Algebra

Important linear algebra operations for Gaussian Process

algebra.diagonal(matrix: numpy.ndarray) → bool

Check if a matrix is diagonal

Param

matrix (np.ndarray) : matrix of size N x N

Returns

cond (bool) : if diagonal, True

algebra.matrix_inverse(matrix: numpy.ndarray, return_chol: bool = False) → numpy.ndarray

Sometimes, we would need the matrix inverse as well

If we are dealing with diagonal matrix, inversion is simple

Param

matrix (np.ndarray) : matrix of size N x N

Param

return_chol (bool) : if True, the Cholesky factor will be returned

Returns

dummy (np.ndarray) : matrix inverse

If we also want the Cholesky factor:

Returns

chol_factor (np.ndarray) : the Cholesky factor

algebra.solve(matrix: numpy.ndarray, b_vec: numpy.ndarray, return_chol: bool = False) → numpy.ndarray

Given a matrix and a vector, this solves for x in the following:

Ax = b

If A is diagonal, the calculations are simpler (do not require any inversions)

Param

matrix (np.ndarray) : ‘A’ matrix of size N x N

Param

b_vec (np.ndarray) : ‘b’ vector of size N

Param

return_chol (bool) : if True, the Cholesky factor will be retuned

Returns

dummy (np.ndarray) : ‘x’ in the equation above

If we want the Cholesky factor:

Returns

chol_factor (np.ndarray) : the Cholesky factor is returned