NumPy, SciPy and SciKits
Python provides a framework on which numerical and scientific data processing can be built. As part of our short course on Python for Physics and Astronomy we will look at the capabilities of the NumPy, SciPy and SciKits packages. This is a brief overview with a few examples drawn primarily from the excellent but short introductory book SciPy and NumPy by Eli Bressert (O'Reilly 2012).
NumPy adds arrays and linear albegra to Python, with special functions, transformations, the ability to operate on all elements of an array in one stroke.
Arrays are at the heart of NumPy. The program
import numpy as np mylist = [1, 3, 5, 7, 11, 13] myarray = np.array(mylist) print myarray
creates a list and makes an array from it. You can create an array of 30 32-bit floating point zeros with
myarray = np.zeros(30, dtype=np.float32)
The dtype argument is optional (defaults to float64) and can be
- unit8, 16, 32, 64
- int8, 16, 32, 64
- float16, 32, 64, 128
- complex64, 128
Arrays may also have character data, as in this
test = np.array(['a very','friendly','dog'])
which will a dtype of
meaning a string of 8 characters (set in this instance by the "friendly" element of the list). Arrays must have all elements the same size.
Arrays can be arranged to be multi-dimensional. In our example of zeros, we could instead have
myarray = np.zeros((3,4,5)) print myarray
which will show
array([[[ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.]],
[[ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.]],
[[ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.]]])
Notice that the array is created with np.zeros(), and the argument is (3,4,5). This means an array of 3x4x5 elements, all zero (float64, by default), grouped as 3 elements, each of 4 elements, each of 5 elements.
An array can be reshaped after it is made. The array stays the same way in memory, but the grouping changes.
myarray = np.array( [1,3,5,7,11,13] )
makes a linear array of 6 elements, and
changes its shape, so it will be
array([[ 1, 3, 5], [ 7, 11, 13]])
To create an array of 1000 elements from 0 to 999, the function
my_1d_array = np.arange(1000)
It is reshaped into an array 10x10x10 with
my_3d_array = my_1d_array.reshape((10,10,10))
or an multi-dimensional array may be flattened
my_new_array = my_3d_array.ravel()
The data remain unchanged, but they are sliced and indexed in different ways depending on the shape of the array.
Once an array is created, you can refer to it as a whole, or to its elements one-by-one. Create a list, turn it into an array, reshape it, and print it with something like this
#Make a list mylist = [1,2,3,4,5,6,7,8,9,10,11,12] #Make an array from a list myarray = np.array(mylist)
#Reshape the array my3by4 = myarray.reshape(3,4) print my3by4
array([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]])
The (2,3) element in the reshaped array is
Remember that indexing is from 0, so the "2" here means the 3 "group", and each group had 4 elements. The "3" means the fourth element of that group, which is 12.
Therefore, the notation is just like matrices, with the first index the row and the second index the column, enumerated from (0,0) at the upper left as printed.
Broadcasting over an array
The term broadcasting in NumPy refers to applying an operation to every element of an array. Consider this simple example
cube = np.zeros((2,2,2))
that makes a 2x2x2 cube of zeros. You can add 1 to every element, then divide them all by 3, with
newcube = (cube + 1.)/3. print newcube
array([[[ 0.33333333, 0.33333333], [ 0.33333333, 0.33333333]],
[[ 0.33333333, 0.33333333], [ 0.33333333, 0.33333333]]])
Perhaps more interestingly, create an array of multiples of Pi with
manypi = np.arange(8)*np.pi/4.
and then find the sine of these angles
manysines = np.sin(manypi)
The first one will produce the array of angles
array([ 0. , 0.78539816, 1.57079633, 2.35619449, 3.14159265, 3.92699082, 4.71238898, 5.49778714])
and the second will give the array of their sines
array([ 0.00000000e+00, 7.07106781e-01, 1.00000000e+00, 7.07106781e-01, 1.22464680e-16, -7.07106781e-01, -1.00000000e+00, -7.07106781e-01])
NumPy math has the usual trigonometric functions, and others. A full list is in the documentation, and some useful ones are
- power(x1,x2) takes x1 to the x2 power, element by element
- negative(x) changes the sign of every element
- sin(x), cos(x), tan(x)
- arcsin(x), arccos(x), arctan(x)
- arctan2(x,y) returns the angle whose tangent is the ratio of x and y
- sinh(x), cosh(x), tanh(x)
- arcsinh(x), arccosh(x), arctanh(x)
- degrees(x) or rad2deg(x) convert from radians
- radians(x) or deg2rad(x) convert from degrees
- rint(x) round to the nearest integer
- fix(x) round to the nearest integer toward zero