def speedTest4(mutate = 2):
"""Test wrt sympy.
Results - sympy is 10 to 24 times faster without using arrays (ouch!).
- diffpy.srfit.equation is slightly slower when using arrays, but
not considerably worse than versus numpy alone.
"""
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 20, 0.05)
qsig = 0.01
sigma = 0.003
eqstr = """\
b1 + b2*x + b3*x**2 + b4*x**3 + b5*x**4 + b6*x**5 + b7*x**6 + b8*x**7\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
from sympy import var, exp, lambdify
from numpy import polyval
b1, b2, b3, b4, b5, b6, b7, b8, xx = vars = var("b1 b2 b3 b4 b5 b6 b7 b8 xx")
f = lambdify(vars, polyval([b1, b2, b3, b4, b5, b6, b7, b8], xx), "numpy")
tnpy = 0
teq = 0
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [1.0]*(len(eq.args))
args.append(x)
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
# Time the different functions with these arguments
teq += timeFunction(eq, *(args[:-1]))
tnpy += timeFunction(f, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "sympy: ", tnpy/numcalls
print "equation: ", teq/numcalls
print "ratio: ", teq/tnpy
return
def speedTest4(mutate=2):
"""Test wrt sympy.
Results - sympy is 10 to 24 times faster without using arrays (ouch!).
- diffpy.srfit.equation is slightly slower when using arrays, but
not considerably worse than versus numpy alone.
"""
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 20, 0.05)
eqstr = """\
b1 + b2*x + b3*x**2 + b4*x**3 + b5*x**4 + b6*x**5 + b7*x**6 + b8*x**7\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
from sympy import var, lambdify
from numpy import polyval
b1, b2, b3, b4, b5, b6, b7, b8, xx = vars = var(
"b1 b2 b3 b4 b5 b6 b7 b8 xx")
f = lambdify(vars, polyval([b1, b2, b3, b4, b5, b6, b7, b8], xx), "numpy")
tnpy = 0
teq = 0
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [1.0] * (len(eq.args))
args.append(x)
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
# Time the different functions with these arguments
teq += timeFunction(eq, *(args[:-1]))
tnpy += timeFunction(f, *args)
print("Average call time (%i calls, %i mutations/call):" %
(numcalls, mutate))
print("sympy: ", tnpy / numcalls)
print("equation: ", teq / numcalls)
print("ratio: ", teq / tnpy)
return
def profileTest():
from diffpy.srfit.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 10, 0.001)
qsig = 0.01
sigma = 0.003
eqstr = """\
b1 + b2*x + b3*x**2 + b4*x**3 + b5*x**4 + b6*x**5 + b7*x**6 + b8*x**7\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
mutate = 8
numargs = len(eq.args)
choices = range(numargs)
args = [0.1] * numargs
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
eq(*args)
return
def profileTest():
from diffpy.srfit.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 10, 0.001)
qsig = 0.01
sigma = 0.003
eqstr = """\
b1 + b2*x + b3*x**2 + b4*x**3 + b5*x**4 + b6*x**5 + b7*x**6 + b8*x**7\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
mutate = 8
numargs = len(eq.args)
choices = range(numargs)
args = [0.1]*numargs
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
eq(*args)
return
def weightedTest(mutate=2):
"""Show the benefits of a properly balanced equation tree."""
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 10, 0.01)
qsig = 0.01
sigma = 0.003
eqstr = """\
b1 + b2*x + b3*x**2 + b4*x**3 + b5*x**4 + b6*x**5 + b7*x**6 + b8*x**7\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
#scale = visitors.NodeWeigher()
#eq.root.identify(scale)
#print scale.output
from numpy import polyval
def f(b1, b2, b3, b4, b5, b6, b7, b8):
return polyval([b8, b7, b6, b5, b4, b3, b2, b1], x)
tnpy = 0
teq = 0
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [0.1] * numargs
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
#print args
# Time the different functions with these arguments
teq += timeFunction(eq, *args)
tnpy += timeFunction(f, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "numpy: ", tnpy / numcalls
print "equation: ", teq / numcalls
print "ratio: ", teq / tnpy
return
def speedTest3(mutate=2):
"""Test wrt sympy.
Results - sympy is 10 to 24 times faster without using arrays (ouch!).
- diffpy.srfit.equation is slightly slower when using arrays, but
not considerably worse than versus numpy alone.
