I want to display a matrix with putting an extracted common factor on outside of the matrix after matrix calculation in sympy.
I wrote below code.
from sympy import *
a = symbols("a")
b = symbols("b")
A = Matrix([exp(I*a),exp(I*a)*exp(I*b)])
print simplify(A)
I got below output.
Matrix([
[ exp(I*a)],
[exp(I*(a + b))]])
However, I want to get below output.
exp(I*a)*Matrix([
[ 1],
[exp(I*b)]])
I tried collect(A,exp(I*a)) and got follow error.
Traceback (most recent call last):
File "<ipython-input-65-834f4c326df4>", line 1, in <module>
runfile('C:/Anaconda2/Programs/test/untitled44.py', wdir='C:/Anaconda2/Programs/test')
File "C:\Anaconda2\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 699, in runfile
execfile(filename, namespace)
File "C:\Anaconda2\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 74, in execfile
exec(compile(scripttext, filename, 'exec'), glob, loc)
File "C:/Anaconda2/Programs/test/untitled44.py", line 14, in <module>
collect(A,exp(I*a))
File "C:\Anaconda2\lib\site-packages\sympy\simplify\simplify.py", line 451, in collect
if expr.is_Mul:
File "C:\Anaconda2\lib\site-packages\sympy\matrices\matrices.py", line 3084, in __getattr__
"%s has no attribute %s." % (self.__class__.__name__, attr))
AttributeError: MutableDenseMatrix has no attribute is_Mul.
I know a way to extract a common factor for a element of a matrix like follow link.
https://github.com/sympy/sympy/issues/8442
But it's not my desire.
How should I do?
I do not think Sympy provides a function for the task you want. However, you can do this manually, as per the method proposed in the accepted answer of a similar question asked in the Mathematica SE (link).
The idea is to extract the common factor of the polynomial elements via gcd and then use MatMul with the evaluate=False option in order to restrict Sympy from performing the scalar-matrix multiplication.
import sympy as sp
a, b = sp.symbols('a, b')
A = sp.Matrix([sp.exp(sp.I * a), sp.exp(sp.I * a) * sp.exp(sp.I * b)])
g = sp.gcd(tuple(A))
A_v2 = sp.MatMul(g,(A/g),evaluate = False)
print(A_v2)
exp(I*a)*Matrix([
[ 1],
[exp(I*b)]])
Related
I have a following problem. I am following this example about spatial regression in Python:
import numpy
import libpysal
import spreg
import pickle
# Read spatial data
ww = libpysal.io.open(libpysal.examples.get_path("baltim_q.gal"))
w = ww.read()
ww.close()
w_name = "baltim_q.gal"
w.transform = "r"
Example above works. But I would like to read my own spatial matrix which I have now as a list of lists. See my approach:
ww = libpysal.io.open(matrix)
But I got this error message:
Traceback (most recent call last):
File "/usr/lib/python3.8/code.py", line 90, in runcode
exec(code, self.locals)
File "<input>", line 1, in <module>
File "/home/vojta/Desktop/INTERNET_HANDEL/ZASILKOVNA/optimal-delivery-branches/venv/lib/python3.8/site-packages/libpysal/io/fileio.py", line 90, in __new__
cls.__registry[cls.getType(dataPath, mode, dataFormat)][mode][0]
File "/home/vojta/Desktop/INTERNET_HANDEL/ZASILKOVNA/optimal-delivery-branches/venv/lib/python3.8/site-packages/libpysal/io/fileio.py", line 105, in getType
ext = os.path.splitext(dataPath)[1]
File "/usr/lib/python3.8/posixpath.py", line 118, in splitext
p = os.fspath(p)
TypeError: expected str, bytes or os.PathLike object, not list
this is how matrix looks like:
[[0, 2, 1], [2, 0, 4], [1, 4, 0]]
EDIT:
If I try to insert my matrix into the GM_Lag like this:
model = spreg.GM_Lag(
y,
X,
w=matrix,
)
I got following error:
warn("w must be API-compatible pysal weights object")
Traceback (most recent call last):
File "/usr/lib/python3.8/code.py", line 90, in runcode
exec(code, self.locals)
File "<input>", line 2, in <module>
File "/home/vojta/Desktop/INTERNET_HANDEL/ZASILKOVNA/optimal-delivery-branches/venv/lib/python3.8/site-packages/spreg/twosls_sp.py", line 469, in __init__
USER.check_weights(w, y, w_required=True)
File "/home/vojta/Desktop/INTERNET_HANDEL/ZASILKOVNA/optimal-delivery-branches/venv/lib/python3.8/site-packages/spreg/user_output.py", line 444, in check_weights
if w.n != y.shape[0] and time == False:
AttributeError: 'list' object has no attribute 'n'
EDIT 2:
This is how I read the list of lists:
import pickle
with open("weighted_matrix.pkl", "rb") as f:
matrix = pickle.load(f)
How can I insert list of lists into spreg.GM_Lag ? Thanks
Why do you want to pass it to the libpysal.io.open method? If I understand correctly this code, you first open a file, then read it (and the read method seems to be returning a List). So in your case, where you already have the matrix, you don't need to neither open nor read any file.
