Numpy array wrong dimensions with calculations

Question

I have a matrix

import numpy as np 
A = np.array([[.7,.2,.1],[0,.6,.4],[.5,0,.5]]);A

I want to make a function that calculate a stationarity :

def statdist(A):
    m = A.shape[0]
    s = (m,m)
    I = np.identity(3)
    return( np.ones(m)@np.linalg.inv(I)- A+np.ones(s))


statdist(A)

The result must be

 0.4761905 0.2380952 0.2857143

but the output from python is a matrix:

array([[1.3, 1.8, 1.9],
       [2. , 1.4, 1.6],
       [1.5, 2. , 1.5]])

What I make wrong ?

In R is simple right :

statdist <- function(gamma){
  m = dim(gamma)[1]
  matrix(1,1,m) %*% solve(diag(1,m) - gamma + matrix(1,m,m))
}

i = matrix(c(.7,.2,.1,0,.6,.4,.5,0,.5),3,3,byrow = TRUE);i
statdist(i)

Check the dimensions of every element in the return statement. The first term is a 1d vector whose shape is (3,) , while the second one - A+np.ones(s) is a sum of two 3x3 matrices. — Andrea Nicolai
– Andrea Nicolai, Commented Jan 21, 2022 at 23:01
Parentheses in the return value seem to be misplaced. It should be np.ones(m)@np.linalg.inv(I- A+np.ones(s)) — bb1
– bb1, Commented Jan 21, 2022 at 23:07
np.ones(m).reshape((1,m) is (3,1) but still the result is wrong — Homer Jay Simpson
– Homer Jay Simpson, Commented Jan 21, 2022 at 23:07

hpaulj · Accepted Answer · 2022-01-22 00:41:07Z

2

A is (3,3)

m = A.shape[0]            # 3
s = (m,m)
I = np.identity(3)        # (3,3)
return( np.ones(m)@np.linalg.inv(I)- A+np.ones(s))

in the last line

(3,) @ (3,3) => (3,3)
(3,3) - (3,3) + (3,) => (3,3)

oops

(3,) @ (3,3) => (3,)
(3,) - (3,3) + (3,3) => (3,3)

with the suggested change

np.ones(m)@np.linalg.inv(I- A+np.ones(s))
                         (3,3)-(3,3)+(3,3) => (3,3)
      (3,) @     (3,3)  => (3,)

With the numbers:

In [621]: A = np.array([[.7,.2,.1],[0,.6,.4],[.5,0,.5]])
In [622]: np.ones(3)@np.linalg.inv(np.eye(3)- A+np.ones((3,3)))
Out[622]: array([0.47619048, 0.23809524, 0.28571429])

edited Jan 22, 2022 at 0:41

answered Jan 21, 2022 at 23:09

hpaulj

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1 Comment

James Over a year ago

See @bb1's post in the main comments. The return has a misplaced parenthesis

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