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Merge branch 'master' into 'master' 

typo & updated notebooks

See merge request fsl/pytreat-2018-practicals!28
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%% Cell type:markdown id: tags:
# Main scientific python libraries
See https://scipy.org/
Most of these packages have or are in thr progress of dropping support for python2.
Most of these packages have or are in the progress of dropping support for python2.
So use python3!
## [Numpy](http://www.numpy.org/): arrays
This is the main library underlying (nearly) all of the scientific python ecosystem.
See the tutorial in the beginner session or [the official numpy tutorial](https://docs.scipy.org/doc/numpy-dev/user/quickstart.html) for usage details.
The usual nickname of numpy is np:
%% Cell type:code id: tags:
``` python
```
import numpy as np
```
%% Cell type:markdown id: tags:
Numpy includes support for:
- N-dimensional arrays with various datatypes
- masked arrays
- matrices
- structured/record array
- basic functions (e.g., sin, log, arctan, polynomials)
- basic linear algebra
- random number generation
## [Scipy](https://scipy.org/scipylib/index.html): most general scientific tools
At the top level this module includes all of the basic functionality from numpy.
You could import this as, but you might as well import numpy directly.
%% Cell type:code id: tags:
``` python
```
import scipy as sp
```
%% Cell type:markdown id: tags:
The main strength in scipy lies in its sub-packages:
%% Cell type:code id: tags:
``` python
```
from scipy import optimize
def costfunc(params):
return params[0] ** 2 * (params[1] - 3) ** 2 + (params[0] - 2) ** 2
optimize.minimize(costfunc, x0=[0, 0], method='l-bfgs-b')
```
%% Cell type:markdown id: tags:
Tutorials for all sub-packages can be found [here](https://docs.scipy.org/doc/scipy-1.0.0/reference/).
## [Matplotlib](https://matplotlib.org/): Main plotting library
%% Cell type:code id: tags:
``` python
```
import matplotlib as mpl
mpl.use('nbagg')
import matplotlib.pyplot as plt
```
%% Cell type:markdown id: tags:
The matplotlib tutorials are [here](https://matplotlib.org/tutorials/index.html)
%% Cell type:code id: tags:
``` python
```
x = np.linspace(0, 2, 100)
plt.plot(x, x, label='linear')
plt.plot(x, x**2, label='quadratic')
plt.plot(x, x**3, label='cubic')
plt.xlabel('x label')
plt.ylabel('y label')
plt.title("Simple Plot")
plt.legend()
plt.show()
```
%% Cell type:markdown id: tags:
Alternatives:
- [Mayavi](http://docs.enthought.com/mayavi/mayavi/): 3D plotting (hard to install)
- [Bokeh](https://bokeh.pydata.org/en/latest/) among many others: interactive plots in the browser (i.e., in javascript)
## [Ipython](http://ipython.org/)/[Jupyter](https://jupyter.org/) notebook: interactive python environments
There are many [useful extensions available](https://github.com/ipython-contrib/jupyter_contrib_nbextensions).
## [Pandas](https://pandas.pydata.org/): Analyzing "clean" data
Once your data is in tabular form (e.g. Biobank IDP's), you want to use pandas dataframes to analyze them.
This brings most of the functionality of R into python.
Pandas has excellent support for:
- fast IO to many tabular formats
- accurate handling of missing data
- Many, many routines to handle data
- group by categorical data (i.e., male/female, or age groups)
- joining/merging data
- time series support
- statistical models through [statsmodels](http://www.statsmodels.org/stable/index.html)
- plotting though seaborn [seaborn](https://seaborn.pydata.org/)
- Use [dask](https://dask.pydata.org/en/latest/) if your data is too big for memory (or if you want to run in parallel)
You should also install `numexpr` and `bottleneck` for optimal performance.
