def _matrix_conv(self, m1, m2):
"""Matrix convolution.
Args:
m1: is a k x k x k dictionary, each element is a n x n matrix.
m2: is a l x l x l dictionary, each element is a n x n matrix.
Returns:
(k + l - 1) x (k + l - 1) x (k + l - 1) dictionary each
element is a n x n matrix.
Raises:
ValueError: if the entries of m1 and m2 are of different dimensions.
"""
n = (m1[0, 0, 0]).shape.as_list()[0]
if n != (m2[0, 0, 0]).shape.as_list()[0]:
raise ValueError("The entries in matrices m1 and m2 "
"must have the same dimensions!")
k = int(np.cbrt(len(m1)))
l = int(np.cbrt(len(m2)))
result = {}
size = k + l - 1
# Compute matrix convolution between m1 and m2.
for i in range(size):
for j in range(size):
for r in range(size):
result[i, j, r] = array_ops.zeros([n, n], self.dtype)
for index1 in range(min(k, i + 1)):
for index2 in range(min(k, j + 1)):
for index3 in range(min(k, r + 1)):
if (i - index1) < l and (j - index2) < l and (r - index3) < l:
result[i, j, r] += math_ops.matmul(m1[index1, index2, index3],
m2[i - index1, j - index2,
r - index3])
return result
def main():
funcs = [lambda x: 1 / (x + np.cbrt(x)), \
lambda x: 1 / math.sqrt(x ** 2 + 3.22), \
lambda x: math.sin(x) ** 3, \
lambda x: 1 / (1 + math.sin(x)), \
lambda x: math.log(x + 2) / x, \
lambda x: math.log(x) / (x ** 2)
]
monte_funcs = [funcs[0], \
lambda x: funcs[0](x[0]) * funcs[1](x[1]), \
lambda x: funcs[0](x[0]) * funcs[1](x[1]) * funcs[2](x[2]), \
lambda x: funcs[0](x[0]) * funcs[1](x[1]) * funcs[2](x[2]) * funcs[3](x[3]), \
lambda x: funcs[0](x[0]) * funcs[1](x[1]) * funcs[2](x[2]) * funcs[3](x[3]) * funcs[4](x[4]), \
lambda x: funcs[0](x[0]) * funcs[1](x[1]) * funcs[2](x[2]) * funcs[3](x[3]) * funcs[4](x[4]) * funcs[5](x[5])
]
anal_funcs = [lambda x: 3 * math.log(np.cbrt(x ** 2) + 1) / 2,\
lambda x: math.log(np.abs(x + math.sqrt(x ** 2 + 3.22))),\
lambda x: (math.cos(3 * x) - 9 *math.cos(x)) / 12,\
lambda x: -2 / (math.tan(x / 2) + 1),
lambda x: 2 * 0.648437 if x == 2 else 0.648437,
lambda x: -(math.log(x) + 1) / x
]
intervals = [(-3, -1), (1, 3), (3, 5), (5, 7), (1.2, 2), (14, 88)]
print("Format in methods is (value, time in seconds)")
for h, experiments_amount in [(0.1, 100), (0.01, 1000)]:
bench_methods(funcs, monte_funcs, anal_funcs, intervals, h, experiments_amount)
def countOptimalBins(self): num = self.dist.shape[0] if num < 100: if num % 2 == 0: num_b = np.sqrt(num) - 1 else: num_b = np.sqrt(num) else: if num % 2 == 0: num_b = np.cbrt(num) - 1 else: num_b = np.cbrt(num) return int(np.floor(num_b))
def calc_prior_n(self, damping_factor=5.):
n_infer = np.zeros((self.students, self.subtopics))
k_infer = np.zeros((self.students, self.subtopics))
for i, node in enumerate(tree.nodes):
n = self.nodes[node][1, :]
p = self.nodes[node][2, :] / (n + 1e-12)
for j in range(self.subtopics):
nmeasure = n * self.tree.damp_factor[i, j]
pmeasure = p * self.tree.pair_cond_true[i, j] + (1 - p) * self.tree.pair_cond_false[i, j]
n_infer[:, j] += nmeasure
k_infer[:, j] += nmeasure * pmeasure
alpha, beta = k_infer + 1., n_infer - k_infer + 1.
means = alpha / (alpha + beta)
weights = (n_infer + 1.)
EX2 = np.sum(weights * (alpha * beta / (alpha + beta) ** 2 / (alpha + beta + 1) + means ** 2), axis=0) / np.sum(
weights, axis=0)
EX = np.sum(weights * means, axis=0) / np.sum(weights, axis=0)
variance = EX2 - EX ** 2
p = np.array([node.prob for node in self.tree.nodes])
b = 7. - p * (1. - p) / variance
c = 16. - 1. / variance
d = 12. - 1. / variance
D0 = b ** 2 - 3. * c
D1 = 2. * b ** 3 - 9. * b * c + 27. * d
C = np.cbrt((D1 + np.sqrt(D1 ** 2 - 4. * D0 ** 3)) / 2.)
ns = -(b + C + D0 / C) / 3.
ns /= damping_factor
for i, node in enumerate(tree.nodes):
node.n_prior = 0 if np.isnan(ns[i]) else ns[i]
def test_unary_ufuncs(self):
v = BlockVector(2)
a = np.ones(3) * 0.5
b = np.ones(2) * 0.8
v[0] = a
v[1] = b
v2 = BlockVector(2)
unary_funcs = [np.log10, np.sin, np.cos, np.exp, np.ceil,
np.floor, np.tan, np.arctan, np.arcsin,
np.arccos, np.sinh, np.cosh, np.abs,
np.tanh, np.arcsinh, np.arctanh,
np.fabs, np.sqrt, np.log, np.log2,
np.absolute, np.isfinite, np.isinf, np.isnan,
np.log1p, np.logical_not, np.exp2, np.expm1,
np.sign, np.rint, np.square, np.positive,
np.negative, np.rad2deg, np.deg2rad,
np.conjugate, np.reciprocal]
for fun in unary_funcs:
v2[0] = fun(v[0])
v2[1] = fun(v[1])
res = fun(v)
self.assertIsInstance(res, BlockVector)
self.assertEqual(res.nblocks, 2)
for i in range(2):
self.assertTrue(np.allclose(res[i], v2[i]))
other_funcs = [np.cumsum, np.cumprod, np.cumproduct]
for fun in other_funcs:
res = fun(v)
self.assertIsInstance(res, BlockVector)
self.assertEqual(res.nblocks, 2)
self.assertTrue(np.allclose(fun(v.flatten()), res.flatten()))
with self.assertRaises(Exception) as context:
np.cbrt(v)
def geostationary(
cls, attractor, angular_velocity=None, period=None, hill_radius=None
):
"""Return the geostationary orbit for the given attractor and its rotational speed.
Parameters
----------
attractor : Body
Main attractor.
angular_velocity : ~astropy.units.Quantity
Rotational angular velocity of the attractor.
period : ~astropy.units.Quantity
Attractor's rotational period, ignored if angular_velocity is passed.
hill_radius : ~astropy.units.Quantity
Radius of Hill sphere of the attractor (optional). Hill sphere radius(in
contrast with Laplace's SOI) is used here to validate the stability of the
geostationary orbit, that is to make sure that the orbital radius required
for the geostationary orbit is not outside of the gravitational sphere of
influence of the attractor.
Hill SOI of parent(if exists) of the attractor is ignored if hill_radius is not provided.
"""
if angular_velocity is None and period is None:
raise ValueError(
"At least one among angular_velocity or period must be passed"
)
if angular_velocity is None:
angular_velocity = 2 * np.pi / period
# Find out geostationary radius using r = cube_root(GM/(angular
# velocity)^2)
with u.set_enabled_equivalencies(u.dimensionless_angles()):
geo_radius = np.cbrt(attractor.k / np.square(angular_velocity.to(1 / u.s)))
if hill_radius is not None and geo_radius > hill_radius:
raise ValueError(
"Geostationary orbit for the given parameters doesn't exist"
)
altitude = geo_radius - attractor.R
return cls.circular(attractor, altitude)
def discretize(self, column):
print("DEB Discretize column " + column)
sorted_col = sorted(column)
l = len(column)
n = int(numpy.floor(l / 2))
if l % 2 == 0:
median_1 = numpy.median(sorted_col[0:n])
median_2 = numpy.median(sorted_col[n:])
else:
median_1 = numpy.median(sorted_col[0:(n + 1)])
median_2 = numpy.median(sorted_col[(n + 1):])
iqr = median_2 - median_1
h = 2 * iqr * (1 / numpy.cbrt(l))
if h > 0:
bins_number = numpy.ceil((column.max() - column.min()) / h)
new_col, bins = pandas.cut(column, bins_number, labels=False, retbins=True, include_lowest=False)
else:
new_col = column
bins = []
return new_col, bins
def form_initial_voxels(xlim, ylim, zlim, num_voxels):
