def choose_points(e, f, nneg, npos):
# Choose first npo+nneg points,
# than pick some points by hands
# For testing purposes
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] = e.conj()[nneg - 1 - i]
ff[i] = f.conj()[nneg - 1 - i]
for i in range(nneg, nneg + npos - 6):
ee[i] = e[i - nneg]
ff[i] = f[i - nneg]
ee[q - 6] = e[750]
ff[q - 6] = f[750]
ee[q - 5] = e[900]
ff[q - 5] = f[900]
ee[q - 4] = e[937]
ff[q - 4] = f[937]
ee[q - 3] = e[960]
ff[q - 3] = f[960]
ee[q - 2] = e[999]
ff[q - 2] = f[999]
ee[q - 1] = e[1000]
ff[q - 1] = f[1000]
return ee, ff
def make_f_prime(f, e, m):
# F'(z) = z^3 * [F(z) - p_n/z - p'_n/z^2 - p''_n/z^3]
r = len(e)
fn = fp.zeros(r, 1)
for i in range(0, r):
fn[i] = (e[i]**3) * (f[i] - m[0] / e[i] - m[1] / (e[i]**2) - m[2] /
(e[i]**3))
return fn
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 choose_seq_points_plus(e, f, nneg, npos):
# Choose first nneg+npos-2 and last two 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] = e.conj()[nneg - 1 - i]
ff[i] = f.conj()[nneg - 1 - i]
for i in range(nneg, nneg + npos - 2):
ee[i] = e[i - nneg]
ff[i] = f[i - nneg]
for i in range(-2, 0):
ee[i] = e[i]
ff[i] = f[i]
return ee, ff
def readsigma(filename):
# Read sigma from AMULET.
print('Input file contains:')
with open(filename, 'r') as f:
data = f.readlines()
# Analyze the file.
# Number of lines.
nlines = len(data)
print(" Number of lines: %i " % nlines)
# Count pairs of blank lines to determine number of datasets.
# Each dataset should be ended by 2 blank lines.
ndatasets = 0
for i in range(0, nlines - 1):
if not data[i].split() and not data[i + 1].split():
ndatasets += 1
blank_lines_ending = 2
# If there are no blank lines at end of file
if ndatasets == 0 and not data[-1].split():
ndatasets += 1
blank_lines_ending = 1
nlinesperblock = (nlines + 1) / ndatasets
elif ndatasets == 0 and data[-1].split():
ndatasets += 1
nlinesperblock = (nlines + 2) / ndatasets
else:
nlinesperblock = nlines / ndatasets
print(" Number of datasets: %i " % ndatasets)
# nlinesperblock = nlines / ndatasets
print(" Number of lines per block: %i " % nlinesperblock)
# Take the last dataset from data file
data = data[nlinesperblock * (ndatasets - 1):(nlinesperblock * ndatasets) -
blank_lines_ending]
nlines = len(data)
s = data[0].split()
# Structure of Sigma file:
# first column -- energy, the next two column are Re and Im parts of sigma majority
# last two column are Re and Im parts of sigma minority (if calc is spin-polarized)
l = len(s)
if l == 3:
e = fp.zeros(nlines, 1)
z = fp.zeros(nlines, 1)
for i in range(0, nlines):
s = data[i].split()
e[i] = 1j * float(s[0])
z[i] = float(s[1]) + 1j * float(s[2])
elif l == 5:
e = fp.zeros(nlines, 1)
z = fp.zeros(nlines, 2)
for i in range(0, nlines):
s = data[i].split()
e[i] = 1j * float(s[0])
z[i, 0] = float(s[1]) + 1j * float(s[2])
z[i, 1] = float(s[3]) + 1j * float(s[4])
else:
print("unknown data format")
return e, z