def energy_density_on_line(k, x0, y0, z0, axis, end):
if (axis not in ['x','y','z']):
raise ValueError("Invalid axis given. Must be one of 'x', 'y', or 'z'")
step_size = 0.02
if (axis == 'x'):
start = x0
elif (axis == 'y'):
start = y0
elif (axis == 'z'):
start = z0
intervals = int(math.ceil((end - start)/step_size))
points = []
for a in range(-2, intervals + 2, 1):
points_y = []
for b in range(-2, 3, 1):
points_z = []
for c in range(-2, 3, 1):
if(b == 0 or c == 0):
if (axis == 'x'):
points_z.append(higgs_squared(k, float(x0 + a * step_size), float(y0 + b * step_size), float(z0 + c * step_size)))
elif (axis == 'y'):
points_z.append(higgs_squared(k, float(x0 + b * step_size), float(y0 + a * step_size), float(z0 + c * step_size)))
elif (axis == 'z'):
points_z.append(higgs_squared(k, float(x0 + c * step_size), float(y0 + b * step_size), float(z0 + a * step_size)))
else:
points_z.append(0) # Value is not used in laplace calculation
points_y.append(points_z)
points.append(points_y)
return five_point_laplace(points, step_size)[0][0]
def higgs_on_line(k, x0, x1, y, z, partition_size):
x_step = (x1 - x0) / partition_size
for i in range(0, partition_size):
x=x0+i*x_step
print higgs_squared(k,x,y,z)
return
def higgs_on_line(k, x0, x1, y, z, partition_size):
x_step = (x1 - x0) / partition_size
for i in range(0, partition_size):
x = x0 + i * x_step
print higgs_squared(k, x, y, z)
return
def test_higgs_exceptional(k):
kk = "%1.2f" % k
points = get_point_tuples(kk, 253, 256)
exceptional=[]
for p in points:
value = higgs_squared(k, p[1], p[0], p[2])
if (value > 1.0 or value <0.0):
exceptional.append(p)
print "Exceptional", p
write_file = '/Users/hwb/Desktop/numerical monopoles/formaple/higgs_' + str(kk) +'.txt'
fo = open(os.path.expanduser(write_file), 'w+')
for i, point in enumerate(exceptional):
point_string = str(point[0]) +' '+ str(point[1]) + ' ' + str(point[2]) +'\n'
if (i != (len(points) - 1)):
point_string = point_string
fo.write(point_string)
fo.close()
return
def higgs_squared_on_xy_plane(
k, x0, x1, y0, y1, z, partition_size
): # If this falls outside of [0,1) an value of maxint-1 will be returned; maxint is globally set.
x_step = (x1 - x0) / partition_size
y_step = (y1 - y0) / partition_size
points = []
for j in xrange(0, partition_size):
# if j % 10 == 0 and j > 0:
# eprint("- rendered %s lines..." % j)
for i in xrange(0, partition_size):
x = x0 + i * x_step
y = y0 + j * y_step
value = higgs_squared(k, x, y, z)
bucket_value = int(floor(maxint * value))
if (bucket_value > maxintr or bucket_value < 0):
print i, j, bucket_value
bucket_value = maxintr
points.append(bucket_value)
return points
def test_higgs_exceptional(k):
kk = "%1.2f" % k
points = get_point_tuples(kk, 253, 256)
exceptional = []
for p in points:
value = higgs_squared(k, p[1], p[0], p[2])
if (value > 1.0 or value < 0.0):
exceptional.append(p)
print "Exceptional", p
write_file = '/Users/hwb/Desktop/numerical monopoles/formaple/higgs_' + str(
kk) + '.txt'
fo = open(os.path.expanduser(write_file), 'w+')
for i, point in enumerate(exceptional):
point_string = str(point[0]) + ' ' + str(point[1]) + ' ' + str(
point[2]) + '\n'
if (i != (len(points) - 1)):
point_string = point_string
fo.write(point_string)
fo.close()
return
def energy_density_on_line(k, x0, y0, z0, axis, end):
if (axis not in ['x', 'y', 'z']):