# TODO: Implement this method!
x_dim = xlim[-1] - xlim[0]
y_dim = ylim[-1] - ylim[0]
z_dim = zlim[-1] - zlim[0]
total_volume = x_dim * y_dim * z_dim
voxel_volume = float(total_volume / num_voxels)
voxel_size = np.cbrt(voxel_volume)
x_voxel_num = np.round(x_dim / voxel_size)
y_voxel_num = np.round(y_dim / voxel_size)
z_voxel_num = np.round(z_dim / voxel_size)
x_coor = np.linspace(xlim[0]+0.5*voxel_size, xlim[0]+(0.5+x_voxel_num-1)*voxel_size, x_voxel_num)
y_coor = np.linspace(ylim[0]+0.5*voxel_size, ylim[0]+(0.5+y_voxel_num-1)*voxel_size, y_voxel_num)
z_coor = np.linspace(zlim[0]+0.5*voxel_size, zlim[0]+(0.5+z_voxel_num-1)*voxel_size, z_voxel_num)
XX, YY, ZZ = np.meshgrid(x_coor, y_coor, z_coor)
voxels = np.vstack((XX.reshape(-1), YY.reshape(-1), ZZ.reshape(-1))).reshape(3, -1).T
return voxels, voxel_size
def sample(number_factors, n_time_steps=50, scenario_type=Collisive, kernel="SingleCPU"):
"""Helper function to sample a scenario for varying number of particles at constant density
:param number_factors: array of factors that will be applied to the scenarios, the length of this determines the number of samples/simulations
:param n_time_steps: how many time steps shall be performed for each sample/simulation
:param scenario_type: determines which scenario shall be run,
:param kernel: string determining the compute kernel of the simulation
:return: performance results (times, counts) and unit-less system variables, these are all dictionaries
"""
n_samples = len(number_factors)
times = get_empty_result_container(n_samples)
counts = get_empty_result_container(n_samples)
system_vars = get_empty_system_variables(n_samples)
box_length_factors = np.cbrt(number_factors)
for i, _ in enumerate(number_factors):
factors = get_identity_factors()
factors["n_particles"] = number_factors[i]
factors["box_length"] = box_length_factors[i]
scenario = scenario_type(kernel, factors)
scenario.run(n_time_steps)
scenario.set_system_vars(system_vars, i)
scenario.set_times(times, i)
scenario.set_counts(counts, i)
return times, counts, system_vars
columns=X_train.columns,
index=trafo_names) # Anderson Darling for all feature transformations
KSstats = pd.DataFrame(
np.zeros((len(trafo_names), X_train.shape[1])),
columns=X_train.columns,
index=trafo_names) # Kolmogorov Smirnov feature transformations
# again: only use training data for the tests!
for i in range(X_train.shape[1]):
feat = X_train.iloc[:, i]
natlog = np.log(feat + 1)
log2 = np.log2(feat + 1)
log10 = np.log10(feat + 1)
sqrt = np.sqrt(feat)
cbrt = np.cbrt(feat)
df_list = list([feat, natlog, log2, log10, sqrt, cbrt])
for j, trafo in zip(range(len(trafo_names)), df_list):
kurtstats.iloc[j, i] = trafo.kurt()
skewstats.iloc[j, i] = trafo.skew()
stdstats.iloc[j, i] = trafo.std()
stat1, pval1 = stats.shapiro(trafo)
stat2, pval2 = stats.jarque_bera(trafo)
AD, crit, sig = stats.anderson(trafo, dist='norm')
stat4, pval4 = stats.kstest(trafo, 'norm')
AD_adj = AD * (1 + (.75 / 50) + 2.25 / (50**2))
def __init__(self, c, Y_b, L_A, whitepoint=whitepoints_cie1931["D65"]):
# step0: Calculate all values/parameters which are independent of input
# samples
Y_w = whitepoint[1]
# Nc and F are modelled as a function of c, and can be linearly interpolated.
c_vals = [0.525, 0.59, 0.69]
F_Nc_vals = [0.8, 0.9, 1.0]
assert 0.535 <= c <= 0.69
F = np.interp(c, c_vals, F_Nc_vals)
self.c = c
self.N_c = F
self.M_cat02 = np.array(
[
[+0.7328, +0.4296, -0.1624],
[-0.7036, +1.6975, +0.0061],
[+0.0030, +0.0136, +0.9834],
]
)
RGB_w = np.dot(self.M_cat02, whitepoint)
D = F * (1 - 1 / 3.6 * np.exp((-L_A - 42) / 92))
D = min(D, 1.0)
D = max(D, 0.0)
self.D_RGB = D * Y_w / RGB_w + 1 - D
k = 1 / (5 * L_A + 1)
k4 = k * k * k * k
l4 = 1 - k4
self.F_L = k4 * L_A + 0.1 * l4 * l4 * np.cbrt(5 * L_A)
self.n = Y_b / Y_w
self.z = 1.48 + np.sqrt(self.n)
self.N_bb = 0.725 / self.n ** 0.2
self.N_cb = self.N_bb
RGB_wc = self.D_RGB * RGB_w
self.M_hpe = np.array(
[
[+0.38971, +0.68898, -0.07868],
[-0.22981, +1.18340, +0.04641],
[+0.00000, +0.00000, +1.00000],
]
)
RGB_w_ = np.dot(self.M_hpe, np.linalg.solve(self.M_cat02, RGB_wc))
alpha = (self.F_L * RGB_w_ / 100) ** 0.42
RGB_aw_ = 400 * alpha / (alpha + 27.13)
self.A_w = np.dot([2, 1, 1 / 20], RGB_aw_) * self.N_bb
self.h = np.array([20.14, 90.00, 164.25, 237.53, 380.14])
self.e = np.array([0.8, 0.7, 1.0, 1.2, 0.8])
self.H = np.array([0.0, 100.0, 200.0, 300.0, 400.0])
# Merge a bunch of matrices together here.
self.M_ = np.dot(
self.M_hpe,
np.linalg.solve(self.M_cat02, (self.M_cat02.T * self.D_RGB).T),
)
# Alternative: LU decomposition. That introduces a scipy dependency
# though and lusolve is slower than dot() as well.
self.invM_ = np.linalg.inv(self.M_)
def test_scafacos(self):
s = self.system
rho = 0.3
# This is only for box size calculation. The actual particle number is
# lower, because particles are removed from the mdlc gap region
n_particle = 100
particle_radius = 0.5
box_l = np.cbrt(4 * n_particle * np.pi / (3 * rho)) * particle_radius
s.box_l = 3 * [box_l]
for dim in (2, 1):
print("Dimension", dim)
# Read reference data
if dim == 2:
file_prefix = "data/mdlc"
s.periodicity = [1, 1, 0]
else:
s.periodicity = [1, 0, 0]
file_prefix = "data/scafacos_dipoles_1d"
ref_E_path = abspath(file_prefix + "_reference_data_energy.dat")
ref_E = float(np.genfromtxt(ref_E_path))
# Particles
data = np.genfromtxt(
abspath(file_prefix + "_reference_data_forces_torques.dat"))
s.part.add(pos=data[:, 1:4], dip=data[:, 4:7])
s.part[:].rotation = (1, 1, 1)
if dim == 2:
scafacos = magnetostatics.Scafacos(
prefactor=1,
method_name="p2nfft",
method_params={
"p2nfft_verbose_tuning": 0,
"pnfft_N": "80,80,160",
"pnfft_window_name": "bspline",
"pnfft_m": "4",
"p2nfft_ignore_tolerance": "1",
"pnfft_diff_ik": "0",
"p2nfft_r_cut": "6",
"p2nfft_alpha": "0.8",
"p2nfft_epsB": "0.05"
})
s.actors.add(scafacos)
# change box geometry in x,y direction to ensure that
# scafacos survives it
s.box_l = np.array((1, 1, 1.3)) * box_l
else:
# 1d periodic in x
scafacos = magnetostatics.Scafacos(
prefactor=1,
method_name="p2nfft",
method_params={
"p2nfft_verbose_tuning": 1,
"pnfft_N": "32,128,128",
"pnfft_direct": 0,
"p2nfft_r_cut": 2.855,
"p2nfft_alpha": "1.5",
"p2nfft_intpol_order": "-1",
"p2nfft_reg_kernel_name": "ewald",
"p2nfft_p": "16",
"p2nfft_ignore_tolerance": "1",
"pnfft_window_name": "bspline",
"pnfft_m": "8",
"pnfft_diff_ik": "1",
"p2nfft_epsB": "0.125"
})
s.box_l = np.array((1, 1, 1)) * box_l
s.actors.add(scafacos)
s.integrator.run(0)
# Calculate errors
err_f = self.vector_error(s.part[:].f, data[:, 7:10])
err_t = self.vector_error(s.part[:].torque_lab, data[:, 10:13])
err_e = s.analysis.energy()["dipolar"] - ref_E
tol_f = 2E-3
tol_t = 2E-3
tol_e = 1E-3
self.assertLessEqual(abs(err_e), tol_e,
"Energy difference too large")
self.assertLessEqual(abs(err_t), tol_t,
"Torque difference too large")
self.assertLessEqual(abs(err_f), tol_f,
"Force difference too large")
s.part.clear()
s.actors.clear()
def freedman_diaconis_bins(data):
"""Number of bins based on Freedman-Diaconis rule."""
h = 2 * (np.percentile(data, 75) - np.percentile(data, 25)) / np.cbrt(
len(data))
return int(np.ceil((data.max() - data.min()) / h))
def __init__(self, vol_bnds, voxel_size, use_gpu=True):
"""Constructor.
Args:
vol_bnds (ndarray): An ndarray of shape (3, 2). Specifies the
xyz bounds (min/max) in meters.
voxel_size (float): The volume discretization in meters.
"""
vol_bnds = np.asarray(vol_bnds)
assert vol_bnds.shape == (
3, 2), "[!] `vol_bnds` should be of shape (3, 2)."