What will be needed though is what w is supposed to look like here: w = ww.read(). If it is a simple matrix, then you can initialize w = matrix. If the read method also format the data a certain way, you'll need to do it another way. If you could describe the expected behavior of the read method (e.g. what does the input file contain, and what is returned), it would be useful.
As mentioned, as the data is formatted into a libpysal.weights object, you must build one yourself. This can supposedly be done with this method libpysal.weights.W. (Read the doc too fast).
I have the following
x=Symbol('x',commutative=False)
y=Symbol('y',commutative=False)
expr = 2*x + 87*x*y + 7*y
Now, this works
integrate(expr,y,manual=True)
because it gives
2*x*y + 87*x*y**2/2 + 7*y**2/2
but the same exact thing with x fails:
integrate(expr,x,manual=True)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py", line 1295, in integrate
risch=risch, manual=manual)
File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py", line 486, in doit
conds=conds)
File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py", line 774, in _eval_integral
poly = f.as_poly(x)
File "/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py", line 706, in as_poly
poly = Poly(self, *gens, **args)
File "/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py", line 113, in __new__
opt = options.build_options(gens, args)
File "/usr/local/lib/python2.7/dist-packages/sympy/polys/polyoptions.py", line 731, in build_options
return Options(gens, args)
File "/usr/local/lib/python2.7/dist-packages/sympy/polys/polyoptions.py", line 154, in __init__
preprocess_options(args)
File "/usr/local/lib/python2.7/dist-packages/sympy/polys/polyoptions.py", line 152, in preprocess_options
self[option] = cls.preprocess(value)
File "/usr/local/lib/python2.7/dist-packages/sympy/polys/polyoptions.py", line 293, in preprocess
raise GeneratorsError("non-commutative generators: %s" % str(gens))
sympy.polys.polyerrors.GeneratorsError: non-commutative generators: (x,)
Why Sympy is so weird? How can I fix this?
You seem satisfied with
integrate(2*x + 87*x*y + 7*y, y, manual=True)
returning
2*x*y + 87*x*y**2/2 + 7*y**2/2
But the first term of this answer could also be 2*y*x. Or x*y + y*x. And these are all different answers. So, is the notion of an integral with noncommutative symbols well-defined to begin with? Maybe it's not that SymPy is weird, but the question you are asking it is.
The concrete reason for this behavior is that manual integration is based on matching certain patterns. Such as "constant times something" pattern:
coeff, f = integrand.as_independent(symbol)
The method as_independent splits the product as independent * possibly_dependent, in this order. So,
(x*y).as_independent(y) # returns (x, y)
(x*y).as_independent(x) # returns (1, x*y)
As a result, constant factors are recognized only in front of the expression, when the product is noncommutative.
I don't think this can be fixed without rewriting one of the core methods as_independent to support noncommutative products (possibly returning independent * dependent * independent2) which looks like a lot of work to me. Before doing that work, I'd want to know whether the objective (antiderivative with noncommuting variables) is well defined.
Good morning,
I am trying to solve a system of equation with 2 variables in Python, but using Tkinter to display the answers on the screen. I did most of it, but I can not display the answes.
That is the error I am seeing:
enter coException in Tkinter callback
Traceback (most recent call last):
File "C:\Users\edwin\AppData\Local\Programs\Python\Python36-32\lib\tkinter\__init__.py", line 1699, in __call__
return self.func(*args)
File "C:\Users\edwin\AppData\Local\Programs\Python\Python36-32\ed.py", line 122, in Calculate
z = np.linalg.solve ( a, b)
File "C:\Users\edwin\AppData\Local\Programs\Python\Python36-32\lib\site-packages\numpy\linalg\linalg.py", line 375, in solve
r = gufunc(a, b, signature=signature, extobj=extobj)
File "C:\Users\edwin\AppData\Local\Programs\Python\Python36-32\lib\site-packages\numpy\linalg\linalg.py", line 90, in _raise_linalgerror_singular
raise LinAlgError("Singular matrix")
numpy.linalg.linalg.LinAlgError: Singular matrixde here
A singular matrix is not invertible. A singular matrix does not satisfy the property: The equation Ax = b has exactly one solution for each b in Kn. This means that the system you are attempting to solve is either incorrectly converted into matrix form, or does not have a unique solution.
