reogranise into a python package

1 files changed, 0 insertions, 531 deletions

diff --git a/utils/fr.py b/utils/fr.py
deleted file mode 100644
index bf0fb56..0000000
--- a/utils/fr.py
+++ /dev/null
@@ -1,531 +0,0 @@
-# author : S. Mandalia
-#          s.p.mandalia@qmul.ac.uk
-#
-# date   : March 17, 2018
-
-"""
-Useful functions for the BSM flavour ratio analysis
-"""
-
-from __future__ import absolute_import, division
-
-from functools import partial
-
-import numpy as np
-
-from utils.enums import ParamTag, Texture
-from utils.misc import enum_parse, parse_bool
-
-import mpmath as mp
-mp.mp.dps = 100 # Computation precision
-
-# DTYPE  = np.float128
-# CDTYPE = np.complex256
-# PI     = np.arccos(DTYPE(-1))
-# SQRT   = np.sqrt
-# COS    = np.cos
-# SIN    = np.sin
-# ACOS   = np.arccos
-# ASIN   = np.arcsin
-# EXP    = np.exp
-
-DTYPE  = mp.mpf
-CDTYPE = mp.mpc
-PI     = mp.pi
-SQRT   = mp.sqrt
-COS    = mp.cos
-SIN    = mp.sin
-ACOS   = mp.acos
-ASIN   = mp.asin
-EXP    = mp.exp
-
-MASS_EIGENVALUES = [7.40E-23, 2.515E-21]
-"""SM mass eigenvalues."""
-
-SCALE_BOUNDARIES = {
-    3 : (-32, -20),
-    4 : (-40, -24),
-    5 : (-48, -27),
-    6 : (-56, -30),
-    7 : (-64, -33),
-    8 : (-72, -36)
-}
-"""Boundaries to scan the NP scale for each dimension."""
-
-
-def determinant(x):
-    """Calculate the determininant of a 3x3 matrix.
-
-    Parameters
-    ----------
-    x : ndarray, shape = (3, 3)
-
-    Returns
-    ----------
-    float determinant
-
-    Examples
-    ----------
-    >>> print determinant(
-    >>>     [[-1.65238188-0.59549718j,  0.27486548-0.18437467j, -1.35524534-0.38542072j],
-    >>>      [-1.07480906+0.29630449j, -0.47808456-0.80316821j, -0.88609356-1.50737308j],
-    >>>      [-0.14924144-0.99230446j,  0.49504234+0.63639805j, 2.29258915-0.36537507j]]
-    >>> )
-    (2.7797571563274688+3.0841795325804848j)
-
-    """
-    return (x[0][0] * (x[1][1] * x[2][2] - x[2][1] * x[1][2])
-           -x[1][0] * (x[0][1] * x[2][2] - x[2][1] * x[0][2])
-           +x[2][0] * (x[0][1] * x[1][2] - x[1][1] * x[0][2]))
-
-
-def angles_to_fr(src_angles):
-    """Convert angular projection of the source flavour ratio back into the
-    flavour ratio.
-
-    Parameters
-    ----------
-    src_angles : list, length = 2
-        sin(phi)^4 and cos(psi)^2
-
-    Returns
-    ----------
-    flavour ratios (nue, numu, nutau)
-
-    Examples
-    ----------
-    >>> print angles_to_fr((0.3, 0.4))
-    (0.38340579025361626, 0.16431676725154978, 0.45227744249483393)
-
-    """
-    sphi4, c2psi = map(DTYPE, src_angles)
-
-    psi = (0.5)*ACOS(c2psi)
-
-    sphi2 = SQRT(sphi4)
-    cphi2 = 1. - sphi2
-    spsi2 = SIN(psi)**2
-    cspi2 = 1. - spsi2
-
-    x = float(abs(sphi2*cspi2))
-    y = float(abs(sphi2*spsi2))
-    z = float(abs(cphi2))
-    return x, y, z
-
-
-def angles_to_u(bsm_angles):
-    """Convert angular projection of the mixing matrix elements back into the
-    mixing matrix elements.