# Define voxel volume parameters
self._vol_bnds = vol_bnds
self._voxel_size = float(voxel_size)
self._trunc_margin = 5 * self._voxel_size # truncation on SDF
self._color_const = 256 * 256
# Adjust volume bounds and ensure C-order contiguous
self._vol_dim = np.ceil((self._vol_bnds[:, 1] - self._vol_bnds[:, 0]) /
self._voxel_size).copy(order='C').astype(int)
self._vol_bnds[:,
1] = self._vol_bnds[:,
0] + self._vol_dim * self._voxel_size
self._vol_origin = self._vol_bnds[:,
0].copy(order='C').astype(np.float32)
print("Voxel volume size: {} x {} x {} - # points: {:,}".format(
self._vol_dim[0], self._vol_dim[1], self._vol_dim[2],
self._vol_dim[0] * self._vol_dim[1] * self._vol_dim[2]))
# Initialize pointers to voxel volume in CPU memory
self._tsdf_vol_cpu = np.ones(self._vol_dim).astype(np.float32)
# for computing the cumulative moving average of observations per voxel
self._weight_vol_cpu = np.zeros(self._vol_dim).astype(np.float32)
self._color_vol_cpu = np.zeros(self._vol_dim).astype(np.float32)
self.gpu_mode = use_gpu and FUSION_GPU_MODE
# Copy voxel volumes to GPU
if self.gpu_mode:
self._tsdf_vol_gpu = cuda.mem_alloc(self._tsdf_vol_cpu.nbytes)
cuda.memcpy_htod(self._tsdf_vol_gpu, self._tsdf_vol_cpu)
self._weight_vol_gpu = cuda.mem_alloc(self._weight_vol_cpu.nbytes)
cuda.memcpy_htod(self._weight_vol_gpu, self._weight_vol_cpu)
self._color_vol_gpu = cuda.mem_alloc(self._color_vol_cpu.nbytes)
cuda.memcpy_htod(self._color_vol_gpu, self._color_vol_cpu)
# Cuda kernel function (C++)
self._cuda_src_mod = SourceModule("""
__global__ void integrate(float * tsdf_vol,
float * weight_vol,
float * color_vol,
float * vol_dim,
float * vol_origin,
float * cam_intr,
float * cam_pose,
float * other_params,
float * color_im,
float * depth_im) {
// Get voxel index
int gpu_loop_idx = (int) other_params[0];
int max_threads_per_block = blockDim.x;
int block_idx = blockIdx.z*gridDim.y*gridDim.x+blockIdx.y*gridDim.x+blockIdx.x;
int voxel_idx = gpu_loop_idx*gridDim.x*gridDim.y*gridDim.z*max_threads_per_block+block_idx*max_threads_per_block+threadIdx.x;
int vol_dim_x = (int) vol_dim[0];
int vol_dim_y = (int) vol_dim[1];
int vol_dim_z = (int) vol_dim[2];
if (voxel_idx > vol_dim_x*vol_dim_y*vol_dim_z)
return;
// Get voxel grid coordinates (note: be careful when casting)
float voxel_x = floorf(((float)voxel_idx)/((float)(vol_dim_y*vol_dim_z)));
float voxel_y = floorf(((float)(voxel_idx-((int)voxel_x)*vol_dim_y*vol_dim_z))/((float)vol_dim_z));
float voxel_z = (float)(voxel_idx-((int)voxel_x)*vol_dim_y*vol_dim_z-((int)voxel_y)*vol_dim_z);
// Voxel grid coordinates to world coordinates
float voxel_size = other_params[1];
float pt_x = vol_origin[0]+voxel_x*voxel_size;
float pt_y = vol_origin[1]+voxel_y*voxel_size;
float pt_z = vol_origin[2]+voxel_z*voxel_size;
// World coordinates to camera coordinates
float tmp_pt_x = pt_x-cam_pose[0*4+3];
float tmp_pt_y = pt_y-cam_pose[1*4+3];
float tmp_pt_z = pt_z-cam_pose[2*4+3];
float cam_pt_x = cam_pose[0*4+0]*tmp_pt_x+cam_pose[1*4+0]*tmp_pt_y+cam_pose[2*4+0]*tmp_pt_z;
float cam_pt_y = cam_pose[0*4+1]*tmp_pt_x+cam_pose[1*4+1]*tmp_pt_y+cam_pose[2*4+1]*tmp_pt_z;
float cam_pt_z = cam_pose[0*4+2]*tmp_pt_x+cam_pose[1*4+2]*tmp_pt_y+cam_pose[2*4+2]*tmp_pt_z;
// Camera coordinates to image pixels
int pixel_x = (int) roundf(cam_intr[0*3+0]*(cam_pt_x/cam_pt_z)+cam_intr[0*3+2]);
int pixel_y = (int) roundf(cam_intr[1*3+1]*(cam_pt_y/cam_pt_z)+cam_intr[1*3+2]);
// Skip if outside view frustum
int im_h = (int) other_params[2];
int im_w = (int) other_params[3];
if (pixel_x < 0 || pixel_x >= im_w || pixel_y < 0 || pixel_y >= im_h || cam_pt_z<0)
return;
// Skip invalid depth
float depth_value = depth_im[pixel_y*im_w+pixel_x];
if (depth_value == 0)
return;
// Integrate TSDF
float trunc_margin = other_params[4];
float depth_diff = depth_value-cam_pt_z;
if (depth_diff < -trunc_margin)
return;
float dist = fmin(1.0f,depth_diff/trunc_margin);
float w_old = weight_vol[voxel_idx];
float obs_weight = other_params[5];
float w_new = w_old + obs_weight;
weight_vol[voxel_idx] = w_new;
tsdf_vol[voxel_idx] = (tsdf_vol[voxel_idx]*w_old+obs_weight*dist)/w_new;
// Integrate color
float old_color = color_vol[voxel_idx];
float old_b = floorf(old_color/(256*256));
float old_g = floorf((old_color-old_b*256*256)/256);
float old_r = old_color-old_b*256*256-old_g*256;
float new_color = color_im[pixel_y*im_w+pixel_x];
float new_b = floorf(new_color/(256*256));
float new_g = floorf((new_color-new_b*256*256)/256);
float new_r = new_color-new_b*256*256-new_g*256;
new_b = fmin(roundf((old_b*w_old+obs_weight*new_b)/w_new),255.0f);
new_g = fmin(roundf((old_g*w_old+obs_weight*new_g)/w_new),255.0f);
new_r = fmin(roundf((old_r*w_old+obs_weight*new_r)/w_new),255.0f);
color_vol[voxel_idx] = new_b*256*256+new_g*256+new_r;
}""")
self._cuda_integrate = self._cuda_src_mod.get_function("integrate")
# Determine block/grid size on GPU
gpu_dev = cuda.Device(0)
self._max_gpu_threads_per_block = gpu_dev.MAX_THREADS_PER_BLOCK
n_blocks = int(
np.ceil(
float(np.prod(self._vol_dim)) /
float(self._max_gpu_threads_per_block)))
#print "Total number of Voxels:",float(np.prod(self._vol_dim))
#print "Max threads per block:",self._max_gpu_threads_per_block
#print "Number of blocks Required:",n_blocks
grid_dim_x = min(gpu_dev.MAX_GRID_DIM_X,
int(np.floor(np.cbrt(n_blocks))))
grid_dim_y = min(gpu_dev.MAX_GRID_DIM_Y,
int(np.floor(np.sqrt(n_blocks / grid_dim_x))))
grid_dim_z = min(
gpu_dev.MAX_GRID_DIM_Z,
int(np.ceil(float(n_blocks) / float(grid_dim_x * grid_dim_y))))
self._max_gpu_grid_dim = np.array(
[grid_dim_x, grid_dim_y, grid_dim_z]).astype(int)
self._n_gpu_loops = int(
np.ceil(
float(np.prod(self._vol_dim)) / float(
np.prod(self._max_gpu_grid_dim) *
self._max_gpu_threads_per_block)))
#print "Grid dimension",self._max_gpu_grid_dim
#print "No of GPU loops",self._n_gpu_loops
else:
# Get voxel grid coordinates
xv, yv, zv = np.meshgrid(range(self._vol_dim[0]),
range(self._vol_dim[1]),
range(self._vol_dim[2]),
indexing='ij')
self.vox_coords = np.concatenate(
[xv.reshape(1, -1),
yv.reshape(1, -1),
zv.reshape(1, -1)],
axis=0).astype(int).T
q = rand_q()
v = rand_v()
J = r.jacob0(q)
Jt = J[:3, :]
# H = r.hessian0(q)
# Ht = H[:3, :, :]
q_n = [10000, 0]
q_m = [10000, 0]
# cond = np.linalg.cond(J[:3, :])
m = r.manipulability(J=J, axes='trans')
# infn = np.linalg.norm(Jt, 2)
psi = (np.cbrt(np.linalg.det(Jt @ np.transpose(Jt)))) / \
(np.trace(Jt @ np.transpose(Jt)) / 3)
for j in range(1000):
qd = np.linalg.pinv(J) @ v
if np.max(qd) > q_m[1]:
q_m[1] = np.max(qd)
if np.min(qd) < q_m[0]:
q_m[0] = np.min(qd)
if np.linalg.norm(qd) > q_n[1]:
q_n[1] = np.linalg.norm(qd)
elif np.linalg.norm(qd) < q_n[0]:
q_n[0] = np.linalg.norm(qd)
import numpy as np
import sys
import os
sys.path.append(os.path.abspath('..'))
