svd(basis_set=' irreducible 5D ' ,
tensors=None,
precision=1)
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Calculate the singular values of all the loaded tensors.
The basis set can be set to one of:
-
'irreducible 5D', the irreducible 5D basis set {A-2, A-1, A0, A1,
A2}. This is a linear map, hence angles are preserved.
-
'unitary 9D', the unitary 9D basis set {Sxx, Sxy, Sxz, Syx, Syy, Syz,
Szx, Szy, Szz}. This is a linear map, hence angles are preserved.
-
'unitary 5D', the unitary 5D basis set {Sxx, Syy, Sxy, Sxz, Syz}.
This is a non-linear map, hence angles are not preserved.
-
'geometric 5D', the geometric 5D basis set {Szz, Sxxyy, Sxy, Sxz,
Syz}. This is a non-linear map, hence angles are not preserved.
This is also the Pales standard notation.
If the selected basis set is the default of 'irreducible 5D', the
matrix on which SVD will be performed will be:
| A-2(1) A-1(1) A0(1) A1(1) A2(1) |
| A-2(2) A-1(2) A0(2) A1(2) A2(2) |
| A-2(3) A-1(3) A0(3) A1(3) A2(3) |
| . . . . . |
| . . . . . |
| . . . . . |
| A-2(N) A-1(N) A0(N) A1(N) A2(N) |
If the selected basis set is 'unitary 9D', the matrix on which SVD
will be performed will be:
| Sxx1 Sxy1 Sxz1 Syx1 Syy1 Syz1 Szx1 Szy1 Szz1 |
| Sxx2 Sxy2 Sxz2 Syx2 Syy2 Syz2 Szx2 Szy2 Szz2 |
| Sxx3 Sxy3 Sxz3 Syx3 Syy3 Syz3 Szx3 Szy3 Szz3 |
| . . . . . . . . . |
| . . . . . . . . . |
| . . . . . . . . . |
| SxxN SxyN SxzN SyxN SyyN SyzN SzxN SzyN SzzN |
Otherwise if the selected basis set is 'unitary 5D', the matrix for
SVD is:
| Sxx1 Syy1 Sxy1 Sxz1 Syz1 |
| Sxx2 Syy2 Sxy2 Sxz2 Syz2 |
| Sxx3 Syy3 Sxy3 Sxz3 Syz3 |
| . . . . . |
| . . . . . |
| . . . . . |
| SxxN SyyN SxyN SxzN SyzN |
Or if the selected basis set is 'geometric 5D', the stretching and
skewing parameters Szz and Sxx-yy will be used instead and the matrix
is:
| Szz1 Sxxyy1 Sxy1 Sxz1 Syz1 |
| Szz2 Sxxyy2 Sxy2 Sxz2 Syz2 |
| Szz3 Sxxyy3 Sxy3 Sxz3 Syz3 |
| . . . . . |
| . . . . . |
| . . . . . |
| SzzN SxxyyN SxyN SxzN SyzN |
For the irreducible basis set, the Am components are defined as:
/ 4pi \ 1/2
A0 = | --- | Szz ,
\ 5 /
/ 8pi \ 1/2
A+/-1 = +/- | --- | (Sxz +/- iSyz) ,
\ 15 /
/ 2pi \ 1/2
A+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
\ 15 /
The relationships between the geometric and unitary basis sets
are:
Szz = - Sxx - Syy,
Sxxyy = Sxx - Syy,
The SVD values and condition number are dependant upon the basis set
chosen.
- Parameters:
basis_set (str) - The basis set to use for the SVD. This can be one of
"irreducible 5D", "unitary 9D", "unitary
5D" or "geometric 5D".
tensors (None or list of str) - The list of alignment tensor IDs to calculate inter-matrix angles
between. If None, all tensors will be used.
precision (int) - The precision of the printed out angles. The number corresponds
to the number of figures to print after the decimal point.
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