Commit b3a06798 by Theo Steininger

### Fixed hermitianization. Moved preserve_gaussian_covariance completely to the Field.

`Made tests more complete.`
parent 4a36f41c
Pipeline #14517 passed with stage
in 6 minutes and 14 seconds
 ... ... @@ -599,58 +599,55 @@ class Field(Loggable, Versionable, object): # hermitianize for the first space (h, a) = domain[spaces[0]].hermitian_decomposition( val, domain_axes[spaces[0]], preserve_gaussian_variance=preserve_gaussian_variance) domain_axes[spaces[0]]) # hermitianize all remaining spaces using the iterative formula for space in xrange(1, len(spaces)): for space in spaces[1:]: (hh, ha) = domain[space].hermitian_decomposition( h, domain_axes[space], preserve_gaussian_variance=False) domain_axes[space]) (ah, aa) = domain[space].hermitian_decomposition( a, domain_axes[space], preserve_gaussian_variance=False) domain_axes[space]) c = (hh - ha - ah + aa).conjugate() full = (hh + ha + ah + aa) h = (full + c)/2. a = (full - c)/2. # correct variance # in principle one must not correct the variance for the fixed # points of the hermitianization. However, for a complex field # the input field loses half of its power at its fixed points # in the `hermitian` part. Hence, here a factor of sqrt(2) is # also necessary! # => The hermitianization can be done on a space level since either # nothing must be done (LMSpace) or ALL points need a factor of sqrt(2) # => use the preserve_gaussian_variance flag in the # hermitian_decomposition method above. # This code is for educational purposes: # fixed_points = [domain[i].hermitian_fixed_points() for i in spaces] # # check if there was at least one flipping during hermitianization # flipped_Q = np.any([fp is not None for fp in fixed_points]) # # if the array got flipped, correct the variance # if flipped_Q: # h *= np.sqrt(2) # a *= np.sqrt(2) # # fixed_points = [[fp] if fp is None else fp for fp in fixed_points] # for product_point in itertools.product(*fixed_points): # slice_object = np.array((slice(None), )*len(val.shape), # dtype=np.object) # for i, sp in enumerate(spaces): # point_component = product_point[i] # if point_component is None: # point_component = slice(None) # slice_object[list(domain_axes[sp])] = point_component # # slice_object = tuple(slice_object) # h[slice_object] /= np.sqrt(2) # a[slice_object] /= np.sqrt(2) if preserve_gaussian_variance: h *= np.sqrt(2) a *= np.sqrt(2) if not issubclass(val.dtype.type, np.complexfloating): # in principle one must not correct the variance for the fixed # points of the hermitianization. However, for a complex field # the input field loses half of its power at its fixed points # in the `hermitian` part. Hence, here a factor of sqrt(2) is # also necessary! # => The hermitianization can be done on a space level since # either nothing must be done (LMSpace) or ALL points need a # factor of sqrt(2) # => use the preserve_gaussian_variance flag in the # hermitian_decomposition method above. # This code is for educational purposes: fixed_points = [domain[i].hermitian_fixed_points() for i in spaces] fixed_points = [[fp] if fp is None else fp for fp in fixed_points] for product_point in itertools.product(*fixed_points): slice_object = np.array((slice(None), )*len(val.shape), dtype=np.object) for i, sp in enumerate(spaces): point_component = product_point[i] if point_component is None: point_component = slice(None) slice_object[list(domain_axes[sp])] = point_component slice_object = tuple(slice_object) h[slice_object] /= np.sqrt(2) a[slice_object] /= np.sqrt(2) return (h, a) def _spec_to_rescaler(self, spec, result_list, power_space_index): ... ...