from two_d_graphs.myfunctions import *
from two_d_graphs.posdef import *
from two_d_graphs.MatrixMaxProj import *
from scipy import io
from statsmodels.stats.moment_helpers import cov2corr
p = 50
d = 2
n_change = 3
len_t = 201
n = 1
h = 5.848 / np.cbrt(len_t - 1)
sigma = 0.1
phi = 0.5
gG = getGraph(p, d)
S, A = gG
A_T = getGraphatT_Shuheng(S, A, n_change)[1]
A_T_list = [lam * A_T + (1 - lam) * A
for lam in np.linspace(0, 1, len_t)] # Omega
C_T_list = [getCov(item) for item in A_T_list] # Cov: 0+class time
gG0 = getGraph(p, d)
S0, A0 = gG0
C0 = getCov(A0)
X = np.random.multivariate_normal(mean=np.zeros(p), cov=C0, size=n)
p = X_list[0][0].shape[1]
set_length_alpha = 51
set_length_beta = 51
indexOfPenalty = 3
alpha_upper = alpha_max(genEmpCov(X_list[3][10].T))
alpha_lower = alpha_max(genEmpCov(X_list[0][0].T))
alpha_set = np.logspace(np.log10(alpha_lower * 5e-2), np.log10(alpha_upper),
set_length_alpha)
beta_set = np.logspace(-2, 0.5, set_length_beta)
parameters_product = itertools.product(alpha_set, beta_set)
mesh_parameters = list(parameters_product)
h = 5.848 / np.cbrt(ni * len_t)
#-------------------------------------------------------------------------------------------------------------------------------
X_array = np.array(X_list) # class by time by ni by p
X_array = np.reshape(X_array,
(len_class, len_t * ni, p)) # class by ni*len_t by p
pool = NoDaemonProcessPool(processes=10)
results_mymethod = [
pool.apply(mtvgl.myTVGL,
args=(X_array, ni, parameters[0], parameters[1], indexOfPenalty,
True, h)) for parameters in mesh_parameters
]
# mtvgl.myTVGL(X_array, ni, 0.5, 1, indexOfPenalty, True, h)
ccb.write_hdf5('testfile_cleanup.hdf5', 3*[M], 3*[delta_x], trunc_triangles, grain_ids_3, phases_3, good_voxels_3, euler_angles_3, surface_voxels_3, gb_voxels_3, interface_voxels_3, overlaps_0)
# Compute actual volume fraction:
print("generated volume fraction of Co (after tweaks):", vol_frac_Co_3)
# final_frac.append(vol_frac_Co_2)
#
# print('************************************* average frac *************************** ', np.mean(final_frac))
# mean_frac.append(np.mean(final_frac))
# print(mean_frac)
# Saving grain volume data
if False:
np.savetxt('d_eq_orig.txt', [t.d_eq for t in trunc_triangles])
np.savetxt('d_eq_0.txt', np.cbrt(6./np.pi * grain_volumes_0 * ((L/M)**3)))
np.savetxt('d_eq_2.txt', np.cbrt(6./np.pi * grain_volumes_2 * ((L/M)**3)))
Plot initial and final distributions
plt.hist(np.array([t.d_eq for t in trunc_triangles]), alpha=0.5, bins=15, normed=True, label='Initial')
plt.hist(np.cbrt(6./np.pi * grain_volumes_2 * ((L/M)**3)), alpha=0.5, bins=15, normed=True, label='Final')
plt.legend(loc='upper right')
plt.show()
# Misorientation:
if False:
angles = compute_all_misorientation_voxel(trunc_triangles, grain_ids_2, [M]*3)
all_angles = np.array(list(angles.values()))
np.savetxt('misorientation.txt', all_angles)
theoretical = np.loadtxt('D3.txt')
plt.hist(np.array(all_angles), bins=20, normed=True)
plt.plot(theoretical[:,0], theoretical[:,1])
def funkcja1(x):
return np.cbrt(-np.exp(-x) -
x) # Przeksztalcenie funkcji do postaci y = ...
def calc_der(self, x):
return 1. / 3 / (np.cbrt(np.log(x + 1e-20)) ** 2) / (x + 1e-20)
def calc(self, x):
return np.cbrt(np.log(x + 1e-20))
print("Prepared", len(trunc_triangles), "triangles")
if use_potential:
ccb.optimize_midpoints(L, trunc_triangles)
grain_ids_0, overlaps_0, voxel_indices_0 = ccb_c.populate_voxels(M, L, trunc_triangles, 1, 0, 1.0)
else:
grain_ids_0, overlaps_0, voxel_indices_0 = ccb_c.populate_voxels(M, L, trunc_triangles, nr_tries, M, 1.0)
phases_0, good_voxels_0, euler_angles_0, phase_volumes_0, grain_volumes_0 = ccb_c.calc_grain_prop(M, grain_ids_0, trunc_triangles)
surface_voxels_0, gb_voxels_0, interface_voxels_0 = ccb_c.calc_surface_prop(M, grain_ids_0)
vol_frac_WC_0 = phase_volumes_0[1]/np.float(np.sum(phase_volumes_0))
vol_frac_Co_0.append( 1 - vol_frac_WC_0 )
sum_gb_voxels_0 = np.sum(gb_voxels_0)
contiguity_0.append( sum_gb_voxels_0 / np.float(sum_gb_voxels_0 + np.sum(interface_voxels_0)) )
d_eq_0.append(np.mean(np.cbrt(6./np.pi * grain_volumes_0 * ((L/M)**3))))
print("********************** Final vol fraction", vol_frac_Co_0[-1])
# Do Potts on coarse grid first for an improved initial guess.
grain_ids_2 = grain_ids_0.copy()
gb_voxels_2 = gb_voxels_0.copy()
if mc_steps > 0:
M_coarse = M//2
print("creating coarse grid")
grain_ids_coarse, overlaps_coarse, voxel_indices_coarse = ccb_c.populate_voxels(M_coarse, L, trunc_triangles, 0, M_coarse, 1.0)
print("coarse grid for potts done")
surface_voxels_coarse, gb_voxels_coarse, interface_voxels_coarse = ccb_c.calc_surface_prop(M_coarse, grain_ids_coarse)
print("starting coarse potts")
ccb_c.make_mcp_bound(M_coarse, grain_ids_coarse, gb_voxels_coarse, overlaps_coarse, voxel_indices_coarse, np.int(mc_steps*M_coarse**4), kBT)
Lsuns = data[:, 1] # data in Lsun units
makesubdir('output') # create file out dir
# conversions and precalculations
radii = np.zeros(Rsuns.size) # convert Rsun to AU
for i, r in enumerate(Rsuns):
radii[i] = r * 0.00465047 # 215 Rsun ~ 1 AU
watts = np.zeros(Lsuns.size) # convert Lsun to W (MKS units)
for i, l in enumerate(Lsuns):
watts[i] = l * 3.828e26 # IAU Resolution B3 conversion
lumins = np.zeros(watts.size) # convert W to sim units
for i, w in enumerate(watts):
lumins[i] = (w * ((6.7e-12)**2) * (5e-31)) / ((3.2e-8)**3)
t_fs = np.zeros(lumins.size) # precalculate t_f (Eq. 1)
for i, l in enumerate(lumins):
t_fs[i] = np.cbrt(masses[i] * radii[i]**2 / l)
taus = np.zeros(t_fs.size) # precalc tau (Eq. 2)
G = 4 * np.pi**2 # units of AU, yr, and Msun
for i, t_f in enumerate(t_fs):
taus[i] = 2. * radii[i]**3 / G / masses[i] / t_f
# main loop
for i, init_a in enumerate(init_as):
# initialize sim and create Interpolator objects
timer_start = time.perf_counter()
sim, rebx, tides = makesim(init_a)
starmass = reboundx.Interpolator(rebx, mtimes, masses, 'spline')
starradius = reboundx.Interpolator(rebx, rtimes, radii, 'spline')
startau = reboundx.Interpolator(rebx, ltimes, taus, 'spline')
# update Sun's mass and radius accordingly
def train_model(model: Model,
dataset_id,
dataset_prefix,
epochs=50,
batch_size=128,
val_subset=None,
cutoff=None,
normalize_timeseries=False,
learning_rate=1e-3):
"""
Trains a provided Model, given a dataset id.
Args:
model: A Keras Model.
dataset_id: Integer id representing the dataset index containd in
`utils/constants.py`.
dataset_prefix: Name of the dataset. Used for weight saving.
epochs: Number of epochs to train.
batch_size: Size of each batch for training.
val_subset: Optional integer id to subset the test set. To be used if
the test set evaluation time significantly surpasses training time
per epoch.
cutoff: Optional integer which slices of the first `cutoff` timesteps
from the input signal.
normalize_timeseries: Bool / Integer. Determines whether to normalize
the timeseries.
If False, does not normalize the time series.
If True / int not equal to 2, performs standard sample-wise
z-normalization.
If 2: Performs full dataset z-normalization.
learning_rate: Initial learning rate.
"""
X_train, y_train, X_test, y_test, is_timeseries = load_dataset_at(
dataset_id, normalize_timeseries=normalize_timeseries)
max_nb_words, sequence_length = calculate_dataset_metrics(X_train)
if sequence_length != MAX_SEQUENCE_LENGTH_LIST[dataset_id]:
if cutoff is None:
choice = cutoff_choice(dataset_id, sequence_length)
else:
assert cutoff in [
'pre', 'post'
], 'Cutoff parameter value must be either "pre" or "post"'
choice = cutoff
if choice not in ['pre', 'post']:
return
else:
X_train, X_test = cutoff_sequence(X_train, X_test, choice,
dataset_id, sequence_length)
if not is_timeseries:
X_train = pad_sequences(X_train,
maxlen=MAX_SEQUENCE_LENGTH_LIST[dataset_id],
padding='post',
truncating='post')
X_test = pad_sequences(X_test,
maxlen=MAX_SEQUENCE_LENGTH_LIST[dataset_id],
padding='post',
truncating='post')
classes = np.unique(y_train)
le = LabelEncoder()
y_ind = le.fit_transform(y_train.ravel())
recip_freq = len(y_train) / (len(le.classes_) *
np.bincount(y_ind).astype(np.float64))
class_weight = recip_freq[le.transform(classes)]
print("Class weights : ", class_weight)
y_train = to_categorical(y_train, len(np.unique(y_train)))
y_test = to_categorical(y_test, len(np.unique(y_test)))
if is_timeseries:
factor = 1. / np.cbrt(2)
else:
factor = 1. / np.sqrt(2)
path_splits = os.path.split(dataset_prefix)
if len(path_splits) > 1:
base_path = os.path.join('weights', *path_splits)
if not os.path.exists(base_path):
os.makedirs(base_path)
base_path = os.path.join(base_path, path_splits[-1])
else:
all_weights_path = os.path.join('weights', dataset_prefix)
if not os.path.exists(all_weights_path):
os.makedirs(all_weights_path)
model_checkpoint = ModelCheckpoint("./weights/%s_weights.h5" %
dataset_prefix,
verbose=1,
monitor='loss',
save_best_only=True,
save_weights_only=True)
reduce_lr = ReduceLROnPlateau(monitor='loss',
patience=100,
mode='auto',
factor=factor,
cooldown=0,
min_lr=1e-4,
verbose=2)
callback_list = [model_checkpoint, reduce_lr]
optm = Adam(lr=learning_rate)
model.compile(optimizer=optm,
loss='categorical_crossentropy',
metrics=['accuracy'])
if val_subset is not None:
X_test = X_test[:val_subset]
y_test = y_test[:val_subset]
model.fit(X_train,
y_train,
batch_size=batch_size,
epochs=epochs,
callbacks=callback_list,
class_weight=class_weight,
verbose=2,
validation_data=(X_test, y_test))
def test_cbrt_array(self):
assert np.all(np.cbrt(np.array([1., 8., 64.]) * u.m**3)
== np.array([1., 2., 4.]) * u.m)
from mpi4py import MPI
from lammps import lammps
import numpy as np
import sys
radius = int(sys.argv[1])
ratio = int(sys.argv[2])
length = radius * ratio * 2 * np.pi
box_sides = radius * np.cbrt(1.5 * ratio * np.pi) + 2
seed = int(sys.argv[3])
A = int(sys.argv[4])
B = 25
density = float(sys.argv[5])
save_dir = sys.argv[6]
lmp = lammps()
initial_commands = [
"units lj", "dimension 3", "boundary p p p", "neighbor 0.3 bin",
"neigh_modify every 1 check yes", "atom_style mdpd"
]
create_commands = [
f"region mdpd block -{box_sides} {box_sides} -{box_sides} {box_sides} 0 {length} units box",
"create_box 1 mdpd", f"lattice fcc {density}",
f"region tube cylinder z 0 0 {radius} INF INF",
"create_atoms 1 region tube", "mass 1 1.0"
def addParticles(self, n, method, mass = 0.0):
"""
Adds n particles to the simulation box using two methods: random
and lattice. The first one inserts particles randomly. The second
inserts them in a lattice.