"""
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 20, 0.05)
qsig = 0.01
sigma = 0.003
eqstr = """\
A0*exp(-(x*qsig)**2)*(exp(-((x-1.0)/sigma1)**2)+exp(-((x-2.0)/sigma2)**2))\
+ polyval(list(b1, b2, b3, b4, b5, b6, b7, b8), x)\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.qsig.setValue(qsig)
eq.sigma1.setValue(sigma)
eq.sigma2.setValue(sigma)
eq.A0.setValue(1.0)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
from sympy import var, exp, lambdify
from numpy import polyval
A0, qsig, sigma1, sigma2, b1, b2, b3, b4, b5, b6, b7, b8, xx = vars = var(
"A0 qsig sigma1 sigma2 b1 b2 b3 b4 b5 b6 b7 b8 xx")
f = lambdify(
vars,
A0 * exp(-(xx * qsig)**2) *
(exp(-((xx - 1.0) / sigma1)**2) + exp(-((xx - 2.0) / sigma2)**2)) +
polyval([b1, b2, b3, b4, b5, b6, b7, b8], xx), "numpy")
tnpy = 0
teq = 0
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [1.0] * (len(eq.args))
args.append(x)
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
# Time the different functions with these arguments
teq += timeFunction(eq, *(args[:-1]))
tnpy += timeFunction(f, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "sympy: ", tnpy / numcalls
print "equation: ", teq / numcalls
print "ratio: ", teq / tnpy
return
def speedTest2(mutate=2):
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 20, 0.05)
qsig = 0.01
sigma = 0.003
eqstr = """\
A0*exp(-(x*qsig)**2)*(exp(-((x-1.0)/sigma1)**2)+exp(-((x-2.0)/sigma2)**2))\
+ polyval(list(b1, b2, b3, b4, b5, b6, b7, b8), x)\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.qsig.setValue(qsig)
eq.sigma1.setValue(sigma)
eq.sigma2.setValue(sigma)
eq.A0.setValue(1.0)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
from numpy import exp
from numpy import polyval
def f(A0, qsig, sigma1, sigma2, b1, b2, b3, b4, b5, b6, b7, b8):
return A0 * exp(-(x * qsig)**2) * (exp(-(
(x - 1.0) / sigma1)**2) + exp(-((x - 2.0) / sigma2)**2)) + polyval(
[b8, b7, b6, b5, b4, b3, b2, b1], x)
tnpy = 0
teq = 0
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [0.0] * (len(eq.args))
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
# Time the different functions with these arguments
tnpy += timeFunction(f, *args)
teq += timeFunction(eq, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "numpy: ", tnpy / numcalls
print "equation: ", teq / numcalls
print "ratio: ", teq / tnpy
return
class RecipeOrganizer(_recipeorganizer_interface, RecipeContainer):
"""Extended base class for organizing pieces of a FitRecipe.
This class extends RecipeContainer by organizing constraints and
Restraints, as well as Equations that can be used in Constraint and
Restraint equations. These constraints and Restraints can be placed at any
level and a flattened list of them can be retrieved with the
_getConstraints and _getRestraints methods.
Attributes
name -- A name for this organizer. Names should be unique
within a RecipeOrganizer and should be valid attribute
names.
_calculators -- A managed dictionary of Calculators, indexed by name.
_parameters -- A managed OrderedDict of contained Parameters.
_constraints -- A dictionary of Constraints, indexed by the constrained
Parameter. Constraints can be added using the
'constrain' method.
_restraints -- A set of Restraints. Restraints can be added using the
'restrain' method.
_eqfactory -- A diffpy.srfit.equation.builder.EquationFactory
instance that is used create Equations from string.
Properties
names -- Variable names (read only). See getNames.
values -- Variable values (read only). See getValues.
Raises ValueError if the name is not a valid attribute identifier
"""
def __init__(self, name):
RecipeContainer.__init__(self, name)
self._restraints = set()
self._constraints = {}
self._eqfactory = EquationFactory()
self._calculators = {}
self._manage(self._calculators)
return
# Parameter management
def _newParameter(self, name, value, check=True):
"""Add a new Parameter to the container.
This creates a new Parameter and adds it to the container using the
_addParameter method.
Returns the Parameter.
"""
p = Parameter(name, value)
self._addParameter(p, check)
return p
def _addParameter(self, par, check=True):
"""Store a Parameter.
Parameters added in this way are registered with the _eqfactory.
par -- The Parameter to be stored.
check -- If True (default), a ValueError is raised a Parameter of
the specified name has already been inserted.
Raises ValueError if the Parameter has no name.
Raises ValueError if the Parameter has the same name as a contained
RecipeContainer.
"""
# Store the Parameter
RecipeContainer._addObject(self, par, self._parameters, check)
# Register the Parameter
self._eqfactory.registerArgument(par.name, par)
return
def _removeParameter(self, par):
"""Remove a parameter.
This de-registers the Parameter with the _eqfactory. The Parameter will
remain part of built equations.
Note that constraints and restraints involving the Parameter are not
modified.
Raises ValueError if par is not part of the RecipeOrganizer.
"""
self._removeObject(par, self._parameters)
self._eqfactory.deRegisterBuilder(par.name)
return
def registerCalculator(self, f, argnames=None):
"""Register a Calculator so it can be used within equation strings.
A Calculator is an elaborate function that can organize Parameters.
This creates a function with this class that can be used within string
equations. The resulting equation can be used in a string with
arguments like a function or without, in which case the values of the
Parameters created from argnames will be be used to compute the value.
f -- The Calculator to register.
argnames -- The names of the arguments to f (list or None).
If this is None, then the argument names will be
extracted from the function.
"""
self._eqfactory.registerOperator(f.name, f)
self._addObject(f, self._calculators)
# Register arguments of the calculator
if argnames is None:
func_code = f.__call__.im_func.func_code
argnames = list(func_code.co_varnames)
argnames = argnames[1 : func_code.co_argcount]
for pname in argnames:
if pname not in self._eqfactory.builders:
par = self._newParameter(pname, 0)
else:
par = self.get(pname)
f.addLiteral(par)
# Now return an equation object
eq = self._eqfactory.makeEquation(f.name)
return eq
def registerFunction(self, f, name=None, argnames=None):
"""Register a function so it can be used within equation strings.
This creates a function with this class that can be used within string
equations. The resulting equation does not require the arguments to be
passed in the equation string, as this will be handled automatically.
f -- The callable to register. If this is an Equation
instance, then all that needs to be provied is a name.
name -- The name of the function to be used in equations. If
this is None (default), the method will try to
determine the name of the function automatically.
argnames -- The names of the arguments to f (list or None).
