ulab.linalg¶
- ulab.linalg.cholesky(A: ulab.array) ulab.array¶
- Parameters
A (array) – a positive definite, symmetric square matrix
- Return ~ulab.array 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.linalg.det(m: ulab.array) float¶
- Param
m, a square matrix
- Return float
The determinant of the matrix
Computes the eigenvalues and eigenvectors of a square matrix
- ulab.linalg.dot(m1: ulab.array, m2: ulab.array) Union[ulab.array, float]¶
-
Computes the product of two matrices, or two vectors. In the letter case, the inner product is returned.
- ulab.linalg.eig(m: ulab.array) Tuple[ulab.array, ulab.array]¶
- Parameters
m – a square matrix
- Return tuple (eigenvectors, eigenvalues)
Computes the eigenvalues and eigenvectors of a square matrix
- ulab.linalg.inv(m: ulab.array) ulab.array¶
- Parameters
m (array) – 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.linalg.norm(x: ulab.array) float¶
- Parameters
x (array) – 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.linalg.trace(m: ulab.array) float¶
- Parameters
m – a square matrix
Compute the trace of the matrix, the sum of its diagonal elements.