Initial Commit

1 files changed, 563 insertions, 0 deletions

diff --git a/mcmc_scan.py b/mcmc_scan.py
new file mode 100755
index 0000000..f79e2af
--- /dev/null
+++ b/mcmc_scan.py
@@ -0,0 +1,563 @@
+#! /usr/bin/env python
+"""
+From a gaussian likelihood run an MCMC scan to find the posteriors
+"""
+
+from __future__ import absolute_import, division
+
+import os, sys
+import errno
+
+import argparse
+import multiprocessing
+
+import numpy as np
+from scipy.stats import multivariate_normal
+from scipy import linalg
+
+import emcee
+import tqdm
+
+import chainer_plot
+
+
+RUN_SCAN = True
+
+FIX_MIXING = False
+FIX_SFR = True
+SOURCE_FR = [1, 2, 0]
+FIX_SCALE = True
+
+DIMENSION = 3
+ENERGY = 1000000 # GeV
+MEASURED_FR = [1, 1, 1]
+SIGMA = 0.001
+SCALE_RATIO = 100.
+MASS_EIGENVALUES = [7.40E-23, 2.515E-21]
+# MASS_EIGENVALUES = [7.40E-100, 2.515E-100]
+FLAT = False
+
+CHANGE_MASS = False
+if CHANGE_MASS:
+    SCALE = 1E-27
+else:
+    SCALE = np.power(10, np.round(np.log10(MASS_EIGENVALUES[1]/ENERGY)) - np.log10(ENERGY**(DIMENSION-3)))
+SCALE2_BOUNDS = (SCALE*1E-10, SCALE*1E10)
+
+
+def test_uni(x):
+    """Test the unitarity of a matrix."""
+    # print 'Unitarity test:\n{0}'.format(abs(np.dot(x, x.conj().T)))
+    return abs(np.dot(x, x.conj().T))
+
+
+def angles_to_fr(angles):
+    sphi4, c2psi = angles
+
+    psi = (0.5)*np.arccos(c2psi)
+
+    sphi2 = np.sqrt(sphi4)
+    cphi2 = 1. - sphi2
+    spsi2 = np.sin(psi)**2
+    cspi2 = 1. - spsi2
+
+    x = sphi2*cspi2
+    y = sphi2*spsi2
+    z = cphi2
+    return x, y, z
+
+
+def angles_to_u(angles):
+    s12_2, c13_4, s23_2, dcp = angles
+    dcp = np.complex128(dcp)
+
+    c12_2 = 1. - s12_2
+    c13_2 = np.sqrt(c13_4)
+    s13_2 = 1. - c13_2
+    c23_2 = 1. - s23_2
+
+    t12 = np.arcsin(np.sqrt(s12_2))
+    t13 = np.arccos(np.sqrt(c13_2))
+    t23 = np.arcsin(np.sqrt(s23_2))
+
+    c12 = np.cos(t12)
+    s12 = np.sin(t12)
+    c13 = np.cos(t13)
+    s13 = np.sin(t13)
+    c23 = np.cos(t23)
+    s23 = np.sin(t23)
+
+    p1 = np.array([[1   , 0   , 0]                   , [0    , c23 , s23] , [0                   , -s23 , c23]] , dtype=np.complex128)
+    p2 = np.array([[c13 , 0   , s13*np.exp(-1j*dcp)] , [0    , 1   , 0]   , [-s13*np.exp(1j*dcp) , 0    , c13]] , dtype=np.complex128)
+    p3 = np.array([[c12 , s12 , 0]                   , [-s12 , c12 , 0]   , [0                   , 0    , 1]]   , dtype=np.complex128)
+
+    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)
+    """
+    a = -np.trace(ham)
+    b = (0.5) * ((np.trace(ham))**2 - np.trace(np.dot(ham, ham)))
+    c = -linalg.det(ham)
+
+    Q = (1/9.) * (a**2 - 3*b)
+    R = (1/54.) * (2*a**3 - 9*a*b + 27*c)
+    theta = np.arccos(R / np.sqrt(Q**3))
+
+    E1 = -2 * np.sqrt(Q) * np.cos(theta/3.) - (1/3.)*a
+    E2 = -2 * np.sqrt(Q) * np.cos((theta - 2.*np.pi)/3.) - (1/3.)*a
+    E3 = -2 * np.sqrt(Q) * np.cos((theta + 2.*np.pi)/3.) - (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 = np.sqrt(abs(A1*B1)**2 + abs(A1*C1)**2 + abs(B1*C1)**2)
+    N2 = np.sqrt(abs(A2*B2)**2 + abs(A2*C2)**2 + abs(B2*C2)**2)
+    N3 = np.sqrt(abs(A3*B3)**2 + abs(A3*C3)**2 + 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