If this is None (default), then the argument names will
be extracted from the function.
Note that name and argnames can be extracted from regular python
functions (of type 'function'), bound class methods and callable
classes.
Raises TypeError if name or argnames cannot be automatically
extracted.
Raises TypeError if an automatically extracted name is '<lambda>'.
Raises ValueError if f is an Equation object and name is None.
Returns the callable Equation object.
"""
# If the function is an equation, we treat it specially. This is
# required so that the objects observed by the root get observed if the
# Equation is used within another equation. It is assumed that a plain
# function is not observable.
if isinstance(f, Equation):
if name is None:
m = "Equation must be given a name"
raise ValueError(m)
self._eqfactory.registerOperator(name, f)
return f
#### Introspection code
if name is None or argnames is None:
import inspect
func_code = None
# This will let us offset the argument list to eliminate 'self'
offset = 0
# check regular functions
if inspect.isfunction(f):
func_code = f.func_code
# check class method
elif inspect.ismethod(f):
func_code = f.im_func.func_code
offset = 1
# check functor
elif hasattr(f, "__call__") and hasattr(f.__call__, "im_func"):
func_code = f.__call__.im_func.func_code
offset = 1
else:
m = "Cannot extract name or argnames"
raise ValueError(m)
# Extract the name
if name is None:
name = func_code.co_name
if name == "<lambda>":
m = "You must supply a name name for a lambda function"
raise ValueError(m)
# Extract the arguments
if argnames is None:
argnames = list(func_code.co_varnames)
argnames = argnames[offset : func_code.co_argcount]
#### End introspection code
# Make missing Parameters
for pname in argnames:
if pname not in self._eqfactory.builders:
self._newParameter(pname, 0)
# Initialize and register
from diffpy.srfit.fitbase.calculator import Calculator
if isinstance(f, Calculator):
for pname in argnames:
par = self.get(pname)
f.addLiteral(par)
self._eqfactory.registerOperator(name, f)
else:
self._eqfactory.registerFunction(name, f, argnames)
# Now we can create the Equation and return it to the user.
eq = self._eqfactory.makeEquation(name)
return eq
def registerStringFunction(self, fstr, name, ns={}):
"""Register a string function.
This creates a function with this class that can be used within string
equations. The resulting equation does not require the arguments to be
passed in the function string, as this will be handled automatically.
fstr -- A string equation to register.
name -- The name of the function to be used in equations.
ns -- A dictionary of Parameters, indexed by name, that are
used in fstr, but not part of the FitRecipe (default
{}).
Raises ValueError if ns uses a name that is already used for another
managed object.
Raises ValueError if the function name is the name of another managed
object.
Returns the callable Equation object.
"""
# Build the equation instance.
eq = equationFromString(fstr, self._eqfactory, ns=ns, buildargs=True)
eq.name = name
# Register any new Parameters.
for par in self._eqfactory.newargs:
self._addParameter(par)
# Register the equation as a callable function.
argnames = eq.argdict.keys()
return self.registerFunction(eq, name, argnames)
def evaluateEquation(self, eqstr, ns={}):
"""Evaluate a string equation.
eqstr -- A string equation to evaluate. The equation is evaluated at
the current value of the registered Parameters.
ns -- A dictionary of Parameters, indexed by name, that are
used in fstr, but not part of the FitRecipe (default {}).
Raises ValueError if ns uses a name that is already used for a
variable.
"""
eq = equationFromString(eqstr, self._eqfactory, ns)
return eq()
def constrain(self, par, con, ns={}):
"""Constrain a parameter to an equation.
Note that only one constraint can exist on a Parameter at a time.
par -- The name of a Parameter or a Parameter to constrain.
con -- A string representation of the constraint equation or a
Parameter to constrain to. A constraint equation must
consist of numpy operators and "known" Parameters.
Parameters are known if they are in the ns argument, or if
they are managed by this object.
ns -- A dictionary of Parameters, indexed by name, that are used
in the parameter, but not part of this object (default {}).
Raises ValueError if ns uses a name that is already used for a
variable.
Raises ValueError if par is a string but not part of this object or in
ns.
Raises ValueError if par is marked as constant.
"""
if isinstance(par, basestring):
name = par
par = self.get(name)
if par is None:
par = ns.get(name)
if par is None:
raise ValueError("The parameter cannot be found")
if par.const:
raise ValueError("The parameter '%s' is constant" % par)
if isinstance(con, basestring):
eqstr = con
eq = equationFromString(con, self._eqfactory, ns)
else:
eq = Equation(root=con)
eqstr = con.name
eq.name = "_constraint_%s" % par.name
# Make and store the constraint
con = Constraint()
con.constrain(par, eq)
# Store the equation string so it can be shown later.
con.eqstr = eqstr
self._constraints[par] = con
# Our configuration changed
self._updateConfiguration()
return
def isConstrained(self, par):
"""Determine if a Parameter is constrained in this object.
par -- The name of a Parameter or a Parameter to check.
"""
if isinstance(par, basestring):
name = par
par = self.get(name)
return par in self._constraints
def unconstrain(self, *pars):
"""Unconstrain a Parameter.
This removes any constraints on a Parameter.
*pars -- The names of Parameters or Parameters to unconstrain.
Raises ValueError if the Parameter is not constrained.
