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The matrix below is singular, and AFAIK attempting to invert it should result in
numpy.linalg.linalg.LinAlgError: Singular matrix
but instead, I do get some output matrix. Note that output matrix is a non-sensical result, because it has a row of 0's (which is impossible, since an inverse of a matrix should itself be invertible)!
Am I missing something here related to floating point precision, or the computation of a pseudoinverse as opposed to a true inverse?
$ np.__version__
'1.13.1'
$ np.linalg.inv(np.array([[2,7,7],[7,7,7],[8,7,7]]))
array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 3.43131400e+15, -2.05878840e+16, 1.71565700e+16],
[ -3.43131400e+15, 2.05878840e+16, -1.71565700e+16]])```
947
A singular matrix does not have an inverse. To find the inverse of a square matrix A , you need to find a matrix A−1 such that the product of A and A−1 is the identity matrix.
We use numpy. linalg. inv() function to calculate the inverse of a matrix. The inverse of a matrix is such that if it is multiplied by the original matrix, it results in identity matrix.
The numpy. linalg. det() function calculates the determinant of the input matrix.
One error you may encounter in Python is: numpy.linalg.LinAlgError: Singular matrix. This error occurs when you attempt to invert a singular matrix, which by definition is a matrix that has a determinant of zero and cannot be inverted.
So let’s see how to inverse the numpy Matrix in Python. The np.linalg.inv () is a numpy library function that computes a matrix’s (multiplicative) inverse. The inverse of a matrix is a reciprocal of a matrix.
If the given input is a numpy matrix, then inv () also returns a matrix. If the input array consists of multiple matrices, the numpy linalg.inv () method computes the inverse of them at once. DelftStack is a collective effort contributed by software geeks like you.
Example Codes: numpy.linalg.inv () Method With matrix Input If the given input is a numpy matrix, then inv () also returns a matrix. import numpy as np arr = np.matrix() arr_inv = np.linalg.inv(arr) print(arr_inv, type(arr_inv))
The inv () function raises a LinAlgError if A is not a square matrix because if A is not a square matrix, inversion fails. Inversion of 4*4 Matrix.
Behind the scenes, NumPy and SciPy (and many other software) fall back to LAPACK implementations (or C translations) of linear equation solvers (in this case GESV).
Since GESV first performs a LU decomposition and then checks the diagonal of U matrix for exact zeros, it is very difficult to hit perfect zeros in the decompositions. That's why you don't get a singular matrix error.
Apart from that you should never ever invert a matrix if you are multiplying with other matrices but instead solve for AX=B.
In SciPy since version 0.19, scipy.linalg.solve uses the "expert" driver GESVX of GESV which also reports back condition number and a warning is emitted. This is similar to matlab behavior in case the singularity is missed.
In [7]: sp.linalg.solve(np.array([[2,7,7],[7,7,7],[8,7,7]]), np.eye(3))
...\lib\site-packages\scipy\linalg\basic.py:223: RuntimeWarning: scipy.linalg.solve
Ill-conditioned matrix detected. Result is not guaranteed to be accurate.
Reciprocal condition number: 1.1564823173178713e-18
' condition number: {}'.format(rcond), RuntimeWarning)
Out[7]:
array([[ 0.00000000e+00, -1.00000000e+00, 1.50000000e+00],
[ 3.43131400e+15, -2.05878840e+16, 1.71565700e+16],
[ -3.43131400e+15, 2.05878840e+16, -1.71565700e+16]])
One note from the numpy team:
The de-facto convention in the field is that errors in matrix inversion are mostly silently ignored --- it is assumed that the user knows if this is something that needs to be checked for (implying that a more controlled approximate inversion method needs to be used --- the regularization is problem-dependent).
https://github.com/numpy/numpy/issues/2074
Seems to give an error on 1.13.0 however
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