Cofinanciación

For those of you who are familiar with programming, it is nearly intuitive that when you create a matrix-variable, say a, and you wish to create its (modified) copy, say b = a + 1, b in fact will be independent of a. This is not a case within older versions of NumPy due to the

"physical" pointing at the same object in the memory. Analyse the following case study:

>>> a = np.array([1,2,3,4,5])

>>> b = a + 1

>>> a; b

array([1, 2, 3, 4, 5]) array([2, 3, 4, 5, 6])

but now, if:

>>> b[0] = 7

>>> a; b

array([7, 2, 3, 4, 5]) array([7, 3, 4, 5, 6])

we affect both 0-th elements in a and b arrays. In order to “break the link” between them, you should create a new copy of a matrix using a

.copy function:

.nonzero()

>>> a = np.array([1,2,3,4,5])

>>> b = a.copy()

>>> b = a + 1

>>> b[0] = 7

>>> a; b

array([1, 2, 3, 4, 5]) array([7, 3, 4, 5, 6])

Fortunately, in Python 3.5 with NumPy 1.10.1+ that problem ceases to exist:

>>> import numpy as np

>>> np.__version__

'1.10.1'

>>> a = np.array([1,2,3,4,5])

>>> b = a + 1

>>> a; b

array([1, 2, 3, 4, 5]) array([2, 3, 4, 5, 6])

>>> b[0] = 7

>>> a; b

array([1, 2, 3, 4, 5]) array([7, 3, 4, 5, 6])

however, keep that pitfall in mind and check for potential errors within your future projects. Just in case. ^☺

3.2.5. 1D Array Flattening and Clipping

For any already existing row vector you can substitute its elements with a desired value. Have a look:

>>> a = np.array([1,2,3,4,5])

>>> a.fill(0);

>>> a

array([0, 0, 0, 0, 0])

or

>>> a = np.array([1,2,3,4,5])

>>> a.flat = -1

>>> a

array([-1, -1, -1, -1, -1])

It is so-called flattening. On the other side, clipping in its simplistic form looks like:

>>> x = np.array([1., -2., 3., 4., -5.])

>>> i = np.where(x < 0)

>>> x.flat[i] = 0

>>> x

array([ 1., 0., 3., 4., 0.])

Let’s consider an example. Working daily with financial time-series, sometimes we wish to separate, e.g. a daily return-series into two sub-series storing negative and positive returns, respectively. To do that, in NumPy we can perform the following logic by employing a .clip

function.

.copy()

.fill

.flat

np.where Returns an array with the indexes corresponding to a specified condition (see Section 3.3.3 and 3.8)

Say, the vector r holds daily returns of a stock. Then:

>>> r = np.array([0.09,-0.03,-0.04,0.07,0.00,-0.02])

>>> rneg = r.clip(-1, 0)

>>> rneg

array([ 0. , -0.03, -0.04, 0. , 0. , -0.02])

>>> rneg = rneg[rneg.nonzero()]

>>> rneg

array([-0.03, -0.04, -0.02])

Here, we end up with rneg array storing all negative daily returns.

The .clip(-1, 0) function should be be understood as: clip all values less than -1 to -1 and greater than 0 to 0. It makes sense in our case as we set a lower boundary of -1 (-100.00% daily loss) on one side and 0.00% on the other side. Since zero is usually considered as a

“positive” return therefore the application of the .nonzero function removes zeros from the rneg array.

The situation becomes a bit steeper in case of positive returns. We cannot simply type rneg=r.clip(0, 1). Why? It will replace all negative returns with zeros. Also, if r contains daily returns equal 0.00, extra zeros from clipping would introduce an undesired input. We solve this problem by replacing “true” 0.00% stock returns with an abstract number of, say, 9 i.e. 900% daily gain, and proceed further as follows:

>>> r2 = r.copy(); r2

array([ 0.09, -0.03, -0.04, 0.07, 0. , -0.02])

>>> i = np.where(r2=0.); r2[i] = 9 # alternatively r2[r2==0.] = 9

>>> rpos = r2.clip(0, 9)

>>> rpos

array([ 0.09, 0. , 0. , 0.07, 9. , 0. ])

>>> rpos = rpos[rpos.nonzero()]

>>> rpos

array([ 0.09, 0.07, 9. ])

>>> rpos[rpos == 9.] = 0.

>>> rpos

array([ 0.09, 0.07, 0. ])

If you think for a while, you will discover that in fact all the effort can be shortened down to two essential lines of code providing us with the same results:

>>> r = np.array([0.09,-0.03,-0.04,0.07,0.00,-0.02])

>>> rneg = r[r < 0] # masking

>>> rpos = r[r >= 0] # masking >>> rneg; rpos

array([-0.03, -0.04, -0.02]) array([ 0.09, 0.07, 0. ])

however by doing so you’d miss a lesson on the .clip function ☺. More on masking for arrays in Section 3.8.

As you can see, Python offers more than one method to solve the same problem. Gaining a flexibility in knowing majority of them will make you a good programmer over time.

By separating two return-series we gain a possibility of conducting an additional research on, for instance, the distribution of extreme losses

.clip

or extreme gains for a specific stock in a given time period the data come from. In the abovementioned example our return-series is too short for a complete demonstration, however in general, if we want to extract from each series two most extreme losses and two highest gains, then:

If repeated for, say, 500 stocks (daily return time-series) traded within S&P 500 index, the same method would lead us to an insight on an empirical distribution of extreme values both negative and positive that could be fitted with a Gumbel distribution and tested against GEV theory.

3.2.6. 1D Special Arrays

NumPy delivers an easy solution in a form of special arrays filled with: zeros, ones, or being “empty”. Suddenly, you stop worrying about creating an array of specified dimensions and flattening it.

Therefore, in our arsenal we have:

>>> x = np.zeros(5); x

The alternative way to derive the same results would be with an aid of the .repeat function acting on a 1-element array:

>>> x = np.array([0])

>>> x2 = np.full((1, 5), 1, dtype=np.int64) .sort()

By default this function sorts all elements of 1D array in an ascending order and alters the matrix itself

>>> x2

array([[1, 1, 1, 1, 1]])

where the shapes of the arrays, x1 and x2, have been provided within the inner round brackets: 1 row and 5 columns.

An additional special array containing numbers from 0 to N-1 we create using the arange function. Analyse the following cases:

>>> a = np.arange(11)

>>> a

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

>>> a = np.arange(10) + 1

>>> a

array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

>>> a = np.arange(0, 11, 2)

>>> a

array([ 0, 2, 4, 6, 8, 10])

>>> a = np.arange(0, 10, 2) + 1

>>> a

array([1, 3, 5, 7, 9])

and also

>>> b = np.arange(5, dtype=np.float32)

>>> b

array([ 0., 1., 2., 3., 4.], dtype=float32)

Array—List—Array

The conversion of 1D array into Python’s list one can achieve by the application of the .tolist() function:

>>> r = np.array([0.09,-0.03,-0.04,0.07,0.00,-0.02])

>>> l = r.tolist()

>>> l

[0.09, -0.03, -0.04, 0.07, 0.0, -0.02]

On the other hand, to go from a flat Python list to NumPy 1D array employ the asarray function:

>>> type(l)

<class 'list'>

>>> a = np.asarray(l)

>>> a

array([ 0.09, -0.03, -0.04, 0.07, 0. , -0.02])

>>> a.dtype dtype('float64')