"""
update = False
for par in pars:
if isinstance(par, basestring):
name = par
par = self.get(name)
if par is None:
raise ValueError("The parameter cannot be found")
if par in self._constraints:
self._constraints[par].unconstrain()
del self._constraints[par]
update = True
if update:
# Our configuration changed
self._updateConfiguration()
else:
raise ValueError("The parameter is not constrained")
return
def getConstrainedPars(self, recurse=False):
"""Get a list of constrained managed Parameters in this object.
recurse -- Recurse into managed objects and retrive their constrained
Parameters as well (default False).
"""
const = self._getConstraints(recurse)
return const.keys()
def clearConstraints(self, recurse=False):
"""Clear all constraints managed by this organizer.
recurse -- Recurse into managed objects and clear all constraints
found there as well.
This removes constraints that are held in this organizer, no matter
where the constrained parameters are from.
"""
if self._constraints:
self.unconstrain(*self._constraints)
if recurse:
f = lambda m: hasattr(m, "clearConstraints")
for m in ifilter(f, self._iterManaged()):
m.clearConstraints(recurse)
return
def restrain(self, res, lb=-inf, ub=inf, sig=1, scaled=False, ns={}):
"""Restrain an expression to specified bounds
res -- An equation string or Parameter to restrain.
lb -- The lower bound on the restraint evaluation (default -inf).
ub -- The lower bound on the restraint evaluation (default inf).
sig -- The uncertainty on the bounds (default 1).
scaled -- A flag indicating if the restraint is scaled (multiplied)
by the unrestrained point-average chi^2 (chi^2/numpoints)
(default False).
ns -- A dictionary of Parameters, indexed by name, that are used
in the equation string, but not part of the RecipeOrganizer
(default {}).
The penalty is calculated as
(max(0, lb - val, val - ub)/sig)**2
and val is the value of the calculated equation. This is multipled by
the average chi^2 if scaled is True.
Raises ValueError if ns uses a name that is already used for a
Parameter.
Raises ValueError if res depends on a Parameter that is not part of
the RecipeOrganizer and that is not defined in ns.
Returns the Restraint object for use with the 'unrestrain' method.
"""
if isinstance(res, basestring):
eqstr = res
eq = equationFromString(res, self._eqfactory, ns)
else:
eq = Equation(root=res)
eqstr = res.name
# Make and store the restraint
res = Restraint(eq, lb, ub, sig, scaled)
res.eqstr = eqstr
self.addRestraint(res)
return res
def addRestraint(self, res):
"""Add a Restraint instance to the RecipeOrganizer.
res -- A Restraint instance.
"""
self._restraints.add(res)
# Our configuration changed. Notify observers.
self._updateConfiguration()
return
def unrestrain(self, *ress):
"""Remove a Restraint from the RecipeOrganizer.
*ress -- Restraints returned from the 'restrain' method or added
with the 'addRestraint' method.
"""
update = False
restuple = tuple(self._restraints)
for res in ress:
if res in restuple:
self._restraints.remove(res)
update = True
if update:
# Our configuration changed
self._updateConfiguration()
return
def clearRestraints(self, recurse=False):
"""Clear all restraints.
recurse -- Recurse into managed objects and clear all restraints
found there as well.
"""
self.unrestrain(*self._restraints)
if recurse:
f = lambda m: hasattr(m, "clearRestraints")
for m in ifilter(f, self._iterManaged()):
m.clearRestraints(recurse)
return
def _getConstraints(self, recurse=True):
"""Get the constrained Parameters for this and managed sub-objects."""
constraints = {}
if recurse:
f = lambda m: hasattr(m, "_getConstraints")
for m in ifilter(f, self._iterManaged()):
constraints.update(m._getConstraints(recurse))
constraints.update(self._constraints)
return constraints
def _getRestraints(self, recurse=True):
"""Get the Restraints for this and embedded ParameterSets.
This returns a set of Restraint objects.
"""
restraints = set(self._restraints)
if recurse:
f = lambda m: hasattr(m, "_getRestraints")
for m in ifilter(f, self._iterManaged()):
restraints.update(m._getRestraints(recurse))
return restraints
def _validate(self):
"""Validate my state.
This performs RecipeContainer validations.
This validates contained Restraints and Constraints.
Raises AttributeError if validation fails.
"""
RecipeContainer._validate(self)
iterable = chain(iter(self._restraints), self._constraints.itervalues())
self._validateOthers(iterable)
return
# For printing the configured recipe to screen
def _formatManaged(self, indent=""):
"""Format fit hierarchy for showing.
Returns the lines of the formatted string in a list.
"""
dashedline = 79 * "-"
lines = []
formatstr = "%-20s %s"
lines.append((indent + self.name)[:79])
# Show parameters
if self._parameters:
lines.append((indent + dashedline)[:79])
items = self._parameters.items()
items.sort()
lines.extend((indent + formatstr % (n, p.value))[:79] for n, p in items)
indent += " "
for obj in self._iterManaged():
if hasattr(obj, "_formatManaged"):
tlines = obj._formatManaged(indent)
lines.append("")
lines.extend(tlines)
return lines
def _formatConstraints(self):
"""Format constraints for showing.
This collects constraints on all levels of the hierarchy and displays
them with respect to this level.
Returns the lines of the formatted string in a list.
"""
cdict = self._getConstraints()
# Find each constraint and format the equation
clines = []
for par, con in cdict.items():
loc = self._locateManagedObject(par)
if loc:
locstr = ".".join(o.name for o in loc)
clines.append("%s <-- %s" % (locstr, con.eqstr))
else:
clines.append("%s <-- %s" % (par.name, con.eqstr))
if clines:
clines.sort()
dashedline = 79 * "-"
clines.insert(0, dashedline)
clines.insert(0, "Constraints")
return clines
def _formatRestraints(self):
"""Format restraints for showing.
