I am trying to evaluate a function (second derivative of another one) but Sympy seems to have a difficulty to do that... ?
from sympy import *
from sympy import Symbol
# Symbols
theta = Symbol('theta')
phi = Symbol('phi')
phi0 = Symbol('phi0')
H0 = Symbol('H0')
# Constants
a = 0.05
t = 100*1e-9
b = 0.05**2/(8*pi*1e-7)
c = 0.001/(4*pi*1e-7)
phi0 = 60*pi/180
H0 = -0.03/(4*pi*1e-7)
def m(theta,phi):
return Matrix([[sin(theta)*cos(phi), sin(theta)*cos(phi), cos(phi)]])
def h(phi0):
return Matrix([[cos(phi0), sin(phi0), 0]])
def k(theta,phi,phi0):
return m(theta,phi).dot(h(phi0))
def F(theta,phi,phi0,H0):
return -(t*a*H0)*k(theta,phi,phi0)+b*t*(cos(theta)**2)+c*t*(sin(2*theta)**2)+t*sin(theta)**4*sin(2*phi)**2
def F_theta(theta,phi,phi0,H0):
return simplify(diff(F(theta,phi,phi0,H0),theta))
def F_thetatheta(theta,phi,phi0,H0):
return simplify(diff(F_theta(theta,phi,phi0,H0),theta))
print F_thetatheta(theta,phi,phi0,H0), F_thetatheta(pi/2,phi,phi0,H0)
As seen below, the general function is evaluated but when I try to replace theta by pi/2 or another value, it does not work.
(4.0e-7*pi*sin(theta)**4*cos(2*phi)**2 - 4.0e-7*pi*sin(theta)**4 + 0.00125*sin(theta)**2 - 0.0001875*sqrt(3)*sin(theta)*cos(phi) - 0.0001875*sin(theta)*cos(phi) + 1.2e-6*pi*cos(2*phi)**2*cos(theta)**4 - 1.2e-6*pi*cos(2*phi)**2*cos(theta)**2 - 1.2e-6*pi*cos(theta)**4 + 1.2e-6*pi*cos(theta)**2 + 0.004*cos(2*theta)**2 - 0.002625)/pi
Traceback (most recent call last):
File "Test.py", line 46, in <module>
print F_thetatheta(theta,phi,phi0,H0), F_thetatheta(pi/2,phi,phi0,H0)
File "Test.py", line 29, in F_thetatheta
return simplify(diff(F_theta(theta,phi,phi0,H0),theta))
File "Test.py", line 27, in F_theta
return simplify(diff(F(theta,phi,phi0,H0),theta))
File "/usr/lib64/python2.7/site-packages/sympy/core/function.py", line 1418, in diff
return Derivative(f, *symbols, **kwargs)
File "/usr/lib64/python2.7/site-packages/sympy/core/function.py", line 852, in __new__
Can\'t differentiate wrt the variable: %s, %s''' % (v, count)))
ValueError:
Can't differentiate wrt the variable: pi/2, 1
The error means you can not differentiate with respect to a number, pi/2. Ie, you derive with respect to a variable (x, y...), not a number.
In an expression with several variables, you can substitute one of them (or more) by its value (or another expression) by using subs:
F_thetatheta(theta,phi,phi0,H0).subs(theta, pi/2)
Then, to evaluate it to the desired accuracy you can use evalf. Compare the two results:
F_thetatheta(theta,phi,phi0,H0).evalf(50, subs={theta:pi/2, phi:0})
F_thetatheta(theta,phi,phi0,H0).subs({theta: pi/2, phi:0})
You should probably have a look at the sympy documentation or follow the tutorial. The documentation is very good, and you can even try the examples in the browser and evaluate code.
Related
Here is my python code:
import sympy as sym
x = sym.Symbol('x')
f = -0.077 * sym.Pow(x - 35.80, 2) + 100
f_prime = f.diff(x)
f_integrate = sym.integrate(sym.sqrt(1 + sym.Pow(f_prime, 2)), x)
I want to be able to write this integral and solve it with Sympy (so, I want to isolate the variable b).
