Module parameters

Module for handling the frame order model parameters.

Functions

numpy rank-1 array assemble_param_vector(sim_index=None)
Assemble and return the parameter vector.

numpy rank-2 array assemble_scaling_matrix(scaling=True)
Create and return the scaling matrix.

numpy rank-2 NxM array, numpy rank-1 N array linear_constraints(scaling_matrix=None)
Create the linear constraint matrices A and b.

int param_num()
Determine the number of parameters in the model.

update_model()
Update the model parameters as necessary.

Variables

__package__ = 'specific_analyses.frame_order'

Imports: pi, array, float64, identity, zeros, pivot_fixed, translation_fixed

Function Details

assemble_param_vector(sim_index=None)

Assemble and return the parameter vector.

Parameters:

• sim_index (int) - The Monte Carlo simulation index.

Returns: numpy rank-1 array

The parameter vector.

assemble_scaling_matrix(scaling=True)

Create and return the scaling matrix.

Parameters:

• scaling (bool) - If False, then the identity matrix will be returned.

Returns: numpy rank-2 array

The square and diagonal scaling matrix.

linear_constraints(scaling_matrix=None)

Create the linear constraint matrices A and b.

Standard notation

The parameter constraints for the motional amplitude parameters are:

   0 <= theta <= pi,
   0 <= theta_x <= theta_y <= pi,
   -0.125 <= S <= 1,
   0 <= sigma_max <= pi,

The pivot point parameter, domain position parameters, and eigenframe parameters are unconstrained.

Matrix notation

In the notation A.x >= b, where A is an matrix of coefficients, x is an array of parameter values, and b is a vector of scalars, these inequality constraints are:

   | 1  0  0  0  0 |                        |   0    |
   |               |                        |        |
   |-1  0  0  0  0 |                        |  -pi   |
   |               |                        |        |
   | 0  1  0  0  0 |                        |   0    |
   |               |                        |        |
   | 0 -1  0  0  0 |     |   theta   |      |  -pi   |
   |               |     |           |      |        |
   | 0 -1  1  0  0 |     |  theta_x  |      |   0    |
   |               |     |           |      |        |
   | 0  0  1  0  0 |  .  |  theta_y  |  >=  |   0    |
   |               |     |           |      |        |
   | 0  0 -1  0  0 |     |    S      |      |  -pi   |
   |               |     |           |      |        |
   | 0  0  0  1  0 |     | sigma_max |      | -0.125 |
   |               |                        |        |
   | 0  0  0 -1  0 |                        |  -1    |
   |               |                        |        |
   | 0  0  0  0  1 |                        |   0    |
   |               |                        |        |
   | 0  0  0  0 -1 |                        |  -pi   |

Parameters:

• scaling_matrix (numpy rank-2 square matrix) - The diagonal, square scaling matrix.

Returns: numpy rank-2 NxM array, numpy rank-1 N array

The matrices A and b.

param_num()

Determine the number of parameters in the model.

Returns: int

The number of model parameters.