Cumulative integration of elements of numpy arrays - python

I would like to to the following type of integration:
Say I have 2 arrays
a = np.array[1,2,3,4]
b = np.array[2,4,6,8]
I know how to integrate these using something like:
c = scipy.integrate.simps(b, a)
where c = 15 for above data set.
What I would like to do is multiply the first elements of each array and add to new array called d, i.e. a[0]*b[0] then integrate the first 2 elements the arrays then the first 3 elements, etc. So eventually for this data set, I would get
d = [2 3 8 15]
I have tried a few things but no luck; I am pretty new to writing code.

If I have understood correctly what you need you could do the following:
import numpy as np
from scipy import integrate
a = np.array([2,4,6,8])
b = np.array([1,2,3,4])
d = np.empty_like(b)
d[0] = a[0] * b[0]
for i in range(2, len(a) + 1):
d[i-1] = integrate.simps(b[0:i], a[0:i])
print(d)

Related

How can I calculate scikit-learn rbf_kernel() with very large array?

While using the rbf_kernel() function the array is too large and there is a memory issue, so I have to separate the data and calculate it.
from sklearn.metrics.pairwise import rbf_kernel
result = rbf_kernel([[1,1],[2,2],[3,3]], gamma=60) # A data:[1,1] , B data:[2,2], C data:[3,3]
And result looks like
A B C
A 1 2 1
B 1 1 1
C 1 1 2
However, if I insert larger data, there is a memory issue.
result = rbf_kernel([[1,1],[2,2],[3,3],[4,4],[5,5],.... ], gamma=60)
How can I extract the result without putting data all at once?
Try using:
l = [[1,1],[2,2],[3,3],[4,4],[5,5], ...]
newl = []
for i in range(0, len(l), 10):
newl.append(rbf_kernel(l[i:i + 10]))

Numpy function operating on two ndarrays

Given two ndarrays a = np.asarray([[0,1,2],[3,4,5]]) and b = np.asarray([[6,7,8],[9,10,11]])I want to write a function that iterates over a and b, such that
[0,1,2] and [6,7,8] are considered
[3,4,5] and [9,10,11] are considered
An example would be a functionn that takes
[0,1,2] and [6,7,8] as an input and outputs 0*6+1*7+2*8 = 23
[3,4,5] and [9,10,11] as an input and outputs 3*9+4*10+5*11 = 122
-> (23,122)
Is there any way to do this efficiently in numpy?
My idea was to zip both arrays, however, this is not efficient.
Edit: I am looking for a way to apply a customizable function myfunc(x,y). In the previous example myfunc(x,y) corresponded to the multipication.
c = a * b
sum1 = c[0].sum()
sum2 = c[1].sum()
if you want the algorithmic way ( custom function )
a = np.asarray([[0,1,2],[3,4,5]])
b = np.asarray([[6,7,8],[9,10,11]])
for i in range(a.shape[0]) :
s = 0
for j in range(a.shape[1]) :
s = s + a[i][j]*b[i][j]
print(s)
import numpy as np
a = np.asarray([[0,1,2],[3,4,5]])
b = np.asarray([[6,7,8],[9,10,11]])
c = a*b
print(sum(c[0]),sum(c1))
ans->23,122
Don't need to use zip both array, you need to understand numpy package help you work well with matrix. So you need the basic knowledge about matrix, i recommend you learn from this link http://cs231n.github.io/python-numpy-tutorial/ , from cs231n of Stanford university.
This is a function can solve your problem:
import numpy as np
def interates(matrix_a, matrix_b):
product = matrix_a*matrix_b
return (np.sum(product,1))
The value product contain a new matrix with same shape of matrix_a and matrix_b, each element in there is the result of matrix_a[i][j] * matrix_b[i][j]with i and j run from 0 to matrix_a.shape[0]and matrix_a.shape[1].
Now check with your example
a = np.asarray([[0,1,2],[3,4,5]])
b = np.asarray([[6,7,8],[9,10,11]])
result = interates(a,b)
Print result
>> print(result)
>> [23 122]
If you want a tuple
>> result = tuple(result)
>> print(result)
>> (23, 122)

Update values in numpy array without tedious for loops

I have a few arrays with data like this:
a = np.random.rand(3,3)
b = np.random.rand(3,3)
Using for loops I construct larger matrix
L = np.zeros((9,9))
for i in range(9):
for j in range(9):
L[i,j] = f(a,b,i,j) # values of L depends on values of a and b
Later in my program I will change a and b and I want my L array to change too. So the logic of my program looks like this (in pseudo code)
Create a
Create b
while True:
Create L using a and b
Do the stuff
Change a
Change b
In my program the size of L is large (10^6 x 10^6 and larger).
Constructing this L matrix again and again is tedious and slow process.
Instead of doing for loops again and again I would like just to update values of L matrix according to changed values of a and b. The structure of L is the same each time, the only difference is values of cells. Something like this:
a[0,0] = 2
b[0,0] = 2
L[3,5] = 2*a[0,0]*b[0,0]
L[3,5]
# >>> 8
a[0,0] = 3
b[0,0] = 1
# do some magic here
L[3,5]
>>> 6
Can something like this solve your problem ?
>>> a = 10
>>> b = 20
>>> def func():
# fetch the values of a and b
... return a+b
...
>>> lis = [func]
>>> lis[0]
<function func at 0x109f70730>
>>> lis[0]()
30
>>> a = 20
>>> lis[0]()
40
Basically every time you fetch the value by calling a function
that computes the latest value.

Numpy where conditional statement along axis 0

I have a 1D vector Zc containing n elements that are 2D arrays. I want to find the index of each 2D array that equals np.ones(Zc[i].shape).
a = np.zeros((5,5))
b = np.ones((5,5))*4
c = np.ones((5,5))
d = np.ones((5,5))*2
Zc = np.stack((a,b,c,d))
for i in range(len(Zc)):
a = np.ones(Zc[i].shape)
b = Zc[i]
if np.array_equal(a,b):
print(i)
else:
pass
Which returns 2. The code above works and returns the correct answer, but I want to know if there a vectorized way to achieve the same result?
Going off of hpaulj's comment:
>>> allones = (Zc == np.array(np.ones(Zc[i].shape))).all(axis=(1,2))
>>> np.where(allones)[0][0]
2

Matrix multiplication with numpy.einsum

I have the following two arrays with shape:
A = (d,w,l)
B = (d,q)
And I want to combine these into a 3d array with shape:
C = (q,w,l)
To be a bit more specific, in my case d (depth of the 3d array) is 2, and i'd first like to multiply all positions out of w * l in the upper layer of A (so d = 0) with the first value of B in the highest row (so d=0, q=0). For d=1 I do the same, and then sum the two so:
C_{q=0,w,l} = A_{d=0,w,l}*B_{d=0,q=0} + A_{d=1,w,l}*B_{d=1,q=0}
I wanted to calculate C by making use of numpy.einsum. I thought of the following code:
A = np.arange(100).reshape(2,10,5)
B = np.arange(18).reshape(2,9)
C = np.einsum('ijk,i -> mjk',A,B)
Where ijk refers to 2,10,5 and mjk refers to 9,10,5. However I get an error. Is there some way to perform this multiplication with numpy einsum?
Thanks
Your shapes A = (d,w,l), B = (d,q), C = (q,w,l) practically write the einsum expression
C=np.einsum('dwl,dq->qwl',A,B)
which I can test with
In [457]: np.allclose(A[0,:,:]*B[0,0]+A[1,:,:]*B[1,0],C[0,:,:])
Out[457]: True

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