For the documentation check [here](http://pandas.pydata.org/pandas-docs/stable/index.html)
### Adjusted example from statsmodels tutorial
%% Cell type:code id: tags:
``` python
```
import statsmodels.api as sm
import statsmodels.formula.api as smf
import numpy as np
```
%% Cell type:code id: tags:
``` python
```
df = sm.datasets.get_rdataset("Guerry", "HistData").data
df
```
%% Cell type:code id: tags:
``` python
```
df.describe()
```
%% Cell type:code id: tags:
``` python
```
df.groupby('Region').mean()
```
%% Cell type:code id: tags:
``` python
```
results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=df).fit()
results.summary()
```
%% Cell type:code id: tags:
``` python
```
df['log_pop'] = np.log(df.Pop1831)
df
```
%% Cell type:code id: tags:
``` python
```
results = smf.ols('Lottery ~ Literacy + log_pop', data=df).fit()
results.summary()
```
%% Cell type:code id: tags:
``` python
```
results = smf.ols('Lottery ~ Literacy + np.log(Pop1831) + Region', data=df).fit()
results.summary()
```
%% Cell type:code id: tags:
``` python
```
results = smf.ols('Lottery ~ Literacy + np.log(Pop1831) + Region + Region * Literacy', data=df).fit()
results.summary()
```
%% Cell type:code id: tags:
``` python
```
%matplotlib nbagg
import seaborn as sns
sns.pairplot(df, hue="Region", vars=('Lottery', 'Literacy', 'log_pop'))
```
%% Cell type:markdown id: tags:
## [Sympy](http://www.sympy.org/en/index.html): Symbolic programming
%% Cell type:code id: tags:
``` python
```
import sympy as sym # no standard nickname
```
%% Cell type:code id: tags:
``` python
```
x, a, b, c = sym.symbols('x, a, b, c')
sym.solve(a * x ** 2 + b * x + c, x)
```
%% Cell type:code id: tags:
``` python
```
sym.integrate(x/(x**2+a*x+2), x)
```
%% Cell type:code id: tags:
``` python
```
f = sym.utilities.lambdify((x, a), sym.integrate((x**2+a*x+2), x))
f(np.random.rand(10), np.random.rand(10))
```
%% Cell type:markdown id: tags:
# Other topics
## [Argparse](https://docs.python.org/3.6/howto/argparse.html): Command line arguments
%% Cell type:code id: tags:
``` python
```
%%writefile test_argparse.py
import argparse
def main():
parser = argparse.ArgumentParser(description="calculate X to the power of Y")
parser.add_argument("-v", "--verbose", action="store_true")
parser.add_argument("x", type=int, help="the base")
parser.add_argument("y", type=int, help="the exponent")
args = parser.parse_args()
answer = args.x**args.y
if args.verbose:
print("{} to the power {} equals {}".format(args.x, args.y, answer))
else:
print("{}^{} == {}".format(args.x, args.y, answer))
if __name__ == '__main__':
main()
```
%% Cell type:code id: tags:
``` python
```
%run test_argparse.py 3 8 -v
```
%% Cell type:code id: tags:
``` python
```
%run test_argparse.py -h
```
%% Cell type:code id: tags:
``` python
```
%run test_argparse.py 3 8.5 -q
```
%% Cell type:markdown id: tags:
Alternatives:
- [docopt](http://docopt.org/): You write a usage string, docopt will generate the parser
> ```
> # example from https://realpython.com/blog/python/comparing-python-command-line-parsing-libraries-argparse-docopt-click/
> """Greeter.
>
> Usage:
> commands.py hello
> commands.py goodbye
> commands.py -h | --help
>
> Options:
> -h --help Show this screen.