UPDATE
Here is now my code.
f_integrate = sym.integrate(sym.sqrt(1 + sym.Pow(f_prime, 2))-c, (x, 0, b))
g = 100
for i in range(10, 72):
bi = sym.nsolve(f_integrate.subs(c,i), g)
g = bi
return g
This code work with the initial function I wrote (f(x)= -0.077 * sym.Pow(x - 35.80, 2) + 100), but with pretty much any other function, I got this error:
Traceback (most recent call last):
File "Dragon_Ball_-_Film_3_-_Effect - Test avec les bézier.py", line 543, in <module>
drawManager(line.copy())
File "Dragon_Ball_-_Film_3_-_Effect - Test avec les bézier.py", line 199, in drawManager
t = createT(FU, f, x, distanceNextSyllable)
File "Dragon_Ball_-_Film_3_-_Effect - Test avec les bézier.py", line 107, in createT
print(getPosition(f, x, 0, distanceNextSyllable))
File "Dragon_Ball_-_Film_3_-_Effect - Test avec les bézier.py", line 95, in getPosition
bi = sym.nsolve(f_integrate.subs(c,i), g)
File "C:\Users\Admin\AppData\Local\Programs\Python\Python38\lib\site-packages\sympy\utilities\decorator.py", line 88, in func_wrapper
return func(*args, **kwargs)
File "C:\Users\Admin\AppData\Local\Programs\Python\Python38\lib\site-packages\sympy\solvers\solvers.py", line 2937, in nsolve
x = sympify(findroot(f, x0, **kwargs))
File "C:\Users\Admin\AppData\Local\Programs\Python\Python38\lib\site-packages\mpmath\calculus\optimization.py", line 985, in findroot
raise ValueError('Could not find root within given tolerance. '
ValueError: Could not find root within given tolerance. (5.9604644775390625e-8 > 2.16840434497100886801e-19)
Try another starting point or tweak arguments.
The sympy solution seems to be correct, at least wolframalpha.com gives the same result for the integral.
It looks like you are using an older version of SymPy that allowed one to write integrate(Eq(x, y), x). The way to do this now is to write integrate(x - y, x). Doing so for your equation, and using nsolve to solve for the numerical value of b, after supplying a value for c, looks like this:
>>> from sympy.abc import b, c
>>> fc = integrate(sqrt(1 + f_prime**2)-c, (x,0,b))
>>> nsolve(fc.subs(c, 10), 111)
186.052268133373
If you have a range of c values to test, use the last solution for a given c as the guess for the next c. e.g. to calculate b for c in [10, 409]
g = 100
for i in range(10, 410):
bi = nsolve(fc.subs(c,i), g)
g = bi
(This takes about 12 seconds on a fairly slow computer.)
I am having the hardest time figuring out why i am getting this error. I have searched a lot but unable to fine any solution
import numpy as np
import warnings
from collections import Counter
import pandas as pd
def k_nearest_neighbors(data, predict, k=3):
if len(data) >= k:
warnings.warn('K is set to a value less than total voting groups!')
