Iterating within a numpy array

Question

I have 3 2x2 Matrices, P1, P2, and P3, which are populated with randomly generated integers. I want to make sure that these matrices are positive definite (i.e. All eigenvalues are all greater than 0). My code is below.

P1 = np.random.randint(10, size=(m,n))
P2 = np.random.randint(10, size=(m,n))
P3 = np.random.randint(10, size=(m,n))
lambda1 = np.linalg.eigvals(P1)
lambda2 = np.linalg.eigvals(P2)
lambda3 = np.linalg.eigvals(P3)
for i in lambda1:  
  if (i <= 0): P1 = np.random.randint(10, size=(m,n))
for i in lambda2:
  if (i <= 0): P2 = np.random.randint(10, size=(m,n))
for i in lambda3:
  if (i <= 0): P3 = np.random.randint(10, size=(m,n))
print('Eigenvalue output to to verify that matrices are positive definite:\n')
print(u'\u03BB(P\u2081) = '  + str(np.linalg.eigvals(P1)))
print(u'\u03BB(P\u2082) = '  + str(np.linalg.eigvals(P2)))
print(u'\u03BB(P\u2083) = '  + str(np.linalg.eigvals(P3)))

Right now, the if statement will pretty much re-generate the matrix once or twice if the eigenvalues are not positive, but it will not verify that the eigenvalues are always positive. My first guess was to nest a while loop within the for loop, but I could not figure out a way to get that to work, and I'm unsure if that is the most efficient way.

user8408080 · Accepted Answer · 2018-11-03 18:16:56Z

2

This function creates an array with positive eigenvalues:

def create_arr_with_pos_ev(m,n):
    ev = np.array([-1,-1])
    while not all(ev>0):
        arr = np.random.randint(10, size=(m,n))
        ev = np.linalg.eigvals(arr)
    return arr, ev

First I define dummy eigenvalues, that are lower than 0. Then I create a new array and calculate its eigenvalues. If there is a negative eigenvalue (while not all(ev>0)), create a new one.

answered Nov 3, 2018 at 18:16

user8408080

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RocketSocks22 · Accepted Answer · 2018-11-03 19:45:14Z

As a supplement to the answer above, this can also be simplified a little further by taking out any input arguments to the function, and just defining the original matrix within the function:

def create_arr_with_pos_ev():
  arr = np.random.randint(10, size=(m,n))
  ev = np.linalg.eigvals(arr)
  while not all (ev >0):
    arr = np.random.randint(10, size=(m,n))
    ev = np.linalg.eigvals(arr)
  print('\nMatrix: \n' + str(arr) + '\nEigenvalues: \n',ev)
  return arr, ev

Print:

P1,eig1=create_arr_with_pos_ev()
P2,eig2=create_arr_with_pos_ev()
P3,eig3=create_arr_with_pos_ev()

Output:

Matrix: 
[[6 0]
 [3 7]]
Eigenvalues: 
 [7. 6.]

Matrix: 
[[9 3]
 [4 2]]
Eigenvalues: 
 [10.4244289  0.5755711]

Matrix: 
[[5 6]
 [3 8]]
Eigenvalues: 
 [ 2. 11.]

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