How do you get the magnitude of a vector in Numpy

Question

In keeping with the  There s only one obvious way to do it   how do you get the magnitude of a vector  1D array  in Numpy   def mag x        return math sqrt sum i  2 for i in x     The above works  but I cannot believe that I must specify such a trivial and core function myself

User · Answer

You can do this concisely using the toolbelt vg. It's a light layer on top of numpy and it supports single values and stacked vectors.

import numpy as np
import vg

x = np.array([1, 2, 3, 4, 5])
mag1 = np.linalg.norm(x)
mag2 = vg.magnitude(x)
print mag1 == mag2
# True

I created the library at my last startup, where it was motivated by uses like this: simple ideas which are far too verbose in NumPy.

User · Answer

Yet another alternative is to use the einsum function in numpy for either arrays   In  1   import numpy as np  In  2   a   np arange 1200 0  reshape  -1 3    In  3    timeit  np linalg norm x  for x in a  100 loops  best of 3  3 86 ms per loop  In  4    timeit np sqrt  a a  sum axis 1   100000 loops  best of 3  15 6   s per loop  In  5    timeit np sqrt np einsum  ij ij- gt i  a a   100000 loops  best of 3  8 71   s per loop   or vectors   In  5   a   np arange 100000   In  6    timeit np sqrt a dot a   10000 loops  best of 3  80 8   s per loop  In  7    timeit np sqrt np einsum  i i   a  a   10000 loops  best of 3  60 6   s per loop   There does  however  seem to be some overhead associated with calling it that may make it slower with small inputs   In  2   a   np arange 100   In  3    timeit np sqrt a dot a   100000 loops  best of 3  3 73   s per loop  In  4    timeit np sqrt np einsum  i i   a  a   100000 loops  best of 3  4 68   s per loop

User · Answer

If you are worried at all about speed  you should instead use   mag   np sqrt x dot x     Here are some benchmarks    gt  gt  gt  import timeit  gt  gt  gt  timeit timeit  np linalg norm x    setup  import numpy as np  x   np arange 100    number 1000  0 0450878  gt  gt  gt  timeit timeit  np sqrt x dot x     setup  import numpy as np  x   np arange 100    number 1000  0 0181372   EDIT  The real speed improvement comes when you have to take the norm of many vectors  Using pure numpy functions doesn t require any for loops  For example   In  1   import numpy as np  In  2   a   np arange 1200 0  reshape  -1 3    In  3    timeit  np linalg norm x  for x in a  100 loops  best of 3  4 23 ms per loop  In  4    timeit np sqrt  a a  sum axis 1   100000 loops  best of 3  18 9 us per loop  In  5   np allclose  np linalg norm x  for x in a  np sqrt  a a  sum axis 1    Out 5   True

User · Answer

The function you re after is numpy linalg norm   I reckon it should be in base numpy as a property of an array -- say x norm   -- but oh well    import numpy as np x   np array  1 2 3 4 5   np linalg norm x    You can also feed in an optional ord for the nth order norm you want  Say you wanted the 1-norm   np linalg norm x ord 1    And so on

User · Answer

use the function norm in scipy linalg  or numpy linalg    gt  gt  gt  from scipy import linalg as LA  gt  gt  gt  a   10 NP random randn 6   gt  gt  gt  a   array    9 62141594    1 29279592    4 80091404   -2 93714318            17 06608678  -11 34617065    gt  gt  gt  LA norm a      23 36461979210312   gt  gt  gt    compare with OP s function   gt  gt  gt  import math  gt  gt  gt  mag   lambda x   math sqrt sum i  2 for i in x    gt  gt  gt  mag a       23 36461979210312

User · Answer

Fastest way I found is via inner1d  Here s how it compares to other numpy methods   import numpy as np from numpy core umath tests import inner1d  V   np random random sample  10  6 3      1 million vectors A   np sqrt np einsum     i    i   V  V   B   np linalg norm V axis 1     C   np sqrt  V    2  sum -1   D   np sqrt  V V  sum axis 1   E   np sqrt inner1d V V    print  np allclose E x  for x in  A B C D      True  True  True  True   import cProfile cProfile run  np sqrt np einsum     i    i   V  V       3 function calls in 0 013 seconds cProfile run  np linalg norm V axis 1                   9 function calls in 0 029 seconds cProfile run  np sqrt  V    2  sum -1                   5 function calls in 0 028 seconds cProfile run  np sqrt  V V  sum axis 1                  5 function calls in 0 027 seconds cProfile run  np sqrt inner1d V V                       2 function calls in 0 009 seconds   inner1d is  3x faster than linalg norm and a hair faster than einsum

[python] How do you get the magnitude of a vector in Numpy?

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