distances = []
for group in data:
for features in data[group]:
euclidean_distance = np.linalg.norm(np.array(features)-
np.array(predict))
distances.append([euclidean_distance,group])
votes = [i[1] for i in sorted(distances)[:k]]
vote_result = Counter(votes).most_common(1)[0][0]
return vote_result
df = pd.read_csv("data.txt")
df.replace('?',-99999, inplace=True)
df.drop(['id'], 1, inplace=True)
full_data = df.astype(float).values.tolist()
print(full_data)
After running. it gives error
Traceback (most recent call last):
File "E:\Jazab\Machine Learning\Lec18(Testing K Neatest Nerighbors
Classifier)\Lec18(Testing K Neatest Nerighbors
Classifier)\Lec18_Testing_K_Neatest_Nerighbors_Classifier_.py", line 25, in
<module>
full_data = df.astype(float).values.tolist()
File "C:\Python27\lib\site-packages\pandas\util\_decorators.py", line 91, in
wrapper
return func(*args, **kwargs)
File "C:\Python27\lib\site-packages\pandas\core\generic.py", line 3299, in
astype
**kwargs)
File "C:\Python27\lib\site-packages\pandas\core\internals.py", line 3224, in
astype
return self.apply('astype', dtype=dtype, **kwargs)
File "C:\Python27\lib\site-packages\pandas\core\internals.py", line 3091, in
apply
applied = getattr(b, f)(**kwargs)
File "C:\Python27\lib\site-packages\pandas\core\internals.py", line 471, in
astype
**kwargs)
File "C:\Python27\lib\site-packages\pandas\core\internals.py", line 521, in
_astype
values = astype_nansafe(values.ravel(), dtype, copy=True)
File "C:\Python27\lib\site-packages\pandas\core\dtypes\cast.py", line 636,
in astype_nansafe
return arr.astype(dtype)
ValueError: invalid literal for float(): 3) <-----Reappears in Group 8 as:
Press any key to continue . . .
if i remove astype(float) program run fine
What should i need to do ?
There are bad data (3)), so need to_numeric with apply because need processes all columns.
Non numeric are converted to NaNs, which are replaced by fillna to some scalar, e.g. 0:
full_data = df.apply(pd.to_numeric, errors='coerce').fillna(0).values.tolist()
Sample:
df = pd.DataFrame({'A':[1,2,7], 'B':['3)',4,5]})
print (df)
A B
0 1 3)
1 2 4
2 7 5
full_data = df.apply(pd.to_numeric, errors='coerce').fillna(0).values.tolist()
print (full_data)
[[1.0, 0.0], [2.0, 4.0], [7.0, 5.0]]
It looks like you have 3) as an entry in your CSV file, and Pandas is complaining because it can't cast it to a float because of the ).
I have a list:
q1 = [0,1.9488e-06,1.5473e-05,5.1829e-05,0.00012192,0.00023633,0.00040526,0.00063862,0.00094596,0.0013365,0.0018192,0.0024025,0.0030949,0.0039041,0.0048379,0.0059036]
which I am trying to integrate.
I have done the following:
def f(x):
if (np.abs(x)<1e-10):
res = x
else:
res = q2[:10]
return res
x = np.arange(0,10,0.001)
def F(x):
res = np.zeros_like(x)
for i,val in enumerate (x):
y,err = integrate.quad(f,0,val)
res[i] = y
return res
plt.plot(F(x))
when I try to run this code I get this error:
Traceback (most recent call last):
File "<ipython-input-88-ca3005760f4b>", line 19, in <module>
plt.plot(F(x))
File "<ipython-input-88-ca3005760f4b>", line 14, in F
y,err = integrate.quad(f,0,val)
File "C:\Anaconda2\lib\site-packages\scipy\integrate\quadpack.py", line 311,
in quad points)
File "C:\Anaconda2\lib\site-packages\scipy\integrate\quadpack.py", line 376,
in _quad
return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
error: Supplied function does not return a valid float.
Can anyone help me understand why I am getting this error?
You're having this error because of these two lines in f:
else:
res = q2[:10]
Here, you're returning a slice of a list from the function. quad doesn't like that; according to its documentation, it expects a function that returns a double (i.e. Python float), not a list.
While your intended output isn't given in your question, changing that line to
res = q2[0]
or any other arbitrary index in q2 corrects the error.
I'm trying to make a Seq2Seq Regression example for time-series analysis and I've used the Seq2Seq library as presented at the Dev Summit, which is currently the code on the Tensorflow GitHub branch r1.0.
I have difficulties understanding how the decoder function works for Seq2Seq, specifically for the "cell_output".
