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# Module alignment_tensor

source code

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. source code

 dAi_dAxx(A) The dAi/dAxx gradient. source code

 dAi_dAyy(A) The dAi/dAyy gradient. source code

 dAi_dAxy(A) The dAi/dAxy gradient. source code

 dAi_dAxz(A) The dAi/dAxz gradient. source code

 dAi_dAyz(A) The dAi/dAyz gradient. source code
float
 kappa(nuc1='15N', nuc2='1H') Function for calculating the kappa constant. source code

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

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

 to_tensor(tensor, vector_5D) Convert the 5D vector alignment tensor form to the rank-2 3D matrix from. source code
 Variables
__package__ = 'lib.alignment'

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

 Function Details

### calc_chi_tensor(A, B0, T)

source code

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)

source code

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)

source code

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)

source code

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)

source code

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)

source code

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')

source code

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)

source code

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)

source code

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)

source code

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}.

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