Module alignment_tensor

Module for the manipulation of alignment tensors.

Functions

numpy array or float calc_chi_tensor(A, B0, T)
Convert the alignment tensor into the magnetic susceptibility (chi) tensor.

dAi_dAxx(A)
The dAi/dAxx gradient.

dAi_dAyy(A)
The dAi/dAyy gradient.

dAi_dAxy(A)
The dAi/dAxy gradient.

dAi_dAxz(A)
The dAi/dAxz gradient.

dAi_dAyz(A)
The dAi/dAyz gradient.

float kappa(nuc1='15N', nuc2='1H')
Function for calculating the kappa constant.

maxA(tensor)
Find the maximal alignment - the Azz component in the alignment frame.

to_5D(vector_5D, tensor)
Convert the rank-2 3D alignment tensor matrix to the 5D vector format.

to_tensor(tensor, vector_5D)
Convert the 5D vector alignment tensor form to the rank-2 3D matrix from.

Variables

__package__ = 'lib.alignment'

Imports: pi, eigvals, periodic_table, h_bar, kB, mu0

Function Details

calc_chi_tensor(A, B0, T)

Convert the alignment tensor into the magnetic susceptibility (chi) tensor.

A can be either the full tensor (3D or 5D), a component Aij of the tensor, Aa, or Ar, anything that can be multiplied by the constants to convert from one to the other.

Parameters:

• A (numpy array or float) - The alignment tensor or alignment tensor component.
• B0 (float) - The magnetic field strength in Hz.
• T (float) - The temperature in Kalvin.

Returns: numpy array or float

A multiplied by the PCS constant.

dAi_dAxx(A)

The dAi/dAxx gradient.

This function will modify the A matrix to be equal to:

 dAi   | 1  0  0 |
---- = | 0  0  0 |
dAxx   | 0  0 -1 |

Parameters:

• A (numpy rank-2 3D tensor) - The alignment tensor object.

dAi_dAyy(A)

The dAi/dAyy gradient.

This function will modify the A matrix to be equal to:

 dAi   | 0  0  0 |
---- = | 0  1  0 |
dAyy   | 0  0 -1 |

Parameters:

• A (numpy rank-2 3D tensor) - The alignment tensor object.

dAi_dAxy(A)

The dAi/dAxy gradient.

This function will modify the A matrix to be equal to:

 dAi   | 0  1  0 |
---- = | 1  0  0 |
dAxy   | 0  0  0 |

Parameters:

• A (numpy rank-2 3D tensor) - The alignment tensor object.

dAi_dAxz(A)

The dAi/dAxz gradient.

This function will modify the A matrix to be equal to:

 dAi   | 0  0  1 |
---- = | 0  0  0 |
dAxz   | 1  0  0 |

Parameters:

• A (numpy rank-2 3D tensor) - The alignment tensor object.

dAi_dAyz(A)

The dAi/dAyz gradient.

This function will modify the A matrix to be equal to:

 dAi   | 0  0  0 |
---- = | 0  0  1 |
dAyz   | 0  1  0 |

Parameters:

• A (numpy rank-2 3D tensor) - The alignment tensor object.

kappa(nuc1='15N', nuc2='1H')

Function for calculating the kappa constant.

The kappa constant is:

   kappa = -3/(8pi^2).gI.gS.mu0.h_bar,

where gI and gS are the gyromagnetic ratios of the I and S spins, mu0 is the permeability of free space, and h_bar is Planck's constant divided by 2pi.

Parameters:

• nuc1 (str) - The first nucleus type.
• nuc2 (str) - The first nucleus type.

Returns: float

The kappa constant value.

maxA(tensor)

Find the maximal alignment - the Azz component in the alignment frame.

Parameters:

• tensor (numpy rank-2 3D tensor) - The alignment tensor object.

Returns:

The Azz component in the alignment frame.

to_5D(vector_5D, tensor)

Convert the rank-2 3D alignment tensor matrix to the 5D vector format.

Parameters:

• vector_5D (numpy 5D vector) - The 5D vector object to populate. The vector format is {Axx, Ayy, Axy, Axz, Ayz}.
• tensor (numpy rank-2 3D tensor) - The alignment tensor object.

to_tensor(tensor, vector_5D)

Convert the 5D vector alignment tensor form to the rank-2 3D matrix from.

Parameters:

• tensor (numpy rank-2 3D tensor) - The alignment tensor object, in matrix format, to populate.
• vector_5D (numpy 5D vector) - The 5D vector object. The vector format is {Axx, Ayy, Axy, Axz, Ayz}.