 ... ... @@ -89,25 +89,21 @@ class LMSpace(Space): super(LMSpace, self).__init__() self._lmax = self._parse_lmax(lmax) def hermitian_decomposition(self, x, axes=None, preserve_gaussian_variance=False): def hermitian_decomposition(self, x, axes=None): if issubclass(x.dtype.type, np.complexfloating): hermitian_part = x.copy_empty() anti_hermitian_part = x.copy_empty() hermitian_part[:] = x.real anti_hermitian_part[:] = x.imag * 1j if preserve_gaussian_variance: hermitian_part *= np.sqrt(2) anti_hermitian_part *= np.sqrt(2) else: hermitian_part = x.copy() anti_hermitian_part = x.copy_empty() anti_hermitian_part.val[:] = 0 anti_hermitian_part[:] = 0 return (hermitian_part, anti_hermitian_part) # def hermitian_fixed_points(self): # return None def hermitian_fixed_points(self): return None # ---Mandatory properties and methods--- ... ...
 ... ... @@ -118,43 +118,25 @@ class RGSpace(Space): # use subtraction since it is faster than flipping another time anti_hermitian_part = (x-hermitian_part) if preserve_gaussian_variance: hermitian_part, anti_hermitian_part = \ self._hermitianize_correct_variance(hermitian_part, anti_hermitian_part, axes=axes) return (hermitian_part, anti_hermitian_part) def _hermitianize_correct_variance(self, hermitian_part, anti_hermitian_part, axes): # Correct the variance by multiplying sqrt(2) hermitian_part = hermitian_part * np.sqrt(2) anti_hermitian_part = anti_hermitian_part * np.sqrt(2) # If the dtype of the input is complex, the fixed points lose the power # of their imaginary-part (or real-part, respectively). Therefore # the factor of sqrt(2) also applies there if not issubclass(hermitian_part.dtype.type, np.complexfloating): # The fixed points of the point inversion must not be averaged. # Hence one must divide out the sqrt(2) again # -> Get the middle index of the array mid_index = np.array(hermitian_part.shape, dtype=np.int) // 2 dimensions = mid_index.size # Use ndindex to iterate over all combinations of zeros and the # mid_index in order to correct all fixed points. ndlist=[1]*dimensions for k in range(len(axes)): i = axes[k] if self.shape[k]%2 == 0: ndlist[i] = 2 ndlist = tuple(ndlist) for i in np.ndindex(ndlist): temp_index = tuple(i * mid_index) hermitian_part[temp_index] /= np.sqrt(2) anti_hermitian_part[temp_index] /= np.sqrt(2) return hermitian_part, anti_hermitian_part def hermitian_fixed_points(self): dimensions = len(self.shape) mid_index = np.array(self.shape)//2 ndlist = [1]*dimensions for k in range(dimensions): if self.shape[k] % 2 == 0: ndlist[k] = 2 ndlist = tuple(ndlist) fixed_points = [] for index in np.ndindex(ndlist): for k in range(dimensions): if self.shape[k] % 2 != 0 and self.zerocenter[k]: index = list(index) index[k] = 1 index = tuple(index) fixed_points += [tuple(index * mid_index)] return fixed_points def _hermitianize_inverter(self, x, axes): # calculate the number of dimensions the input array has ... ...