This collects restraints on all levels of the hierarchy and displays
them with respect to this level.
Returns the lines of the formatted string in a list.
"""
rset = self._getRestraints()
rlines = []
for res in rset:
line = "%s: lb = %f, ub = %f, sig = %f, scaled = %s" % (res.eqstr, res.lb, res.ub, res.sig, res.scaled)
rlines.append(line)
if rlines:
rlines.sort()
dashedline = 79 * "-"
rlines.insert(0, dashedline)
rlines.insert(0, "Restraints")
return rlines
def show(self):
"""Show the configuration on screen.
This will print a summary of all contained objects.
"""
# Show sub objects and their parameters
lines = []
tlines = self._formatManaged()
lines.extend(tlines)
# FIXME - parameter names in equations not particularly informative
# Show constraints
tlines = self._formatConstraints()
lines.append("")
lines.extend(tlines)
# FIXME - parameter names in equations not particularly informative
# Show restraints
tlines = self._formatRestraints()
lines.append("")
lines.extend(tlines)
print "\n".join(lines)
return
class RecipeOrganizer(_recipeorganizer_interface, RecipeContainer):
"""Extended base class for organizing pieces of a FitRecipe.
This class extends RecipeContainer by organizing constraints and
Restraints, as well as Equations that can be used in Constraint and
Restraint equations. These constraints and Restraints can be placed at any
level and a flattened list of them can be retrieved with the
_getConstraints and _getRestraints methods.
Attributes
name -- A name for this organizer. Names should be unique
within a RecipeOrganizer and should be valid attribute
names.
_calculators -- A managed dictionary of Calculators, indexed by name.
_parameters -- A managed OrderedDict of contained Parameters.
_constraints -- A dictionary of Constraints, indexed by the constrained
Parameter. Constraints can be added using the
'constrain' method.
_restraints -- A set of Restraints. Restraints can be added using the
'restrain' method.
_eqfactory -- A diffpy.srfit.equation.builder.EquationFactory
instance that is used create Equations from string.
Properties
names -- Variable names (read only). See getNames.
values -- Variable values (read only). See getValues.
Raises ValueError if the name is not a valid attribute identifier
"""
def __init__(self, name):
RecipeContainer.__init__(self, name)
self._restraints = set()
self._constraints = {}
self._eqfactory = EquationFactory()
self._calculators = {}
self._manage(self._calculators)
return
# Parameter management
def _newParameter(self, name, value, check=True):
"""Add a new Parameter to the container.
This creates a new Parameter and adds it to the container using the
_addParameter method.
Returns the Parameter.
"""
p = Parameter(name, value)
self._addParameter(p, check)
return p
def _addParameter(self, par, check=True):
"""Store a Parameter.
Parameters added in this way are registered with the _eqfactory.
par -- The Parameter to be stored.
check -- If True (default), a ValueError is raised a Parameter of
the specified name has already been inserted.
Raises ValueError if the Parameter has no name.
Raises ValueError if the Parameter has the same name as a contained
RecipeContainer.
"""
# Store the Parameter
RecipeContainer._addObject(self, par, self._parameters, check)
# Register the Parameter
self._eqfactory.registerArgument(par.name, par)
return
def _removeParameter(self, par):
"""Remove a parameter.
This de-registers the Parameter with the _eqfactory. The Parameter will
remain part of built equations.
Note that constraints and restraints involving the Parameter are not
modified.
Raises ValueError if par is not part of the RecipeOrganizer.
"""
self._removeObject(par, self._parameters)
self._eqfactory.deRegisterBuilder(par.name)
return
def registerCalculator(self, f, argnames=None):
"""Register a Calculator so it can be used within equation strings.
A Calculator is an elaborate function that can organize Parameters.
This creates a function with this class that can be used within string
equations. The resulting equation can be used in a string with
arguments like a function or without, in which case the values of the
Parameters created from argnames will be be used to compute the value.
f -- The Calculator to register.
argnames -- The names of the arguments to f (list or None).
If this is None, then the argument names will be
extracted from the function.
"""
self._eqfactory.registerOperator(f.name, f)
self._addObject(f, self._calculators)
# Register arguments of the calculator
if argnames is None:
func_code = f.__call__.im_func.func_code
argnames = list(func_code.co_varnames)
argnames = argnames[1:func_code.co_argcount]
for pname in argnames:
if pname not in self._eqfactory.builders:
par = self._newParameter(pname, 0)
else:
par = self.get(pname)
f.addLiteral(par)
# Now return an equation object
eq = self._eqfactory.makeEquation(f.name)
return eq
def registerFunction(self, f, name=None, argnames=None):
"""Register a function so it can be used within equation strings.
This creates a function with this class that can be used within string
equations. The resulting equation does not require the arguments to be
passed in the equation string, as this will be handled automatically.
f -- The callable to register. If this is an Equation
instance, then all that needs to be provied is a name.
name -- The name of the function to be used in equations. If
this is None (default), the method will try to
determine the name of the function automatically.
argnames -- The names of the arguments to f (list or None).
If this is None (default), then the argument names will
be extracted from the function.
Note that name and argnames can be extracted from regular python
functions (of type 'function'), bound class methods and callable
classes.
Raises TypeError if name or argnames cannot be automatically
extracted.
Raises TypeError if an automatically extracted name is '<lambda>'.
Raises ValueError if f is an Equation object and name is None.
Returns the callable Equation object.
