Symbolic Potential¶

The SymbolicPotential class is defined below, along with some child classes:

the WoodsSaxonPotential class,
the TwoGaussianPotential class,
the FourGaussianPotential class.

class siegpy.symbolicpotentials.SymbolicPotential(sym_func, grid=None)[source]¶

Bases: siegpy.potential.Potential

A Symbolic potential is defined by a symbolic function using the sympy package. The symbolic function can be encoded in a string. The function must be a function of x only (no other parameters).

Parameters:	sym_func (str or sympy symbolic function) – Symbolic function of the potential. grid (list or numpy array or NoneType) – Discretization grid of the potential (optional).
Raises:	`ValueError` – If a parameter of the symbolic function is not \(x\).

Examples

The symbolic function can be a string:

>>> f = "1 / (x**2 + 1)"
>>> pot = SymbolicPotential(f)

Updating the grid automatically updates the values of the potential:

>>> xgrid = [-1, 0, 1]
>>> pot.grid = xgrid
>>> pot.values
array([ 0.5,  1. ,  0.5])

The symbolic function must be a function of x only:

>>> from sympy.abc import a, b, x
>>> f = a / (x**2 + b)
>>> SymbolicPotential(f)
Traceback (most recent call last):
ValueError: The only variable of the analytic function should be x.

This means you must assign values to the parameters beforehand:

>>> pot = SymbolicPotential(f.subs([(a, 1), (b, 1)]), grid=xgrid)
>>> pot.values
array([ 0.5,  1. ,  0.5])

symbolic¶

Returns:	Symbolic function of the potential.
Return type:	Sympy symbolic function

grid¶

Returns:	Values of the grid.
Return type:	NoneType or numpy array

_compute_values(grid)[source]¶

Evaluate the values of the potential for a given grid.

Parameters:	grid (list or numpy array) – Discretization grid or complex scaled grid.
Returns:	Values of the potential according to its grid.
Return type:	numpy array

complex_scaled_values(coord_map)[source]¶

Evaluate the complex scaled potential for a given coordinate mapping.

Parameters:	coord_map (CoordMap) – Coordinate mapping.
Returns:	Complex scaled values of the potential.
Return type:	numpy array

__add__(other)[source]¶

Parameters:	other (Potential) – Another potential.
Returns:	Sum of both potentials.
Return type:	SymbolicPotential or Potential
Raises:	`ValueError` – If the other potential is not symbolic and both potentials have no grid.

class siegpy.symbolicpotentials.WoodsSaxonPotential(l, V0, lbda, grid=None)[source]¶

Bases: siegpy.symbolicpotentials.SymbolicPotential

This class defines a symmetric and smooth Woods-Saxon potential of the form:

\[V(x) = V_0 \left( \frac{1}{1 + e^{\lambda(x+l/2)}} - \frac{1}{1 + e^{\lambda(x-l/2)}} \right)\]

where \(V_0\) is the potential depth, \(l\) is the potential characteristic width and \(\lambda\) is the sharpness parameter.

Parameters:	l (float) – Characteristic width of the potential. V0 (float) – Potential depth (if negative, it corresponds to a potential barrier). lbda (float) – Sharpness of the potential. grid (numpy array) – Discretization grid of the potential (optional).
Raises:	`ValueError` – If the width or the sharpness parameters is strictly negative.

width¶

Returns:	Width of the potential.
Return type:	float

depth¶

Returns:	Depth of the potential.
Return type:	float

sharpness¶

Returns:	Sharpness of the potential.
Return type:	float

class siegpy.symbolicpotentials.MultipleGaussianPotential(sym_func, grid=None)[source]¶

Bases: siegpy.symbolicpotentials.SymbolicPotential

This class avoids some code repetition inside the classes TwoGaussianPotential and FourGaussianPotential.

Parameters:	sym_func (str or sympy symbolic function) – Symbolic function of the potential. grid (list or numpy array or NoneType) – Discretization grid of the potential (optional).
Raises:	`ValueError` – If a parameter of the symbolic function is not \(x\).

Examples

The symbolic function can be a string:

>>> f = "1 / (x**2 + 1)"
>>> pot = SymbolicPotential(f)

Updating the grid automatically updates the values of the potential:

>>> xgrid = [-1, 0, 1]
>>> pot.grid = xgrid
>>> pot.values
array([ 0.5,  1. ,  0.5])

The symbolic function must be a function of x only:

>>> from sympy.abc import a, b, x
>>> f = a / (x**2 + b)
>>> SymbolicPotential(f)
Traceback (most recent call last):
ValueError: The only variable of the analytic function should be x.