 ... ... @@ -20,21 +20,17 @@ import unittest import numpy as np from numpy.testing import assert_,\ assert_equal,\ assert_almost_equal from itertools import product from nifty import Field,\ RGSpace,\ FieldArray RGSpace from d2o import distributed_data_object,\ STRATEGIES from d2o import distributed_data_object from test.common import expand np.random.seed(123) SPACES = [RGSpace((4,)), RGSpace((5))] SPACE_COMBINATIONS = [(), SPACES[0], SPACES[1], SPACES] ... ... @@ -56,46 +52,31 @@ class Test_Interface(unittest.TestCase): f = Field(domain=domain) assert_(isinstance(getattr(f, attribute), desired_type)) def test_hermitian_decomposition0(self): s1=(25,) s2=(16,) r1 = RGSpace(s1, harmonic=True) r2 = RGSpace(s2, harmonic=True) ra = RGSpace(s1+s2, harmonic=True) v = np.random.random(s1+s2) + 1j*np.random.random(s1+s2) f1=Field(ra,val=v,copy=True) f2=Field((r1,r2),val=v,copy=True) h1,a1 = Field._hermitian_decomposition((ra,),f1.val,(0,),((0,1,),),False) h2,a2 = Field._hermitian_decomposition((r1,r2),f2.val,(0,1),((0,),(1,)),False) h3,a3 = Field._hermitian_decomposition((r1,r2),f2.val,(1,0),((0,),(1,)),False) assert_almost_equal(h1.get_full_data(),h2.get_full_data()) assert_almost_equal(a1.get_full_data(),a2.get_full_data()) assert_almost_equal(h1.get_full_data(),h3.get_full_data()) assert_almost_equal(a1.get_full_data(),a3.get_full_data()) @expand(product([False,True],[False,True])) def test_hermitian_decomposition1(self, complexdata, preserve): s0=(1,) s1=(56,25) r0 = RGSpace(s0, harmonic=True) r1 = RGSpace(s1, harmonic=True) ra = RGSpace(s0+s1, harmonic=True) v = np.random.random(s1) if (complexdata): v = v + 1j*np.random.random(s1) f1=Field(r1,val=v,copy=True) f2=Field((r0,r1),val=v,copy=True) h1,a1 = Field._hermitian_decomposition((r1,),f1.val,(0,),((0,1,),),preserve) h2,a2 = Field._hermitian_decomposition((r0,r1),f2.val,(0,1),((0,),(1,2)),preserve) h2=h2[0,:,:] a2=a2[0,:,:] assert_almost_equal(h1.get_full_data(),h2.get_full_data()) assert_almost_equal(a1.get_full_data(),a2.get_full_data()) class Test_Functionality(unittest.TestCase): @expand(product([True, False], [True, False], [True, False], [True, False], [(1,), (4,), (5,)], [(1,), (6,), (7,)])) def test_hermitian_decomposition(self, z1, z2, preserve, complexdata, s1, s2): np.random.seed(123) r1 = RGSpace(s1, harmonic=True, zerocenter=(z1,)) r2 = RGSpace(s2, harmonic=True, zerocenter=(z2,)) ra = RGSpace(s1+s2, harmonic=True, zerocenter=(z1, z2)) #class Test_Initialization(unittest.TestCase): # # @parameterized.expand( # itertools.product(SPACE_COMBINATIONS, # [] # ) # def test_ v = np.random.random(s1+s2) if complexdata: v = v + 1j*np.random.random(s1+s2) f1 = Field(ra, val=v, copy=True) f2 = Field((r1, r2), val=v, copy=True) h1, a1 = Field._hermitian_decomposition((ra,), f1.val, (0,), ((0, 1,),), preserve) h2, a2 = Field._hermitian_decomposition((r1, r2), f2.val, (0, 1), ((0,), (1,)), preserve) h3, a3 = Field._hermitian_decomposition((r1, r2), f2.val, (1, 0), ((0,), (1,)), preserve) assert_almost_equal(h1.get_full_data(), h2.get_full_data()) assert_almost_equal(a1.get_full_data(), a2.get_full_data()) assert_almost_equal(h1.get_full_data(), h3.get_full_data()) assert_almost_equal(a1.get_full_data(), a3.get_full_data())
 ... ... @@ -130,3 +130,7 @@ class LMSpaceFunctionalityTests(unittest.TestCase): def test_distance_array(self, lmax, expected): l = LMSpace(lmax) assert_almost_equal(l.get_distance_array('not').data, expected) def test_hermitian_fixed_points(self): x = LMSpace(5) assert_equal(x.hermitian_fixed_points(), None)
