relax SVN archive

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.

Expanded the N_state_model.test_5_state_xz system test.

This now covers the new 'unitary 9D' basis set for the align_tensor.svd user function and the new
'matrix' basis set for the align_tensor.matrix_angles user function.

Conversion of the basis_set argument for the align_tensor.svd user function.

The argument is now a string that accepts the values of 'unitary 9D', 'unitary 5D', and 'geometric
5D' to select between the different SVD matrices. This has been updated in the test suite as well.

Printout improvements clarifying the align_tensor.matrix_angles user function.

Added a check for the values of the basis_set argument.

This is to the align_tensor.matrix_angles user function backend.

Conversion of the basis_set argument for the align_tensor.matrix_angles user function.

The argument is now a string that accepts the values of 'matrix', 'unitary 5D', and 'geometric 5D'
to select between the different matrix angles techniques. This has been updated in the test suite
as well.