Parameters
----------
method : string
Method to insert particles. Values can be "random" or "lattice".
n : integer
Number of molecules to be inserted in the box.
Returns
----------
None
Raises
----------
None
Notes
----------
None
"""
self.box.mass = mass / 6.023e23 * 10.0**-3
self.box.numParticles = n
if method == "random":
self.box.coordinates = (0.5 - np.random.rand(n,3)) * self.box.length
elif method == "lattice":
# nSide = 1
# self.box.coordinates = np.zeros((n,3))
# while np.power(nSide, 3) < n:
# nSide += 1
# counterPosition = np.zeros((3, ))
# for iParticle in range(0, n):
# self.box.coordinates[iParticle] = \
# (counterPosition + 0.5)*self.box.length / nSide \
# - 0.5*self.box.length
# counterPosition[0] += 1
# if counterPosition[0] == nSide:
# counterPosition[0] = 0
# counterPosition[1] += 1
# if counterPosition[1] == nSide:
# counterPosition[1] = 0
# counterPosition[2] += 1
# for iParticle in range(0, self.box.numParticles):
# self.box.coordinates[iParticle] -= 0.5
xVector = np.linspace(0.0,self.box.length,np.cbrt(self.box.numParticles) + 1)
yVector = np.linspace(0.0,self.box.length,np.cbrt(self.box.numParticles) + 1)
zVector = np.linspace(0.0,self.box.length,np.cbrt(self.box.numParticles) + 1)
self.box.coordinates = np.vstack(np.meshgrid(xVector,yVector,zVector)).reshape(3,-1).T
excess = len(self.box.coordinates) - self.box.numParticles
self.box.coordinates = self.box.coordinates[:-excess]
self.box.coordinates *= 0.98
def generate_lattice(sg,
volume,
minvec=tol_m,
minangle=pi / 6,
max_ratio=10.0,
maxattempts=100):
"""
generate the lattice according to the space group symmetry and number of atoms
if the space group has centering, we will transform to conventional cell setting
If the generated lattice does not meet the minimum angle and vector requirements,
we try to generate a new one, up to maxattempts times
args:
sg: International number of the space group
volume: volume of the lattice
minvec: minimum allowed lattice vector length (among a, b, and c)
minangle: minimum allowed lattice angle (among alpha, beta, and gamma)
max_ratio: largest allowed ratio of two lattice vector lengths
"""
maxangle = pi - minangle
for n in range(maxattempts):
#Triclinic
if sg <= 2:
#Derive lattice constants from a random matrix
mat = random_shear_matrix(width=0.2)
a, b, c, alpha, beta, gamma = matrix2para(mat)
x = sqrt(1 - cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2 + 2 *
(cos(alpha) * cos(beta) * cos(gamma)))
vec = random_vector()
abc = volume / x
xyz = vec[0] * vec[1] * vec[2]
a = vec[0] * np.cbrt(abc) / np.cbrt(xyz)
b = vec[1] * np.cbrt(abc) / np.cbrt(xyz)
c = vec[2] * np.cbrt(abc) / np.cbrt(xyz)
#Monoclinic
elif sg <= 15:
alpha, gamma = pi / 2, pi / 2
beta = gaussian(minangle, maxangle)
x = sin(beta)
vec = random_vector()
xyz = vec[0] * vec[1] * vec[2]
abc = volume / x
a = vec[0] * np.cbrt(abc) / np.cbrt(xyz)
b = vec[1] * np.cbrt(abc) / np.cbrt(xyz)
c = vec[2] * np.cbrt(abc) / np.cbrt(xyz)
#Orthorhombic
elif sg <= 74:
alpha, beta, gamma = pi / 2, pi / 2, pi / 2
x = 1
vec = random_vector()
xyz = vec[0] * vec[1] * vec[2]
abc = volume / x
a = vec[0] * np.cbrt(abc) / np.cbrt(xyz)
b = vec[1] * np.cbrt(abc) / np.cbrt(xyz)
c = vec[2] * np.cbrt(abc) / np.cbrt(xyz)
#Tetragonal
elif sg <= 142:
alpha, beta, gamma = pi / 2, pi / 2, pi / 2
x = 1
vec = random_vector()
c = vec[2] / (vec[0] * vec[1]) * np.cbrt(volume / x)
a = b = sqrt((volume / x) / c)
#Trigonal/Rhombohedral/Hexagonal
elif sg <= 194:
alpha, beta, gamma = pi / 2, pi / 2, pi / 3 * 2
x = sqrt(3.) / 2.
vec = random_vector()
c = vec[2] / (vec[0] * vec[1]) * np.cbrt(volume / x)
a = b = sqrt((volume / x) / c)
#Cubic
else:
alpha, beta, gamma = pi / 2, pi / 2, pi / 2
s = (volume)**(1. / 3.)
a, b, c = s, s, s
#Check that lattice meets requirements
maxvec = (a * b * c) / (minvec**2)
if minvec < maxvec:
#Check minimum Euclidean distances
smallvec = min(a * cos(max(beta, gamma)),
b * cos(max(alpha, gamma)),
c * cos(max(alpha, beta)))
if (a > minvec and b > minvec and c > minvec and a < maxvec
and b < maxvec and c < maxvec and smallvec < minvec
and alpha > minangle and beta > minangle
and gamma > minangle and alpha < maxangle
and beta < maxangle and gamma < maxangle
and a / b < max_ratio and a / c < max_ratio
and b / c < max_ratio and b / a < max_ratio
and c / a < max_ratio and c / b < max_ratio):
return np.array([a, b, c, alpha, beta, gamma])
#else:
#print([a, b, c, maxvec, minvec, maxvec*minvec*minvec])
#If maxattempts tries have been made without success
print(
"Error: Could not generate lattice after " + str(n + 1) +
" attempts for volume ", volume)
return
def fit(self, text_list):
"""
The fit method.
:param text_list: List of input texts
"""
if not type(text_list) == list:
text_list = text_list.values.tolist()
# Subsample the document space to reduce graph size.
if len(text_list) > self.doc_limit:
if self.targets is None:
if not self.doc_limit is None:
text_list = text_list[:self.doc_limit]
else:
unique_targets = np.unique(self.targets)
utx = defaultdict(list)
for utarget in unique_targets:
indices = np.where(self.targets == utarget)[0]
utx[utarget] = indices.tolist()
sampled_docs = []
while len(sampled_docs) < self.doc_limit:
for k, v in utx.items():
if len(v) > 0:
relevant_index = v.pop()
sampled_docs.append(text_list[relevant_index])
self.subsample_classes.append(k)
assert len(sampled_docs) == self.doc_limit
text_list = sampled_docs
del sampled_docs
t_tokens = OrderedDict()
for a in text_list:
t_tokens[a] = set(
[x.lower()[:self.ed_cutoff] for x in a.strip().split(" ")])
nlist = {}
for a in tqdm.tqdm(range(len(text_list))):
for b in range(a, len(text_list)):
set1 = t_tokens[text_list[a]]
set2 = t_tokens[text_list[b]]
jaccard = self.jaccard_index(set1, set2)
nlist[(a, b)] = jaccard
self.core_documents = t_tokens
self.G = self.get_graph(nlist, len(text_list))
G = nx.to_scipy_sparse_matrix(self.G,
nodelist=list(range(len(text_list))))
if self.verbose:
logging.info("Graph normalization in progress.")
laplacian = csgraph.laplacian(G, normed=True)
if self.verbose:
logging.info("SVD of the graph relation space in progress.")
if self.ndim >= len(text_list): self.ndim = len(text_list) - 1
svd = TruncatedSVD(n_components=self.ndim,
random_state=self.random_seed)
self.node_embeddings = svd.fit_transform(laplacian)
if self.neigh_size is None:
self.neigh_size = int(np.cbrt(self.node_embeddings.shape[0]))
# Number of client processes NUM_OF_CLIENTS = 2 # Global number of particles GLOBAL_NUM_PART = args.N assert (GLOBAL_NUM_PART % 2) == 0, "The number of particles must be even" # Init particle density init_density = args.density # Global volume GLOBAL_VOLUME = GLOBAL_NUM_PART / init_density # Init box _length init_box_length = np.cbrt(GLOBAL_VOLUME / NUM_OF_CLIENTS) # Temperature kT = args.T # Displacement DX_MAX = 0.4 DV_MAX = 0.2 # Number of steps, warmup steps steps = args.steps warmup = args.warmup # Perform about 100 system checks during the simulation check = int(steps / 1000) # Trial move probabilities
def inner_distance_transform_3d(mask,
bins=None,
erosion_width=None,
alpha=0.1,
beta=1,
sampling=[0.5, 0.217, 0.217]):
"""Transform a label mask for a z-stack with an inner distance transform.
