\[\DeclareMathOperator{\erf}{erf} \DeclareMathOperator{\argmin}{argmin} \newcommand{\R}{\mathbb{R}} \newcommand{\n}{\boldsymbol{n}}\]

Module pyqt_fit.utils

Author:Pierre Barbier de Reuille <pierre.barbierdereuille@gmail.com>

Module contained a variety of small useful functions.

pyqt_fit.utils.namedtuple(typename, field_names, verbose=False, rename=False)

Returns a new subclass of tuple with named fields.

>>> Point = namedtuple('Point', 'x y')
>>> Point.__doc__                   # docstring for the new class
'Point(x, y)'
>>> p = Point(11, y=22)             # instantiate with positional args or keywords
>>> p[0] + p[1]                     # indexable like a plain tuple
33
>>> x, y = p                        # unpack like a regular tuple
>>> x, y
(11, 22)
>>> p.x + p.y                       # fields also accessable by name
33
>>> d = p._asdict()                 # convert to a dictionary
>>> d['x']
11
>>> Point(**d)                      # convert from a dictionary
Point(x=11, y=22)
>>> p._replace(x=100)               # _replace() is like str.replace() but targets named fields
Point(x=100, y=22)

pyqt_fit.utils.approx_jacobian(x, func, epsilon, *args)

Approximate the Jacobian matrix of callable function func

Parameters:

• x (ndarray) – The state vector at which the Jacobian matrix is desired
• func (callable) – A vector-valued function of the form f(x,*args)
• epsilon (ndarray) – The peturbation used to determine the partial derivatives
• args (tuple) – Additional arguments passed to func

Returns:

An array of dimensions (lenf, lenx) where lenf is the length of the outputs of func, and lenx is the number of

Note

The approximation is done using forward differences