> """
> from docopt import docopt
>
> if __name__ == '__main__':
> arguments = docopt(__doc__)
> ```
- [clize](http://clize.readthedocs.io/en/stable/why.html): You write a function, clize will generate the parser
> ```
> from clize import run
>
> def echo(word):
> return word
>
> if __name__ == '__main__':
> run(echo)
> ```
### [Gooey](https://github.com/chriskiehl/Gooey): GUI from command line tool
%% Cell type:code id: tags:
``` python
```
%%writefile test_gooey.py
import argparse
from gooey import Gooey
@Gooey
def main():
parser = argparse.ArgumentParser(description="calculate X to the power of Y")
parser.add_argument("-v", "--verbose", action="store_true")
parser.add_argument("x", type=int, help="the base")
parser.add_argument("y", type=int, help="the exponent")
args = parser.parse_args()
answer = args.x**args.y
if args.verbose:
print("{} to the power {} equals {}".format(args.x, args.y, answer))
else:
print("{}^{} == {}".format(args.x, args.y, answer))
if __name__ == '__main__':
main()
```
%% Cell type:code id: tags:
``` python
```
%run test_gooey.py
```
%% Cell type:code id: tags:
``` python
```
!gcoord_gui
```
%% Cell type:markdown id: tags:
## [Jinja2](http://jinja.pocoo.org/docs/2.10/): Templating language
Jinja2 allows to create templates of files with placeholders, where future content will go.
This allows for the creation of a large number of similar files.
This can for example be used to produce static HTML output in a highly flexible manner.
%% Cell type:code id: tags:
``` python
```
%%writefile image_list.jinja2
<!DOCTYPE html>
<html lang="en">
<head>
{% block head %}
<title>{{ title }}</title>
{% endblock %}
</head>
<body>
<div id="content">
{% block content %}
{% for description, filenames in images %}
<p>
{{ description }}
</p>
{% for filename in filenames %}
<a href="{{ filename }}">
<img src="{{ filename }}">
</a>
{% endfor %}
{% endfor %}
{% endblock %}
</div>
<footer>
Created on {{ time }}
</footer>
</body>
</html>
```
%% Cell type:code id: tags:
``` python
```
def plot_sine(amplitude, frequency):
x = np.linspace(0, 2 * np.pi, 100)
y = amplitude * np.sin(frequency * x)
plt.plot(x, y)
plt.xticks([0, np.pi, 2 * np.pi], ['0', '$\pi$', '$2 \pi$'])
plt.ylim(-1.1, 1.1)
filename = 'plots/A{:.2f}_F{:.2f}.png'.format(amplitude, frequency)
plt.title('A={:.2f}, F={:.2f}'.format(amplitude, frequency))
plt.savefig(filename)
plt.close(plt.gcf())
return filename
!mkdir plots
amplitudes = [plot_sine(A, 1.) for A in [0.1, 0.3, 0.7, 1.0]]
frequencies = [plot_sine(1., F) for F in [1, 2, 3, 4, 5, 6]]
```
%% Cell type:code id: tags:
``` python
```
from jinja2 import Environment, FileSystemLoader
from datetime import datetime
loader = FileSystemLoader('.')
env = Environment(loader=loader)
template = env.get_template('image_list.jinja2')
images = [
('Varying the amplitude', amplitudes),
('Varying the frequency', frequencies),
]
with open('image_list.html', 'w') as f:
f.write(template.render(title='Lots of sines',
images=images, time=datetime.now()))
```
%% Cell type:code id: tags:
``` python
```
!open image_list.html
```
%% Cell type:markdown id: tags:
## Neuroimage packages
The [nipy](http://nipy.org/) ecosystem covers most of these.
## [networkx](https://networkx.github.io/): graph theory
## GUI
- [tkinter](https://docs.python.org/3.6/library/tkinter.html): thin wrapper around Tcl/Tk; included in python
- [wxpython](https://www.wxpython.org/): Wrapper around the C++ wxWidgets library
%% Cell type:code id: tags:
``` python
```
%%writefile wx_hello_world.py
#!/usr/bin/env python
"""
Hello World, but with more meat.
