When I use sympy to get the square root of 8, the output is ugly:
2*2**(1/2)
import sympy
In [2]: sympy.sqrt(8)
Out[2]: 2*2**(1/2)
Is there any way to make sympy print output in proper mathematical notation (i.e. using the proper symbol for square root) ?
UPDATE:
when I follow the suggestions from #pqnet:
from sympy import *
x, y, z = symbols('x y z')
init_printing()
init_session()
I get following error:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-23-21d886bf3e54> in <module>()
2 x, y, z = symbols('x y z')
3 init_printing()
----> 4 init_session()
/usr/lib/python2.7/dist-packages/sympy/interactive/session.pyc in init_session(ipython, pretty_print, order, use_unicode, quiet, argv)
154 # and False means don't add the line to IPython's history.
155 ip.runsource = lambda src, symbol='exec': ip.run_cell(src, False)
--> 156 mainloop = ip.mainloop
157 else:
158 mainloop = ip.interact
AttributeError: 'ZMQInteractiveShell' object has no attribute 'mainloop'
In an ipython notebook you can enable Sympy's graphical math typesetting with the init_printing function:
import sympy
sympy.init_printing(use_latex='mathjax')
After that, sympy will intercept the output of each cell and format it using math fonts and symbols. Try:
sympy.sqrt(8)
See also:
Printing section in the Sympy Tutorial.
The simplest way to do it is this:
sympy.pprint(sympy.sqrt(8))
For me (using rxvt-unicode and ipython) it gives
___
2⋅╲╱ 2
Related
For a long time I was able to add data and fit, then plot the curve with data. But recently I get this:
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last)
<ipython-input-6-6f645a2744bc> in <module>
1 poland = prepare_data(europe_data, 'Poland')
----> 2 plot_all(poland, max_y=400000)
3 poland
~/Pulpit/library.py in plot_all(country, max_x, max_y)
43 def plot_all(country, max_x = 1000, max_y = 500000):
44
---> 45 parameters_logistic = scipy.optimize.curve_fit(func_logistic, country['n'], country['all'])[0]
46 parameters_expo = scipy.optimize.curve_fit(func_expo, country['n'], country['all'])[0]
47
/usr/local/lib64/python3.6/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
787 cost = np.sum(infodict['fvec'] ** 2)
788 if ier not in [1, 2, 3, 4]:
--> 789 raise RuntimeError("Optimal parameters not found: " + errmsg)
790 else:
791 # Rename maxfev (leastsq) to max_nfev (least_squares), if specified.
RuntimeError: Optimal parameters not found: Number of calls to function has reached maxfev = 800.
Here are all Python Jupyter Notebook files: https://files.fm/u/zj7cc6ne#sign_up
How to solve this?
scipy.optimize.curve_fit takes a keyword argument p0.
Initial guess for the parameters (length N). If None, then the initial
values will all be 1 (if the number of parameters for the function can
be determined using introspection, otherwise a ValueError is raised).
If the defaults 1 are too far of from the result the algorithm may not converge. Try to put some values that make sense for your problem.
I have question about the data type of the result returned by Sympy Poly.all_coeffs(). I have started to use Sympy just recently.
My Sympy transfer function is following:
Then I run this code:
n,d = fraction(Gs)
num = Poly(n,s)
den = Poly(d,s)
num_c = num.all_coeffs()
den_c = den.all_coeffs()
I get:
Then I run this code:
from scipy import signal
#nu = [5000000.0]
#de = [4.99, 509000.0]
nu = num_c
de = den_c
sys = signal.lti(nu, de)
w,mag,phase = signal.bode(sys)
plt.plot(w/(2*np.pi), mag)
and the result is:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-131-fb960684259c> in <module>
4 nu = num_c
5 de = den_c
----> 6 sys = signal.lti(nu, de)
But if I use those commented line 'nu' and 'de' straight python lists instead, the program works. So what is wrong here?
Why did you just show a bit the error? Why not the full message, maybe even the full traceback!
