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.