+
+
+# s_12^2, c_13^4, s_23^2, dcp
+NUFIT_U = angles_to_u((0.307, (1-0.02195)**2, 0.565, 3.97935))
+
+
+def params_to_BSMu(theta):
+    if FIX_MIXING:
+        s12_2, c13_4, s23_2, dcp, sc2 = 0.5, 1.0-1E-6, 0.5, 0., theta
+    elif FIX_SCALE:
+        s12_2, c13_4, s23_2, dcp = theta
+        sc2 = np.log10(SCALE)
+    else:
+        s12_2, c13_4, s23_2, dcp, sc2 = theta
+    sc2 = np.power(10., sc2)
+    sc1 = sc2 / SCALE_RATIO
+
+    mass_matrix = np.array(
+        [[0, 0, 0], [0, MASS_EIGENVALUES[0], 0], [0, 0, MASS_EIGENVALUES[1]]]
+    )
+    sm_ham = (1./(2*ENERGY))*np.dot(NUFIT_U, np.dot(mass_matrix, NUFIT_U.conj().T))
+
+    new_physics_u = angles_to_u((s12_2, c13_4, s23_2, dcp))
+    scale_matrix = np.array(
+        [[0, 0, 0], [0, sc1, 0], [0, 0, sc2]]
+    )
+    bsm_term = (ENERGY**(DIMENSION-3)) * np.dot(new_physics_u, np.dot(scale_matrix, new_physics_u.conj().T))
+
+    bsm_ham = sm_ham + bsm_term
+
+    eg_vector = cardano_eqn(bsm_ham)
+    tu = test_uni(eg_vector)
+    if not abs(np.trace(tu) - 3.) < 1e-5 or not abs(np.sum(tu) - 3.) < 1e-5:
+	raise AssertionError('Matrix is not unitary!\neg_vector\n{0}\ntest u\n{1}'.format(eg_vector, tu))
+    return eg_vector
+
+
+def u_to_fr(initial_fr, matrix):
+    """Compute the observed flavour ratio assuming decoherence."""
+    # TODO(shivesh): energy dependence
+    composition = np.einsum(
+        'ai, bi, a -> b', abs(matrix)**2, abs(matrix)**2, initial_fr
+    )
+    ratio = composition / np.sum(initial_fr)
+    return ratio
+
+
+def triangle_llh(theta):
+    """-Log likelihood function for a given theta."""
+    if FIX_SFR:
+        fr1, fr2, fr3 = SOURCE_FR
+        u = params_to_BSMu(theta)
+    else:
+        fr1, fr2, fr3 = angles_to_fr(theta[-2:])
+        u = params_to_BSMu(theta[:-2])
+
+    fr = u_to_fr((fr1, fr2, fr3), u)
+    fr_bf = MEASURED_FR
+    cov_fr = np.identity(3) * SIGMA
+    if FLAT:
+        return 10.
+    else:
+        return np.log(multivariate_normal.pdf(fr, mean=fr_bf, cov=cov_fr))
+
+
+def lnprior(theta):
+    """Priors on theta."""
+    if FIX_SFR:
+        if FIX_MIXING:
+            s12_2, sc2 = theta
+        elif FIX_SCALE:
+            s12_2, c13_4, s23_2, dcp = theta
+        else:
+            s12_2, c13_4, s23_2, dcp, sc2 = theta
+    else:
+        if FIX_MIXING:
+            sc2, sphi4, c2psi = theta
+        elif FIX_SCALE:
+            s12_2, c13_4, s23_2, dcp, sphi4, c2psi = theta
+        else:
+            s12_2, c13_4, s23_2, dcp, sc2, sphi4, c2psi = theta
+    if not FIX_SCALE:
+        sc2 = np.power(10., sc2)
+
+    if not FIX_SFR:
+        # Flavour ratio bounds
+        if 0. <= sphi4 <= 1.0 and -1.0 <= c2psi <= 1.0:
+            pass
+        else: return -np.inf
+
+    # Mixing angle bounds
+    if not FIX_MIXING:
+        if 0. <= s12_2 <= 1. and 0. <= c13_4 <= 1. and 0. <= s23_2 <= 1. \
+           and 0. <= dcp <= 2*np.pi:
+            pass
+        else: return -np.inf
+
+    # Scale bounds
+    if not FIX_SCALE:
+        if SCALE2_BOUNDS[0] <= sc2 <= SCALE2_BOUNDS[1]:
+            pass
+        else: return -np.inf
+
+    return 0.