-
-    Parameters
-    ----------
-    bsm_angles : list, length = 4
-        sin(12)^2, cos(13)^4, sin(23)^2 and deltacp
-
-    Returns
-    ----------
-    unitary numpy ndarray of shape (3, 3)
-
-    Examples
-    ----------
-    >>> from fr import angles_to_u
-    >>> print angles_to_u((0.2, 0.3, 0.5, 1.5))
-    array([[ 0.66195018+0.j        ,  0.33097509+0.j        ,  0.04757188-0.6708311j ],
-           [-0.34631487-0.42427084j,  0.61741198-0.21213542j,  0.52331757+0.j        ],
-           [ 0.28614067-0.42427084j, -0.64749908-0.21213542j,  0.52331757+0.j        ]])
-
-    """
-    s12_2, c13_4, s23_2, dcp = map(DTYPE, bsm_angles)
-    dcp = CDTYPE(dcp)
-
-    c12_2 = 1. - s12_2
-    c13_2 = SQRT(c13_4)
-    s13_2 = 1. - c13_2
-    c23_2 = 1. - s23_2
-
-    t12 = ASIN(SQRT(s12_2))
-    t13 = ACOS(SQRT(c13_2))
-    t23 = ASIN(SQRT(s23_2))
-
-    c12 = COS(t12)
-    s12 = SIN(t12)
-    c13 = COS(t13)
-    s13 = SIN(t13)
-    c23 = COS(t23)
-    s23 = SIN(t23)
-
-    p1 = np.array([[1   , 0   , 0]                , [0    , c23 , s23] , [0                , -s23 , c23]] , dtype=CDTYPE)
-    p2 = np.array([[c13 , 0   , s13*EXP(-1j*dcp)] , [0    , 1   , 0]   , [-s13*EXP(1j*dcp) , 0    , c13]] , dtype=CDTYPE)
-    p3 = np.array([[c12 , s12 , 0]                , [-s12 , c12 , 0]   , [0                , 0    , 1]]   , dtype=CDTYPE)
-
-    u = np.dot(np.dot(p1, p2), p3)
-    return u
-
-
-def cardano_eqn(ham):
-    """Diagonalise the effective Hamiltonian 3x3 matrix into the form
-    h_{eff} = UE_{eff}U^{dagger} using the procedure in PRD91, 052003 (2015).
-
-    Parameters
-    ----------
-    ham : numpy ndarray of shape (3, 3)
-        sin(12)^2, cos(13)^4, sin(23)^2 and deltacp
-
-    Returns
-    ----------
-    unitary numpy ndarray of shape (3, 3)
-
-    Examples
-    ----------
-    >>> import numpy as np
-    >>> from fr import cardano_eqn
-    >>> ham = np.array(
-    >>>     [[ 0.66195018+0.j        ,  0.33097509+0.j        ,  0.04757188-0.6708311j ],
-    >>>      [-0.34631487-0.42427084j,  0.61741198-0.21213542j,  0.52331757+0.j        ],
-    >>>      [ 0.28614067-0.42427084j, -0.64749908-0.21213542j,  0.52331757+0.j        ]]
-    >>> )
-    >>> print cardano_eqn(ham)
-    array([[-0.11143379-0.58863683j, -0.09067747-0.48219068j, 0.34276625-0.08686465j],
-           [ 0.14835519+0.47511473j, -0.18299305+0.40777481j, 0.31906300+0.82514223j],
-           [-0.62298966+0.07231745j, -0.61407815-0.42709603j, 0.03660313+0.30160428j]])
-
-    """
-    if np.shape(ham) != (3, 3):
-        raise ValueError(
-            'Input matrix should be a square and dimension 3, '
-            'got\n{0}'.format(ham)
-        )
-
-    a = -np.trace(ham)
-    b = DTYPE(1)/2 * ((np.trace(ham))**DTYPE(2) - np.trace(np.dot(ham, ham)))
-    c = -determinant(ham)
-
-    Q = (DTYPE(1)/9) * (a**DTYPE(2) - DTYPE(3)*b)
-    R = (DTYPE(1)/54) * (DTYPE(2)*a**DTYPE(3) - DTYPE(9)*a*b + DTYPE(27)*c)
-    theta = ACOS(R / SQRT(Q**DTYPE(3)))
-
-    E1 = -DTYPE(2) * SQRT(Q) * COS(theta/DTYPE(3)) - (DTYPE(1)/3)*a
-    E2 = -DTYPE(2) * SQRT(Q) * COS((theta - DTYPE(2)*PI)/DTYPE(3)) - (DTYPE(1)/3)*a
-    E3 = -DTYPE(2) * SQRT(Q) * COS((theta + DTYPE(2)*PI)/DTYPE(3)) - (DTYPE(1)/3)*a
-
