Tests for path deformation in 1d and 2d

test/pd_1d_test.py

@@ -0,0 +1,81 @@
+"""
+Path deformation from CT
+========================
+
+Tests for path deformation applied to 1d potentials parameterised by E and
+alpha. For tunneling, E < 0 and 0.5 < alpha < 0.75.
+
+    V(f) = E * ((4. * alpha - 3.) / 2. * f**2 + f**3 - alpha * f**4)
+
+Spot check:
+
+>>> action_1d(0.6, -1.)
+7.445...
+
+>>> action_1d(0.55, -3.)
+19.157...
+
+Exception checks:
+
+>>> action_1d(0.6, 1.)
+Traceback (most recent call last):
+...
+ValueError: Maximum allowed size exceeded
+
+
+>>> action_1d(0.45, -1.)
+Traceback (most recent call last):
+...
+PotentialError: ('V(phi_metaMin) <= V(phi_absMin); tunneling cannot occur.', 'stable, not metastable')
+
+>>> action_1d(0.75, -1.)
+Traceback (most recent call last):
+...
+PotentialError: ('Barrier height is not positive, does not exist.', 'no barrier')
+
+Systematic check:
+
+>>> alpha = np.linspace(0.51, 0.749, 100)
+>>> E = -2.
+>>> action = [action_1d(a, E) for a in alpha]
+>>> expected = [562.92647189163586, 367.22180702340177, 258.65337026110859, 192.16481782909108, 148.47724421863325, 118.21852370609565, 96.383901938278768, 80.10344033396747, 67.6338797886024, 57.867532657401441, 50.072509618002243, 43.749156396166121, 38.547529535514386, 34.185909646521978, 30.543307423766056, 27.449313535197856, 24.800526223895005, 22.521447676079379, 20.574731459115796, 18.739223251865461, 17.169513582514359, 15.783149791721431, 14.5618758060631, 13.550904635140817, 12.565608908901291, 11.685280247098385, 10.869010755096969, 10.124142157820726, 9.44568875467181, 8.8279916343178222, 8.2632875985544647, 7.7452570926690365, 7.2676652494380605, 6.8267494245346443, 6.4175373784126162, 6.0376747548013547, 5.6914389287941276, 5.3554165827426816, 5.0705221440255359, 4.791996484443354, 4.5297073497757996, 4.2828914791509032, 4.0515569635462247, 3.8349094334723897, 3.6305752360114112, 3.4409770755842342, 3.2539978584608633, 3.0846092986447409, 2.9108358431735608, 2.7567245469680777, 2.6100700583506056, 2.4692584724608619, 2.3361399373781113, 2.210043151988573, 2.0904092847286364, 1.9764226992197085, 1.8678050154027728, 1.7655240012880855, 1.6679023775534181, 1.574854526781746, 1.4861153844329582, 1.4015387097538872, 1.3208902612276427, 1.2440384090792016, 1.1706648551024457, 1.1006590141085129, 1.0338216147825368, 0.97001008256914778, 0.90908200299037412, 0.85084046161777072, 0.79529828754359988, 0.74225104545346365, 0.69160841561155051, 0.64330682019730134, 0.59719197729990947, 0.55326396110926002, 0.51134154764300899, 0.4713569883129578, 0.43331005578464654, 0.39710922709558727, 0.36268780622023838, 0.32999460918823814, 0.29898581222260556, 0.26953408837941223, 0.24173476590470569, 0.21544404973607681, 0.19058184362100905, 0.16724757117510367, 0.14533602663807349, 0.12484511253240671, 0.1060537896725911, 0.088430534225688806, 0.072172325551223424, 0.057410548616978113, 0.043843863175876768, 0.031886858346490562, 0.021371414033251414, 0.012563681812002497, 0.0055929259686676863, 0.0009435456878673107]
+>>> assert all(np.isclose(action, expected))
+"""
+
+from cosmoTransitions.pathDeformation import fullTunneling as path_deform
+import numpy as np
+
+
+def action_1d(alpha, E):
+    """
+    :param alpha: Parametrises shape of 1d potential
+    :param E: Parameteries height of 1d potential
+
+    :returns: Action from path deformation
+    """
+    def V(f):
+        """
+        :returns: 1d potential
+        """
+        return E * ((4. * alpha - 3.) / 2. * f**2 + f**3 - alpha * f**4)
+
+    def dV(f):
+        """
+        :returns: Derivative of 1d potential
+        """
+        return E *((4. * alpha - 3.) * f + 3. * f**2 - 4. * alpha * f**3)
+
+    n_points = 100
+    guess_phi = np.linspace(1., 0., n_points)  # Extrema always at 1 and 0
+    guess_phi = np.reshape(guess_phi, (n_points, 1))
+
+    kwargs = {'deformation_deform_params': {'verbose': False}}
+
+    profile_1d, phi, action = path_deform(guess_phi, V, dV, **kwargs)[:3]
+
+    return action
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod(optionflags=doctest.ELLIPSIS ^ doctest.REPORT_NDIFF)

test/pd_2d_test.py

@@ -0,0 +1,78 @@
+"""
+Path deformation from CT
+========================
+
+Tests for path deformation applied to a 2d potential.
+
+The potential is eq. 13 in https://arxiv.org/pdf/1109.4189.pdf parameterised
+by the variable delta. The true vacuum was found by Mathematica in the below
+test cases.
+
+>>> action_2d(1., [1.06561, 2.24282])
+2.0901...
+
+>>> action_2d(0.5, [1.05114, 1.77899])
+8.7948...
+
+>>> action_2d(0.4, [1.04637, 1.66349])
+12.972...
+
+>>> action_2d(0.3, [1.0403, 1.53521])
+21.024...
+
+>>> action_2d(0.2, [1.03213, 1.38923])
+39.648...
+
+>>> action_2d(0.1, [1.0202, 1.21683])
+119.83...
+
+>>> action_2d(0.01, [1.00267, 1.02459])
+7853.5...
+
+>>> action_2d(0.001, [1.00028, 1.0025])
+639494.2...
+"""
+
+from cosmoTransitions.pathDeformation import fullTunneling as path_deform
+import numpy as np
+
+
+def action_2d(delta, true_vacuum):
+    """
+    :param alpha: Parametrises shape of 1d potential
+    :param E: Parameteries height of 1d potential
+
+    :returns: Action from path deformation
+    """
+    def V(fields):
+        """
+        :returns: 2d potential
+        """
+        f, g = fields[..., 0], fields[..., 1]
+        return (f**2 + g**2) * (1.8 * (f - 1.)**2 + 0.2 * (g - 1.)**2 - delta)
+
+    def dV(fields):
+        """
+        :returns: Derivative of 2d potential
+        """
+        f, g = fields[..., 0], fields[..., 1]
+        df = -10.8 * f**2 + 7.2 * f**3 - 3.6 * g**2 - 2. * f * (-2. + delta + 0.4 * g - 2. * g**2)
+        dg = -7.2 * f * g + f**2 * (-0.4 + 4. * g) + g * (4. - 2. * delta - 1.2 * g + 0.8 * g**2)
+        rval = np.empty_like(fields)
+        rval[..., 0] = df
+        rval[..., 1] = dg
+        return rval
+
+    n_points = 100
+    guess_phi = np.array([np.linspace(t, 0., n_points) for t in true_vacuum]).T
+
+    kwargs = {'deformation_deform_params': {'verbose': False}}
+
+    profile_1d, phi, action = path_deform(guess_phi, V, dV, **kwargs)[:3]
+
+    return action
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod(optionflags=doctest.ELLIPSIS ^ doctest.REPORT_NDIFF)