+
+
+def lnprob(theta):
+    """Prob function for mcmc."""
+    lp = lnprior(theta)
+    if not np.isfinite(lp):
+        return -np.inf
+    return lp + triangle_llh(theta)
+
+
+def parse_args():
+    """Parse command line arguments"""
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument(
+        '--measured-ratio', type=int, nargs=3, default=[1, 1, 1],
+        help='Set the central value for the measured flavour ratio at IceCube'
+    )
+    parser.add_argument(
+        '--sigma-ratio', type=float, default=0.01,
+        help='Set the 1 sigma for the measured flavour ratio'
+    )
+    parser.add_argument(
+        '--fix-source-ratio', type=str, default='False',
+        help='Fix the source flavour ratio'
+    )
+    parser.add_argument(
+        '--source-ratio', type=int, nargs=3, default=[2, 1, 0],
+        help='Set the source flavour ratio for the case when you want to fix it'
+    )
+    parser.add_argument(
+        '--fix-mixing', type=str, default='False',
+        help='Fix all mixing parameters except one'
+    )
+    parser.add_argument(
+        '--fix-scale', type=str, default='False',
+        help='Fix the new physics scale'
+    )
+    parser.add_argument(
+        '--scale', type=float, default=1e-30,
+        help='Set the new physics scale'
+    )
+    parser.add_argument(
+        '--dimension', type=int, default=3,
+        help='Set the new physics dimension to consider'
+    )
+    parser.add_argument(
+        '--energy', type=float, default=1000,
+        help='Set the energy scale'
+    )
+    parser.add_argument(
+        '--flat-llh', type=str, default='False',
+        help='Run with a flat likelihood'
+    )
+    parser.add_argument(
+        '--burnin', type=int, default=100,
+        help='Amount to burnin'
+    )
+    parser.add_argument(
+        '--nwalkers', type=int, default=100,
+        help='Number of walkers'
+    )
+    parser.add_argument(
+        '--nsteps', type=int, default=2000,
+        help='Number of steps to run'
+    )
+    parser.add_argument(
+        '--seed', type=int, default=99,
+        help='Set the random seed value'
+    )
+    parser.add_argument(
+        '--outfile', type=str, default='./untitled',
+        help='Path to output chains'
+    )
+    args = parser.parse_args()
+    return args
+
+
+def main():
+    args = parse_args()
+
+    np.random.seed(args.seed)
+
+    global DIMENSION
+    global ENERGY
+    global MEASURED_FR
+    global SIGMA
+    global FLAT
+    global FIX_SFR
+    global SOURCE_FR
+    global FIX_MIXING
+    global FIX_SCALE
+    global SCALE
+    global SCALE2_BOUNDS
+
+    DIMENSION = args.dimension
+    ENERGY = args.energy
+
+    MEASURED_FR = np.array(args.measured_ratio) / float(np.sum(args.measured_ratio))
+    SIGMA = args.sigma_ratio
+
+    if args.flat_llh.lower() == 'true':
+        FLAT = True
+    elif args.flat_llh.lower() == 'false':
+        FLAT = False
+    else:
+        raise ValueError
+
+    if args.fix_source_ratio.lower() == 'true':
+        FIX_SFR = True
+    elif args.fix_source_ratio.lower() == 'false':
+        FIX_SFR = False
+    else:
+        raise ValueError
+
+    if args.fix_mixing.lower() == 'true':
+        FIX_MIXING = True
+    elif args.fix_mixing.lower() == 'false':
+        FIX_MIXING = False
+    else:
+        raise ValueError
+
+    if args.fix_scale.lower() == 'true':
+        FIX_SCALE = True
+    elif args.fix_scale.lower() == 'false':
+        FIX_SCALE = False
+    else:
+        raise ValueError
+
+    if FIX_SFR:
