def testDiag2Chain(self):
# Perform the diagonalization for a 2-site chain. Compare
# an exact diagonalization against scipy.
# First calculate X,P
calc = Calculate()
polygon = sp.array([[0,0],[2,0]])
maple_link = maple.MapleLink("/opt/maple13/bin/maple -tu")
precision = 25
X,P = calc.correlations(polygon, maple_link, precision)
entropy = calc.entropy(X, P, 1, precision,False)
# Manual diag.
# [ a, b,
# c, d]
XP = X*P
a = XP[0,0]
b = XP[0,1]
c = XP[1,0]
d = XP[1,1]
eig_plus = ((a+d)+sympy.mpmath.sqrt((a+d)**2-4*(a*d-b*c)))/2
eig_minus = ((a+d)-sympy.mpmath.sqrt((a+d)**2-4*(a*d-b*c)))/2
sqrt_eigs = [sympy.mpmath.sqrt(eig_plus),sympy.mpmath.sqrt(eig_minus)]
S = 0
for vk in sqrt_eigs:
S += ((vk + 0.5)*sympy.mpmath.log(vk + 0.5) - (vk - 0.5)*sympy.mpmath.log(vk - 0.5))
# Scipy operates in double, so we check equality up to a tolerance
bound = 10**(-13)
eq_(True, abs(S - entropy) < bound)
def testPolygonScramble(self):
# Here, rearrange polygon randomly and repeatedly get results. See if come out different.
# Presets.
precision = 20
maple_link = maple.MapleLink(
"/opt/maple13/bin/maple -tu"
) #TODO: hopefully remove this maple dependency...too hardwirey.
L = 3
calc = Calculate()
polygon = calc.square_lattice(L)
X, P = calc.correlations(polygon, maple_link, precision)
# Get eigenvals
with sympy.mpmath.extraprec(500):
XP = X * P
XPnum = sympy.matrix2numpy(XP)
sqrt_eigs = sp.sqrt(linalg.eigvals(XPnum))
sqrt_eigs_orig = sqrt_eigs.real
# Scramble polygon.
sp.random.shuffle(polygon)
# Perform the integration again.
X, P = calc.correlations(polygon, maple_link, precision)
# Get eigenvals
with sympy.mpmath.extraprec(500):
XP = X * P
XPnum = sympy.matrix2numpy(XP)
sqrt_eigs = sp.sqrt(linalg.eigvals(XPnum))
sqrt_eigs_scrambled = sqrt_eigs.real
# Compare.
a = set(tuple([round(float(x), 10) for x in sqrt_eigs_orig]))
b = set(tuple([round(float(x), 10) for x in sqrt_eigs_scrambled]))
eq_(a, b)
def testPolygonScramble(self):
# Here, rearrange polygon randomly and repeatedly get results. See if come out different.
# Presets.
precision = 20
maple_link = maple.MapleLink("/opt/maple13/bin/maple -tu") #TODO: hopefully remove this maple dependency...too hardwirey.
L = 3
calc = Calculate()
polygon = calc.square_lattice(L)
X,P = calc.correlations(polygon, maple_link, precision)
# Get eigenvals
with sympy.mpmath.extraprec(500):
XP = X*P
XPnum = sympy.matrix2numpy(XP)
sqrt_eigs = sp.sqrt(linalg.eigvals(XPnum))
sqrt_eigs_orig = sqrt_eigs.real
# Scramble polygon.
sp.random.shuffle(polygon)
# Perform the integration again.
X,P = calc.correlations(polygon, maple_link, precision)
# Get eigenvals
with sympy.mpmath.extraprec(500):
XP = X*P
XPnum = sympy.matrix2numpy(XP)
sqrt_eigs = sp.sqrt(linalg.eigvals(XPnum))
sqrt_eigs_scrambled = sqrt_eigs.real
# Compare.
a = set(tuple([round(float(x),10) for x in sqrt_eigs_orig]))
b = set(tuple([round(float(x),10) for x in sqrt_eigs_scrambled]))
eq_(a,b)
def testDiag2Chain(self):
# Perform the diagonalization for a 2-site chain. Compare
# an exact diagonalization against scipy.
# First calculate X,P
calc = Calculate()
polygon = sp.array([[0, 0], [2, 0]])
maple_link = maple.MapleLink("/opt/maple13/bin/maple -tu")
precision = 25
X, P = calc.correlations(polygon, maple_link, precision)
entropy = calc.entropy(X, P, 1, precision, False)
