def choose_seq_points(e, f, nneg, npos):
# Pick first nneg+npos points
if (nneg + npos) % 2 != 0:
print('Number of chosen points should be even!', nneg, npos,
nneg + npos)
npos += 1
q = nneg + npos
# ee = np.zeros(q, dtype=mp.mpc)
# ff = np.zeros((q, f.shape[1]), dtype=mp.mpc)
ee = fp.zeros(q, 1)
ff = fp.zeros(q, f.cols)
for i in range(0, nneg):
ee[i] = mp.conj(e[nneg - 1 - i])
ff[i] = mp.conj(f[nneg - 1 - i])
for i in range(nneg, nneg + npos):
ee[i] = e[i - nneg]
ff[i] = f[i - nneg]
return ee, ff
def choose_prandom_points(e, f, nneg, npos):
# Subroutine selects from input nneg+npos points
# first nneg+npos-nrnd points are selected sequently,
# then nrnd points are picked randomly
# Number of randomly selected points nrnd is determined randomly in interval (4, 18)
# e -- input complex array with energy points
# f -- input complex array with values of function in points e[i]
nrnd = random.randrange(4, 18, 2)
if (nneg + npos) % 2 != 0:
print('Number of chosen points should be even!', nneg, npos,
nneg + npos)
npos += 1
q = nneg + npos
r = len(e)
ee = fp.zeros(q, 1)
ff = fp.zeros(q, f.cols)
for i in range(0, nneg):
ee[i] = mp.conj(e[nneg - 1 - i])
ff[i] = mp.conj(f[nneg - 1 - i])
for i in range(nneg, q - nrnd):
ee[i] = e[i - nneg]
ff[i] = f[i - nneg]
# Make list of random points
pp = random.sample(range(q - nrnd, r - 1), nrnd)
# Sort them
pp.sort()
# Fix repeated points (if there are)
for i in range(0, nrnd - 1):
if pp[i] == pp[i + 1]:
pp[i + 1] += 1
# The last two points should be sequential to fix diff at the tail of F(z).
pp[nrnd - 1] = pp[nrnd - 2] + 1
# Construct
for i in range(0, nrnd):
ee[q - nrnd + i] = e[pp[i]]
ff[q - nrnd + i] = f[pp[i]]
return ee, ff
def test_eighe_randmatrix():
N = 5
for a in xrange(10):
A = (2 * mp.randmatrix(N, N) - 1) + 1j * (2 * mp.randmatrix(N, N) - 1)
for i in xrange(0, N):
A[i, i] = mp.re(A[i, i])
for j in xrange(i + 1, N):
A[j, i] = mp.conj(A[i, j])
run_eighe(A)
def test_eighe_randmatrix():
N = 5
for a in xrange(10):
A = (2 * mp.randmatrix(N, N) - 1) + 1j * (2 * mp.randmatrix(N, N) - 1)
for i in xrange(0, N):
A[i,i] = mp.re(A[i,i])
for j in xrange(i + 1, N):
A[j,i] = mp.conj(A[i,j])
run_eighe(A)
def test_eighe_irandmatrix():
N = 4
R = 4
for a in xrange(10):
A = irandmatrix(N, R) + 1j * irandmatrix(N, R)
for i in xrange(0, N):
A[i, i] = mp.re(A[i, i])
for j in xrange(i + 1, N):
A[j, i] = mp.conj(A[i, j])
run_eighe(A)
def test_eighe_irandmatrix():
N = 4
R = 4
for a in xrange(10):
A=irandmatrix(N, R) + 1j * irandmatrix(N, R)
for i in xrange(0, N):
A[i,i] = mp.re(A[i,i])
for j in xrange(i + 1, N):
A[j,i] = mp.conj(A[i,j])
run_eighe(A)
def mp_normsqr(cplx):
return mp.re(mp.conj(cplx) * cplx)
def E_pi_minus(lx, ly):
fle = float(mp.re(mp.sqrt(mp.conj(fl(lx, ly, 0) * fl(lx, ly, 0)))))
return -1 * t * fle / (1 + s * fle)
def createP_sigma(lx, ly, band):
C = table.C_Sigma(ly / (2 / mp.sqrt(3)), lx / (mp.sqrt(3) / 2), band)
#Values tabulated on a rectangular grid, flipped and compensated for.
C = [
C[0], C[1], C[2], C[3] / (3**(1 / 2)), C[4] / (3**(1 / 2)),
C[5] / (3**(1 / 2))
]
#For sqrt(3) normalisation, see paper for reference.
f = lambda kx, ky, kz: C[0] * fi_As(lx, ly, kx, ky, kz) + C[1] * fi_Ax(
lx, ly, kx, ky, kz) + C[2] * fi_Ay(lx, ly, kx, ky, kz) + C[3] * fi_Bs(
lx, ly, kx, ky, kz) + C[4] * fi_Bx(lx, ly, kx, ky, kz) + C[
5] * fi_By(lx, ly, kx, ky, kz)
nrm = 1 / mp.sqrt(
mp.conj(C[0]) * C[0] + mp.conj(C[1]) * C[1] + mp.conj(C[2]) * C[2] +
3 *
(mp.conj(C[3]) * C[3] + mp.conj(C[4]) * C[4] + mp.conj(C[5]) * C[5]) +
2 * mp.re((mp.conj(C[0]) * C[3] * pss + mp.conj(C[0]) * C[4] * psx +
mp.conj(C[0]) * C[5] * psy + mp.conj(C[1]) * C[3] * psx +
mp.conj(C[1]) * C[4] * pxx + mp.conj(C[1]) * C[5] * pxy +
mp.conj(C[2]) * C[3] * psy + mp.conj(C[2]) * C[4] * pxy +
mp.conj(C[2]) * C[5] * pyy) *
(mp.exp(1j * mp.fdot([lx, ly, 0], R_1)) +
mp.exp(1j * mp.fdot([lx, ly, 0], R_2)) +
mp.exp(1j * mp.fdot([lx, ly, 0], R_3)))))
return lambda kx, ky, kz: f(kx, ky, kz) * nrm
def get_G_from_U(U, chi):
n = U.rows
Vinvdagger = mp.eye(n) * mp.one / mp.conj(chi)
Gdagger = Vinvdagger - U
return Gdagger.H