+        SOURCE_FR = np.array(args.source_ratio) / float(np.sum(args.source_ratio))
+
+    if FIX_SCALE:
+	SCALE = args.scale
+    else:
+        if CHANGE_MASS:
+            SCALE = 1E-27
+        else:
+            SCALE = np.power(10, np.round(np.log10(MASS_EIGENVALUES[1]/ENERGY)) - np.log10(ENERGY**(DIMENSION-3)))
+
+    if FIX_MIXING and FIX_SFR:
+        raise NotImplementedError('Fixed mixing and sfr not implemented')
+    if FIX_MIXING and FIX_SCALE:
+        raise NotImplementedError('Fixed mixing and scale not implemented')
+
+    SCALE2_BOUNDS = (SCALE*1E-10, SCALE*1E10)
+
+    print 'RUN_SCAN = {0}'.format(RUN_SCAN)
+    print 'MEASURED_FR = {0}'.format(MEASURED_FR)
+    print 'SIGMA = {0}'.format(SIGMA)
+    print 'FLAT = {0}'.format(FLAT)
+    print 'ENERGY = {0}'.format(ENERGY)
+    print 'DIMENSION = {0}'.format(DIMENSION)
+    print 'SCALE2_BOUNDS = {0}'.format(SCALE2_BOUNDS)
+    print 'FIX_SFR = {0}'.format(FIX_SFR)
+    if FIX_SFR:
+        print 'SOURCE_FR = {0}'.format(SOURCE_FR)
+    print 'FIX_MIXING = {0}'.format(FIX_MIXING)
+    print 'FIX_SCALE = {0}'.format(FIX_SCALE)
+    if FIX_SCALE:
+        print 'SCALE = {0}'.format(SCALE)
+
+    if FIX_SFR:
+        if FIX_MIXING:
+            ndim = 2
+        elif FIX_SCALE:
+            ndim = 4
+        else:
+            ndim = 5
+    else:
+        if FIX_MIXING:
+            ndim = 3
+        elif FIX_SCALE:
+            ndim = 6
+        else:
+            ndim = 7
+    nwalkers = args.nwalkers
+    ntemps = 1
+    burnin = args.burnin
+    betas = np.array([1e0, 1e-1, 1e-2, 1e-3, 1e-4])
+    s2 = np.average(np.log10(SCALE2_BOUNDS))
+    if FIX_SFR:
+        if FIX_MIXING:
+            p0_base = [0.5, s2]
+            p0_std = [0.2, 3]
+        elif FIX_SCALE:
+            p0_base = [0.5, 0.5, 0.5, np.pi]
+            p0_std = [0.2, 0.2, 0.2, 0.2]
+        else:
+            p0_base = [0.5, 0.5, 0.5, np.pi, s2]
+            p0_std = [0.2, 0.2, 0.2, 0.2, 3]
+    else:
+        if FIX_MIXING:
+            p0_base = [s2, 0.5, 0.0]
+            p0_std = [3, 0.2, 0.2]
+        elif FIX_SCALE:
+            p0_base = [0.5, 0.5, 0.5, np.pi, 0.5, 0.0]
+            p0_std = [0.2, 0.2, 0.2, 0.2, 0.2, 0.2]
+        else:
+            p0_base = [0.5, 0.5, 0.5, np.pi, s2, 0.5, 0.0]
+            p0_std = [0.2, 0.2, 0.2, 0.2, 3, 0.2, 0.2]
+
+    print 'p0_base', p0_base
+    print 'p0_std', p0_std
+    p0 = np.random.normal(p0_base, p0_std, size=[ntemps, nwalkers, ndim])
+    print map(lnprior, p0[0])
+
+    if RUN_SCAN:
+        # threads = multiprocessing.cpu_count()
+        threads = 1
+        sampler = emcee.PTSampler(
+            ntemps, nwalkers, ndim, triangle_llh, lnprior, threads=threads
+        )
+
+    if RUN_SCAN:
+        print "Running burn-in"
+        for result in tqdm.tqdm(sampler.sample(p0, iterations=burnin), total=burnin):
+            pos, prob, state = result
+        sampler.reset()
+        print "Finished burn-in"
+
+        nsteps = args.nsteps
+
+        print "Running"
+        for _ in tqdm.tqdm(sampler.sample(pos, iterations=nsteps), total=nsteps):
+            pass
+        print "Finished"
+
+    if FIX_SFR:
+        if FIX_MIXING:
+            outfile = args.outfile+'_{0:03d}_{1:03d}_{2:03d}_{3:04d}_sfr_{4:03d}_{5:03d}_{6:03d}_DIM{7}_fix_mixing'.format(
+                int(MEASURED_FR[0]*100), int(MEASURED_FR[1]*100), int(MEASURED_FR[2]*100), int(SIGMA*1000),
+                int(SOURCE_FR[0]*100), int(SOURCE_FR[1]*100), int(SOURCE_FR[2]*100), DIMENSION
+            )