"""
# If the function is an equation, we treat it specially. This is
# required so that the objects observed by the root get observed if the
# Equation is used within another equation. It is assumed that a plain
# function is not observable.
if isinstance(f, Equation):
if name is None:
m = "Equation must be given a name"
raise ValueError(m)
self._eqfactory.registerOperator(name, f)
return f
#### Introspection code
if name is None or argnames is None:
import inspect
func_code = None
# This will let us offset the argument list to eliminate 'self'
offset = 0
# check regular functions
if inspect.isfunction(f):
func_code = f.func_code
# check class method
elif inspect.ismethod(f):
func_code = f.im_func.func_code
offset = 1
# check functor
elif hasattr(f, "__call__") and hasattr(f.__call__, 'im_func'):
func_code = f.__call__.im_func.func_code
offset = 1
else:
m = "Cannot extract name or argnames"
raise ValueError(m)
# Extract the name
if name is None:
name = func_code.co_name
if name == '<lambda>':
m = "You must supply a name name for a lambda function"
raise ValueError(m)
# Extract the arguments
if argnames is None:
argnames = list(func_code.co_varnames)
argnames = argnames[offset:func_code.co_argcount]
#### End introspection code
# Make missing Parameters
for pname in argnames:
if pname not in self._eqfactory.builders:
self._newParameter(pname, 0)
# Initialize and register
from diffpy.srfit.fitbase.calculator import Calculator
if isinstance(f, Calculator):
for pname in argnames:
par = self.get(pname)
f.addLiteral(par)
self._eqfactory.registerOperator(name, f)
else:
self._eqfactory.registerFunction(name, f, argnames)
# Now we can create the Equation and return it to the user.
eq = self._eqfactory.makeEquation(name)
return eq
def registerStringFunction(self, fstr, name, ns={}):
"""Register a string function.
This creates a function with this class that can be used within string
equations. The resulting equation does not require the arguments to be
passed in the function string, as this will be handled automatically.
fstr -- A string equation to register.
name -- The name of the function to be used in equations.
ns -- A dictionary of Parameters, indexed by name, that are
used in fstr, but not part of the FitRecipe (default
{}).
Raises ValueError if ns uses a name that is already used for another
managed object.
Raises ValueError if the function name is the name of another managed
object.
Returns the callable Equation object.
"""
# Build the equation instance.
eq = equationFromString(fstr, self._eqfactory, ns=ns, buildargs=True)
eq.name = name
# Register any new Parameters.
for par in self._eqfactory.newargs:
self._addParameter(par)
# Register the equation as a callable function.
argnames = eq.argdict.keys()
return self.registerFunction(eq, name, argnames)
def evaluateEquation(self, eqstr, ns={}):
"""Evaluate a string equation.
eqstr -- A string equation to evaluate. The equation is evaluated at
the current value of the registered Parameters.
ns -- A dictionary of Parameters, indexed by name, that are
used in fstr, but not part of the FitRecipe (default {}).
Raises ValueError if ns uses a name that is already used for a
variable.
"""
eq = equationFromString(eqstr, self._eqfactory, ns)
return eq()
def constrain(self, par, con, ns={}):
"""Constrain a parameter to an equation.
Note that only one constraint can exist on a Parameter at a time.
par -- The name of a Parameter or a Parameter to constrain.
con -- A string representation of the constraint equation or a
Parameter to constrain to. A constraint equation must
consist of numpy operators and "known" Parameters.
Parameters are known if they are in the ns argument, or if
they are managed by this object.
ns -- A dictionary of Parameters, indexed by name, that are used
in the parameter, but not part of this object (default {}).
Raises ValueError if ns uses a name that is already used for a
variable.
Raises ValueError if par is a string but not part of this object or in
ns.
Raises ValueError if par is marked as constant.
"""
if isinstance(par, basestring):
name = par
par = self.get(name)
if par is None:
par = ns.get(name)
if par is None:
raise ValueError("The parameter cannot be found")
if par.const:
raise ValueError("The parameter '%s' is constant" % par)
if isinstance(con, basestring):
eqstr = con
eq = equationFromString(con, self._eqfactory, ns)
else:
eq = Equation(root=con)
eqstr = con.name
eq.name = "_constraint_%s" % par.name
# Make and store the constraint
con = Constraint()
con.constrain(par, eq)
# Store the equation string so it can be shown later.
con.eqstr = eqstr
self._constraints[par] = con
# Our configuration changed
self._updateConfiguration()
return
def isConstrained(self, par):
"""Determine if a Parameter is constrained in this object.
par -- The name of a Parameter or a Parameter to check.
"""
if isinstance(par, basestring):
name = par
par = self.get(name)
return (par in self._constraints)
def unconstrain(self, *pars):
"""Unconstrain a Parameter.
This removes any constraints on a Parameter.
*pars -- The names of Parameters or Parameters to unconstrain.
Raises ValueError if the Parameter is not constrained.
"""
update = False
for par in pars:
if isinstance(par, basestring):
name = par
par = self.get(name)
if par is None:
raise ValueError("The parameter cannot be found")
if par in self._constraints:
self._constraints[par].unconstrain()
del self._constraints[par]
update = True
if update:
# Our configuration changed
self._updateConfiguration()
else:
raise ValueError("The parameter is not constrained")
return
def getConstrainedPars(self, recurse=False):
"""Get a list of constrained managed Parameters in this object.
recurse -- Recurse into managed objects and retrive their constrained
Parameters as well (default False).