# Manual diag.
# [ a, b,
# c, d]
XP = X * P
a = XP[0, 0]
b = XP[0, 1]
c = XP[1, 0]
d = XP[1, 1]
eig_plus = ((a + d) + sympy.mpmath.sqrt((a + d)**2 - 4 *
(a * d - b * c))) / 2
eig_minus = ((a + d) - sympy.mpmath.sqrt((a + d)**2 - 4 *
(a * d - b * c))) / 2
sqrt_eigs = [sympy.mpmath.sqrt(eig_plus), sympy.mpmath.sqrt(eig_minus)]
S = 0
for vk in sqrt_eigs:
S += ((vk + 0.5) * sympy.mpmath.log(vk + 0.5) -
(vk - 0.5) * sympy.mpmath.log(vk - 0.5))
# Scipy operates in double, so we check equality up to a tolerance
bound = 10**(-13)
eq_(True, abs(S - entropy) < bound)
class CorrelationsTest(unittest.TestCase):
#TODO: Currently limited to a small case. In future, when program optimized, expand this!
maple_link = None
# For L = 3...
X = None
P = None
XP = None
precision = None
@classmethod
def setUpClass(cls):
cls.calc = Calculate()
if cls.X is None and cls.P is None:
# Startup Maple. #TODO: Replace with sympy when they fix bug (see src.main). This is ugly since relying on a hardcoded dir.
cls.maple_link = maple.MapleLink("/opt/maple13/bin/maple -tu")
cls.precision = 25
lattice = cls.calc.square_lattice(5)
cls.X,cls.P = cls.calc.correlations(lattice,cls.maple_link,cls.precision)
else:
# TODO: rremove this if this doesn't show up
print "Bug: This function has been called twice"
def setUp(self):
self.calc = Calculate()
def testSymmetric(self):
eq_(True,self.X.is_symmetric())
eq_(True,self.P.is_symmetric())
def testReal(self):
eq_(True, self.X == self.X.conjugate())
eq_(True, self.P == self.P.conjugate())
def testPrecision(self):
"""
See if the precision increases with the variable.
"""
polygon = self.calc.square_lattice(1)
precisions = [20,30,40,50]
# Find X,P for each precision
corrs_collection = []
for precision in precisions:
X,P = self.calc.correlations(polygon, self.maple_link, precision)
corrs_collection.append([X,P])
for i in range(0, len(precisions)-1):
# get X and P pairs for precisions[i] and precisions[i+1]
pairX = sp.array([corrs_collection[i][0],corrs_collection[i+1][0]])
pairP = sp.array([corrs_collection[i][1],corrs_collection[i+1][1]])
# Check if increasing the precision variable actually does this.
bound = 10**(-precisions[i])
eq_(True, ( abs(pairX[0] - pairX[1]) < bound ).all())
eq_(True, ( abs(pairP[0] - pairP[1]) < bound ).all())
def testPrecomputed(self):
"""
Test the precomputed correlations feature.
"""
precision = 25
lattice3 = self.calc.square_lattice(3)
lattice4 = self.calc.square_lattice(4)
X3,P3 = self.calc.correlations(lattice3, self.maple_link, precision, verbose=True)
X4,P4 = self.calc.correlations(lattice4, self.maple_link, precision, verbose=True)
# With precomputed.
precomputed_correlations = {}
X3_quick, P3_quick, precomputed_correlations = self.calc.correlations(lattice3, self.maple_link, precision, precomputed_correlations, verbose=True)
X4_quick, P4_quick, precomputed_correlations = self.calc.correlations(lattice4, self.maple_link, precision, precomputed_correlations, verbose=True)
eq_(True, X3 == X3_quick)
eq_(True, P3 == P3_quick)
eq_(True, X4 == X4_quick)
eq_(True, P4 == P4_quick)
def testMatrixSymmetries(self):
"""
X and P should have the same pattern as the distance matrix defined by
the lattice.
