Adding a 0 in the beginning of a 2D numpy array

Question

import numpy as np
import math as m
from matplotlib import pyplot as plt

#Q1
def bm(s,n):
    np.random.seed(222)
    dw = np.random.normal(0,1,size=(s,n))*m.sqrt(1/n)
    w = np.cumsum(dw, axis=1)
    a = np.mean(w, axis=0)
    b = np.std(w, axis=0)
    plt.plot(np.arange(n),w[:10:,:].T)
    plt.plot(np.arange(n),a.T)
    plt.plot(np.arange(n),b.T)
    plt.show()

bm(1000,600)

This code creates Brownian Motions generated from random standard normal distributions. Every graph needs to start at 0, so I need to append 0 to the beginning of each graph. How can I do this?

Conventionally, pyplot is imported as plt rather than pt. — Mad Physicist
– Mad Physicist, Commented Oct 12, 2020 at 15:59

Mad Physicist · Accepted Answer · 2020-10-12 16:13:53Z

1

You can always subtract off the first delta:

w = np.cumsum(dw, axis=1) - dw[:, :1]

The elements of w are normally given by

 dw[:, :1]
 dw[:, :1] + dw[:, 1:2]
 dw[:, :1] + dw[:, 1:2] + dw[:, 2:3]
 ...

Clearly removing dw[:, :1] offsets the sum by the first element. The difference between dw[:, 0] and dw[:, :1] is that the latter preserves the shape for proper broadcasting, as if you did dw[:, 0][:, None]. If you insist on removing the last element rather than the first, you can do

 w = np.empty_like(dw)
 np.cumsum(dw[:, :-1], axis=1, out=w[:, 1:])
 w[:, 0] = 0

You can actually prepend a zero in a couple of different ways. A concatenation is one way:

np.concatenate((np.zeros((dw.shape[0], 1)), np.cumsum(dw, axis=1)), axis=1)

A potentially better way, hinted above, might be to pre-allocate the output buffer:

w = np.empty((dw.shape[0], dw.shape[1] + 1))
np.cumsum(dw, axis=1, out=w[:, 1:])
w[:, 0] = 0

edited Oct 12, 2020 at 16:13

answered Oct 12, 2020 at 15:58

Mad Physicist

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4 Comments

Mad Physicist Over a year ago

@user14369387. What does that mean?

Unholier Than Thou Over a year ago

I am trying to map this function so that it takes each x and turns these into e to the power (a+(b times x)), how can I do it?

Unholier Than Thou Over a year ago

I upvoted your answer afterwards :) and yes i just deleted it

Unholier Than Thou Over a year ago

Let us continue this discussion in chat.

tom10 · Accepted Answer · 2020-10-12 16:25:00Z

1

In general, you can use numpy.concatenate to append arrays.

But in this specific case, I'd just do

dw[:, 0] = 0.0

after you create dw.

edited Oct 12, 2020 at 16:25

answered Oct 12, 2020 at 16:16

tom10

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1 Comment

Mad Physicist Over a year ago

Took me a second to realize that that won't alter the distribution of steps. Just the initial value.

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