I want print a polynomial equation for the given data. I am using this line of code, however I am not sure this the correct way to get the polynomial equation for the given data
fit2 = numpy.polyfit(temp[0][0],temp[0][1],deg=2)
y1=numpy.poly1d(fit2)
Please advise
Sympy has some nice features do that simply:
from sympy import Symbol,expand
fit2 = numpy.polyfit(temp[0][0],temp[0][1],deg=2)
y1=numpy.poly1d(fit2)
x=Symbol('x')
print(expand(y1(x)))
for:
-2.6666666666668*x**3 + 41.0000000000018*x**2 - 195.333333333342*x + 323.000000000013
Related
I'm trying to compose two functions and I get a bizzare result
'''
#!/usr/bin/python
from sympy import *
init_printing(use_unicode=True)
x= symbols('x')
f = x/(x+1);
g = x/(x+2);
print(compose(f,g))
This shows : x/((x + 1)*(x + 2))
Should be x/(2x+2)
I don't get it. Does anyone has an idea?
Thanks
Despite being available in the top-level sympy namespace under the plain name compose, sympy.compose doesn't actually do general function composition.
sympy.compose is actually sympy.polys.polytools.compose. It's actually a function for polynomial composition. When you try to compose x/(x+1) and x/(x+2), it ends up interpreting these inputs as multivariate polynomials in 3 variables, x, 1/(x+1), and 1/(x+2), and the results are total nonsense.
I am using Sympy to integrate a Sympy Matrix whose components depend on variables (x,y). Integrating with respect to a single variable x (or y) works, and returns the expected Matrix whose components are the integrals of the components of the original vector.
import sympy as sp
from sympy.abc import x,y
V = sp.Matrix(4,1,[1,x,y,x*y])
display(V)
# This works
I = sp.integrate(V,(x,0,1))
display(I)
Ultimately, I would like a double integral. I can accomplish this with the following
Ix = sp.integrate(V,(x,0,1))
I = sp.integrate(Ix,(y,0,1))
display(I)
My question is why the following does not seem to work.
I = sp.integrate(V,(x,0,1),(y,0,1))
The error I get is :
ValueError: Invalid limits given: (((x, 0, 1), (y, 0, 1)),)
Is this a bug? Or am I using the wrong syntax for the double integral with a Matrix type? This syntax works on components of the Matrix, i.e.
# This works
I3 = sp.integrate(V[3,0],(x,0,1),(y,0,1))
Thanks for confirming that this was a bug in SymPy. This is now fixed in SymPy. See https://github.com/sympy/sympy/pull/23277.
The other suggestion - using
I = V.integrate((x,0,1),(y,0,1))
may even be a nicer solution.
Given a symbol s, which ultimately will be an Array, I want to define the following expression
A = Array([-s[1]/2, s[0]/2])
but I'd like A to be evaluated only when I compute some other expressions containing it, because s changes over time. I tried
A = UnevaluatedExpr(Array([-s[1]/2,s[0]/2]))
but I got the error TypeError: 'Symbol' object is not subscriptable, which make me think that some evaluation is performed on s.
Thanks for your patience, I'm just learning Sympy and I'm used to Maxima where this kind of construct is straightforward. To be more precise, with Maxima the full working code I'm trying to translate into Sympy is (in Maxima everything is a symbol, colon is the assignment operator, ev forces evaluation with custom values, the dot before diff is the vector scalar product):
A: [-s[2],s[1]]/2; /* define A in terms of subscripted symbols */
P1: [x1,y1];
P2: [x2,y2];
segment: P1+t*(P2-P1); /* --> [t*(x2-x1)+x1,t*(y2-y1)+y1] */
factor(integrate(ev(A,s=segment).diff(segment,t),t,0,1)); /* integrates the scalar product of A evaluated over segment and the derivative of segment */
Follow up
Thanks to Oscar answer I was able to come up with a working Sympy translation of the above Maxima code (improvements are welcomed!):
from sympy import *
def dotprod(*vectors): # scalar product, is there a built in better way?
return sum(Mul(*x) for x in zip(*vectors))
s = IndexedBase('s')
A = Array([-s[1]/2,s[0]/2])
t,x1,y1,x2,y2 = symbols('t x1 y1 x2 y2')
P1 = Array([x1,y1])
P2 = Array([x2,y2])
segment = P1 + t * (P2-P1)
dotprod(A.subs(s,segment),segment.diff(t)).integrate((t,0,1)).factor()
Apart from the IndexedBase magic the structure of the code in Maxima and Sympy is very similar.
I'm not sure I understand what you want. It's possible that your problem is better approached in a different way rather than using Array. In any case a direct answer to your question is that you can use IndexedBase to make a subscriptable symbol:
In [1]: s = IndexedBase('s')
In [2]: A = Array([-s[1]/2, s[0]/2])
In [3]: A
Out[3]:
⎡-s[1] s[0]⎤
⎢────── ────⎥
⎣ 2 2 ⎦
I have got the following situation (in Sympy 1.8):
from sympy import *
u = symbols('u') # not necessarily positive
term = sqrt(1/u**2)/sqrt(u**2)
The term renders as
How can I simplify this to 1/u**2, i.e. ?
I have tried many functions from https://docs.sympy.org/latest/tutorial/simplification.html, and some arguments listed in https://docs.sympy.org/latest/modules/simplify/simplify.html but could not get it to work.
The variable needs to be declared as real number:
u=symbols('u', real=True)
Then the term is auto-simplified.
(I suggested a corresponding Sympy documentation change.)
I consider following matrices:
M1 = Matrix([[1/7,2/7],[3/7,4/7]])
M2 = Matrix([[1,2],[3,4]])/7
which are evidently identical, but when I determine their determinant I obtain different results:
print(M1.det())
print(M2.det())
giving the following results:
-0.0408163265306122
-2/49
I would like the first result to be expressed as a rational and not as a floating point.
This is an example of one of the gochas and pitfalls from SymPy's documentation. My answer will basically reiterate what is said there. I highly recommend going through it.
When you type 1/7, the Python interpreter changes it into a float before SymPy has a chance to identify it as a rational number. In order for SymPy to evaluate it before Python does, you need to use some other method. You have already shown one of those other methods with M2: divide a SymPy object by 7 instead of a Python int by 7. Here are a few other ways:
from sympy import *
M = Matrix([[Rational(1, 7),Rational(2, 7)],[Rational(3, 7),Rational(4, 7)]]) # create a Rational object
print(det(M))
M = Matrix([[S(1)/7,S(2)/7],[S(3)/7,S(4)/7]]) # divide a SymPy Integer by 7
print(det(M))
M = Matrix([[S("1/7"),S("2/7")],[S("3/7"),S("4/7")]]) # let SymPy interpret it
print(det(M))
M = Matrix([[1,2],[3,4]])/7 # divide a SymPy Matrix by 7
print(det(M))
M = S("Matrix([[1/7,2/7],[3/7,4/7]])") # throw the whole thing into SymPy
print(det(M))
All of the above will give rational determinants. There are probably many more ways to make SymPy identify a rational number.