.. code-block:: python
inner_distance = 1 / (1 + beta * alpha * distance_to_center)
Args:
mask (numpy.array): A label mask (``y`` data).
bins (int): The number of transformed distance classes.
erosion_width (int): Number of pixels to erode edges of each labels
alpha (float, str): Coefficent to reduce the magnitude of the distance
value. If ``'auto'``, determines alpha for each cell based on the
cell area.
beta (float): Scale parameter that is used when ``alpha`` is "auto".
sampling (list): Spacing of pixels along each dimension.
Returns:
numpy.array: A mask of same shape as input mask,
with each label being a distance class from 1 to ``bins``.
Raises:
ValueError: ``alpha`` is a string but not set to "auto".
"""
# Check input to alpha
if isinstance(alpha, str):
if alpha.lower() != 'auto':
raise ValueError('alpha must be set to "auto"')
mask = np.squeeze(mask)
mask = erode_edges(mask, erosion_width)
distance = ndimage.distance_transform_edt(mask, sampling=sampling)
distance = distance.astype(K.floatx())
label_matrix = label(mask)
inner_distance = np.zeros(distance.shape, dtype=K.floatx())
for prop in regionprops(label_matrix, distance):
coords = prop.coords
center = prop.weighted_centroid
distance_to_center = (coords - center) * np.array(sampling)
distance_to_center = np.sum(distance_to_center**2, axis=1)
# Determine alpha to use
if str(alpha).lower() == 'auto':
_alpha = 1 / np.cbrt(prop.area)
else:
_alpha = float(alpha)
center_transform = 1 / (1 + beta * _alpha * distance_to_center)
coords_z = coords[:, 0]
coords_x = coords[:, 1]
coords_y = coords[:, 2]
inner_distance[coords_z, coords_x, coords_y] = center_transform
if bins is None:
return inner_distance
# divide into bins
min_dist = np.amin(inner_distance.flatten())
max_dist = np.amax(inner_distance.flatten())
distance_bins = np.linspace(min_dist - K.epsilon(),
max_dist + K.epsilon(),
num=bins + 1)
inner_distance = np.digitize(inner_distance, distance_bins, right=True)
return inner_distance - 1 # minimum distance should be 0, not 1
y,
nd2,
cmap=matplotlib.colors.ListedColormap(clrs),
alpha=1.0,
shading='gouraud',
zorder=10)
# Plot the stripes
ax = fig.add_axes([0, 0, 1, 1],
facecolor='black',
xlim=((start + datetime.timedelta(days=1)).timestamp(),
(end - datetime.timedelta(days=1)).timestamp()),
ylim=(0, 1))
ax.set_axis_off()
ndata = numpy.transpose(ndata)
s = ndata.shape
y = numpy.linspace(0, 1, s[0] + 1)
x = [(a - datetime.timedelta(days=15)).timestamp() for a in dts]
x.append((dts[-1] + datetime.timedelta(days=15)).timestamp())
img = ax.pcolorfast(x,
y,
numpy.cbrt(ndata),
cmap='RdYlBu_r',
alpha=1.0,
vmin=-1.7,
vmax=1.7,
zorder=100)
fig.savefig('20CRv3.png')
import numpy as np import matplotlib.pyplot as plt a = 0.1 n = int(1e7) t = np.random.random(n) r = a / np.cbrt(1 - t) x = np.linspace(a, 10 * a, num=100) y = 3 * a**3 / x**4 hist, edge = np.histogram(r, x) hist = hist / hist[0] * y[0] plt.figure() plt.plot(x, y, linewidth=3, color='b') plt.draw() # plt.figure() # plt.hist(r, bins=100, edgecolor="w") plt.plot(edge[:-1], hist, linewidth=3, color='r') plt.show()
def gen_each(inlist): """ Function for generating synthetic data inlist[0] - dist of x inlist[1] - f1 inlist[2] - dist of noise inlist[3] - f2 inlist[4] - number of pts """ if len(inlist) != 5: print 'not enough parameters!' return -1 n = inlist[4] # ----- dist of x ----- if inlist[0] == 1: x = np.random.rand(n, 1) elif inlist[0] == 2: x = np.random.randn(n, 1) elif inlist[0] == 3: x = np.random.exponential(0.5, [n, 1]) elif inlist[0] == 4: x = np.random.laplace(0, 1, [n, 1]) elif inlist[0] == 5: x = np.random.lognormal(0, 1, [n, 1]) # ----- f_1 ----- if inlist[1] == 0: f1 = -x elif inlist[1] == 1: f1 = np.exp( -(np.random.rand() * 0.1 + 1) * x ) elif inlist[1] == 2: f1 = np.exp( -(np.random.rand() * 0.1 + 3) * x ) # ----- noise ----- if inlist[2] == 0: t = f1 elif inlist[2] == 1: t = f1 + 0.2 * np.random.rand(n, 1) elif inlist[2] == 2: t = f1 + 0.05*np.random.randn(n, 1) elif inlist[2] == 3: t = f1 + np.random.exponential(0.5, [n, 1]) elif inlist[2] == 4: t = f1 + np.random.laplace(0, 1, [n, 1]) elif inlist[2] == 5: t = f1 + np.random.lognormal(0, 1, [n, 1]) # ----- f_2 ----- if inlist[3] == 0: y = t elif inlist[3] == 1: y = 1 / (t**2 + 1) elif inlist[3] == 2: y = t**2 elif inlist[3] == 3: y = np.sin(t) elif inlist[3] == 4: y = np.cos(t) elif inlist[3] == 5: y = np.cbrt(t) xy = np.hstack((x, y)) return xy
for n in range(0,len(axs)):
axs[n].hist(white_wine.iloc[:,n],bins=50)
axs[n].set_title('name={}'.format(cols[n]))
# Obs 4 = "volatile acidity" and "residual sugar" are right skewed
###-----Since this is imbalanced class dataset we will try to achieve higher recall and use roc_auc as evaluation metric----###
#%%
#-- removing features which are highly correlated or zero correlated: ('citric acid','free sulfur dioxide')
col = ['fixed_acidity','volatile_acidity','residual_sugar','chlorides','total_sulfur_dioxide','density','sulphates', 'alcohol']
white_wine.head()
# Working with right skewed data--> cube root
white_wine_mod = pd.DataFrame()
for n in col:
white_wine_mod[col] = white_wine[col].apply(lambda x: np.cbrt(x))
white_wine_mod['pH']=white_wine['pH']
white_wine_mod['quality']=white_wine['quality']
# Working with normal data
white_wine_nor = white_wine[['fixed_acidity','volatile_acidity','residual_sugar','chlorides','total_sulfur_dioxide','density','sulphates', 'alcohol','pH','quality']]
#%%
#-- detecting outliers, transforming data can also help in handling outliers.
