relax SVN archive

Editing of the align_tensor.svd user function description.

Editing of the description for the align_tensor.matrix_angles user function.

Editing of the description for the 'irreducible 5D' alignment tensor basis set.

This is for the align_tensor.matrix_angles and align_tensor.svd user functions. All Sm element have
been converted to Am.

Added the 'irreducible 5D' basis set option to the align_tensor.svd user function.

This is for the inter-tensor vector angle for the irreducible 5D basis set {A-2, A-1, A0, A1, A2}.
Its results match that of the 'unitary 9D' basis set.

Added the 'irreducible 5D' basis set option to the align_tensor.matrix_angles user function.

This is for the inter-tensor vector angle for the irreducible 5D basis set {S-2, S-1, S0, S1, S2}.
Its results match that of the standard tensor angle as well as the 'unitary 9D' basis sets.

Created functions in the relax library for calculating the inter-vector angle for complex vectors.

This is in the lib.geometry.vectors module. The function vector_angle_complex_conjugate() has been
created to calculate the angle between two complex vectors. This uses the new auxiliary function
complex_inner_product() to calculate <v1|v2>.

Expanded the unit test of the alignment tensor {A-2, A-1, A0, A1, A2} parameters to cover all values.

Added the irreducible tensor notation of {A-2, A-1, A0, A1, A2} to the alignment tensor object.

This follows from the definition of Sass et al, J. Am. Chem. Soc. 1999, 121, 2047-2055,
http://dx.doi.org/10.1021/ja983887w.

The equations of (2) were converted using Gaussian elimination to obtain a reduced row echelon form,
so that the equations in terms of {A-2, A-1, A0, A1, A2} were derived. These have been coded into
the alignment tensor object calc_Am2, calc_Am1, calc_A0, calc_A1 and calc_A2 methods respectively,
and the values can be obtained by accessing the Am2, Am1, A0, A1, and A2 objects.

To check that the implementation is correct, a unit test has been created to compare the calculated
values with those determined using Pales.

Updated the script and log file for demonstrating differences between alignment tensor basis sets.

This now handles the changes to the basis_set arguments used in the align_tensor.matrix_angles and
align_tensor.svd user functions, and includes the new basis sets.

Expansion of the align_tensor.matrix_angles user function.

The new basis set 'unitary 9D' has been introduced. This creates vectors as {Sxx, Sxy, Sxz, Syx,
Syy, Syz, Szx, Szy, Szz} and computes the inter-vector angles. These match the 'matrix' basis set
whereby the Euclidean inner product divided by the Frobenius norms is used to calculate the
inter-tensor angles.

In addition, the user function documentation and printouts have been improved. And the backend code
has been simplified.