"""
const = self._getConstraints(recurse)
return const.keys()
def clearConstraints(self, recurse=False):
"""Clear all constraints managed by this organizer.
recurse -- Recurse into managed objects and clear all constraints
found there as well.
This removes constraints that are held in this organizer, no matter
where the constrained parameters are from.
"""
if self._constraints:
self.unconstrain(*self._constraints)
if recurse:
f = lambda m: hasattr(m, "clearConstraints")
for m in ifilter(f, self._iterManaged()):
m.clearConstraints(recurse)
return
def restrain(self, res, lb=-inf, ub=inf, sig=1, scaled=False, ns={}):
"""Restrain an expression to specified bounds
res -- An equation string or Parameter to restrain.
lb -- The lower bound on the restraint evaluation (default -inf).
ub -- The lower bound on the restraint evaluation (default inf).
sig -- The uncertainty on the bounds (default 1).
scaled -- A flag indicating if the restraint is scaled (multiplied)
by the unrestrained point-average chi^2 (chi^2/numpoints)
(default False).
ns -- A dictionary of Parameters, indexed by name, that are used
in the equation string, but not part of the RecipeOrganizer
(default {}).
The penalty is calculated as
(max(0, lb - val, val - ub)/sig)**2
and val is the value of the calculated equation. This is multipled by
the average chi^2 if scaled is True.
Raises ValueError if ns uses a name that is already used for a
Parameter.
Raises ValueError if res depends on a Parameter that is not part of
the RecipeOrganizer and that is not defined in ns.
Returns the Restraint object for use with the 'unrestrain' method.
"""
if isinstance(res, basestring):
eqstr = res
eq = equationFromString(res, self._eqfactory, ns)
else:
eq = Equation(root=res)
eqstr = res.name
# Make and store the restraint
res = Restraint(eq, lb, ub, sig, scaled)
res.eqstr = eqstr
self.addRestraint(res)
return res
def addRestraint(self, res):
"""Add a Restraint instance to the RecipeOrganizer.
res -- A Restraint instance.
"""
self._restraints.add(res)
# Our configuration changed. Notify observers.
self._updateConfiguration()
return
def unrestrain(self, *ress):
"""Remove a Restraint from the RecipeOrganizer.
*ress -- Restraints returned from the 'restrain' method or added
with the 'addRestraint' method.
"""
update = False
restuple = tuple(self._restraints)
for res in ress:
if res in restuple:
self._restraints.remove(res)
update = True
if update:
# Our configuration changed
self._updateConfiguration()
return
def clearRestraints(self, recurse=False):
"""Clear all restraints.
recurse -- Recurse into managed objects and clear all restraints
found there as well.
"""
self.unrestrain(*self._restraints)
if recurse:
f = lambda m: hasattr(m, "clearRestraints")
for m in ifilter(f, self._iterManaged()):
m.clearRestraints(recurse)
return
def _getConstraints(self, recurse=True):
"""Get the constrained Parameters for this and managed sub-objects."""
constraints = {}
if recurse:
f = lambda m: hasattr(m, "_getConstraints")
for m in ifilter(f, self._iterManaged()):
constraints.update(m._getConstraints(recurse))
constraints.update(self._constraints)
return constraints
def _getRestraints(self, recurse=True):
"""Get the Restraints for this and embedded ParameterSets.
This returns a set of Restraint objects.
"""
restraints = set(self._restraints)
if recurse:
f = lambda m: hasattr(m, "_getRestraints")
for m in ifilter(f, self._iterManaged()):
restraints.update(m._getRestraints(recurse))
return restraints
def _validate(self):
"""Validate my state.
This performs RecipeContainer validations.
This validates contained Restraints and Constraints.
Raises AttributeError if validation fails.
"""
RecipeContainer._validate(self)
iterable = chain(iter(self._restraints),
self._constraints.itervalues())
self._validateOthers(iterable)
return
# For printing the configured recipe to screen
def _formatManaged(self, indent=""):
"""Format fit hierarchy for showing.
Returns the lines of the formatted string in a list.
"""
dashedline = 79 * '-'
lines = []
formatstr = "%-20s %s"
lines.append((indent + self.name)[:79])
# Show parameters
if self._parameters:
lines.append((indent + dashedline)[:79])
items = self._parameters.items()
items.sort()
lines.extend(
(indent + formatstr % (n, p.value))[:79] for n, p in items)
indent += " "
for obj in self._iterManaged():
if hasattr(obj, "_formatManaged"):
tlines = obj._formatManaged(indent)
lines.append("")
lines.extend(tlines)
return lines
def _formatConstraints(self):
"""Format constraints for showing.
This collects constraints on all levels of the hierarchy and displays
them with respect to this level.
Returns the lines of the formatted string in a list.
"""
cdict = self._getConstraints()
# Find each constraint and format the equation
clines = []
for par, con in cdict.items():
loc = self._locateManagedObject(par)
if loc:
locstr = ".".join(o.name for o in loc)
clines.append("%s <-- %s" % (locstr, con.eqstr))
else:
clines.append("%s <-- %s" % (par.name, con.eqstr))
if clines:
clines.sort()
dashedline = 79 * '-'
clines.insert(0, dashedline)
clines.insert(0, "Constraints")
return clines
def _formatRestraints(self):
"""Format restraints for showing.
This collects restraints on all levels of the hierarchy and displays
them with respect to this level.
Returns the lines of the formatted string in a list.