I'm trying to solve two simultaneous nonlinear equations using the scipy.optimize.brute function
import numpy as np
import scipy.optimize as so
def root2d(x,a,b):
F1 = np.exp(-np.exp(-(x[0]+x[1]))) - x[1]*(b+x[0]**2)
F2 = x[0]*np.cos(x[1]) + x[1]*np.sin(x[0]) - a
return (F1,F2)
a = 0.5
b = 1
x0 = np.array([-0.1,0.1]) # initial guesses
rranges = (slice(-4,4,0.2),slice(-4,4,0.2))
print(so.brute(root2d,rranges,args=(a,b),finish=so.fmin))
I get an error that I don't understand: AttributeError: 'tuple' object has no attribute 'ravel'. What does this mean and how do I fix my code (if it's possible)?
Edit: full error message
Traceback (most recent call last):
File "<ipython-input-2-29b9507fcb99>", line 1, in <module>
runfile('.../test')
File "C:\WinPython\WinPython-64bit-3.5.2.3\python-3.5.2.amd64\lib\site-packages\spyder\utils\site\sitecustomize.py", line 866, in runfile
execfile(filename, namespace)
File "C:\WinPython\WinPython-64bit-3.5.2.3\python-3.5.2.amd64\lib\site-packages\spyder\utils\site\sitecustomize.py", line 102, in execfile
exec(compile(f.read(), filename, 'exec'), namespace)
File "../test.py", line 111, in <module>
print(so.brute(root2d,rranges,args=(a,b),finish=so.fmin))
File "C:\WinPython\WinPython-64bit-3.5.2.3\python-3.5.2.amd64\lib\site-packages\scipy\optimize\optimize.py", line 2711, in brute
indx = argmin(Jout.ravel(), axis=-1)
AttributeError: 'tuple' object has no attribute 'ravel'
You return 2 variables F1 and F2 and reveive them using a single variable obj.(say) This is what is called a tuple obj,it is associated with 2 values, the values of F1 and F2. So, use index as you use in a list to get the value you want, in order.
in the example below, there is a 3d numpy matrix of size (4, 3, 3)+ a solution about how to calculate pinv of each of 4 of those 3*3 matrices in numpy. I also tried to use the same function worked in numpy, in theano hoping that it is implemented the same, but it failed. Any idea how to do it in theano?
dt = np.dtype(np.float32)
a=[[[12,3,1],
[2,4,1],
[2,4,2],],
[[12,3,3],
[2,4,4],
[2,4,5],],
[[12,3,6],
[2,4,5],
[2,4,4],],
[[12,3,3],
[2,4,5],
[2,4,6]]]
a=np.asarray(a,dtype=dt)
print(a.shape)
apinv=np.zeros((4,3,3))
print(np.linalg.pinv(a[0,:,:]).shape)
#numpy solution
apinv = map(lambda n: np.linalg.pinv(n), a)
apinv = np.asarray(apinv,dtype=dt)
#theano solution (not working)
at=T.tensor3('a')
apinvt = map(lambda n: T.nlinalg.pinv(n), at)
The error is:
Original exception was:
Traceback (most recent call last):
File "pydevd.py", line 2403, in <module>
globals = debugger.run(setup['file'], None, None, is_module)
File "pydevd.py", line 1794, in run
launch(file, globals, locals) # execute the script
File "exp_thn_pinv_map.py", line 35, in <module>
apinvt = map(lambda n: T.nlinalg.pinv(n), at)
File "theano/tensor/var.py", line 549, in __iter__
raise TypeError(('TensorType does not support iteration. '
TypeError: TensorType does not support iteration. Maybe you are using builtin.sum instead of theano.tensor.sum? (Maybe .max?)
The error message is
Traceback (most recent call last):
File "D:/Dropbox/source/intro_theano/pinv.py", line 32, in <module>
apinvt = map(lambda n: T.nlinalg.pinv(n), at)
File "d:\dropbox\source\theano\theano\tensor\var.py", line 549, in __iter__
raise TypeError(('TensorType does not support iteration. '
TypeError: TensorType does not support iteration. Maybe you are using builtin.sum instead of theano.tensor.sum? (Maybe .max?)
This is occurring because, as the error message indicates, the symbolic variable at is not iterable.
The fundamental problem here is that you're incorrectly mixing immediately executed Python code with delayed execution Theano symbolic code.
You need to use a symbolic loop, not a Python loop. The correct solution is to use Theano's scan operator:
at=T.tensor3('a')
apinvt, _ = theano.scan(lambda n: T.nlinalg.pinv(n), at, strict=True)
f = theano.function([at], apinvt)
print np.allclose(f(a), apinv)