+        elif FIX_SCALE:
+            outfile = args.outfile+'_{0:03d}_{1:03d}_{2:03d}_{3:04d}_sfr_{4:03d}_{5:03d}_{6:03d}_DIM{7}_fixed_scale_{8}'.format(
+                int(MEASURED_FR[0]*100), int(MEASURED_FR[1]*100), int(MEASURED_FR[2]*100), int(SIGMA*1000),
+                int(SOURCE_FR[0]*100), int(SOURCE_FR[1]*100), int(SOURCE_FR[2]*100), DIMENSION, SCALE
+            )
+        else:
+            outfile = args.outfile+'_{0:03d}_{1:03d}_{2:03d}_{3:04d}_sfr_{4:03d}_{5:03d}_{6:03d}_DIM{7}_single_scale'.format(
+                int(MEASURED_FR[0]*100), int(MEASURED_FR[1]*100), int(MEASURED_FR[2]*100), int(SIGMA*1000),
+                int(SOURCE_FR[0]*100), int(SOURCE_FR[1]*100), int(SOURCE_FR[2]*100), DIMENSION
+            )
+    else:
+        if FIX_MIXING:
+            outfile = args.outfile+'_{0:03d}_{1:03d}_{2:03d}_{3:04d}_DIM{4}_fix_mixing'.format(
+                int(MEASURED_FR[0]*100), int(MEASURED_FR[1]*100), int(MEASURED_FR[2]*100),
+                int(SIGMA*1000), DIMENSION
+            )
+        elif FIX_SCALE:
+            outfile = args.outfile+'_{0:03d}_{1:03d}_{2:03d}_{3:04d}_DIM{4}_fixed_scale_{5}'.format(
+                int(MEASURED_FR[0]*100), int(MEASURED_FR[1]*100), int(MEASURED_FR[2]*100),
+                int(SIGMA*1000), DIMENSION, SCALE
+            )
+        else:
+            outfile = args.outfile+'_{0:03d}_{1:03d}_{2:03d}_{3:04d}_DIM{4}'.format(
+                int(MEASURED_FR[0]*100), int(MEASURED_FR[1]*100), int(MEASURED_FR[2]*100),
+                int(SIGMA*1000), DIMENSION
+            )
+
+    if RUN_SCAN:
+        samples = sampler.chain[0, :, :, :].reshape((-1, ndim))
+        print 'acceptance fraction', sampler.acceptance_fraction
+        print 'sum of acceptance fraction', np.sum(sampler.acceptance_fraction)
+        print 'np.unique(samples[:,0]).shape', np.unique(samples[:,0]).shape
+
+        try:
+            print 'autocorrelation', sampler.acor
+        except:
+            print 'WARNING : NEED TO RUN MORE SAMPLES FOR FILE ' + outfile
+
+    if FLAT:
+	outfile += '_flat'
+
+    if RUN_SCAN:
+        try:
+            os.makedirs(outfile[:-len(os.path.basename(outfile))])
+        except OSError as exc:  # Python >2.5
+            if exc.errno == errno.EEXIST and os.path.isdir(outfile[:-len(os.path.basename(outfile))]):
+                pass
+            else:
+                raise
+        np.save(outfile+'.npy', samples)
+
+    # print "Making triangle plots"
+    # chainer_plot.plot(
+    #     infile=outfile+'.npy',
+    #     angles=True,
+    #     outfile=outfile[:5]+outfile[5:].replace('data', 'plots')+'_angles.pdf',
+    #     measured_ratio=MEASURED_FR,
+    #     sigma_ratio=SIGMA,
+    #     fix_sfr=FIX_SFR,
+    #     fix_mixing=FIX_MIXING,
+    #     fix_scale=FIX_SCALE,
+    #     source_ratio=SOURCE_FR,
+    #     scale=SCALE,
+	# dimension=DIMENSION,
+	# energy=ENERGY,
+	# scale_bounds=SCALE2_BOUNDS,
+    # )
+    # chainer_plot.plot(
+    #     infile=outfile+'.npy',
+    #     angles=False,
+    #     outfile=outfile[:5]+outfile[5:].replace('data', 'plots')+'.pdf',
+    #     measured_ratio=MEASURED_FR,
+    #     sigma_ratio=SIGMA,
+    #     fix_sfr=FIX_SFR,
+    #     fix_mixing=FIX_MIXING,
+    #     fix_scale=FIX_SCALE,
+    #     source_ratio=SOURCE_FR,
+    #     scale=SCALE,
+    #     dimension=DIMENSION,
+    #     energy=ENERGY,
+    #     scale_bounds=SCALE2_BOUNDS,
+    # )
+    print "DONE!"
+
+
+main.__doc__ = __doc__
+
+
+if __name__ == '__main__':
+    main()
+