 ... ... @@ -23,7 +23,6 @@ import numpy as np from numpy.testing import assert_, assert_equal, assert_almost_equal from nifty import RGSpace from nifty import Field from test.common import expand from itertools import product ... ... @@ -153,47 +152,59 @@ class RGSpaceFunctionalityTests(unittest.TestCase): for key, value in expected.iteritems(): assert_equal(getattr(x, key), value) @expand(product([(10,),(11,),(1,1),(4,4),(5,7),(8,12),(7,16),(4,6,8), (17,5,3)],)) def test_hermitian_decomposition(self, shape): r = RGSpace(shape, harmonic=True) v = np.empty(shape,dtype=np.complex128) @expand(product([(10,), (11,), (1, 1), (4, 4), (5, 7), (8, 12), (7, 16), (4, 6, 8), (17, 5, 3)], [True, False])) def test_hermitian_decomposition(self, shape, zerocenter): r = RGSpace(shape, harmonic=True, zerocenter=zerocenter) v = np.empty(shape, dtype=np.complex128) v.real = np.random.random(shape) v.imag = np.random.random(shape) h,a = r.hermitian_decomposition(v) h, a = r.hermitian_decomposition(v) # make sure that data == h + a # NOTE: this is only correct for preserve_gaussian_variance==False, # but I consider this an intrinsic property of a hermitian decomposition. assert_almost_equal(v,h+a) # but I consider this an intrinsic property of a hermitian # decomposition. assert_almost_equal(v, h+a) print (h, a) # test hermitianity of h it = np.nditer (h, flags=['multi_index']) it = np.nditer(h, flags=['multi_index']) while not it.finished: i1 = it.multi_index i2 = [] for i in range(len(i1)): i2.append(h.shape[i]-i1[i] if i1[i]>0 else 0) if r.zerocenter[i] and r.shape[i] % 2 != 0: i2.append(h.shape[i]-i1[i]-1) else: i2.append(h.shape[i]-i1[i] if i1[i] > 0 else 0) i2 = tuple(i2) assert_almost_equal(h[i1],np.conj(h[i2])) assert_almost_equal(a[i1],-np.conj(a[i2])) assert_almost_equal(h[i1], np.conj(h[i2])) assert_almost_equal(a[i1], -np.conj(a[i2])) it.iternext() @expand(product([(10,),(11,),(1,1),(4,4),(5,7),(8,12),(7,16),(4,6,8), (17,5,3)],)) def test_hermitian_decomposition2(self, shape): r = RGSpace(shape, harmonic=True) @expand(product([(10,), (11,), (1, 1), (4, 4), (5, 7), (8, 12), (7, 16), (4, 6, 8), (17, 5, 3)], [True, False])) def test_hermitian_decomposition2(self, shape, zerocenter): r = RGSpace(shape, harmonic=True, zerocenter=zerocenter) v = np.random.random(shape) h,a = r.hermitian_decomposition(v) h, a = r.hermitian_decomposition(v) # make sure that data == h + a assert_almost_equal(v,h+a) assert_almost_equal(v, h+a) # test hermitianity of h it = np.nditer (h, flags=['multi_index']) it = np.nditer(h, flags=['multi_index']) while not it.finished: i1 = it.multi_index i2 = [] for i in range(len(i1)): i2.append(h.shape[i]-i1[i] if i1[i]>0 else 0) if r.zerocenter[i] and r.shape[i] % 2 != 0: i2.append(h.shape[i]-i1[i]-1) else: i2.append(h.shape[i]-i1[i] if i1[i] > 0 else 0) i2 = tuple(i2) assert_almost_equal(h[i1],np.conj(h[i2])) assert_almost_equal(a[i1],-np.conj(a[i2])) assert_almost_equal(h[i1], np.conj(h[i2])) assert_almost_equal(a[i1], -np.conj(a[i2])) it.iternext() @expand(get_distance_array_configs()) ... ... @@ -209,3 +220,8 @@ class RGSpaceFunctionalityTests(unittest.TestCase): assert_almost_equal(res, expected) if inplace: assert_(x is res) def test_hermitian_fixed_points(self): x = RGSpace((5, 6, 5, 6), zerocenter=[False, False, True, True]) assert_equal(x.hermitian_fixed_points(), [(0, 0, 2, 0), (0, 0, 2, 3), (0, 3, 2, 0), (0, 3, 2, 3)])
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