I need to know how transfer string input into executable function.
For example - user write string 'x*Sin(x**2)' and then programm takes it as function, can calculate a value for given x, can plot derivation of this function etc. I've read that there is module called scitools.stringfunction, but as far as I know this module is not callable in python-3.
Any ideas how to make it?
For Python 2.X
f = lambda x: input() # the user inputs: x**2 + 1
y = f(3)
print y # outputs: 10
For Python 3.X
f = lambda x: eval(input())
y = f(5)
print y
Just make sure to import the required mathematical functions. And make sure the user inputs a valid Python arithmetic expression.
using sympy you could do something like this:
from sympy import var
from sympy import sympify
x = var('x') # the possible variable names must be known beforehand...
user_input = 'x * sin(x**2)'
expr = sympify(user_input)
res = expr.subs(x, 3.14)
print(res) # -1.322...
if you want to turn the user input into a function you can call you could to this:
from sympy.utilities.lambdify import lambdify
f = lambdify(x, expr)
# f(3.14) -> -1.322...
sympy can do sybolic calculations (including derivatives); if you want to make plots i strongly suggest matplotlib.
the advantage of using a math library opposed to eval is that you do not need to sanitize the user input (against malicious code).
(deleted this thanks to a comment from ejm).
Related
I was wondering if is there is a way to define a function that is a derivative of a function. I'm new to python so I don't no much, I tired looking up stuff that might be similar but nothing has worked so far. This is what I have for my code right now.
import sympy as sp
import math
x = sp.Symbol('x')
W = 15 #kN/m
E = 70 # Gpa
I = 52.9*10**(-6) #m**4
L = 3 #m
e = 0.01
xi = 1.8
y = 9
def f(x):
return ( ( y*3*(math.pi**4)*E*I/(W*L) ) - ( 48*(L**3)*math.cos(math.pi*x/(2*L)) ) + ( 48*(L**3) ) + ( (math.pi**3)*(x**3) ) )/(3*L*(math.pi**3))**(1/2)
def derv(f,x):
return sp.diff(f)
print (derv(f,x))
Also, I don't understand whatx = sp.Symbol('x') does, so if someone could explain that, that would be awesome.
Any help is appreciated.
You are conflating two different things: python functions like f and math functions, which you can express with sympy like y = π * x/3. f is a python function that returns a sympy expression. sympy lets you stay in the world of symbolic math functions by defining variables like x = sp.Symbol('x') So calling f() produces a symbolic math function like:
You can use sympy to find the derivative of the symbolic function returned by f() but you need to define it with the sympy versions of the cos() function (and sp.pi if you want to keep it symbolic).
For example:
import sympy as sp
x = sp.Symbol('x')
W = 15 #kN/m
E = 70 # Gpa
I = 52.9*10**(-6) #m**4
L = 3 #m
e = 0.01
xi = 1.8
y = 9
def f(x):
return ( ( y*3*(sp.pi**4)*E*I/(W*L) ) - ( 48*(L**3)*sp.cos(sp.pi*x/(2*L)) ) + ( 48*(L**3) ) + ( (sp.pi**3)*(x**3) ) )/(3*L*(sp.pi**3))**(1/2)
def derv(f,x):
return sp.diff(f(x)) # pass the result of f() which is a sympy function
derv(f,x)
You've programmed the function. it appears to be a simple function of two independent variables x and y.
Could be that x = sp.Symbol('x') is how SymPy defines the independent variable x. I don't know if you need one or another one for y.
You know enough about calculus to know that you need a derivative. Do you know how to differentiate a function of a single independent variable? It helps to know the answer before you start coding.
y*3*(math.pi**4)*E*I/(W*L) ) - ( 48*(L**3)*math.cos(math.pi*x/(2*L)) ) + ( 48*(L**3) ) + ( (math.pi**3)*(x**3) ) )/(3*L*(math.pi**3))**(1/2)
Looks simple.
There's only one term with y in it. The partial derivative w.r.t. y leaves you with 3*(math.pi**4)*E*I/(W*L) )
There's only one term with Cx**3 in it. That's easy to differentiate: 3C*x**2.
What's so hard? What's the problem?
In traditional programming, each function you write is translated to a series of commands that are then sent to the CPU and the result of the calculation is returned. Therefore, symbolic manipulation, like what we humans do with algebra and calculus, doesn't make any sense to the computer. Sympy gets around this by overriding Python's normal arithmetic operators, allowing you to do generate algebraic functions that can be manipulated similarly to how we humans do math. That's what sp.Symbols('x') is doing: providing you with a symbolic variable you can work with (you're also naming it in sympy).
If you want to evaluate your derivative, simply call evalf with the numerical value you want to assign to x.
I am trying to use the symbolic libraries of the python Symp. I am getting lots of errors. How to overcome this. every time I don't want to type sym.symobls for defining some thing new.
from sympy import *
from math import *
W1, W2, W3,z1, z2, b, a,g,l = symbols('W1 W2 W3 z1 z2 b a g l')
l = b**2(g/sqrt(a));
#Beam Functions
W1 = simplify(c1*cos(b*x) + c2*sin(b*x) + c3*cosh(b*x) + c4*sinh(b*x));
The expression l = b**2(g/sqrt(a)) isn't valid. You need e.g. a * between the 2 and the opening bracket. Also note that after the assignment, l isn't a symbol anymore, but a symbolic expression.
You can avoid declaring many variables by using sympify(). That function gets a string as input and creates symbolic variables on the fly. With sympify a lot of standard functions also get their correct symbolic version.
As mentioned in the comments, from sympy import * can be problematic, especially if you also work with other libraries. For convenience, a lot of examples in the docs do use import *, but only for short programs which don't use other libraries.
