ulab.numpy.linalg
- ulab.numpy.linalg.cholesky(A: ulab.numpy.ndarray) ulab.numpy.ndarray
- Parameters:
A (ndarray) – a positive definite, symmetric square matrix
- Return ~ulab.numpy.ndarray L:
a square root matrix in the lower triangular form
- Raises:
ValueError – If the input does not fulfill the necessary conditions
The returned matrix satisfies the equation m=LL*
- ulab.numpy.linalg.det(m: ulab.numpy.ndarray) float
- Param:
m, a square matrix
- Return float:
The determinant of the matrix
Computes the eigenvalues and eigenvectors of a square matrix
- ulab.numpy.linalg.eig(m: ulab.numpy.ndarray) Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]
- Parameters:
m – a square matrix
- Return tuple (eigenvectors, eigenvalues):
Computes the eigenvalues and eigenvectors of a square matrix
- ulab.numpy.linalg.inv(m: ulab.numpy.ndarray) ulab.numpy.ndarray
- Parameters:
m (ndarray) – a square matrix
- Returns:
The inverse of the matrix, if it exists
- Raises:
ValueError – if the matrix is not invertible
Computes the inverse of a square matrix
- ulab.numpy.linalg.norm(x: ulab.numpy.ndarray) float
- Parameters:
x (ndarray) – a vector or a matrix
Computes the 2-norm of a vector or a matrix, i.e.,
sqrt(sum(x*x))
, however, without the RAM overhead.
- ulab.numpy.linalg.qr(m: ulab.numpy.ndarray) Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]
- Parameters:
m – a matrix
- Return tuple (Q, R):
Factor the matrix a as QR, where Q is orthonormal and R is upper-triangular.