"""
import wx
class HelloFrame(wx.Frame):
"""
A Frame that says Hello World
"""
def __init__(self, *args, **kw):
# ensure the parent's __init__ is called
super(HelloFrame, self).__init__(*args, **kw)
# create a panel in the frame
pnl = wx.Panel(self)
# and put some text with a larger bold font on it
st = wx.StaticText(pnl, label="Hello World!", pos=(25,25))
font = st.GetFont()
font.PointSize += 10
font = font.Bold()
st.SetFont(font)
# create a menu bar
self.makeMenuBar()
# and a status bar
self.CreateStatusBar()
self.SetStatusText("Welcome to wxPython!")
def makeMenuBar(self):
"""
A menu bar is composed of menus, which are composed of menu items.
This method builds a set of menus and binds handlers to be called
when the menu item is selected.
"""
# Make a file menu with Hello and Exit items
fileMenu = wx.Menu()
# The "\t..." syntax defines an accelerator key that also triggers
# the same event
helloItem = fileMenu.Append(-1, "&Hello...\tCtrl-H",
"Help string shown in status bar for this menu item")
fileMenu.AppendSeparator()
# When using a stock ID we don't need to specify the menu item's
# label
exitItem = fileMenu.Append(wx.ID_EXIT)
# Now a help menu for the about item
helpMenu = wx.Menu()
aboutItem = helpMenu.Append(wx.ID_ABOUT)
# Make the menu bar and add the two menus to it. The '&' defines
# that the next letter is the "mnemonic" for the menu item. On the
# platforms that support it those letters are underlined and can be
# triggered from the keyboard.
menuBar = wx.MenuBar()
menuBar.Append(fileMenu, "&File")
menuBar.Append(helpMenu, "&Help")
# Give the menu bar to the frame
self.SetMenuBar(menuBar)
# Finally, associate a handler function with the EVT_MENU event for
# each of the menu items. That means that when that menu item is
# activated then the associated handler function will be called.
self.Bind(wx.EVT_MENU, self.OnHello, helloItem)
self.Bind(wx.EVT_MENU, self.OnExit, exitItem)
self.Bind(wx.EVT_MENU, self.OnAbout, aboutItem)
def OnExit(self, event):
"""Close the frame, terminating the application."""
self.Close(True)
def OnHello(self, event):
"""Say hello to the user."""
wx.MessageBox("Hello again from wxPython")
def OnAbout(self, event):
"""Display an About Dialog"""
wx.MessageBox("This is a wxPython Hello World sample",
"About Hello World 2",
wx.OK|wx.ICON_INFORMATION)
if __name__ == '__main__':
# When this module is run (not imported) then create the app, the
# frame, show it, and start the event loop.
app = wx.App()
frm = HelloFrame(None, title='Hello World 2')
frm.Show()
app.MainLoop()
```
%% Cell type:code id: tags:
``` python
```
%run wx_hello_world.py
```
%% Cell type:markdown id: tags:
## Machine learning
- scikit-learn
- theano/tensorflow/pytorch
- keras
## [Pycuda](https://documen.tician.de/pycuda/): Programming the GPU
Wrapper around [Cuda](https://developer.nvidia.com/cuda-zone).
The alternative [Pyopencl](https://documen.tician.de/pyopencl/) provides a very similar wrapper around [OpenCL](https://www.khronos.org/opencl/).
%% Cell type:code id: tags:
``` python
```
import pycuda.autoinit
import pycuda.driver as drv
from pycuda.compiler import SourceModule
mod = SourceModule("""
__global__ void multiply_them(double *dest, double *a, double *b)
{
const int i = threadIdx.x;
dest[i] = a[i] * b[i];
}
""")
multiply_them = mod.get_function("multiply_them")
a = np.random.randn(400)
b = np.random.randn(400)
dest = np.zeros_like(a)
multiply_them(
drv.Out(dest), drv.In(a), drv.In(b),
block=(400,1,1), grid=(1,1))
print(dest-a*b)
```
%% Cell type:markdown id: tags:
Also see [pyopenGL](http://pyopengl.sourceforge.net/): graphics programming in python (used in FSLeyes)
## Testing
- [unittest](https://docs.python.org/3.6/library/unittest.html): python built-in testing
> ```
> import unittest
>
> class TestStringMethods(unittest.TestCase):
>
> def test_upper(self):
> self.assertEqual('foo'.upper(), 'FOO')
>
> def test_isupper(self):
> self.assertTrue('FOO'.isupper())
> self.assertFalse('Foo'.isupper())
>
> def test_split(self):
> s = 'hello world'
> self.assertEqual(s.split(), ['hello', 'world'])
> # check that s.split fails when the separator is not a string
> with self.assertRaises(TypeError):
> s.split(2)
>
> if __name__ == '__main__':
> unittest.main()
> ```
- [doctest](https://docs.python.org/3.6/library/doctest.html): checks the example usage in the documentation
> ```
> def factorial(n):
> """Return the factorial of n, an exact integer >= 0.
