How to apply a function for each element in a matrix in Python?

Question

I have a matrix of triangles where each line has 3 verticies: elementSet:

Element Number      Vertices 
    2           473    1159   917
    3           271    1026   816

And I also have a matrix of nodes that assign a 2d coordinated for every vertice nodeSet:

Vertice Number                 (X,Y)
917             5.487167292060809 2.195789288329368 
271             5.448888739433895 2.38822856765269

I've written some methods to handle the area calculation, they are contained in a class:

  def findArea(self):
        self.elementsArea = nu.zeros((self.elementSet.shape[0],1))
        self.elementsArea[:] = self.calcArea(*self.elementSet[:,-3:])

  #Calculate the area of 3 points
  def calcArea (self,p1,p2,p3):
      [p1,p2,p3] = [self.nodeCoord(p1),self.nodeCoord(p2),self.nodeCoord(p3)]

      return 0.5*abs(p1[Xc]*(p2[Yc] - p3[Yc]) + p2[Xc]*(p3[Yc]-p1[Yc]) + p3[Xc]*(p1[Yc] - p2[Yc]))


  # returns the vertices of a point
  def nodeCoord(self, point):
        return(self.nodeSet[point-1,-3:-1])

where the function calcArea works fine but I want to apply a function to every element of a matrix and assign to another matrix without using a loop.

I have to write something like:

A[:] = func(B[:])

In def findArea() I tried to do something like this but it gives me the following error:

calcArea() takes 4 positional arguments but 2171 were given

I wanna use calcArea() to calculate the area passing arrays as arguments the same way I did in this exemple:

import numpy as np


def test(x,y):
    return x*y

f = np.array([[1,2,5,6,7] , [3,4,9,6,7] ,[6,7,23,34,32]])

print(test(f[0,:],f[1,:]))

I am trying to apply calcArea method but I am getting now only a 2 dimmensions array when I was suppose to get an array the same dimmension the original vectors

a.calcArea(f[0,:],f[1,:],f[2,:])
 array([ 7.5,  0. ])

Do you have to do this manually, can't you use other packages such as pandas — Leb
– Leb, Commented Oct 31, 2015 at 12:51
I have to do it manually =(. if you use numpy.sin() you can apply to a matrix and I have to do the same — Artur Castiel
– Artur Castiel, Commented Oct 31, 2015 at 13:19
Do you understand the error? Do us a favor add a small script, function and data that reproduces the error - something we can run with a quick cut-n-paste. — hpaulj
– hpaulj, Commented Oct 31, 2015 at 14:59
I am really trying to emulate the error somehow so I show you guys. — Artur Castiel
– Artur Castiel, Commented Oct 31, 2015 at 15:17

ali_m · Accepted Answer · 2015-10-31 16:00:05Z

If you can rearrange your data into a set of three 2D arrays containing the x,y coordinates for the first, second and third vertices of all your triangles (e.g. with dimensions (2, n) where n is the number of triangles) then you can easily vectorize the computation over all triangles:

import numpy as np

# adapted from your code. here p1, p2 and p3 are (2, ...) vectors of x,y coords.
def triangle_area(p1, p2, p3):
      return 0.5 * np.abs(p1[0] * (p2[1] - p3[1]) +
                          p2[0] * (p3[1] - p1[1]) +
                          p3[0] * (p1[1] - p2[1]))

n = 100000

# some random vertex data
vert_data = np.random.randn(3, 2, n)

# each of these is a (2, n) vector of x,y coordinates
P1, P2, P3 = vert_data

# a 100000-long vector of areas
areas = triangle_area(P1, P2, P3)

Timing:

In [41]: %%timeit P1, P2, P3 = np.random.randn(3, 2, 100000)
   ....: triangle_area(P1, P2, P3)
   ....: 
1000 loops, best of 3: 1.09 ms per loop

hpaulj · Accepted Answer · 2015-10-31 17:08:08Z

1

Using your test and f:

In [420]: test(f[0,:],f[1,:])
Out[420]: array([ 3,  8, 45, 36, 49])
In [421]: test(*f[:2,:])
Out[421]: array([ 3,  8, 45, 36, 49])

When indexing on the 1st dimension, (*...) does the same thing. But in your class case you are trying to select columns, not rows

In [422]: f1=f.T
In [423]: test(f1[:,1],f1[:,2])
Out[423]: array([ 18,  28, 207, 204, 224])
In [424]: test(*f1[:,:2])
...
TypeError: test() takes 2 positional arguments but 5 were given

(*f1...) expands to (f1[0,:2],f1[1,:2],f1[2,:2],etc). * expansion is in effect an interation on the 1st dimensions.

calcArea takes 3 arguments, but self.calcArea(*self.elementSet[:,-3:]) expands along the 1st dimension of elementSet, not the last size 3 dimension. Try

self.calcArea(self.elementSet[:,0], self.elementSet[:,1], self.elementSet[:,2])

edited Oct 31, 2015 at 17:08

answered Oct 31, 2015 at 16:33

hpaulj

233k14 gold badges260 silver badges392 bronze badges

1 Comment

Artur Castiel Over a year ago

I understand that. What it does not make sense is why it works with test but not with calcArea()

Collectives™ on Stack Overflow

How to apply a function for each element in a matrix in Python?

2 Answers 2

Comments

1 Comment

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

2 Answers 2

Comments

1 Comment

Your Answer

Sign up or log in

Post as a guest

Related