Package maths_fns :: Module alignment_tensor

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Module alignment_tensor

source code

Module for the manipulation of alignment tensors.

Functions

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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

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.

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

source code

Variables

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__package__ = 'maths_fns'

Imports: eigvals

Function Details

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dAi_dAxx(A)

source code

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)

source code

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)

source code

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)

source code

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)

source code

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.

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}.