raise ValueError("Invalid axis given. Must be one of 'x', 'y', or 'z'")
step_size = 0.02
if (axis == 'x'):
start = x0
elif (axis == 'y'):
start = y0
elif (axis == 'z'):
start = z0
intervals = int(math.ceil((end - start) / step_size))
points = []
for a in range(-2, intervals + 2, 1):
points_y = []
for b in range(-2, 3, 1):
points_z = []
for c in range(-2, 3, 1):
if (b == 0 or c == 0):
if (axis == 'x'):
points_z.append(
higgs_squared(k, float(x0 + a * step_size),
float(y0 + b * step_size),
float(z0 + c * step_size)))
elif (axis == 'y'):
points_z.append(
higgs_squared(k, float(x0 + b * step_size),
float(y0 + a * step_size),
float(z0 + c * step_size)))
elif (axis == 'z'):
points_z.append(
higgs_squared(k, float(x0 + c * step_size),
float(y0 + b * step_size),
float(z0 + a * step_size)))
else:
points_z.append(
0) # Value is not used in laplace calculation
points_y.append(points_z)
points.append(points_y)
return five_point_laplace(points, step_size)[0][0]
def test_on_line(k, x0, x1, y, z, partition_size):
k1 = sqrt(1 - k**2)
a = k1 + complex(0, 1) * k
b = k1 - complex(0, 1) * k
x_step = (x1 - x0) / partition_size
for i in range(0, partition_size):
x = x0 + i * x_step
zeta = calc_zeta(k, x, y, z)
eta = calc_eta(k, x, y, z)
abel = calc_abel(k, zeta, eta)
mu = calc_mu(k, x, y, z, zeta, abel)
print "zeta/a", zeta[0] / a, zeta[1] / a, zeta[2] / a, zeta[3] / a, '\n'
print "eta", eta[0], eta[1], eta[2], eta[3], '\n'
print "abel", abel[0], abel[1], abel[2], abel[3], '\n'
abel_tmp= map(lambda zetai : \
complex(0, 1) * 1/(complex64(ellipk(k**2))*2*b) \
* complex64(ellipf( asin( (zetai )/a), mfrom(k=a/b))) \
- taufrom(k=k)/2,
zeta)
print "abel_tmp", abel_tmp[0], abel_tmp[1], abel_tmp[2], abel_tmp[
3], '\n'
print abel[0] + conj(abel[2]), abel[1] + conj(abel[3]), '\n'
print -taufrom(k=k) / 2, '\n'
for l in range(0, 4):
tmp = abs(complex64(calc_eta_by_theta(k, abel[l])) - eta[l])
print tmp
value = higgs_squared(k, x, y, z)
print "higgs", higgs_squared(k, x, y, z)
if (value > 1.0 or value < 0.0):
print "Exception"
print '\n'
# print mu[0]+mu[2], mu[1]+mu[3], '\n'
return
def test_on_line(k, x0, x1, y, z, partition_size):
k1 = sqrt(1-k**2)
a=k1+complex(0, 1)*k
b=k1-complex(0, 1)*k
x_step = (x1 - x0) / partition_size
for i in range(0, partition_size):
x=x0+i*x_step
zeta = calc_zeta(k ,x, y, z)
eta = calc_eta(k, x, y, z)
abel = calc_abel(k, zeta, eta)
mu = calc_mu(k, x, y, z, zeta, abel)
print "zeta/a", zeta[0]/a, zeta[1]/a, zeta[2]/a, zeta[3]/a, '\n'
print "eta", eta[0], eta[1], eta[2], eta[3], '\n'
print "abel", abel[0], abel[1],abel[2],abel[3],'\n'
abel_tmp= map(lambda zetai : \
complex(0, 1) * 1/(complex64(ellipk(k**2))*2*b) \
* complex64(ellipf( asin( (zetai )/a), mfrom(k=a/b))) \
- taufrom(k=k)/2,
zeta)
print "abel_tmp", abel_tmp[0], abel_tmp[1],abel_tmp[2],abel_tmp[3],'\n'
print abel[0]+conj(abel[2]), abel[1]+conj(abel[3]), '\n'
print - taufrom(k=k)/2, '\n'
for l in range(0,4):
tmp= abs(complex64(calc_eta_by_theta(k, abel[l])) - eta[l])
print tmp
value = higgs_squared(k, x, y, z)
print "higgs", higgs_squared(k,x,y,z)
if (value > 1.0 or value <0.0):
print "Exception"
print '\n'
# print mu[0]+mu[2], mu[1]+mu[3], '\n'
return
def energy_density_numerical(k, x1, x2, x3):
step_size = 0.02
points = []
for a in range(-2, 3, 1):
points_y = []
for b in range(-2, 3, 1):
points_z = []
for c in range(-2, 3, 1):