"""
precision = 20
polygon = self.calc.square_lattice(5)
X,P = self.calc.correlations(polygon, self.maple_link, precision)
# Round X and P down so we can see if elements are distinct or not.
X = sympy.matrix2numpy(X)
P = sympy.matrix2numpy(P)
X = X.astype('float')
P = P.astype('float')
# Get the pattern of the distance matrix.
D = spatial.distance.cdist(polygon,polygon)
# The pattern of the distance matrix
D_pat = sp.zeros(D.shape)
getSignatureMatrix(D_pat,sp.nditer(D),D.shape)
# Get the pattern of X and P.
X_pat = sp.zeros(X.shape)
P_pat = sp.zeros(P.shape)
getSignatureMatrix(X_pat,sp.nditer(X),X.shape)
getSignatureMatrix(P_pat,sp.nditer(P),P.shape)
# Check if patterns match.
eq_(False,(D_pat - X_pat).all())
eq_(False,(D_pat - P_pat).all())
class CorrelationsTest(unittest.TestCase):
#TODO: Currently limited to a small case. In future, when program optimized, expand this!
maple_link = None
# For L = 3...
X = None
P = None
XP = None
precision = None
@classmethod
def setUpClass(cls):
cls.calc = Calculate()
if cls.X is None and cls.P is None:
# Startup Maple. #TODO: Replace with sympy when they fix bug (see src.main). This is ugly since relying on a hardcoded dir.
cls.maple_link = maple.MapleLink("/opt/maple13/bin/maple -tu")
cls.precision = 25
lattice = cls.calc.square_lattice(5)
cls.X, cls.P = cls.calc.correlations(lattice, cls.maple_link,
cls.precision)
else:
# TODO: rremove this if this doesn't show up
print "Bug: This function has been called twice"
def setUp(self):
self.calc = Calculate()
def testSymmetric(self):
eq_(True, self.X.is_symmetric())
eq_(True, self.P.is_symmetric())
def testReal(self):
eq_(True, self.X == self.X.conjugate())
eq_(True, self.P == self.P.conjugate())
def testPrecision(self):
"""
See if the precision increases with the variable.
"""
polygon = self.calc.square_lattice(1)
precisions = [20, 30, 40, 50]
# Find X,P for each precision
corrs_collection = []
for precision in precisions:
X, P = self.calc.correlations(polygon, self.maple_link, precision)
corrs_collection.append([X, P])
for i in range(0, len(precisions) - 1):
# get X and P pairs for precisions[i] and precisions[i+1]
pairX = sp.array(
[corrs_collection[i][0], corrs_collection[i + 1][0]])
pairP = sp.array(
[corrs_collection[i][1], corrs_collection[i + 1][1]])
# Check if increasing the precision variable actually does this.
bound = 10**(-precisions[i])
eq_(True, (abs(pairX[0] - pairX[1]) < bound).all())
eq_(True, (abs(pairP[0] - pairP[1]) < bound).all())
def testPrecomputed(self):
"""
Test the precomputed correlations feature.
"""
precision = 25
lattice3 = self.calc.square_lattice(3)
lattice4 = self.calc.square_lattice(4)
X3, P3 = self.calc.correlations(lattice3,
self.maple_link,
precision,
verbose=True)
X4, P4 = self.calc.correlations(lattice4,
self.maple_link,
precision,
verbose=True)
# With precomputed.
precomputed_correlations = {}
X3_quick, P3_quick, precomputed_correlations = self.calc.correlations(
lattice3,
self.maple_link,
precision,
precomputed_correlations,
verbose=True)
X4_quick, P4_quick, precomputed_correlations = self.calc.correlations(
lattice4,
self.maple_link,
precision,
precomputed_correlations,
verbose=True)
eq_(True, X3 == X3_quick)
eq_(True, P3 == P3_quick)
eq_(True, X4 == X4_quick)
eq_(True, P4 == P4_quick)
def testMatrixSymmetries(self):
"""
X and P should have the same pattern as the distance matrix defined by
the lattice.
"""
precision = 20
polygon = self.calc.square_lattice(5)
X, P = self.calc.correlations(polygon, self.maple_link, precision)
# Round X and P down so we can see if elements are distinct or not.
X = sympy.matrix2numpy(X)
P = sympy.matrix2numpy(P)
X = X.astype('float')
P = P.astype('float')
# Get the pattern of the distance matrix.
D = spatial.distance.cdist(polygon, polygon)
# The pattern of the distance matrix
D_pat = sp.zeros(D.shape)
getSignatureMatrix(D_pat, sp.nditer(D), D.shape)
# Get the pattern of X and P.
X_pat = sp.zeros(X.shape)
P_pat = sp.zeros(P.shape)
getSignatureMatrix(X_pat, sp.nditer(X), X.shape)
getSignatureMatrix(P_pat, sp.nditer(P), P.shape)
# Check if patterns match.
eq_(False, (D_pat - X_pat).all())
eq_(False, (D_pat - P_pat).all())