>
> >>> [factorial(n) for n in range(6)]
> [1, 1, 2, 6, 24, 120]
> >>> factorial(30)
> 265252859812191058636308480000000
> >>> factorial(-1)
> Traceback (most recent call last):
> ...
> ValueError: n must be >= 0
>
> Factorials of floats are OK, but the float must be an exact integer:
> >>> factorial(30.1)
> Traceback (most recent call last):
> ...
> ValueError: n must be exact integer
> >>> factorial(30.0)
> 265252859812191058636308480000000
>
> It must also not be ridiculously large:
> >>> factorial(1e100)
> Traceback (most recent call last):
> ...
> OverflowError: n too large
> """
>
> import math
> if not n >= 0:
> raise ValueError("n must be >= 0")
> if math.floor(n) != n:
> raise ValueError("n must be exact integer")
> if n+1 == n: # catch a value like 1e300
> raise OverflowError("n too large")
> result = 1
> factor = 2
> while factor <= n:
> result *= factor
> factor += 1
> return result
>
>
> if __name__ == "__main__":
> import doctest
> doctest.testmod()
> ```
Two external packages provide more convenient unit tests:
- [py.test](https://docs.pytest.org/en/latest/)
- [nose2](http://nose2.readthedocs.io/en/latest/usage.html)
> ```
> # content of test_sample.py
> def inc(x):
> return x + 1
>
> def test_answer():
> assert inc(3) == 5
> ```
- [coverage](https://coverage.readthedocs.io/en/coverage-4.5.1/): measures which part of the code is covered by the tests
## Linters
Linters check the code for any syntax errors, [style errors](https://www.python.org/dev/peps/pep-0008/), unused variables, unreachable code, etc.
- [pylint](https://pypi.python.org/pypi/pylint): most extensive linter
- [pyflake](https://pypi.python.org/pypi/pyflakes): if you think pylint is too strict
- [pep8](https://pypi.python.org/pypi/pep8): just checks for style errors
- [mypy](http://mypy-lang.org/): adding explicit typing to python
## Web frameworks
- [Django2](https://www.djangoproject.com/): includes the most features, but also forces you to do things their way
- [Pyramid](https://trypyramid.com): Intermediate options
- [Flask](http://flask.pocoo.org/): Bare-bone web framework, but many extensions available
There are also many, many libraries to interact with databases, but you will have to google those yourself.
# Several honourable mentions
- [trimesh](https://github.com/mikedh/trimesh): Triangular mesh algorithms
- [Pillow](https://pillow.readthedocs.io/en/latest/): Read/write/manipulate a wide variety of images (png, jpg, tiff, etc.)