points_z.append(higgs_squared(k, float(x1 + a * step_size), float(x2 + b * step_size), float(x3 + c * step_size)))
points_y.append(points_z)
points.append(points_y)
return five_point_laplace(points, step_size)[0][0]
def xhiggs_on_line(k, x0, x1, y, z, partition_size):
x_step = (x1 - x0) / partition_size
points = []
for i in range(0, partition_size):
x = x0 + i * x_step
value = higgs_squared(k, x, y, z)
bucket_value = int(floor(maxint * value))
points.append(bucket_value)
# print higgs_squared(k,x,y,z)
return points
def xhiggs_on_line(k, x0, x1, y, z, partition_size):
x_step = (x1 - x0) / partition_size
points = []
for i in range(0, partition_size):
x=x0+i*x_step
value = higgs_squared(k, x, y, z)
bucket_value = int(floor(maxint * value))
points.append(bucket_value)
# print higgs_squared(k,x,y,z)
return points
def test_on_line(k, x0, x1, y, z, partition_size):
k1 = sqrt(1-k**2)
a=k1+complex(0, 1)*k
b=k1-complex(0, 1)*k
# x_step = (x1 - x0) / partition_size
x_step = 0.05
for i in range(0, partition_size):
x=x0+i*x_step
zeta = calc_zeta(k ,x, y, z)
eta = calc_eta(k, x, y, z)
abel = calc_abel(k, zeta, eta)
mu = calc_mu(k, x, y, z, zeta, abel)
print i,'\n'
print "zeta", zeta[0], zeta[1], zeta[2], zeta[3], '\n'
# print "eta", eta[0], eta[1], eta[2], eta[3], '\n'
# print "mu", mu[0], mu[1], mu[2], mu[3], '\n'
# print mu[0]+conj(mu[2]), mu[1]+conj( mu[3]), '\n'
# print "abel", abel[0], abel[1],abel[2],abel[3],'\n'
# abel_tmp= map(lambda zetai : \
# complex(0, 1) * 1/(complex64(ellipk(k**2))*2*b) \
# * complex64(ellipf( asin( (zetai )/a), mfrom(k=a/b))) \
# - taufrom(k=k)/2,
# zeta)
# print "abel_tmp", abel_tmp[0], abel_tmp[1],abel_tmp[2],abel_tmp[3],'\n'
#
# print abel[0]+conj(abel[2]), abel[1]+conj(abel[3]), '\n'
# print - taufrom(k=k)/2, '\n'
# for l in range(0,4):
# tmp= abs(complex64(calc_eta_by_theta(k, abel[l])) - eta[l])
# print tmp
value = higgs_squared(k, x, y, z)
print "higgs", value, int(floor(maxint *value))
# if (value > 1.0 or value <0.0):
# print "Exception"
#
print '\n'
# # print mu[0]+mu[2], mu[1]+mu[3], '\n'
return
def energy_density_numerical(k, x1, x2, x3):
step_size = 0.02
points = []
for a in range(-2, 3, 1):
points_y = []
for b in range(-2, 3, 1):
points_z = []
for c in range(-2, 3, 1):
points_z.append(
higgs_squared(k, float(x1 + a * step_size),
float(x2 + b * step_size),
float(x3 + c * step_size)))
points_y.append(points_z)
points.append(points_y)
return five_point_laplace(points, step_size)[0][0]
def test_on_line(k, x0, x1, y, z, partition_size):
k1 = sqrt(1 - k**2)
a = k1 + complex(0, 1) * k
b = k1 - complex(0, 1) * k
# x_step = (x1 - x0) / partition_size
x_step = 0.05
for i in range(0, partition_size):
x = x0 + i * x_step
zeta = calc_zeta(k, x, y, z)
eta = calc_eta(k, x, y, z)
abel = calc_abel(k, zeta, eta)
mu = calc_mu(k, x, y, z, zeta, abel)
print i, '\n'
print "zeta", zeta[0], zeta[1], zeta[2], zeta[3], '\n'
# print "eta", eta[0], eta[1], eta[2], eta[3], '\n'
# print "mu", mu[0], mu[1], mu[2], mu[3], '\n'
# print mu[0]+conj(mu[2]), mu[1]+conj( mu[3]), '\n'
# print "abel", abel[0], abel[1],abel[2],abel[3],'\n'
# abel_tmp= map(lambda zetai : \
# complex(0, 1) * 1/(complex64(ellipk(k**2))*2*b) \
# * complex64(ellipf( asin( (zetai )/a), mfrom(k=a/b))) \
# - taufrom(k=k)/2,
# zeta)
# print "abel_tmp", abel_tmp[0], abel_tmp[1],abel_tmp[2],abel_tmp[3],'\n'
#
# print abel[0]+conj(abel[2]), abel[1]+conj(abel[3]), '\n'
# print - taufrom(k=k)/2, '\n'
# for l in range(0,4):
# tmp= abs(complex64(calc_eta_by_theta(k, abel[l])) - eta[l])
# print tmp
value = higgs_squared(k, x, y, z)
