Sheshuk/update flavor matrix interface

[Sheshuk]

This is a first part of changes, needed for #344

Expanding the interface of FlavorScheme and FlavorMatrix with useful methods and syntactic sugar. The goal is to make the code using these classes more expressive and look more similar to the formulas in the papers.

Example

This allows us to access and define individual matrix elements as well as whole submatrices with a clear interface (example from #344 defining the elements of matrix in mass_basis<<flavor_basis space)

snewpy/python/snewpy/neutrino.py

Lines 178 to 193 in 8181503

	# The NMO case. Matter state 3 is the electron neutrino, matter state 1bar is the electron antineutrino.
	k1 = T - np.sqrt(D)
	k2 = T + np.sqrt(D)
	k2bar = Tbar - np.sqrt(Dbar)
	k3bar = Tbar + np.sqrt(Dbar)
	PmfHDL['1','mu'] = (HV['tau','tau'].real - k1)/(k2-k1)
	PmfHDL['1','tau'] = (HV['mu','mu'].real - k1)/(k2-k1)
	PmfHDL['2','mu'] = (HV['tau','tau'].real - k2)/(k1-k2)
	PmfHDL['2','tau'] = (HV['mu','mu'].real - k2)/(k1 -k2)
	PmfHDL['3','e'] = 1
	PmfHDL['1_bar','e_bar'] = 1
	PmfHDL['2_bar','mu_bar'] = (HV['tau_bar','tau_bar'].real - k2bar ) / ( k3bar - k2bar )
	PmfHDL['2_bar','tau_bar'] = (HV['mu_bar','mu_bar'].real - k2bar ) / ( k3bar - k2bar )
	PmfHDL['3_bar','mu_bar'] = (HV['tau_bar','tau_bar'].real - k3bar ) / ( k2bar - k3bar )
	PmfHDL['3_bar','tau_bar'] = (HV['mu_bar','mu_bar'].real - k3bar ) / ( k2bar - k3bar )

Changes in FlavorScheme

1. Allowing to use shorter names for neutrinos, omitting NU_ prefix. Also ignoring the case.
2. Adding the 'NU' and 'NU_BAR' names to access the list of all neutrinos or antineutrinos

Changes in FlavorMatrix

1. Useful methods for complex matrix: real,imag,abs, abs2, conjugate
2. In the __matmul__ method: added check if the flavor schemes of the matrices' dimensions are compatible.
3. Adding the extra_dims options to constructors FlavorMatrix.eye and FlavorMatrix.zeros - to initialize arrays of size (N x M x extra_dims). These extra dimensions can be energy and/or time dependency of the transformation
4. Added conversion methods: convert_to_flavor method, and also << and >> operators, which allows to do the flavor bases conversion in one line, for example M_3f = (ThreeFlavor<<M<<ThreeFlavor)
5. Using np.einsum to perform the correct matrix multiplication of the matrices and matrix to flux
6. When creating conversion matrix, for example(ThreeFlavor<<FourFlavor), it will check that the matrix is non-zero - to prevent silent zeroing out when there was an intrinsic conversion to an incompatible flavor scheme

See the changes in test/test_flavors.py for the demonstration of some new functionality

[sybenzvi]

Integration tests are failing because of this obsolete flavor transformation (line 152 of base.py) in the SupernovaModel base class.

[sybenzvi]

Suggestion: while we have this PR open, rename the EnumMeta child class in flavor.py toFlavorEnumMeta.

Otherwise this looks pretty good.

[sybenzvi]

Integration tests are failing because of this obsolete flavor transformation (line 152 of base.py) in the SupernovaModel base class.

After discussion on Zoom, we agree that the failing integration tests are all due to the obsolete code in get_transformed_spectra that will be not be addressed until PR #351. So this should not hold up the merge.

[sybenzvi]

I made a cosmetic change of snewpy.flavor.EnumMeta to snewpy.flavor.FlavorEnumMeta, which feels a bit safer. Otherwise we can commit this, with the understanding that integration tests will fail in release_2.0.