z = np.abs(stats.zscore(white_wine_mod)) # Calculating Z-score
threshold = 3
np.where(z > 3)
white_wine_mod_o = white_wine_mod[(z < 3).all(axis=1)]
white_wine_mod_o.shape # (4616, 10) # without outliers
white_wine_mod.shape #(4898, 10) # with outliers
def post_process(data, calib, M):
import time
started = time.time()
mask, Fs, quality = [], [], []
for i,d in enumerate(data):
if i % 100 == 0:
print(".", end="", flush=True)
xy, uv, q = d[:,:2], d[:,2:4], d[:,4:]
# represent as matrix [[a, b], [b, c]]
# flip signs since maximum is negative definite
a, b, c = -q[:,3], -q[:,4]/2, -q[:,5]
# asses quality by determinant
d = a*c-b*b
m = d > 1e-6
quality.append(np.median(d))
if m.sum() > 10:
F = algebraic_fit(xy[m], (xy+uv)[m], calib)
mask.append(True)
Fs.append(F)
else:
mask.append(False)
print()
F = np.asarray(Fs)
mask = np.asarray(mask)
quality = np.asarray(quality)
# camera to sample coordinates
#F = F.dot(M.T)
# set volumetric scale to 1
scale = np.cbrt(np.linalg.det(F))
F /= scale[...,np.newaxis,np.newaxis]
#
# Finite strain theory
#
# Polar decomposition
U, S, V = np.linalg.svd(F)
R = U @ V
#P = (V_T*S[:,np.newaxis,:]) @ V # == V.T @ diag(S) @ V
V_T = V.transpose(0,2,1)
R_T = R.transpose(0,2,1)
epsilon = (V_T*np.log(S[:,np.newaxis,:])) @ V # == logm(P)
k = (R - R_T)/2 # inverse or Rodrigez formula
sintheta = np.sqrt((k*k).sum(axis=(1,2))/2)
#costheta = (R.trace(0,1,2)-1)/2
#theta = np.arctan2(sintheta, costheta)
#omega = k*(theta/np.sin(theta))[:,np.newaxis,np.newaxis] # == logm(R)
omega = k*(np.arcsin(sintheta)/sintheta)[:,np.newaxis,np.newaxis] # == logm(R)
#
# Infinitesimal strain theory
#
#F_T = F.transpose(0,2,1)
#epsilon = (F+F_T)/2 - np.eye(3)[np.newaxis,:,:]
#omega = (F-F_T)/2
print("post_processed in", time.time()-started, "s")
return mask, F, epsilon, omega, quality
#Import Data and remove outliers model = pd.read_csv(r"E:\TAMIDS 2019\Data\pred.csv", low_memory=False, parse_dates=["Time"]) model = model[np.abs(model["Count"]-model["Count"].mean())<=(model["Count"].std()*3)] # In[11]: #Data Distribution and Probability Plots: Count fig,ax = plt.subplots(ncols=2,nrows=3) fig.set_size_inches(15,15) sns.distplot(model['Count'], ax=ax[0][0]) stats.probplot(model["Count"], dist='norm', fit=True, plot=ax[0][1]) sns.distplot(stats.boxcox(model['Count'], 0), ax=ax[1][0]) stats.probplot(stats.boxcox(model["Count"], .5), dist='norm', fit=True, plot=ax[1][1]) sns.distplot(np.cbrt(model['Count']), ax=ax[2][0]) stats.probplot(np.cbrt(model["Count"]), dist='norm', fit=True, plot=ax[2][1]) # In[12]: #Data Distribution and Probability Plots: Total Cost fig,ax = plt.subplots(ncols=2,nrows=2) fig.set_size_inches(15,15) sns.distplot(model['total_cost'], ax=ax[0][0]) stats.probplot(model["total_cost"], dist='norm', fit=True, plot=ax[0][1]) sns.distplot(np.cbrt(model['total_cost']), ax=ax[1][0]) stats.probplot(np.cbrt(model["total_cost"]), dist='norm', fit=True, plot=ax[1][1])
def scale_const_density(scale_factor):
factors = ps.get_identity_factors()
factors["n_particles"] = scale_factor
factors["box_length"] = np.cbrt(scale_factor)
return factors
ax2 = fig.add_axes([0,0,1,1],facecolor='green')
ax2.set_axis_off() # Don't want surrounding x and y axis
nd2=numpy.random.rand(s[1],s[0])
clrs=[]
for shade in numpy.linspace(.42+.01,.36+.01):
clrs.append((shade,shade,shade,1))
y = numpy.linspace(0,1,s[1])
x = numpy.linspace(0,1,s[0])
img = ax2.pcolormesh(x,y,nd2,
cmap=matplotlib.colors.ListedColormap(clrs),
alpha=1.0,
shading='gouraud',
zorder=10)
ax = fig.add_axes([0,0,1,1],facecolor='black',xlim=(0,1),ylim=(0,1))
ax.set_axis_off() # Don't want surrounding x and y axis
ndata=numpy.transpose(ndata)
s=ndata.shape
y = numpy.linspace(0,1,s[0])
x = numpy.linspace(0,1,s[1])
img = ax.pcolorfast(x,y,numpy.cbrt(ndata),
cmap='RdYlBu_r',
alpha=1.0,
vmin=-1.7,
vmax=1.7,
zorder=100)
fig.savefig('ensemble.pdf')
def test_cbrt_array(self):
# Calculate cbrt on both sides since on Windows the cube root of 64
# does not exactly equal 4. See 4388.
values = np.array([1., 8., 64.])
assert np.all(np.cbrt(values * u.m**3) ==
np.cbrt(values) * u.m)
def test_cbrt_scalar(self):
assert np.cbrt(8. * u.m**3) == 2. * u.m
def solve_four(a,b,c,d): if (a == 0): roots = solve_three(b,c,d) return [roots[0],roots[1],roots[1]] # http://www.it.uom.gr/teaching/linearalgebra/NumericalRecipiesInC/c5-6.pdf # http://web.archive.org/web/20120321013251/http://linus.it.uts.edu.au/~don/pubs/solving.html p = b/a q = c/a r = d/a u = q - np.square(p)/3 v = r - p*q/3 + 2*p*p*p/27 j = 4*u*u*u/27 * v*v if (b == 0 and c == 0): return [np.cbrt(-d),np.cbrt(-d),np.cbrt(-d)] elif (abs(p) > 10e100): return [-p,-p,-p] elif (abs(q) > 10e100): return [-np.cbrt(v),-np.cbrt(v),-np.cbrt(v)] elif (abs(u) > 10e100): #some big number return [np.cbrt(4)*u/3,np.cbrt(4)*u/3,np.cbrt(4)*u/3] if (j > 0): #one real root w = sqrt(j) if (v > 0): y = (u / 3)*np.cbrt(2 / (w + v)) - np.cbrt((w + v) / 2) - p / 3; else: y = np.cbrt((w - v) / 2) - (u / 3)*np.cbrt(2 / (w - v)) - p / 3; return else: s = np.sqrt(-u/3) t = -v/ (2*s*s*s) k = np.arccos(t)/3 y1 = 2 * s*np.cos(k) - p / 3; y2 = s*(-np.cos(k) + np.sqrt(3.)*np.sin(k)) - p / 3; y3 = s*(-np.cos(k) - np.sqrt(3.)*np.sin(k)) - p / 3; return [float(y1[0]),float(y2[0]),float(y3[0])]
def forward(self, pos, index_voxels):
print("-------------------- In RVS --------------------")
B = len(index_voxels) # batch_size
#print(B)
device = pos.device
vs = int(np.cbrt(len(index_voxels[0]))) # 64 -> 4, voxel_size
centroids = torch.zeros(B, self.npoints, dtype=torch.long).to(device)
centroids_index = []
#print(index_voxels[0])
#print('-------------------------------------------------------------')
for batch in range(B):
#print(batch)
voxels_per_batch = index_voxels[batch]
indexes = []
dict_keys = voxels_per_batch.keys()
len_key = len(dict_keys)
#print("npoints")
#print(self.npoints)
#print("len key")
#print(len_key)
if self.npoints <= len_key:
#print(list(voxels_per_batch.items()))
#print("npoints: "+str(self.npoints)+" "+"length: "+str(len_key))
selected_keys = random.sample(dict_keys, self.npoints)
#print(selected_keys)
i = 0
for per_key in selected_keys:
#int_index = int(per_key)
#indexes.append([batch, int_index//10000, int_index//100, int_index%100])
indexes.append([batch, per_key[0], per_key[1], per_key[2]])
val = voxels_per_batch.get(per_key)
#print(val)
length = len(val)
#print(str(length)+'====================')
#print(val.shape)
if (length == 1):
tem = 0
else:
tem = random.randint(0, len(val) - 1)
#index = int(random.sample(val, 1)[0])
index = int(val[tem])
centroids[batch, i] = index
i = i + 1
#print(centroids[batch])
else:
#self.npoints > len(voxels_per_batch):
#print(list(voxels_per_batch.items()))
selected_keys = dict_keys
i = 0
added = []
for per_key in selected_keys:
#int_index = int(per_key)
#indexes.append([batch, int_index//10000, int_index//100, int_index%100])
indexes.append([batch, per_key[0], per_key[1], per_key[2]])
val = voxels_per_batch.get(per_key)
#print(val)
#index = int(random.sample(val, 1)[0])
#print("perkey")
#print(per_key)
#print("val")
#print(val)
length = len(val)
#print("length")
#print(length)
if (length == 1):
tem = 0
else:
tem = random.randint(0, len(val) - 1)
index = int(val[tem])
centroids[batch, i] = index
added.append(index)
#print("index")
#print(index)
i = i + 1
add_num = 0
while add_num < (self.npoints - len_key):
index = int(random.sample(range(pos.shape[1]), 1)[0])
#print(index)
if index not in added:
centroids[batch, len_key + add_num] = index
indexes.append(index)
add_num += 1
added.append(index)
#print(index)
#print(centroids[batch])
centroids_index.append(indexes)
i = 0
return centroids, centroids_index # centroid_index is not used
def cal_nL(self,theta,rho):
self.L_k = np.cbrt(self.particle_num/(1.0*rho))
self.n_k = np.arange(-1*self.N_max,self.N_max+1)
self.k_step = (2*np.pi/self.L_k)
self.k_vec = self.n_k * self.k_step
def test_cbrt_array(self):
assert np.all(np.cbrt(np.array([1., 8., 64.]) * u.m**3)
== np.array([1., 2., 4.]) * u.m)
def test_flattened_hernquist():
"""
This test compares the coefficients against some computed in the mathematica
notebook 'flattened-hernquist.nb'. nmax and lmax here must match nmax and lmax
in that notebook.
"""
coeff_path = os.path.abspath(get_pkg_data_filename('data/Snlm-mathematica.csv'))
G = 1.
M = 1
a = 1.
q = 0.9
# Note: this must be the same as in the mathematica notebook
nmax = 8
lmax = 8
(Snlm,Serr),(Tnlm,Terr) = compute_coeffs(flattened_hernquist_density,
nmax=nmax, lmax=lmax, skip_odd=True, skip_m=True,
M=M, r_s=a, args=(M,a,q))
for l in range(1, lmax+1, 2):
for m in range(lmax+1):
assert Snlm[0,l,m] == 0.