In [60]: sys = signal.lti(num_c, den_c)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-60-21f71ecd8884> in <module>
----> 1 sys = signal.lti(num_c, den_c)
/usr/local/lib/python3.6/dist-packages/scipy/signal/ltisys.py in __init__(self, *system, **kwargs)
590 self._den = None
591
--> 592 self.num, self.den = normalize(*system)
593
594 def __repr__(self):
/usr/local/lib/python3.6/dist-packages/scipy/signal/filter_design.py in normalize(b, a)
1609 leading_zeros = 0
1610 for col in num.T:
-> 1611 if np.allclose(col, 0, atol=1e-14):
1612 leading_zeros += 1
1613 else:
<__array_function__ internals> in allclose(*args, **kwargs)
/usr/local/lib/python3.6/dist-packages/numpy/core/numeric.py in allclose(a, b, rtol, atol, equal_nan)
2169
2170 """
-> 2171 res = all(isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan))
2172 return bool(res)
2173
<__array_function__ internals> in isclose(*args, **kwargs)
/usr/local/lib/python3.6/dist-packages/numpy/core/numeric.py in isclose(a, b, rtol, atol, equal_nan)
2267 y = array(y, dtype=dt, copy=False, subok=True)
2268
-> 2269 xfin = isfinite(x)
2270 yfin = isfinite(y)
2271 if all(xfin) and all(yfin):
TypeError: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''
Now look at the elements of the num_c list (same for den_c):
In [55]: num_c[0]
Out[55]: 500000.000000000
In [56]: type(_)
Out[56]: sympy.core.numbers.Float
The scipy code is doing numpy testing on the inputs. So it's first turned the lists into arrays:
In [61]: np.array(num_c)
Out[61]: array([500000.000000000], dtype=object)
This array contains sympy object(s). It can't cast that to numpy float with 'safe'. But an explicit astype uses unsafe as the default:
In [63]: np.array(num_c).astype(float)
Out[63]: array([500000.])
So lets convert both lists into valid numpy float arrays:
In [64]: sys = signal.lti(np.array(num_c).astype(float), np.array(den_c).astype(float))
In [65]: sys
Out[65]:
TransferFunctionContinuous(
array([100200.4008016]),
array([1.00000000e+00, 1.02004008e+05]),
dt: None
)
Conversion in a list comprehension also works:
sys = signal.lti([float(i) for i in num_c],[float(i) for i in den_c])
You likely need to conver sympy objects to floats / lists of floats.
I am trying to visualize data using Seaborn. I have created a dataframe using SQLContext in pyspark. However, when I call lmplot it results in an error. I am not sure what I am missing. Given below is my code(I am using jupyter notebook):
import pandas as pd
from matplotlib import pyplot as plt
import seaborn as sns
from pyspark.sql import SQLContext
sqlContext = SQLContext(sc)
df = sqlContext.read.load('file:///home/cloudera/Downloads/WA_Sales_Products_2012-14.csv',
format='com.databricks.spark.csv',
header='true',inferSchema='true')
sns.lmplot(x='Quantity', y='Year', data=df)
Error trace:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-86-2a2b43993475> in <module>()
----> 2 sns.lmplot(x='Quantity', y='Year', data=df)
/home/cloudera/anaconda3/lib/python3.5/site-packages/seaborn/regression.py in lmplot(x, y, data, hue, col, row, palette, col_wrap, size, aspect, markers, sharex, sharey, hue_order, col_order, row_order, legend, legend_out, x_estimator, x_bins, x_ci, scatter, fit_reg, ci, n_boot, units, order, logistic, lowess, robust, logx, x_partial, y_partial, truncate, x_jitter, y_jitter, scatter_kws, line_kws)
557 hue_order=hue_order, size=size, aspect=aspect,
558 col_wrap=col_wrap, sharex=sharex, sharey=sharey,
--> 559 legend_out=legend_out)
560
561 # Add the markers here as FacetGrid has figured out how many levels of the
/home/cloudera/anaconda3/lib/python3.5/site-packages/seaborn/axisgrid.py in __init__(self, data, row, col, hue, col_wrap, sharex, sharey, size, aspect, palette, row_order, col_order, hue_order, hue_kws, dropna, legend_out, despine, margin_titles, xlim, ylim, subplot_kws, gridspec_kws)
255 # Make a boolean mask that is True anywhere there is an NA
256 # value in one of the faceting variables, but only if dropna is True
--> 257 none_na = np.zeros(len(data), np.bool)
258 if dropna:
259 row_na = none_na if row is None else data[row].isnull()
TypeError: object of type 'DataFrame' has no len()
Any help or pointer is appreciated. Thank you in advance:-)
sqlContext.read.load(...) returns a Spark-DataFrame. I am not sure, whether seaborn can automatically cast a Spark-DataFrame into a Pandas-Dataframe.
