def framePotentialSeparated(elementArray):
## get frame potential from a FLATTENED ELEMENT ARRAY ##
d = len(elementArray) / 2
elements = []
for i in range(0, len(elementArray) - 1, 2):
elements.append(elementArray[i] + elementArray[i + 1] * 1j)
vec = mathBackBone.vector(elements)
framePotentialSum = 0
for k in range(d):
for l in range(d):
# middleOperator = mathBackBone.matrix(mathBackBone.X(d=d, power=k).dot(mathBackBone.Z(d=d, power=l)), size=d)
# middleOperatorDotVector = mathBackBone.vector(middleOperator.dot(vec))
# framePotentialSum += numpy.abs(mathBackBone.vector(vec.conjugate).dot(middleOperatorDotVector))**4
XpowerK = mathBackBone.X(d=d, power=k)
ZpowerL = mathBackBone.Z(d=d, power=l)
# print "X", XpowerK.matrix
# print "Z", ZpowerL.matrix
conjugateVector = mathBackBone.vector(vec.conjugate)
lastTwo = mathBackBone.vector(ZpowerL.dot(vec))
# print "Last two: ", lastTwo.elements
lastThree = mathBackBone.vector(XpowerK.dot(lastTwo))
# print "Last three:", lastThree.elements
# print conjugateVector.dot(lastThree)
framePotentialSum += abs(conjugateVector.dot(lastThree))**4
return framePotentialSum
def framePotentialReal(elementArray):
## (MINIMIZE) get frame potential from a FLATTENED ELEMENT ARRAY ##
d = len(elementArray) / 2
vec = elementArray
elements = []
for i in range(0, len(elementArray) - 1, 2):
# print "REAL", elementArray[i]
# print "COMPLEX", elementArray[i+1]
elements.append(
complex(elementArray[i], elementArray[i + 1]) /
numpy.linalg.norm(elementArray))
vec = mathBackBone.vector(elements)
framePotentialSum = 0
for k in range(d):
for l in range(d):
# middleOperator = mathBackBone.matrix(mathBackBone.X(d=d, power=k).dot(mathBackBone.Z(d=d, power=l)), size=d)
# middleOperatorDotVector = mathBackBone.vector(middleOperator.dot(vec))
# framePotentialSum += numpy.abs(mathBackBone.vector(vec.conjugate).dot(middleOperatorDotVector))**4
XpowerK = mathBackBone.X(d=d, power=k)
ZpowerL = mathBackBone.Z(d=d, power=l)
# print "X", XpowerK.matrix
# print "Z", ZpowerL.matrix
conjugateVector = mathBackBone.vector(vec.conjugate)
lastTwo = mathBackBone.vector(ZpowerL.dot(vec))
# print "Last two: ", lastTwo.elements
lastThree = mathBackBone.vector(XpowerK.dot(lastTwo))
# print "Last three:", lastThree.elements
# print conjugateVector.dot(lastThree)
framePotentialSum += abs(conjugateVector.dot(lastThree))**4
return ((framePotentialSum) -
(2. * d /
(d + 1.)))**2. + (1. - numpy.linalg.norm(vec.elements))**2
def framePotential(vec):
## get frame potential from a VECTOR OBJECT ##
d = vec.length
framePotentialSum = 0
for k in range(d):
for l in range(d):
# middleOperator = mathBackBone.matrix(mathBackBone.X(d=d, power=k).dot(mathBackBone.Z(d=d, power=l)), size=d)
# middleOperatorDotVector = mathBackBone.vector(middleOperator.dot(vec))
# framePotentialSum += numpy.abs(mathBackBone.vector(vec.conjugate).dot(middleOperatorDotVector))**4
XpowerK = mathBackBone.X(d=d, power=k)
ZpowerL = mathBackBone.Z(d=d, power=l)
# print "X", XpowerK.matrix
# print "Z", ZpowerL.matrix
conjugateVector = mathBackBone.vector(vec.conjugate)
lastTwo = mathBackBone.vector(ZpowerL.dot(vec))
# print "Last two: ", lastTwo.elements
lastThree = mathBackBone.vector(XpowerK.dot(lastTwo))
# print "Last three:", lastThree.elements
# print conjugateVector.dot(lastThree)
framePotentialSum += abs(conjugateVector.dot(lastThree))**4
return framePotentialSum
def sicTest():
sic = (1./numpy.sqrt(2.))*numpy.array([1, 0, -1, 0, 0, 0])
print mathBackBone.vector(sic).elements
print FramePotential.framePotentialReal(sic)
def framePotentialTest2():
testVec = mathBackBone.vector([0.0723391 - 0.19082j, 0.0792411 + 0.2153j, 0.536444 + 0.199117j, 0.137276 + 0.0599187j, -0.312771 - 0.439084j, 0.447471 + 0.254983j]) ## frame potential should be 2.27671
return FramePotential.framePotential(testVec)
def generateRandomVector(d):
elems = [complex(random.random(), random.random()) for i in range(d)]
vec = mathBackBone.vector(elems)
print list(vec.elements)
return vec