
# print "\n".join("%s:%s"%(id(p),p) for p in pars)
# Also walk parameter expressions
pars = pars + flatten([p.parameters() for p in pars])
# print "====== extended"
# print "\n".join("%s:%s"%(id(p),p) for p in pars)
# TODO: implement n log n rather than n^2 uniqueness algorithm
# problem is that the sorting has to be unique across a pickle.
result = []
for p in pars:
if not any(p is q for q in result):
result.append(p)
# print "====== unique"
# print "\n".join("%s:%s"%(id(p),p) for p in result)
# Return the complete set of parameters
return result
[docs]
def fittable(s):
"""
Return the list of fittable parameters in no paraticular order.
Note that some fittable parameters may be fixed during the fit.
"""
return [p for p in unique(s) if not p.fittable]
[docs]
def varying(s):
"""
Return the list of fitted parameters in the model.
This is the set of parameters that will vary during the fit.
"""
return [p for p in unique(s) if not p.fixed]
[docs]
def randomize(s):
"""
Set random values to the parameters in the parameter set, with
values chosen according to the bounds.
"""
for p in s:
p.value = p.bounds.random(1)[0]
[docs]
def current(s):
return [p.value for p in s]
# ========= trash ===================
[docs]
class IntegerParameter(Parameter):
discrete = True
def _get_value(self):
return self._value
def _set_value(self, value):
self._value = int(value)
value = property(_get_value, _set_value)
[docs]
class Alias(object):
"""
Parameter alias.
Rather than modifying a model to contain a parameter slot,
allow the parameter to exist outside the model. The resulting
parameter will have the full parameter semantics, including
the ability to replace a fixed value with a parameter expression.
**Deprecated** :class:`Reference` does this better.
"""
def __init__(self, obj, attr, p=None, name=None):
self.obj = obj
self.attr = attr
if name is None:
name = ".".join([obj.__class__.__name__, attr])
self.p = Parameter.default(p, name=name)
[docs]
def update(self):
setattr(self.obj, self.attr, self.p.value)
[docs]
def parameters(self):
return self.p.parameters()
[docs]
def to_dict(self):
return {
'type': type(self).__name__,
'p': to_dict(self.p),
# TODO: can't json pickle arbitrary objects
'obj': to_dict(self.obj),
'attr': self.attr,
}
[docs]
def test_operator():
a = Parameter(1, name='a')
b = Parameter(2, name='b')
a_b = a + b
a.value = 3
assert a_b.value == 5.
assert a_b.name == '(a + b)'