-    A1 = ham[1][2] * (ham[0][0] - E1) - ham[1][0]*ham[0][2]
-    A2 = ham[1][2] * (ham[0][0] - E2) - ham[1][0]*ham[0][2]
-    A3 = ham[1][2] * (ham[0][0] - E3) - ham[1][0]*ham[0][2]
-
-    B1 = ham[2][0] * (ham[1][1] - E1) - ham[2][1]*ham[1][0]
-    B2 = ham[2][0] * (ham[1][1] - E2) - ham[2][1]*ham[1][0]
-    B3 = ham[2][0] * (ham[1][1] - E3) - ham[2][1]*ham[1][0]
-
-    C1 = ham[1][0] * (ham[2][2] - E1) - ham[1][2]*ham[2][0]
-    C2 = ham[1][0] * (ham[2][2] - E2) - ham[1][2]*ham[2][0]
-    C3 = ham[1][0] * (ham[2][2] - E3) - ham[1][2]*ham[2][0]
-
-    N1 = SQRT(np.abs(A1*B1)**2 + np.abs(A1*C1)**2 + np.abs(B1*C1)**2)
-    N2 = SQRT(np.abs(A2*B2)**2 + np.abs(A2*C2)**2 + np.abs(B2*C2)**2)
-    N3 = SQRT(np.abs(A3*B3)**2 + np.abs(A3*C3)**2 + np.abs(B3*C3)**2)
-
-    mm = np.array([
-        [np.conjugate(B1)*C1 / N1, np.conjugate(B2)*C2 / N2, np.conjugate(B3)*C3 / N3],
-        [A1*C1 / N1, A2*C2 / N2, A3*C3 / N3],
-        [A1*B1 / N1, A2*B2 / N2, A3*B3 / N3]
-    ])
-    return mm
-
-
-def normalise_fr(fr):
-    """Normalise an input flavour combination to a flavour ratio.
-
-    Parameters
-    ----------
-    fr : list, length = 3
-        flavour combination
-
-    Returns
-    ----------
-    numpy ndarray flavour ratio
-
-    Examples
-    ----------
-    >>> from fr import normalise_fr
-    >>> print normalise_fr((1, 2, 3))
-    array([ 0.16666667,  0.33333333,  0.5       ])
-
-    """
-    return np.array(fr) / float(np.sum(fr))
-
-
-def fr_argparse(parser):
-    parser.add_argument(
-        '--injected-ratio', type=float, nargs=3, required=False,
-        help='Injected ratio if not using data'
-    )
-    parser.add_argument(
-        '--source-ratio', type=float, nargs=3, default=[1, 2, 0],
-        help='Set the source flavour ratio for the case when you want to fix it'
-    )
-    parser.add_argument(
-        '--no-bsm', type=parse_bool, default='False',
-        help='Turn off BSM terms'
-    )
-    parser.add_argument(
-        '--dimension', type=int, default=3,
-        help='Set the new physics dimension to consider'
-    )
-    parser.add_argument(
-        '--texture', type=partial(enum_parse, c=Texture),
-        default='none', choices=Texture, help='Set the BSM mixing texture'
-    )
-    parser.add_argument(
-        '--binning', default=[6e4, 1e7, 20], type=float, nargs=3,
-        help='Binning for spectral energy dependance'
-    )
-
-
-def fr_to_angles(ratios):
-    """Convert from flavour ratio into the angular projection of the flavour
-    ratios.
-
-    Parameters
-    ----------
-    TODO(shivesh)
-    """
-    fr0, fr1, fr2 = normalise_fr(ratios)
-
-    cphi2 = fr2
-    sphi2 = (1.0 - cphi2)
-
-    if sphi2 == 0.:
-        return (0., 0.)
-    else:
-        cpsi2 = fr0 / sphi2
-
-    sphi4 = sphi2**2
-    c2psi = COS(ACOS(SQRT(cpsi2))*2)
-
-    return map(float, (sphi4, c2psi))
-
-
-NUFIT_U = angles_to_u((0.307, (1-0.02195)**2, 0.565, 3.97935))
-"""NuFIT mixing matrix (s_12^2, c_13^4, s_23^2, dcp)"""
-
-
-def params_to_BSMu(bsm_angles, dim, energy, mass_eigenvalues=MASS_EIGENVALUES,
-                   sm_u=NUFIT_U, no_bsm=False, texture=Texture.NONE,
-                   check_uni=True, epsilon=1e-7):
-    """Construct the BSM mixing matrix from the BSM parameters.