This means you must assign values to the parameters beforehand:

>>> pot = SymbolicPotential(f.subs([(a, 1), (b, 1)]), grid=xgrid)
>>> pot.values
array([ 0.5,  1. ,  0.5])

classmethod from_Gaussians(*args, **kwargs)[source]¶

Note

This is an asbtract class method.

Initalization of the potential from Gaussian functions and not from the parameters allowing to define these Gaussian functions.

Returns:	Potential initialized from multiple Gaussian functions.
Return type:	MultipleGaussianPotential

gaussians¶

Note

This is an asbtract property.

Returns:	All the Gaussian functions used to create the potential.
Return type:	list

sigmas¶

Returns:	Sigma of the Gaussian functions of the potential.
Return type:	list

centers¶

Returns:	Center of the Gaussian functions of the potential.
Return type:	list

amplitudes¶

Returns:	Amplitude of the Gaussian functions of the potential.
Return type:	list

class siegpy.symbolicpotentials.TwoGaussianPotential(sigma1, xc1, h1, sigma2, xc2, h2, grid=None)[source]¶

Bases: siegpy.symbolicpotentials.MultipleGaussianPotential

This class defines a potential made of the sum of two Gaussian functions.

Parameters:

sigma1 (float) – Sigma of the first Gaussian function.
xc1 (float) – Center of the first Gaussian function.
h1 (float) – Amplitude of the first Gaussian function.
sigma2 (float) – Sigma of the second Gaussian function.
xc2 (float) – Center of the second Gaussian function.
h2 (float) – Amplitude of the second Gaussian function.
grid (numpy array) – Discretization grid of the potential (optional).

classmethod from_Gaussians(gauss1, gauss2, grid=None)[source]¶

Initialization of a TwoGaussianPotential instance from two Gaussian functions.

Parameters:	gauss1 (Gaussian) – First Gaussian function. gauss2 (Gaussian) – Second Gaussian function. grid (numpy array) – Discretization grid of the potential (optional).
Returns:	Potential initialized from two Gaussian functions.
Return type:	TwoGaussianPotential

gaussian1¶

Returns:	First Gaussian function of the potential.
Return type:	Gaussian

gaussian2¶

Returns:	Second Gaussian function of the potential.
Return type:	Gaussian

gaussians¶

Returns:	Both Gaussian functions of the potential.
Return type:	list

class siegpy.symbolicpotentials.FourGaussianPotential(sigma1, xc1, h1, sigma2, xc2, h2, sigma3, xc3, h3, sigma4, xc4, h4, grid=None)[source]¶

Bases: siegpy.symbolicpotentials.MultipleGaussianPotential

This class defines a potential made of the sum of four Gaussian functions.

Parameters:

sigma1 (float) – Sigma of the first Gaussian function.
xc1 (float) – Center of the first Gaussian function.
h1 (float) – Amplitude of the first Gaussian function.
sigma2 (float) – Sigma of the second Gaussian function.
xc2 (float) – Center of the second Gaussian function.
h2 (float) – Amplitude of the second Gaussian function.
sigma3 (float) – Sigma of the third Gaussian function.
xc3 (float) – Center of the third Gaussian function.
h3 (float) – Amplitude of the third Gaussian function.
sigma4 (float) – Sigma of the fouth Gaussian function.
xc4 (float) – Center of the fouth Gaussian function.
h4 (float) – Amplitude of the fouth Gaussian function.
grid (numpy array) – Discretization grid of the potential (optional).

classmethod from_Gaussians(gauss1, gauss2, gauss3, gauss4, grid=None)[source]¶

Initialization of a FourGaussianPotential instance from four Gaussian functions.

Parameters:	gauss1 (Gaussian) – First Gaussian function. gauss2 (Gaussian) – Second Gaussian function. gauss3 (Gaussian) – Third Gaussian function. gauss4 (Gaussian) – Fourth Gaussian function. grid (numpy array) – Discretization grid of the potential (optional).
Returns:	Potential initialized from four Gaussian functions.
Return type:	FourGaussianPotential

gaussian1¶

Returns:	First Gaussian function of the potential.
Return type:	Gaussian

gaussian2¶

Returns:	Second Gaussian function of the potential.
Return type:	Gaussian

gaussian3¶

Returns:	Third Gaussian function of the potential.
Return type:	Gaussian

gaussian4¶

Returns:	Fouth Gaussian function of the potential.
Return type:	Gaussian

gaussians¶

Returns:	Four Gaussian functions of the potential.
Return type:	list