- [psychopy](http://www.psychopy.org/): equivalent of psychtoolbox (workshop coming up in April in Nottingham)
- [Buit-in libraries](https://docs.python.org/3/py-modindex.html)
- [collections](https://docs.python.org/3.6/library/collections.html): deque, OrderedDict, namedtuple, and more
- [datetime](https://docs.python.org/3/library/datetime.html): Basic date and time types
- [enum](https://docs.python.org/3/library/enum.html): Enumerators
- [fractions](https://docs.python.org/3/library/fractions.html): rational numbers
- [functools](https://docs.python.org/3/library/functools.html): caching, decorators, and support for functional programming
- [json](https://docs.python.org/3/library/json.html)/[ipaddress](https://docs.python.org/3/library/ipaddress.html)/[xml](https://docs.python.org/3/library/xml.html#module-xml): parsing/writing
- [itertools](https://docs.python.org/3/library/itertools.html): more tools to loop over sequences
- [logging](https://docs.python.org/3/library/logging.htm): log your output to stdout or a file (more flexible than print statements)
- [multiprocessing](https://docs.python.org/3/library/multiprocessing.html)
- [os](https://docs.python.org/3/library/os.html#module-os)/[sys](https://docs.python.org/3/library/sys.html): Miscellaneous operating system interfaces
- [os.path](https://docs.python.org/3/library/os.path.html)/[pathlib](https://docs.python.org/3/library/pathlib.html): utilities to deal with filesystem paths (latter provides an object-oriented interface)
- [pickle](https://docs.python.org/3/library/pickle.html): Store/load any python object
- [shutil](https://docs.python.org/3/library/shutil.html): copy/move files
- [subprocess](https://docs.python.org/3/library/subprocess.html): call shell commands
- [time](https://docs.python.org/3/library/time.html)/[timeit](https://docs.python.org/3/library/timeit.html): keeping track of it
- [turtule](https://docs.python.org/3/library/turtle.html#module-turtle): teach python to your kids!
- [warnings](https://docs.python.org/3/library/warnings.html#module-warnings): tell people they are not using your code properly
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# Main scientific python libraries
See https://scipy.org/
Most of these packages have or are in thr progress of dropping support for python2.
Most of these packages have or are in the progress of dropping support for python2.
So use python3!
## [Numpy](http://www.numpy.org/): arrays
......
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......@@ -53,14 +53,14 @@
{
"ename": "ValueError",
"evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-19-5d1fed3ed2df>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1e6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1e6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mroot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m<ipython-input-18-54b500cd66b1>\u001b[0m in \u001b[0;36mroot\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mroot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mD\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0mD\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mx1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"
]
],
"output_type": "error"
}
],
"source": [
......@@ -253,7 +253,6 @@
{
"ename": "SystemError",
"evalue": "CPUDispatcher(<function root at 0x114035620>) returned a result with an error set",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
......@@ -262,7 +261,8 @@
"\u001b[0;31mSystemError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<timed eval>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n",
"\u001b[0;31mSystemError\u001b[0m: CPUDispatcher(<function root at 0x114035620>) returned a result with an error set"
]
],
"output_type": "error"
}
],
"source": [
......@@ -350,7 +350,6 @@
{
"ename": "NotImplementedError",
"evalue": "(float64 x 2) cannot be represented as a Numpy dtype",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNotImplementedError\u001b[0m Traceback (most recent call last)",
......@@ -360,7 +359,8 @@
"\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/numba/npyufunc/ufuncbuilder.py\u001b[0m in \u001b[0;36m_build_element_wise_ufunc_wrapper\u001b[0;34m(cres, signature)\u001b[0m\n\u001b[1;32m 163\u001b[0m \u001b[0;31m# Get dtypes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 164\u001b[0m \u001b[0mdtypenums\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mas_dtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 165\u001b[0;31m \u001b[0mdtypenums\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mas_dtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 166\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mdtypenums\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mptr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 167\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/numba/numpy_support.py\u001b[0m in \u001b[0;36mas_dtype\u001b[0;34m(nbtype)\u001b[0m\n\u001b[1;32m 134\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mas_dtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnbtype\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 135\u001b[0m raise NotImplementedError(\"%r cannot be represented as a Numpy dtype\"\n\u001b[0;32m--> 136\u001b[0;31m % (nbtype,))\n\u001b[0m\u001b[1;32m 137\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 138\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mNotImplementedError\u001b[0m: (float64 x 2) cannot be represented as a Numpy dtype"
]
],
"output_type": "error"
}
],
"source": [
......@@ -2049,7 +2049,7 @@
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": 4,
"threshold": 4.0,
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": true
......
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