-
-    Parameters
-    ----------
-    bsm_angles : list, length > 3
-        BSM parameters
-
-    dim : int
-        Dimension of BSM physics
-
-    energy : float
-        Energy in GeV
-
-    mass_eigenvalues : list, length = 2
-        SM mass eigenvalues
-
-    sm_u : numpy ndarray, dimension 3
-        SM mixing matrix
-
-    no_bsm : bool
-        Turn off BSM behaviour
-
-    texture : Texture
-        BSM mixing texture
-
-    check_uni : bool
-        Check the resulting BSM mixing matrix is unitary
-
-    Returns
-    ----------
-    unitary numpy ndarray of shape (3, 3)
-
-    Examples
-    ----------
-    >>> from fr import params_to_BSMu
-    >>> print params_to_BSMu((0.2, 0.3, 0.5, 1.5, -20), dim=3, energy=1000)
-    array([[ 0.18658169 -6.34190523e-01j, -0.26460391 +2.01884200e-01j, 0.67247096 -9.86808417e-07j],
-           [-0.50419832 +2.14420570e-01j, -0.36013768 +5.44254868e-01j, 0.03700961 +5.22039894e-01j],
-           [-0.32561308 -3.95946524e-01j,  0.64294909 -2.23453580e-01j, 0.03700830 +5.22032403e-01j]])
-
-    """
-    if np.shape(sm_u) != (3, 3):
-        raise ValueError(
-            'Input matrix should be a square and dimension 3, '
-            'got\n{0}'.format(sm_u)
-        )
-
-    if not isinstance(bsm_angles, (list, tuple)):
-        bsm_angles = [bsm_angles]
-
-    z = 0.+1e-9
-    if texture is Texture.OEU:
-        np_s12_2, np_c13_4, np_s23_2, np_dcp, sc2 = 0.5, 1.0, z, z, bsm_angles
-    elif texture is Texture.OET:
-        np_s12_2, np_c13_4, np_s23_2, np_dcp, sc2 = z, 0.25,  z, z, bsm_angles
-    elif texture is Texture.OUT:
-        np_s12_2, np_c13_4, np_s23_2, np_dcp, sc2 = z, 1.0, 0.5, z, bsm_angles
-    else:
-        np_s12_2, np_c13_4, np_s23_2, np_dcp, sc2 = bsm_angles
-
-    sc2 = np.power(10., sc2)
-    sc1 = sc2 / 100.
-
-    mass_matrix = np.array(
-        [[0, 0, 0], [0, mass_eigenvalues[0], 0], [0, 0, mass_eigenvalues[1]]]
-    )
-    sm_ham = (1./(2*energy))*np.dot(sm_u, np.dot(mass_matrix, sm_u.conj().T))
-    if no_bsm:
-        eg_vector = cardano_eqn(sm_ham)
-    else:
-        NP_U = angles_to_u((np_s12_2, np_c13_4, np_s23_2, np_dcp))
-        SC_U = np.array(
-            [[0, 0, 0], [0, sc1, 0], [0, 0, sc2]]
-        )
-        bsm_term = (energy**(dim-3)) * np.dot(NP_U, np.dot(SC_U, NP_U.conj().T))
-        bsm_ham = sm_ham + bsm_term
-        eg_vector = cardano_eqn(bsm_ham)
-
-    if check_uni:
-        test_unitarity(eg_vector, rse=True, epsilon=epsilon)
-    return eg_vector
-
-
-def flux_averaged_BSMu(theta, args, spectral_index, llh_paramset):
-    if len(theta) != len(llh_paramset):
-        raise AssertionError(
-            'Length of MCMC scan is not the same as the input '
-            'params\ntheta={0}\nparamset]{1}'.format(theta, llh_paramset)
-        )
-
-    for idx, param in enumerate(llh_paramset):
-        param.value = theta[idx]
-
-    bin_centers = np.sqrt(args.binning[:-1]*args.binning[1:])
-    bin_width = np.abs(np.diff(args.binning))
-
-    source_flux = np.array(
-        [fr * np.power(bin_centers, spectral_index)
-         for fr in args.source_ratio]
-    ).T
-
-    bsm_angles = llh_paramset.from_tag(
-        [ParamTag.SCALE, ParamTag.MMANGLES], values=True
-    )
-
-    m_eig_names = ['m21_2', 'm3x_2']
-    ma_names = ['s_12_2', 'c_13_4', 's_23_2', 'dcp']