print "higgs", value, int(floor(maxint * value))
# if (value > 1.0 or value <0.0):
# print "Exception"
#
print '\n'
# # print mu[0]+mu[2], mu[1]+mu[3], '\n'
return
def energy_density_volume(k, x0, x1, y0, y1, z0, z1):
step_size = 0.02
xintervals = int(math.ceil((x1 - x0)/step_size))
yintervals = int(math.ceil((y1 - y0)/step_size))
zintervals = int(math.ceil((z1 - z0)/step_size))
points = []
for a in range(-2, xintervals + 2, 1):
points_y = []
for b in range(-2, yintervals + 2, 1):
points_z = []
for c in range(-2, zintervals + 2, 1):
points_z.append(higgs_squared(k, float(x0 + a * step_size), float(y0 + b * step_size), float(z0 + c * step_size)))
points_y.append(points_z)
points.append(points_y)
return five_point_laplace(points, step_size)
def higgs_squared_on_yz_plane(k, y0, y1, z0, z1, x, partition_size): # If this falls outside of [0,1) an value of maxint-1 will be returned; maxint is globally set.
y_step = (y1 - y0) / partition_size
z_step = (z1 - z0) / partition_size
points = []
for j in range(0, partition_size):
for i in range(0, partition_size):
y = y0 + i * y_step
z = z0 + j * z_step
value = higgs_squared(k, x, y, z)
bucket_value = int(floor(maxint * value))
if(bucket_value > maxintr or bucket_value < 0):
print i, j, bucket_value
bucket_value = maxintr
points.append(bucket_value)
return points
def higgs_squared_on_yz_plane(
k, y0, y1, z0, z1, x, partition_size
): # If this falls outside of [0,1) an value of maxint-1 will be returned; maxint is globally set.
y_step = (y1 - y0) / partition_size
z_step = (z1 - z0) / partition_size
points = []
for j in range(0, partition_size):
for i in range(0, partition_size):
y = y0 + i * y_step
z = z0 + j * z_step
value = higgs_squared(k, x, y, z)
bucket_value = int(floor(maxint * value))
if (bucket_value > maxintr or bucket_value < 0):
print i, j, bucket_value
bucket_value = maxintr
points.append(bucket_value)
return points
def energy_density_volume(k, x0, x1, y0, y1, z0, z1):
step_size = 0.02
xintervals = int(math.ceil((x1 - x0) / step_size))
yintervals = int(math.ceil((y1 - y0) / step_size))
zintervals = int(math.ceil((z1 - z0) / step_size))
points = []
for a in range(-2, xintervals + 2, 1):
points_y = []
for b in range(-2, yintervals + 2, 1):
points_z = []
for c in range(-2, zintervals + 2, 1):
points_z.append(
higgs_squared(k, float(x0 + a * step_size),
float(y0 + b * step_size),
float(z0 + c * step_size)))
points_y.append(points_z)
points.append(points_y)
return five_point_laplace(points, step_size)
def higgs_squared_on_xy_plane(k, x0, x1, y0, y1, z, partition_size): # If this falls outside of [0,1) an value of maxint-1 will be returned; maxint is globally set.
x_step = (x1 - x0) / partition_size
y_step = (y1 - y0) / partition_size
points = []
for j in xrange(0, partition_size):
# if j % 10 == 0 and j > 0:
# eprint("- rendered %s lines..." % j)
for i in xrange(0, partition_size):
x = x0 + i * x_step
y = y0 + j * y_step
value = higgs_squared(k, x, y, z)
bucket_value = int(floor(maxint * value))
if(bucket_value > maxintr or bucket_value < 0):
print i, j, bucket_value
bucket_value = maxintr
points.append(bucket_value)
return points