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<section begin=description/>
This is a major feature and bugfix release. It fixes a failure when loading relaxation data and adds Python 3 support for using the NMRPipe showApod software. Features include a large expansion for the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles] and [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd] user functions to support the standard inter-matrix angles, the unitary 9D vector notation {SxxS<sub>xx</sub>, SxyS<sub>xy</sub>, SxzS<sub>xz</sub>, SyxS<sub>yx</sub>, SyyS<sub>yy</sub>, SyzS<sub>yz</sub>, SzxS<sub>zx</sub>, SzyS<sub>zy</sub>, SzzS<sub>zz</sub>}, and the irreducible spherical tensor 5D basis set of {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>} for correctly calculating the inter-tensor angles, singular values and condition numbers.
<section end=description/>
* Implemented the lib.geometry.vectors.vector_angle_atan2() relax library function. This is for calculating the inter-vector angle using the more numerically stable atan2() formula.
* Implemented the lib.geometry.vectors.vector_angle_acos() relax library function. This is used to calculate the inter-vector angle using the arccos of the dot product formula. The function has been introduced into the relax library as the calculation is repeated throughout relax.
* Expanded the basis sets for the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles user function] to allow the correct inter-tensor angles to be calculated. This includes the standard inter-matrix angles via the arccos of the Euclidean inner product of the alignment matrices in rank-2, 3D form divided by the Frobenius norm of the matrices, irreducible spherical tensor 5D basis set {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>}, and the unitary 9D basis set {SxxS<sub>xx</sub>, SxyS<sub>xy</sub>, SxzS<sub>xz</sub>, SyxS<sub>yx</sub>, SyyS<sub>yy</sub>, SyzS<sub>yz</sub>, SzxS<sub>zx</sub>, SzyS<sub>zy</sub>, SzzS<sub>zz</sub>} (all of which produce the same result).* Expanded the basis sets for the [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd user function] to allow the correct singular values and condition number to be calculated. This includes the irreducible spherical tensor 5D basis set {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>} and the unitary 9D basis set {SxxS<sub>xx</sub>, SxyS<sub>xy</sub>, SxzS<sub>xz</sub>, SyxS<sub>yx</sub>, SyyS<sub>yy</sub>, SyzS<sub>yz</sub>, SzxS<sub>zx</sub>, SzyS<sub>zy</sub>, SzzS<sub>zz</sub>} (both of which produce the same result).
* Added the angle_units and precision arguments to the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles user function] to allow either degrees or radians to be output and the number of decimal points to be specified.
* Added the precision argument to the [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd user function] to allow the number of decimal points for the singular values and condition number to be specified.
* Updated the [http://www.nmr-relax.com/manual/align_tensor_display.html align_tensor.display user function] to output the irreducible spherical harmonic weights. This is the alignment tensor in the {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>} notation.
<section end=features/>
* Conversion of the basis_set argument for the [http://www.nmr-relax.com/manual/align_tensor_svd.html 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.
* Expanded the N_state_model.test_5_state_xz system test. This now covers the new 'unitary 9D' basis set for the [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd user function] and the new 'matrix' basis set for the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles user function].
* Expansion of the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles user function]. The new basis set 'unitary 9D' has been introduced. This creates vectors as {SxxS<sub>xx</sub>, SxyS<sub>xy</sub>, SxzS<sub>xz</sub>, SyxS<sub>yx</sub>, SyyS<sub>yy</sub>, SyzS<sub>yz</sub>, SzxS<sub>zx</sub>, SzyS<sub>zy</sub>, SzzS<sub>zz</sub>} 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.
* 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 [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles] and [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd] user functions, and includes the new basis sets.
* Added the irreducible tensor notation of {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>} 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 DOI: 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<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>} 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.* Expanded the unit test of the alignment tensor {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>} parameters to cover all values.
* 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>.
* Added the 'irreducible 5D' basis set option to the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles user function]. This is for the inter-tensor vector angle for the irreducible 5D basis set {S<sub>-2</sub>, S<sub>-1</sub>, S0S<sub>0</sub>, S1S<sub>1</sub>, S2S<sub>2</sub>}. Its results match that of the standard tensor angle as well as the 'unitary 9D' basis sets.* Added the 'irreducible 5D' basis set option to the [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd user function]. This is for the inter-tensor vector angle for the irreducible 5D basis set {A<sub>-2</sub>, A<sub>-1</sub>, A0A<sub>0</sub>, A1A<sub>1</sub>, A2A<sub>2</sub>}. Its results match that of the 'unitary 9D' basis set.
* Editing of the description for the 'irreducible 5D' alignment tensor basis set. This is for the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles] and [http://www.nmr-relax.com/manual/align_tensor_svd.html align_tensor.svd] user functions. All Sm element have been converted to Am.
* Editing of the description for the [http://www.nmr-relax.com/manual/align_tensor_matrix_angles.html align_tensor.matrix_angles user function].
