false_position

torchdr.false_position(f, n, begin=None, end=None, max_iter=1000, tol=1e-09, verbose=False, dtype=torch.float64, device='cpu')

Implement the false position root finding method.

Perform a batched false position method to find the root of an increasing function f. The domain of f is restricted to positive floats.

Parameters:

• f (function \(\mathbb{R}_{>0} \to \mathbb{R}\)) – increasing function which root should be computed.

• n (int) – size of the input of f.

• begin (torch.Tensor of shape (n) or float, optional) – initial lower bound of the root.

• end (torch.Tensor of shape (n) or float, optional) – initial upper bound of the root.

• max_iter (int, optional) – maximum iterations of search.

• tol (float, optional) – precision threshold at which the algorithm stops.

• verbose (bool, optional) – if True, prints current bounds.

• dtype (torch.dtype, optional) – data type of the input.

• device (str, optional) – device on which the computation is performed.

Returns:

m – root of f.

Return type:

torch.Tensor of shape (n)