m_Snl0 = np.loadtxt(coeff_path, delimiter=',')
m_Snl0 = m_Snl0[:,::2] # every other l
assert np.allclose(Snlm[0,::2,0], m_Snl0[0])
# check that random points match in gradient and density
np.random.seed(42)
n_test = 1024
r = 10.*np.cbrt(np.random.uniform(0.1**3,1,size=n_test)) # 1 to 10
t = np.arccos(2*np.random.uniform(size=n_test) - 1)
ph = np.random.uniform(0, 2*np.pi, size=n_test)
x = r*np.cos(ph)*np.sin(t)
y = r*np.sin(ph)*np.sin(t)
z = r*np.cos(t)
xyz = np.vstack((x, y, z))
# confirmed by testing...
tru_dens = flattened_hernquist_density(xyz[0], xyz[1], xyz[2], M, a, q)
bfe_dens = density(np.ascontiguousarray(xyz.T), Snlm, Tnlm, M, a)
assert np.all((np.abs(bfe_dens - tru_dens) / tru_dens) < 0.05) # <5%
tru_grad = np.array([flattened_hernquist_gradient(xyz[0,i], xyz[1,i], xyz[2,i], G, M, a, q)
for i in range(xyz.shape[1])]).T
bfe_grad = gradient(np.ascontiguousarray(xyz.T), Snlm, Tnlm, G, M, a).T
# check what typical errors are
# for j in range(3):
# pl.hist(np.abs((bfe_grad[j]-tru_grad[j])/tru_grad[j]))
for j in range(3):
assert np.all(np.abs((bfe_grad[j]-tru_grad[j])/tru_grad[j]) < 0.005) # 0.5%
return
# ------------------------------------------------------------------------
# plots:
# coefficients
fig,ax = pl.subplots(1,1,figsize=(10,8))
n,l = np.mgrid[:nmax+1, :lmax+1]
c = ax.scatter(n.ravel(), l.ravel(), c=Snlm[:,:,0].ravel(), s=64,
norm=mpl.colors.SymLogNorm(1E-5), cmap='RdBu_r',
vmin=-100, vmax=100, linewidths=1., edgecolors='#666666')
ax.xaxis.set_ticks(np.arange(0,nmax+1,1))
ax.yaxis.set_ticks(np.arange(0,lmax+1,1))
ax.set_xlim(-0.5, nmax+0.5)
ax.set_ylim(-0.5, lmax+0.5)
ax.set_xlabel('$n$')
ax.set_ylabel('$l$')
tickloc = np.concatenate((-10.**np.arange(2,-5-1,-1),
10.**np.arange(-5,2+1,1)))
fig.colorbar(c, ticks=tickloc, format='%.0e')
fig.tight_layout()
# contour plot in r,t at ph=0
rgrid = np.logspace(-1, 1., 128)
tgrid = np.linspace(0, np.pi, 128)
r,t = np.meshgrid(rgrid,tgrid)
x = r*np.sin(t)
z = r*np.cos(t)
_xyz = np.vstack((x.ravel(),np.zeros_like(x.ravel()),z.ravel()))
bfe_dens = density(np.ascontiguousarray(_xyz.T), Snlm, Tnlm, M, a)
true_dens = flattened_hernquist_density(_xyz[0], _xyz[1], _xyz[2], M, a, q)
fig,ax = pl.subplots(1, 1, figsize=(8,8))
levels = 10**np.linspace(-4.5, 1, 16)
ax.contour(np.log10(r), t, true_dens.reshape(x.shape),
levels=levels, colors='k',
locator=mpl.ticker.LogLocator(), label='True')
ax.contour(np.log10(r), t, bfe_dens.reshape(x.shape),
levels=levels, colors='r',
locator=mpl.ticker.LogLocator(), label='BFE')
ax.legend()
fig.tight_layout()
pl.show()
ax[1].plot(dataBJ2_70['Dmax'], dataBJ2_70['CscaKa'], label='BJ_70')
ax[2].plot(dataDO['Dmax'], dataDO['Ka'], label='DO_00', linestyle='-.')
ax[2].plot(meltedDO30['Dmax'], meltedDO30['Ka'], label='DO_30', linestyle='-.')
ax[2].plot(meltedDO70['Dmax'], meltedDO70['Ka'], label='DO_70', linestyle='-.')
ax[2].plot(dataBJ2['Dmax'], dataBJ2['Ka'], label='BJ_00')
ax[2].plot(dataBJ2_30['Dmax'], dataBJ2_30['Ka'], label='BJ_30')
ax[2].plot(dataBJ2_70['Dmax'], dataBJ2_70['Ka'], label='BJ_70')
ax[2].set_title('Copol Xsec Ka [mm$^2$]')
ax[2].set_xlabel('Dmax [mm]')
ax[2].legend()
ax[2].set_yscale('log')
fig.savefig('DO_BJ_comp_Xpol2.png')
# %%
plt.close('all')
reff = lambda mass: np.cbrt(3.0 * mass / (4.0 * np.pi * 916.0))
xeff = lambda r, l: 2.0 * np.pi * r / l
qeff = lambda C, r: C / (np.pi * r**2.0)
def reff2rhoBr07(r, ar):
mass = 4.0 * np.pi * r**3.0 * 916.0 / 3.0
size = 0.001 * (mass * 1000.0 / 8.9e-5)**(1.0 / 2.1)
# print(mass,size)
vol = np.pi * size**3.0 * ar / 6.0
den = mass / vol
for i, d in enumerate(den):
if d > 916.0:
den[i] = 916.0
size[i] = np.cbrt(6.0 * (mass[i] / den[i]) / (np.pi * ar))
return size, den
# For a very coarse grid, we should check the voxel indices. Requires Cython implementation for efficiency.
gid = grain_ids_coarse[ci]
for ii, g in zip(i, gid):
if g != grain_ids_2[ii] and np.searchsorted(voxel_indices_0[g-2], ii) < len(voxel_indices_0[g-2]):
grain_ids_2[ii] = g
# This might change a few voxels to a value that they shouldn't obtain, but it's barely noticeable
#grain_ids_2[i] = grain_ids_coarse[ci]
surface_voxels_2, gb_voxels_2, interface_voxels_2 = ccb_c.calc_surface_prop(M, grain_ids_2)
ccb_c.make_mcp_bound(M, grain_ids_2, gb_voxels_2, overlaps_0, voxel_indices_0, np.int(mc_steps*M**4), kBT)
sum_gb_voxels_2 = np.sum(gb_voxels_2)
contiguity_2.append( sum_gb_voxels_2 / np.float(sum_gb_voxels_2 + np.sum(interface_voxels_2)) )
print("Contiguity is at", contiguity_2[-1])
phases_2, good_voxels_2, euler_angles_2, phase_volumes_0, grain_volumes_2 = ccb_c.calc_grain_prop(M, grain_ids_2, trunc_triangles)
d_eq_mean.append(np.mean(np.cbrt(6./np.pi * grain_volumes_2 * ((L/M)**3))))
d_eq_std.append(np.std(np.cbrt(6./np.pi * grain_volumes_2 * ((L/M)**3))))
if False:
import matplotlib.pyplot as plt
plt.plot(np.array(mc_stepss), contiguity_2)
plt.show()
fname = 'stat_mc_steps'
if use_potential:
fname += '_U'
elif nr_tries == 0:
fname += '_random'
else:
fname += '_transl'
def test_cbrt_scalar(self):
assert np.cbrt(8. * u.m**3) == 2. * u.m
def test_cbrt_array(self):
# Calculate cbrt on both sides since on Windows the cube root of 64
# does not exactly equal 4. See 4388.
values = np.array([1., 8., 64.])
assert np.all(np.cbrt(values * u.m**3) == np.cbrt(values) * u.m)
[-np.sin(th), 0., np.cos(th)]])
return matrix.dot(vec)
def rotate_z(th, vec):
matrix = np.array([[np.cos(th), -np.sin(th), 0.],
[np.sin(th), np.cos(th), 0.], [0., 0., 1.]])
return matrix.dot(vec)
def angle_between(v1, v2):
cs = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
return np.arccos(cs)
a = np.cbrt(G * M * T**2 / 4. / np.pi**2)
c = a * e
b = np.sqrt(a**2 - c**2)
J = m * np.sqrt(G * M * a * (1. - e**2))
perihelion = a * (1. - e)
aphelion = a * (1. + e)
vPerihelion = np.sqrt(G * M * (1. + e) / perihelion)
vAphelion = np.sqrt(G * M * (1. - e) / aphelion)
omegaEarth = 2 * np.pi * (T / Day + 1) / T
print("earth orbit semimajor axis: a={}".format(a))
print("earth rotation angular speed: omegaEarth={}".format(omegaEarth))
# Axis configuration:
# Set theta(th) coordinate of perihelion to 0.
# Set theta(th) axis direction the same as earth's orbital direction.
def predict():
net = unet_model_3d((1, 64, 64, 64))
net.load_weights("./data/logs/network_weights_loss.h5")
global_tp = 0
global_fn = 0
global_fp = 0
for patient in os.listdir(path):
f = h5py.File(path + patient, "r")
amount_of_subvolumes = len(f["images/images"])
tp = 0
fp = 0
fn = 0
for i in range(amount_of_subvolumes):
images = np.array(np.reshape(f["images/images"][i], (1, 1, 64, 64, 64)))
labels = np.array(np.reshape(f["labels/labels"][i], (1, 1, 64, 64, 64)))
# if len(np.nonzero(labels)[1]) == 0:
# continue
prediction = net.predict(images, batch_size=1, verbose=1)
highly_conf_predicted = len(np.where(prediction[0][0] > 0.99)[0])
# plot(prediction, labels)
# aneurysm in mask -> dice can be considered as measure
if len(np.nonzero(labels)[1]) != 0:
dc = 1 - distance.dice(
np.reshape(labels, (-1,)), np.reshape(prediction, (-1,))
)
if dc > 0.30:
# aneurysm detected correctly
tp += 1
visualize_mask(prediction[0][0])
visualize_mask(labels[0][0])
else:
# aneurysm not detected correctly
fn += 1
visualize_mask(prediction[0][0])
visualize_mask(labels[0][0])
# no aneurysm in mask but in prediction
elif highly_conf_predicted > 50:
# check whether this is predicted aneurysm or random activation (check is across one axis only)
max_index = np.max((np.where(prediction[0][0] > 0.99)[0]))
min_index = np.min((np.where(prediction[0][0] > 0.99)[0]))
if max_index - min_index < np.cbrt(highly_conf_predicted) + 5:
fp += 1
# compute precision and recall per patient
precision = tp + 0.0001 / (tp + fp + 0.0001)
recall = tp + 0.0001 / (tp + fn + 0.0001)
print("precision: " + str(precision) + " recall: " + str(recall))
global_fn += fn
global_fp += fp
global_tp += tp
precision = global_tp / (global_tp + global_fp)
recall = global_tp / (global_tp + global_fn)
print("precision: " + str(precision) + " recall: " + str(recall))