-
-    if set(m_eig_names+ma_names).issubset(set(llh_paramset.names)):
-        mass_eigenvalues = [x.value for x in llh_paramset if x.name in m_eig_names]
-        sm_u = angles_to_u(
-            [x.value for x in llh_paramset if x.name in ma_names]
-        )
-    else:
-        mass_eigenvalues = MASS_EIGENVALUES
-        sm_u = NUFIT_U
-
-    if args.no_bsm:
-        fr = u_to_fr(source_flux, np.array(sm_u, dtype=np.complex256))
-    else:
-        mf_perbin = []
-        for i_sf, sf_perbin in enumerate(source_flux):
-            u = params_to_BSMu(
-                bsm_angles        = bsm_angles,
-                dim               = args.dimension,
-                energy            = bin_centers[i_sf],
-                mass_eigenvalues  = mass_eigenvalues,
-                sm_u              = sm_u,
-                no_bsm            = args.no_bsm,
-                texture           = args.texture,
-            )
-            fr = u_to_fr(sf_perbin, u)
-            mf_perbin.append(fr)
-        measured_flux = np.array(mf_perbin).T
-        intergrated_measured_flux = np.sum(measured_flux * bin_width, axis=1)
-        averaged_measured_flux = (1./(args.binning[-1] - args.binning[0])) * \
-            intergrated_measured_flux
-        fr = averaged_measured_flux / np.sum(averaged_measured_flux)
-    return fr
-
-
-def test_unitarity(x, prnt=False, rse=False, epsilon=None):
-    """Test the unitarity of a matrix.
-
-    Parameters
-    ----------
-    x : numpy ndarray
-        Matrix to evaluate
-
-    prnt : bool
-        Print the result
-
-    rse : bool
-        Raise Assertion if matrix is not unitary
-
-    Returns
-    ----------
-    numpy ndarray
-
-    Examples
-    ----------
-    >>> from fr import test_unitarity
-    >>> x = np.identity(3)
-    >>> print test_unitarity(x)
-    array([[ 1.,  0.,  0.],
-           [ 0.,  1.,  0.],
-           [ 0.,  0.,  1.]])
-
-    """
-    f = np.abs(np.dot(x, x.conj().T), dtype=DTYPE)
-    if prnt:
-        print 'Unitarity test:\n{0}'.format(f)
-    if rse:
-        if not np.abs(np.trace(f) - 3.) < epsilon or \
-           not np.abs(np.sum(f) - 3.) < epsilon:
-            raise AssertionError(
-                'Matrix is not unitary!\nx\n{0}\ntest '
-                'u\n{1}'.format(x, f)
-            )
-    return f
-
-
-def u_to_fr(source_fr, matrix):
-    """Compute the observed flavour ratio assuming decoherence.
-
-    Parameters
-    ----------
-    source_fr : list, length = 3
-        Source flavour ratio components
-
-    matrix : numpy ndarray, dimension 3
-        Mixing matrix
-
-    Returns
-    ----------
-    Measured flavour ratio
-
-    Examples
-    ----------
-    >>> from fr import params_to_BSMu, u_to_fr
-    >>> print u_to_fr((1, 2, 0), params_to_BSMu((0.2, 0.3, 0.5, 1.5, -20), 3, 1000))
-        array([ 0.33740075,  0.33176584,  0.33083341])
-
-    """
-    try:
-        composition = np.einsum(
-            'ai, bi, a -> b', np.abs(matrix)**2, np.abs(matrix)**2, source_fr,
-        )
-    except:
-        matrix = np.array(matrix, dtype=np.complex256)
-        composition = np.einsum(
-            'ai, bi, a -> b', np.abs(matrix)**2, np.abs(matrix)**2, source_fr,
-        )
-        pass
-
-    ratio = composition / np.sum(source_fr)
-    return ratio