I understand that the num_decoder_symbols is the number of classes/words to decode at each time step. I have it working at a point where I can do training. However, I don't get why I can't just substitute the number of features (num_features) instead of num_decoder_symbols. Basically, I want to be able to run the decoder without teacher forcing, in other words pass the output of the previous time step as the input to the next time step.
with ops.name_scope(name, "simple_decoder_fn_inference",
[time, cell_state, cell_input, cell_output,
context_state]):
if cell_input is not None:
raise ValueError("Expected cell_input to be None, but saw: %s" %
cell_input)
if cell_output is None:
# invariant that this is time == 0
next_input_id = array_ops.ones([batch_size,], dtype=dtype) * (
start_of_sequence_id)
done = array_ops.zeros([batch_size,], dtype=dtypes.bool)
cell_state = encoder_state
cell_output = array_ops.zeros([num_decoder_symbols],
dtype=dtypes.float32)
Here is a link to the original code: https://github.com/tensorflow/tensorflow/blob/r1.0/tensorflow/contrib/seq2seq/python/ops/decoder_fn.py
Why don't I need to pass batch_size for the cell output?
cell_output = array_ops.zeros([batch_size, num_decoder_symbols],
dtype=dtypes.float32)
When trying to use this code to create my own regressive Seq2Seq example, where instead of having an output of probabilities/classes, I have a real valued vector of dimension num_features, instead of an array of probability of classes. As I understood, I thought I could replace num_decoder_symbols with num_features, like below:
def decoder_fn(time, cell_state, cell_input, cell_output, context_state):
"""
Again same as in simple_decoder_fn_inference but for regression on sequences with a fixed length
"""
with ops.name_scope(name, "simple_decoder_fn_inference", [time, cell_state, cell_input, cell_output, context_state]):
if cell_input is not None:
raise ValueError("Expected cell_input to be None, but saw: %s" % cell_input)
if cell_output is None:
# invariant that this is time == 0
next_input = array_ops.ones([batch_size, num_features], dtype=dtype)
done = array_ops.zeros([batch_size], dtype=dtypes.bool)
cell_state = encoder_state
cell_output = array_ops.zeros([num_features], dtype=dtypes.float32)
else:
cell_output = output_fn(cell_output)
done = math_ops.equal(0,1) # hardcoded hack just to properly define done
next_input = cell_output
# if time > maxlen, return all true vector
done = control_flow_ops.cond(math_ops.greater(time, maximum_length),
lambda: array_ops.ones([batch_size,], dtype=dtypes.bool),
lambda: done)
return (done, cell_state, next_input, cell_output, context_state)
return decoder_fn
But, I get the following error:
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/contrib/seq2seq/python/ops/seq2seq.py", line 212, in dynamic_rnn_decoder
swap_memory=swap_memory, scope=scope)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/rnn.py", line 1036, in raw_rnn
swap_memory=swap_memory)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/control_flow_ops.py", line 2605, in while_loop
result = context.BuildLoop(cond, body, loop_vars, shape_invariants)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/control_flow_ops.py", line 2438, in BuildLoop
pred, body, original_loop_vars, loop_vars, shape_invariants)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/control_flow_ops.py", line 2388, in _BuildLoop
body_result = body(*packed_vars_for_body)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/rnn.py", line 980, in body
(next_output, cell_state) = cell(current_input, state)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/contrib/rnn/python/ops/core_rnn_cell_impl.py", line 327, in __call__
input_size = inputs.get_shape().with_rank(2)[1]
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/framework/tensor_shape.py", line 635, in with_rank
raise ValueError("Shape %s must have rank %d" % (self, rank))
ValueError: Shape (100,) must have rank 2
As a result, I passed in the batch_size like this in order to get a Shape of rank 2:
