def matrixExpGEMM():
eta = .2
gsT = 10.
gsJ = 1.
H = numHamiltonians.setupPhotonHamiltonianInf(gsT, gsJ, eta)
expH1 = sciLin.expm(H)
eVals, eVecs = np.linalg.eigh(H)
expH2 = np.dot(
eVecs, np.dot(np.diag(np.exp(eVals)), np.transpose(np.conj(eVecs))))
#print(np.abs(expH1 - expH2))
diff = np.sum(np.abs(expH1 - expH2)) / (np.sum(np.abs(expH1)))
print("rel diff exp summed = {}".format(diff))
fail = diff > 1e-5
if (fail):
print(
" Diagonalization with matrix multiplication failed!!! ------ CHECK FAILED!!!"
)
return False
else:
print(
" Diagonalization via matrix multiplication worked! ------ CHECK PASSED :)"
)
return True
def setupHOrder(TJ, eta, orderH):
if (orderH == 1):
return numH.setupPhotonHamiltonian1st(TJ[0], TJ[1], eta)
elif (orderH == 2):
return numH.setupPhotonHamiltonian2nd(TJ[0], TJ[1], eta)
else:
return numH.setupPhotonHamiltonianInf(TJ[0], TJ[1], eta)
def getH(eta):
gsJ = 0.
gsE = np.zeros(prms.chainLength)
gsE[0:prms.numberElectrons // 2 + 1] = 1.
gsE[-prms.numberElectrons // 2 + 1:] = 1.
kVec = np.linspace(0, 2. * np.pi, prms.chainLength, endpoint=False)
cosK = np.cos(kVec)
gsT = 2. * prms.t * np.sum(np.multiply(cosK, gsE))
return numH.setupPhotonHamiltonianInf(gsT, gsJ, eta)
def matrixDiagGEMM():
eta = .2
gsT = 10.
gsJ = 1.
H = numHamiltonians.setupPhotonHamiltonianInf(gsT, gsJ, eta)
eVals, eVecs = np.linalg.eigh(H)
HDiag1 = np.diag(eVals)
HDiag2 = np.dot(np.transpose(np.conj(eVecs)), np.dot(H, eVecs))
diff = np.sum(np.abs(HDiag1 - HDiag2))
fail = diff > 1e-10
if (fail):
print(
" Diagonalization with matrix multiplication failed!!! ------ CHECK FAILED!!!"
)
return False
else:
print(
" Diagonalization via matrix multiplication worked! ------ CHECK PASSED :)"
)
return True
def getH(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
return numH.setupPhotonHamiltonianInf(gsT, gsJ, eta)