"""
rset = self._getRestraints()
rlines = []
for res in rset:
line = "%s: lb = %f, ub = %f, sig = %f, scaled = %s"%\
(res.eqstr, res.lb, res.ub, res.sig, res.scaled)
rlines.append(line)
if rlines:
rlines.sort()
dashedline = 79 * '-'
rlines.insert(0, dashedline)
rlines.insert(0, "Restraints")
return rlines
def show(self):
"""Show the configuration on screen.
This will print a summary of all contained objects.
"""
# Show sub objects and their parameters
lines = []
tlines = self._formatManaged()
lines.extend(tlines)
# FIXME - parameter names in equations not particularly informative
# Show constraints
tlines = self._formatConstraints()
lines.append("")
lines.extend(tlines)
# FIXME - parameter names in equations not particularly informative
# Show restraints
tlines = self._formatRestraints()
lines.append("")
lines.extend(tlines)
print "\n".join(lines)
return
def weightedTest(mutate = 2):
"""Show the benefits of a properly balanced equation tree."""
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 10, 0.01)
qsig = 0.01
sigma = 0.003
eqstr = """\
b1 + b2*x + b3*x**2 + b4*x**3 + b5*x**4 + b6*x**5 + b7*x**6 + b8*x**7\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
#scale = visitors.NodeWeigher()
#eq.root.identify(scale)
#print scale.output
from numpy import polyval
def f(b1, b2, b3, b4, b5, b6, b7, b8):
return polyval([b8, b7, b6, b5,b4,b3,b2,b1],x)
tnpy = 0
teq = 0
import random
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [0.1]*numargs
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
#print args
# Time the different functions with these arguments
teq += timeFunction(eq, *args)
tnpy += timeFunction(f, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "numpy: ", tnpy/numcalls
print "equation: ", teq/numcalls
print "ratio: ", teq/tnpy
return
def speedTest3(mutate = 2):
"""Test wrt sympy.
Results - sympy is 10 to 24 times faster without using arrays (ouch!).
- diffpy.srfit.equation is slightly slower when using arrays, but
not considerably worse than versus numpy alone.
"""
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 20, 0.05)
qsig = 0.01
sigma = 0.003
eqstr = """\
A0*exp(-(x*qsig)**2)*(exp(-((x-1.0)/sigma1)**2)+exp(-((x-2.0)/sigma2)**2))\
+ polyval(list(b1, b2, b3, b4, b5, b6, b7, b8), x)\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.qsig.setValue(qsig)
eq.sigma1.setValue(sigma)
eq.sigma2.setValue(sigma)
eq.A0.setValue(1.0)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
from sympy import var, exp, lambdify
from numpy import polyval
A0, qsig, sigma1, sigma2, b1, b2, b3, b4, b5, b6, b7, b8, xx = vars = var("A0 qsig sigma1 sigma2 b1 b2 b3 b4 b5 b6 b7 b8 xx")
f = lambdify(vars, A0*exp(-(xx*qsig)**2)*(exp(-((xx-1.0)/sigma1)**2)+exp(-((xx-2.0)/sigma2)**2)) + polyval([b1, b2, b3, b4, b5, b6, b7, b8], xx), "numpy")
tnpy = 0
teq = 0
import random
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [1.0]*(len(eq.args))
args.append(x)
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
# Time the different functions with these arguments
teq += timeFunction(eq, *(args[:-1]))
tnpy += timeFunction(f, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "sympy: ", tnpy/numcalls
print "equation: ", teq/numcalls
print "ratio: ", teq/tnpy
return
def speedTest2(mutate = 2):
from diffpy.srfit.equation.builder import EquationFactory
factory = EquationFactory()
x = numpy.arange(0, 20, 0.05)
qsig = 0.01
sigma = 0.003
eqstr = """\
A0*exp(-(x*qsig)**2)*(exp(-((x-1.0)/sigma1)**2)+exp(-((x-2.0)/sigma2)**2))\
+ polyval(list(b1, b2, b3, b4, b5, b6, b7, b8), x)\
"""
factory.registerConstant("x", x)
eq = factory.makeEquation(eqstr)
eq.qsig.setValue(qsig)
eq.sigma1.setValue(sigma)
eq.sigma2.setValue(sigma)
eq.A0.setValue(1.0)
eq.b1.setValue(0)
eq.b2.setValue(1)
eq.b3.setValue(2.0)
eq.b4.setValue(2.0)
eq.b5.setValue(2.0)
eq.b6.setValue(2.0)
eq.b7.setValue(2.0)
eq.b8.setValue(2.0)
from numpy import exp
from numpy import polyval
def f(A0, qsig, sigma1, sigma2, b1, b2, b3, b4, b5, b6, b7, b8):
return A0*exp(-(x*qsig)**2)*(exp(-((x-1.0)/sigma1)**2)+exp(-((x-2.0)/sigma2)**2)) + polyval([b8, b7, b6, b5,b4,b3,b2,b1],x)
tnpy = 0
teq = 0
import random
# Randomly change variables
numargs = len(eq.args)
choices = range(numargs)
args = [0.0]*(len(eq.args))
# The call-loop
random.seed()
numcalls = 1000
for _i in xrange(numcalls):
# Mutate values
n = mutate
if n == 0:
n = random.choice(choices)
c = choices[:]
for _j in xrange(n):
idx = random.choice(c)
c.remove(idx)
args[idx] = random.random()
# Time the different functions with these arguments
tnpy += timeFunction(f, *args)
teq += timeFunction(eq, *args)
print "Average call time (%i calls, %i mutations/call):" % (numcalls,
mutate)
print "numpy: ", tnpy/numcalls
print "equation: ", teq/numcalls
print "ratio: ", teq/tnpy
return