helpers

Functions:

make_hash_md5(obj)	param obj: anything that can be hashed.
make_hashable(obj)	Recursive calls to elements of tuples, lists, dicts, set, and frozensets.
m_power_x(m, x)	Apply numpy.linalg.matrix_power to last 2 dimensions of 4-dimensional input matrix.
m_times_n(m, n)	Matrix multiplication of last 2 dimensions for two 4-dimensional input matrices.
finderb(key, array)	Binary search algorithm for sorted array.
multi_gauss(x[, s, x0, A])	Multiple gauss functions with width s given as FWHM and area normalized to input A and maximum of gauss at x0.
convert_cartesian_to_polar(cartesian)	Convert a vector or field from cartesian coordinates \((x, y, z)\) to polar coordinates \((r, \phi, \gamma)\):
convert_polar_to_cartesian(polar)	Convert a vector or field from polar coordinates \((r, \phi, \gamma)\) to cartesian coordinates \((x, y, z)\):

udkm1Dsim.helpers.make_hash_md5(obj)

Parameters:

obj (any) – anything that can be hashed.

Returns:

hash (str) – hash from object.

udkm1Dsim.helpers.make_hashable(obj)

Recursive calls to elements of tuples, lists, dicts, set, and frozensets.

Parameters:

obj (any) – anything that can be hashed..

Returns:

obj (tuple) – hashable object.

udkm1Dsim.helpers.m_power_x(m, x)

Apply numpy.linalg.matrix_power to last 2 dimensions of 4-dimensional input matrix.

Parameters:

• m (ndarray[float, complex]) – 4-dimensional input matrix.

• x (float) – exponent.

Returns:

m (ndarray[float, complex]) – resulting matrix.

udkm1Dsim.helpers.m_times_n(m, n)

Matrix multiplication of last 2 dimensions for two 4-dimensional input matrices.

Parameters:

• m (ndarray[float, complex]) – 4-dimensional input matrix.

• n (ndarray[float, complex]) – 4-dimensional input matrix.

Returns:

res (ndarray[float, complex]) – 4-dimensional multiplication result.

udkm1Dsim.helpers.finderb(key, array)

Binary search algorithm for sorted array. Searches for the first index i of array where key >= array[i]. key can be a scalar or a np.ndarray of keys. array must be a sorted np.ndarray.

Author: André Bojahr. Licence: BSD.

Parameters:

• key (float, ndarray[float]) – single or multiple sorted keys.

• array (ndarray[float]) – sorted array.

Returns:

i (ndarray[float]) – position indices for each key in the array.

udkm1Dsim.helpers.multi_gauss(x, s=[1], x0=[0], A=[1])

Multiple gauss functions with width s given as FWHM and area normalized to input A and maximum of gauss at x0.

Parameters:

• x (ndarray[float]) – argument of multi_gauss.

• s (ndarray[float], optional) – FWHM of Gaussians. Defaults to 1.

• x0 (ndarray[float], optional) – centers of Gaussians. Defaults to 0.

• A (ndarray[float], optional) – amplitudes of Gaussians. Defaults to 1.

Returns:

y (ndarray[float]) – multiple Gaussians.

udkm1Dsim.helpers.convert_cartesian_to_polar(cartesian)

Convert a vector or field from cartesian coordinates \((x, y, z)\) to polar coordinates \((r, \phi, \gamma)\):

\[\begin{split}F_r & = \sqrt{F_x^2 + F_y^2+F_z^2}\\ F_{\phi} & = \begin{cases}\\ \arctan\left(\frac{F_y}{F_x} \right) & \mathrm{for}\ F_x > 0 \\ \pi + \arctan\left(\frac{F_y}{F_x}\right) & \mathrm{for}\ F_x < 0 \ \mathrm{and}\ F_y \geq 0 \\ \arctan\left(\frac{F_y}{F_x}\right) - \pi & \mathrm{for}\ F_x < 0 \ \mathrm{and}\ F_y < 0 \\ 0 & \mathrm{for}\ F_x = F_y = 0 \end{cases} \\ F_{\gamma} & = \arccos\left(\frac{F_z}{F_r} \right)\end{split}\]

where \(F_r\), \(F_{\phi}\), \(F_{\gamma}\) are the radial (amplitude), azimuthal, and polar component of vector field \(\mathbf{F}\), respectively.

Parameters:

cartesian (ndarray[float]) – vector of field to convert.

Returns:

polar (ndarray[float]) – converted vector or field.

udkm1Dsim.helpers.convert_polar_to_cartesian(polar)

Convert a vector or field from polar coordinates \((r, \phi, \gamma)\) to cartesian coordinates \((x, y, z)\):

\[\begin{split}F_x & = r \sin(\phi)\cos(\gamma) \\ F_y & = r \sin(\phi)\sin(\gamma) \\ F_z & = r \cos(\phi)\end{split}\]

where \(r\), \(\phi\), \(\gamma\) are the radius (amplitude), azimuthal, and polar angles of vector field \(\mathbf{F}\), respectively.

Parameters:

polar (ndarray[float]) – vector of field to convert.

Returns:

cartesian (ndarray[float]) – converted vector or field.