cell_output = array_ops.zeros([batch_size, num_features],
dtype=dtypes.float32)
But I get the following error, where Shape is of rank 3 and wants a rank 2 instead:
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/contrib/seq2seq/python/ops/seq2seq.py", line 212, in dynamic_rnn_decoder
swap_memory=swap_memory, scope=scope)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/rnn.py", line 1036, in raw_rnn
swap_memory=swap_memory)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/control_flow_ops.py", line 2605, in while_loop
result = context.BuildLoop(cond, body, loop_vars, shape_invariants)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/control_flow_ops.py", line 2438, in BuildLoop
pred, body, original_loop_vars, loop_vars, shape_invariants)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/control_flow_ops.py", line 2388, in _BuildLoop
body_result = body(*packed_vars_for_body)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/ops/rnn.py", line 980, in body
(next_output, cell_state) = cell(current_input, state)
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/contrib/rnn/python/ops/core_rnn_cell_impl.py", line 327, in __call__
input_size = inputs.get_shape().with_rank(2)[1]
File "/opt/DL/tensorflow/lib/python2.7/site-packages/tensorflow/python/framework/tensor_shape.py", line 635, in with_rank
raise ValueError("Shape %s must have rank %d" % (self, rank))
ValueError: Shape (10, 10, 100) must have rank 2
I am trying to implement a logistic classifier using python. The goal is to train the algo to identify digits 0-9 using the mnist handwritten digits data set. However, fmin_cg seems to be changing the dimensions of my input arguments. I have tried reshaping the arguements inside cost() and gradient() with no luck; just more errors.
from scipy.io import loadmat
from numpy import shape, zeros, ones, dot, hstack, vstack, log, transpose, kron
from scipy.special import expit as sigmoid
import scipy.optimize
def cost(theta, X, y):
h = sigmoid( X.dot(theta) )
pos_class = y.T.dot( log(h) )
neg_class = (1.0-y).T.dot( log(1.0-h) )
cost = ((-1.0/m)*(pos_class+neg_class))
return cost
def gradient(theta, X, y):
h = sigmoid( X.dot(theta) )
grad = (1.0/m)*(X.T.dot((h-y)))
return grad
def one_vs_all(X, y, theta):
# add x1 feature,x1 = 1, to each example set
X = hstack( (ones((m,1)),X) )
# train the classifier for digit 9.0
temp_y = (y == 9.0)+0
result = scipy.optimize.fmin_cg( cost, fprime=gradient, x0=theta, \
args=(X, temp_y), maxiter=50, disp=False, full_output=True )
print result[1]
# Load data from Matlab file
data = loadmat('data.mat')
X,y = data['X'],data['y']
m,n = shape(X)
theta = zeros((n+1, 1))
one_vs_all(X, y, theta)
The error I receive:
Traceback (most recent call last):
File "/Users/jkarimi91/Documents/Digit Recognizer/Digit_Recognizer.py", line 36, in <module>
one_vs_all(X, y, theta)
File "/Users/jkarimi91/Documents/Digit Recognizer/Digit_Recognizer.py", line 26, in one_vs_all
args=(X, temp_y), maxiter=50, disp=False, full_output=True )
File "/anaconda/lib/python2.7/site-packages/scipy/optimize/optimize.py", line 1092, in fmin_cg
res = _minimize_cg(f, x0, args, fprime, callback=callback, **opts)
File "/anaconda/lib/python2.7/site-packages/scipy/optimize/optimize.py", line 1156, in _minimize_cg
deltak = numpy.dot(gfk, gfk)
ValueError: shapes (401,5000) and (401,5000) not aligned: 5000 (dim 1) != 401 (dim 0)
[Finished in 1.0s with exit code 1]
With the current code, the cost & gradient function are each returning a 2-D array. For fmin_cg to function properly, these functions must each return a 1-D array (as noted by the documentation).
I know this might be a little late but this is supposed to work
.In your gradient function I got several memory errors,So I changed the code a little and added regularization, check it out
def gradients (theta,X,y,Lambda):
m,n = shape(X)
theta = reshape(theta,(n,1))
h = sigmoid(X.dot(theta))
h = h-y
theta[0,0] = 0
grad = ((X.T.dot(h)) / m) + (Lambda / m * theta)
return grad.ravel()