Inverse of a matrix using numpy

Question

I\'d like to use numpy to calculate the inverse. But I\'m getting an error:

\'numpy.ndarry\' object has no attribute I

To calculate inver

Answer 1

What about inv?

e.g.: my_inverse_array = inv(my_array)

Answer 2

The I attribute only exists on matrix objects, not ndarrays. You can use numpy.linalg.inv to invert arrays:

inverse = numpy.linalg.inv(x)

Note that the way you're generating matrices, not all of them will be invertible. You will either need to change the way you're generating matrices, or skip the ones that aren't invertible.

try:
    inverse = numpy.linalg.inv(x)
except numpy.linalg.LinAlgError:
    # Not invertible. Skip this one.
    pass
else:
    # continue with what you were doing

Also, if you want to go through all 3x3 matrices with elements drawn from [0, 10), you want the following:

for comb in itertools.product(range(10), repeat=9):

rather than combinations_with_replacement, or you'll skip matrices like

numpy.array([[0, 1, 0],
             [0, 0, 0],
             [0, 0, 0]])

Answer 3

Inverse of a matrix using python and numpy:

>>> import numpy as np
>>> b = np.array([[2,3],[4,5]])
>>> np.linalg.inv(b)
array([[-2.5,  1.5],
       [ 2. , -1. ]])

Not all matrices can be inverted. For example singular matrices are not Invertable:

>>> import numpy as np
>>> b = np.array([[2,3],[4,6]])
>>> np.linalg.inv(b)

LinAlgError: Singular matrix

Solution to singular matrix problem:

try-catch the Singular Matrix exception and keep going until you find a transform that meets your prior criteria AND is also invertable.

Intuition for why matrix inversion can't always be done; like in singular matrices:

Imagine an old overhead film projector that shines a bright light through film onto a white wall. The pixels in the film are projected to the pixels on the wall.

If I stop the film projection on a single frame, you will see the pixels of the film on the wall and I ask you to regenerate the film based on what you see. That's easy, you say, just take the inverse of the matrix that performed the projection. An Inverse of a matrix is the reversal of the projection.

Now imagine if the projector was corrupted, and I put a distorted lens in front of the film. Now multiple pixels are projected to the same spot on the wall. I asked you again to "undo this operation with the matrix inverse". You say: "I can't because you destroyed information with the lens distortion, I can't get back to where we were, because the matrix is either Singular or Degenerate."

A matrix that can be used to transform some data into other data is invertable only if the process can be reversed with no loss of information. If your matrix can't be inverted, perhaps you are defining your projection using a guess-and-check methodology rather than using a process that guarantees a non-corrupting transform.

If you're using a heuristic or anything less than perfect mathematical precision, then you'll have to define another process to manage and quarantine distortions so that programming by Brownian motion can resume.

Source:

http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.inv.html#numpy.linalg.inv

Answer 4

Another way to do this is to use the numpy matrix class (rather than a numpy array) and the I attribute. For example:

>>> m = np.matrix([[2,3],[4,5]])
>>> m.I
matrix([[-2.5,  1.5],
       [ 2. , -1. ]])