Let x,y be two numpy arrays of N elements. I want to create a numpy matrix whose columns are scaled-shifted versions of x. For instance, say
m=[0.2, 0.4, 1.2]
Then I want the matrix
X = [0.2x+y, 0.4x+y, 1.2x+y]
What's the fastest (easiest as well, easiest being second priority) way to do this.
Currently I am doing something like this.
ListVec = [m[i]*x+y for i in numpy.arange(len(m))]
X = numpy.array(ListVec).T
import numpy as np
m = np.array([0.2, 0.4, 1.2])
x = 5
y = 3
X = m*x+y
This is called broadcasting in numpy (both easy and fast ;))
use Einstein Summation for case when X and Y are arrays
In [70]: Y
Out[76]: array([5, 6, 7, 8, 9])
In [71]: X
Out[71]: array([0, 1, 2, 3, 4])
In [72]: m
Out[72]: [0.2, 0.4, 1.2]
In [73]: np.einsum('i,j', X, m)
Out[73]:
array([[0. , 0. , 0. ],
[0.2, 0.4, 1.2],
[0.4, 0.8, 2.4],
[0.6, 1.2, 3.6],
[0.8, 1.6, 4.8]])
In [74]: Y[...,np.newaxis] + np.einsum('i,j', X, m)
Out[74]:
array([[ 5. , 5. , 5. ],
[ 6.2, 6.4, 7.2],
[ 7.4, 7.8, 9.4],
[ 8.6, 9.2, 11.6],
[ 9.8, 10.6, 13.8]])
It would have helped if you'd given example x
and y
as well as m
, but:
In [435]: x,y = np.array([1,2,3,4]), np.array([.1,.2,.3,.4])
In [436]: m = [.2,.4,1.2]
So the result is (3,N):
In [437]: np.array([i*x+y for i in m])
Out[437]:
array([[0.3, 0.6, 0.9, 1.2],
[0.5, 1. , 1.5, 2. ],
[1.3, 2.6, 3.9, 5.2]])
broadcasting with m
:
In [438]: np.array(m)[:,None]*x + y
Out[438]:
array([[0.3, 0.6, 0.9, 1.2],
[0.5, 1. , 1.5, 2. ],
[1.3, 2.6, 3.9, 5.2]])
oops, I missed your transpose,
In [440]: np.array(m)*x[:,None] + y[:,None]
Out[440]:
array([[0.3, 0.5, 1.3],
[0.6, 1. , 2.6],
[0.9, 1.5, 3.9],
[1.2, 2. , 5.2]])
I'd go ahead a apply the transpose to [438]
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