Try:
sns.lmplot(x='Quantity', y='Year', data=df.toPandas())
df.toPandas() returns the the pandas-DF from the Spark-DF.
I have a problem in using pep8 to check the coding style in jupyter notebook.
install by:
in[1]
%install_ext https://raw.githubusercontent.com/SiggyF/notebooks/master/pep8_magic.py
out
Installed pep8_magic.py. To use it, type:
%load_ext pep8_magic
load by
in[2]
%load_ext pep8_magic
out
The pep8_magic extension is already loaded. To reload it, use:
%reload_ext pep8_magic
use it by
in[3]
%%pep8
a=1
out
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-5-3b6f6dbc7761> in <module>()
----> 1 get_ipython().run_cell_magic(u'pep8', u'', u'\na = 1')
/usr/local/lib/python2.7/dist-packages/IPython/core/interactiveshell.pyc in run_cell_magic(self, magic_name, line, cell)
2118 magic_arg_s = self.var_expand(line, stack_depth)
2119 with self.builtin_trap:
-> 2120 result = fn(magic_arg_s, cell)
2121 return result
2122
/home/cs/.ipython/extensions/pep8_magic.pyc in pep8(line, cell)
38 with tempfile.NamedTemporaryFile() as f:
39 # save to file
---> 40 f.write(bytes(cell + '\n', 'UTF-8'))
41 # make sure it's written
42 f.flush()
TypeError: str() takes at most 1 argument (2 given)
It seems that I have installed and loaded it successfully but I can not run the cell magic.
Later I found the problem was caused by some differences between python2 and python3. By using io.Bytes and f.write(cell+'\n') in pep2_magic.py, it worked. But unfortunately, it still can't output information of pep8, like the example here pep8 style guide
After importing this data file from Matlab with scipy.io.loadmat, things appeared to work fine until we tried to calculate the conditioning number of one of the matrixes within.
Here's the minimum amount of code that reproduces for us:
import scipy
import numpy
stuff = scipy.io.loadmat("dati-esercizio1.mat")
numpy.linalg.cond(stuff["A"])
Here's the extended stacktrace courtesy of iPython:
In [3]: numpy.linalg.cond(A)
---------------------------------------------------------------------------
LapackError Traceback (most recent call last)
/snip/<ipython-input-3-15d9ef00a605> in <module>()
----> 1 numpy.linalg.cond(A)
/snip/python2.7/site-packages/numpy/linalg/linalg.py in cond(x, p)
1409 x = asarray(x) # in case we have a matrix
1410 if p is None:
-> 1411 s = svd(x,compute_uv=False)
1412 return s[0]/s[-1]
1413 else:
/snip/python2.7/site-packages/numpy/linalg/linalg.py in svd(a, full_matrices, compute_uv)
1313 work = zeros((lwork,), t)
1314 results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
-> 1315 work, -1, iwork, 0)
1316 lwork = int(work[0])
1317 work = zeros((lwork,), t)
LapackError: Parameter a has non-native byte order in lapack_lite.dgesdd
All obvious ideas (like flattening and reshaping the matrix or recreating the matrix from scratch reassigning it element by element) failed. How can I want to massage the data, then, in order to make it more agreeable with numpy?
It's a bug, fixed some time ago: https://github.com/numpy/numpy/pull/235
Workaround:
np.linalg.cond(stuff['A'].newbyteorder('='))
This works for me:
In [33]: stuff = loadmat('dati-esercizio1.mat')
In [34]: a = stuff['A']
In [35]: try: np.linalg.cond(a)
....: except: print "Fail!"
Fail!
In [36]: b = np.array(a, dtype='>d')
In [37]: np.linalg.cond(b)
Out[37]: 62493201976.673141
In [38]: np.all(a == b) # Verify they hold the same data.
Out[38]: True
Apparently it's something wrong with the byte order (endianness?) of each number in the resulting ndarray and not just with the ndarray object itself.
Something like this but more elegant should do the trick:
n, m = A.shape()
B = numpy.empty_like(A)
for i in xrange(n):
for j in xrange(m):
B[i,j] = float(A[i,j])
del A
B = A
print numpy.linalg.cond(A) # 62493210091.354507
(For some reason an in-place replacement still gives that error - so there's something wrong with the byte order of the whole object, too.)