Here is a simple standalone example which assigns a symbolic expression to l and shows the internal representation (note that the expression is placed into quotes):
from sympy import sympify, srepr
l = sympify("b**2*(g/sqrt(a))")
print(srepr(l))
W1 = sympify("simplify(c1*cos(b*x) + c2*sin(b*x) + c3*cosh(b*x) + c4*sinh(b*x))")
print(srepr(W1))
Output:
Mul(Pow(Symbol('a'), Rational(-1, 2)), Pow(Symbol('b'), Integer(2)), Symbol('g'))
Add(Mul(Symbol('c1'), cos(Mul(Symbol('b'), Symbol('x')))), Mul(Symbol('c2'), sin(Mul(Symbol('b'), Symbol('x')))), Mul(Symbol('c3'), cosh(Mul(Symbol('b'), Symbol('x')))), Mul(Symbol('c4'), sinh(Mul(Symbol('b'), Symbol('x')))))
Often, routines will allow string input so you can just refer to variables created automatically through sympifying an expression with a string:
>>> from sympy import S
>>> S('x')
x
>>> _.subs('x',42)
42
>>> S('2*x').coeff('x')
2
If all you are doing is working with single letter symbols and SymPy functions (and no other libraries) you can (and this is how I always start my sessions):
>>> from sympy.abc import *
>>> from sympy import *
I put the second import there so I get S as the shortcut to sympify rather than as symbol S.
I'm writing a program which needs a user input for an polynomial function of x. I'm using Tkinter and python 2.5.
I have a parser method which so far takes the inputted equation and splits it into terms without dropping the signs.
I want to take each term and parse it to get a tuple of the (coefficient, degree). For example, -2x^3 returns (-2,3). I can then add these to an array and manipulate them accordingly in the program.
Is there a way or standard module that can do this?
Here is the beginning of the parse method.
def parse(a):
termnum=[]
terms=[]
hi=[]
num1=0
num=0
f=list(a)
count=0
negative=False
coef=0.0
deg=0.0
codeg=[]
for item in f:
if (item=='-' or item=='+') and count!=0:
termnum.append(count)
count+=1
for item in termnum:
num1=num
num=item
current=''
while num1<num:
current=current+f[num1]
num1+=1
terms.append(current)
num1=num
num=len(f)
current=''
while num1<num:
current=current+f[num1]
num1+=1
terms.append(current)
print terms
parse('-x^2+3x+2x^3-x')
Thanks!
P.S I don't want to use external packages.
you can use regular expressions,
import re
test = '-x^2+3x+2x^3-x'
for m in re.finditer( r'(-{0,1}\d*)x\^{0,1}(-{0,1}\d*)', test ):
coef, expn = list( map( lambda x: x if x != '' and x != '-' else x + '1' ,
m.groups( ) ))
print ( 'coef:{}, exp:{}'.format( coef, expn ))
output:
coef:-1, exp:2
coef:3, exp:1
coef:2, exp:3
coef:-1, exp:1
Look for "recursive descent parser". It's the canonical method for analysis of strings where some operator precedence is involved.
It looks like you're implementing something that already exists, in python and other math languages. See for example:
http://www.gnu.org/software/octave/doc/interpreter/Solvers.html
http://stat.ethz.ch/R-manual/R-devel/library/base/html/solve.html
I wrote a function in Python 2.7:
# Python #
def function_py(par):
#something happens
return(value)
and I want to use this function as an argument for another function in R. More precisely, I want to perform to compute the Sobol' indices using the following function:
# R #
library('sensitivity')
sobol(function_py_translated, X1,X2)
where function_py_translated would b the R equivalent of function_py.
I'm trying to use the rpy2 module, and for a simple function, I could make a working case:
import rpy2.rinterface as ri
import rpy2.robjects.numpy2ri
sensitivity = importr('sensitivity')
radd = ri.baseenv.get('+')
def costfun(X):
a = X[0]
b = X[1]
return(radd(a,b))
costfunr=ri.rternalize(costfun)
X1 = robjects.r('data.frame(matrix(rnorm(2*1000), nrow = 1000))')
X2 = robjects.r('data.frame(matrix(rnorm(2*1000), nrow = 1000))')
sobinde = sensitivity.sobol(costfunr,X1,X2)
print(sobinde.__getitem__(11))
The main problem is that I had to redefine the "+". Is there a way to work around this ? Being able to pass an arbitrary function without prior transformation ? The function I want to analyze is much more complicated.
Thank you very much for your time
I'm writing a program to calculate the volume of a solid of rotation. The first step of this is to calculate an integral. I'm using scipy.integrate for this, but I can't figure out the best way to have a equation (like x=x**2 input at the command line. I was originally planning on adding an argument 'with respect to: x|y' and then taking the function as a lambda. Unfortunately, argparse won't take lambda as an argument type, and trying to use a string to construct a lambda (f = lambda x: args.equation) just returns a string (understandably really).
Here's what I've got so far:
import sys
import argparse
import math
from scipy import integrate
parser = argparse.ArgumentParser(description='Find the volume of the solid of rotation defined')
parser.add_argument('equation', help='continous function')
parser.add_argument('a', type=float, help='bound \'a\'')
parser.add_argument('b', type=float, help='bound \'b\'')
parser.add_argument('-axis', metavar='x|y', help='axis of revolution')
args = parser.parse_args()
def volume(func, a, b, axis=None):
integral = integrate.quad(func, a, b)
return scipy.py * integral
print volume(args.equation, args.a, args.b)
Any advice will be appreciated
thanks
If there are absolutely no concerns about security risks from letting the user run arbitrary Python code, then you can use eval to create a callable object:
volume(eval('lambda x: %s' % args.equation), args.a, args.b)
You should be able to use eval() on the string you get from your arguments:
>>> f = eval("lambda x: x**2")
>>> f(5)
25