Lambdify
This module provides convenient functions to transform diofant expressions to lambda functions which can be used to calculate numerical values very fast.
- diofant.utilities.lambdify.implemented_function(symfunc, implementation)[source]
Add numerical
implementation
to functionsymfunc
.symfunc
can be anUndefinedFunction
instance, or a name string. In the latter case we create anUndefinedFunction
instance with that name.Be aware that this is a quick workaround, not a general method to create special symbolic functions. If you want to create a symbolic function to be used by all the machinery of Diofant you should subclass the
Function
class.- Parameters:
symfunc (
str
orUndefinedFunction
instance) – Ifstr
, then create newUndefinedFunction
with this as name. If \(symfunc\) is a diofant function, attach implementation to it.implementation (callable) – numerical implementation to be called by
evalf()
orlambdify
- Returns:
afunc (diofant.FunctionClass instance) – function with attached implementation
Examples
>>> f = implemented_function(Function('f'), lambda x: x+1) >>> lam_f = lambdify(x, f(x)) >>> lam_f(4) 5
- diofant.utilities.lambdify.lambdastr(args, expr, printer=None, dummify=False)[source]
Returns a string that can be evaluated to a lambda function.
Examples
>>> lambdastr(x, x**2) 'lambda x: (x**2)' >>> lambdastr((x, y, z), [z, y, x]) 'lambda x,y,z: ([z, y, x])'
Although tuples may not appear as arguments to lambda in Python 3, lambdastr will create a lambda function that will unpack the original arguments so that nested arguments can be handled:
>>> lambdastr((x, (y, z)), x + y) 'lambda _0,_1: (lambda x,y,z: (x + y))(*list(__flatten_args__([_0,_1])))'
- diofant.utilities.lambdify.lambdify(args, expr, modules=None, printer=None, use_imps=True, dummify=True)[source]
Returns a lambda function for fast calculation of numerical values.
If not specified differently by the user,
modules
defaults to["numpy"]
if NumPy is installed, and["math", "mpmath", "sympy"]
if it isn’t, that is, Diofant functions are replaced as far as possible by eithernumpy
functions if available, and Python’s standard librarymath
, ormpmath
functions otherwise. To change this behavior, the “modules” argument can be used. It accepts:the strings “math”, “mpmath”, “numpy”, “diofant”
any modules (e.g. math)
dictionaries that map names of diofant functions to arbitrary functions
lists that contain a mix of the arguments above, with higher priority given to entries appearing first.
The default behavior is to substitute all arguments in the provided expression with dummy symbols. This allows for applied functions (e.g. f(t)) to be supplied as arguments. Call the function with dummify=False if dummy substitution is unwanted (and \(args\) is not a string). If you want to view the lambdified function or provide “diofant” as the module, you should probably set dummify=False.
In previous releases
lambdify
replacedMatrix
withnumpy.matrix
by default. As of release 0.7.7numpy.array
is the default. To get the old default behavior you must pass in[{'ImmutableMatrix': numpy.matrix}, 'numpy']
to themodules
kwarg.Use one of the provided modules:
>>> f = lambdify(x, sin(x), 'math')
- Attention: Functions that are not in the math module will throw a name
error when the lambda function is evaluated! So this would be better:
>>> f = lambdify(x, sin(x)*gamma(x), ('math', 'mpmath', 'diofant'))
Use some other module:
>>> import numpy >>> f = lambdify((x, y), tan(x*y), numpy)
- Attention: There are naming differences between numpy and diofant. So if
you simply take the numpy module, e.g. diofant.atan will not be translated to numpy.arctan. Use the modified module instead by passing the string “numpy”:
>>> f = lambdify((x, y), tan(x*y), 'numpy') >>> f(1, 2) -2.18503986326 >>> from numpy import array >>> f(array([1, 2, 3]), array([2, 3, 5])) [-2.18503986 -0.29100619 -0.8559934 ]
Use a dictionary defining custom functions:
>>> def my_cool_function(x): ... return f'sin({x}) is cool' >>> myfuncs = {'sin': my_cool_function} >>> f = lambdify(x, sin(x), myfuncs) >>> f(1) 'sin(1) is cool'
Examples
>>> from diofant.abc import w
>>> f = lambdify(x, x**2) >>> f(2) 4 >>> f = lambdify((x, y, z), [z, y, x]) >>> f(1, 2, 3) [3, 2, 1] >>> f = lambdify(x, sqrt(x)) >>> f(4) 2.0 >>> f = lambdify((x, y), sin(x*y)**2) >>> f(0, 5) 0.0 >>> row = lambdify((x, y), Matrix((x, x + y)).T, modules='diofant') >>> row(1, 2) Matrix([[1, 3]])
Tuple arguments are handled and the lambdified function should be called with the same type of arguments as were used to create the function.:
>>> f = lambdify((x, (y, z)), x + y) >>> f(1, (2, 4)) 3
A more robust way of handling this is to always work with flattened arguments:
>>> args = w, (x, (y, z)) >>> vals = 1, (2, (3, 4)) >>> f = lambdify(flatten(args), w + x + y + z) >>> f(*flatten(vals)) 10
Functions present in \(expr\) can also carry their own numerical implementations, in a callable attached to the
_imp_
attribute. Usually you attach this using theimplemented_function
factory:>>> f = implemented_function(Function('f'), lambda x: x+1) >>> func = lambdify(x, f(x)) >>> func(4) 5
lambdify
always prefers_imp_
implementations to implementations in other namespaces, unless theuse_imps
input parameter is False.