def solve(x0, A, b, omega, tol):
'''Wrapper function to use SOR algorithm to solve Ax = b
Parameters
===========
x0: numpy array
First guess for solution
A: numpy array
matrix describing linear system
b: numpy array
vector of constants
omega: float
relaxation factor
tol: float
error tolerancd for stopping iteration (error for convergence)
'''
# Format dtype of all parameters to numba double precision float
# this helps @njit work correctly
x0 = f8(x0)
A = f8(A)
b = f8(b)
omega = f8(omega)
M = u8(10**6)
tol = f8(tol)
# call actual SOR algorithm (need the numba dtypes to allow njit compile)
x = solve_body(x0, A, b, omega, M, tol)
return x
def solve_body(x0, A, b, omega, M, tol):
'''SOR function. Iterates until errror is less than specified, or M
iterations, whichever comes first.
Parameters
===========
x0: numpy array
First guess for solution
A: numpy array
matrix describing linear system
b: numpy array
vector of constants
omega: float
relaxation factor
M: integer
maximum number of steps while seeking convergence
tol: float
error size for stopping iteration (error for convergence)
'''
x = x0 # set initial guess
err = f8(tol + 1000000) # initial error level
# While loop. Main loop exit after M iterations, but has a secondary break
# that stops when the observed error is less than selected tolerance
for i in range(M):
x_new = SOR_iter(x, A, b, omega) # perform SOR iteration
err = resid(x_new, A, b) # compute new residual
x = x_new # reset x for new pass (or for output)
# second break parameter (under error tolerance)
if err < tol:
break
return x
def resid(x_new, x):
''' Calculate L2-norm of x and x_new'''
# need to be numba double precision float so njit will work in body of
# solve function
err = f8(np.linalg.norm(x_new - x))
return err
def resid(x, A, b):
''' Calculate L2-norm of b and x dot A '''
# need to be numba double precision float so njit will work in body of
# solve function
err = f8(np.linalg.norm(b - np.dot(A, x)))
return err
def convolve(signal, ref, window, result):
smem = cuda.shared.array(0, f8)
i, j = cuda.grid(2)
S = signal.size
W = window.size
R = ref.shape[0]
Bix = cuda.blockIdx.x # Block index along the x dimension -> indexing the signal
BDx = cuda.blockDim.x # Number of threads along x -> Many things
tix = cuda.threadIdx.x # x thread id within block [0,blockdim.x) -> indexing the window
tiy = cuda.threadIdx.y # y thread id within block [0,blockdim.y) -> indexing of memory
tif = tix + tiy * BDx # thread index within a block (flat) -> indexing lines and shared memory
index = j + tix # reference and signal index
value = f8(0)
if (tix < W) & (index < S):
value = window[tix] * (ref[R, index] * signal[index])
value = reduce_warp(value, u4(0xffffffff))
# Reduced sum should be present in the value of all threads with lane index == 0
# Store the warp reduction in the shared memory
if tif % 32 == 0: # For all threads with lane index == 0
smem[tif // 32] = value # Flat warp id
cuda.syncthreads()
# When the blocksize is smaller than a single warp (32), we are done.
# In this case we can be very specific about the locations we need
if (BDx <= 32) and (tix == 0):
result[Bix, j] = smem[tiy]
# Otherwise, take values from the shared memory van reduce.
# NOTE: maximum number of threads is 1024 which is 32 times a warp (consisting of 32 threads)
# This means, the warp reductions of 32 warps, fit baxck into a single warp.
# Disperse the reduction values from the memory over the first threads along the x direction.
# All others become 0
Nwx = (BDx - 1) // 32 + 1
if (tix < BDx // 32):
values = smem[tix + Nwx * tiy]
else:
values = 0
# Perhaps its better to put the index definition outside the if-else block and remove this barrier
cuda.syncthreads()
# All threads in a first warp along x
if tix // 32 == 0:
value = reduce_warp(value, u4(0xffffffff))
cuda.syncthreads()
if (tix == 0) and (j < S):
result[Bix, j] = value
def MC_Amer_call(S0, K, mu, r, d, sigma, t, T, delta_t, N):
'''
Parameters
==========
S0: float
Initial value of stock process
mu: float
Drift of stock process
r: float
Risk Free rate
delta: float
Continuous dividend yield
sigma: float
Volatility of stock process
T: float
Time horizon
delta_t: float
Time step size
N: integer
Number of paths to generate
Returns
=======
C: Float
Value of American call option
'''
M = int((T - t) / delta_t) # number of steps. Must be an integer.
S = generate_paths(S0, mu, d, sigma, delta_t, N, M)
h = np.maximum(S - K, 0) #compute exercise values
g = h[M] #set up excercised value vector
tau = np.repeat(T, N) #set up stopping time vector
for j in range(M - 1, 0, -1):
k = S[j] > K #in the money boolean vector
x = S[j, k] # in the money points
y = g[k] * np.exp(-(r - d) * (tau[k] - t * delta_t))
a, __ = fit(func, x, y) #regression step
C_hat = func(S[j, k], a[0], a[1], a[2],
a[3]) #find estimated continuation value
g[k][C_hat >= h[j, k]] = h[j, k][
C_hat >= h[j, k]] #update g where excercise more than continuation
tau[k][C_hat >= h[j, k]] = j / f8(M) * (
T - t) #update optimal excercise time
C_0 = np.sum(np.exp(-(r - d) * delta_t * tau).T * g) / N
V_0 = np.maximum(C_0, h[0, 0])
return V_0
def solve(A, d):
'''Helper function for Thomas algorith. Breaks matrix into tridiagonal
elements for easier processing by algorithm. '''
# pass numba float64 dtype np.arrays to the solve function - need to
# perform this step to allow for nopython execution of thomas algorithm
# which yields maximum speed
a = f8(np.diagonal(A, offset=0))
b = f8(np.diagonal(A, offset=1))
c = f8(np.diagonal(A, offset=-1))
dfloat = f8(d)
D = np.diag(a, 0) + np.diag(b, 1) + np.diag(c, -1) #create test matrix
# test if D is 'close enough' to A - if not that means A was not
# tridiagonal and the function raises an exception
if not np.allclose(A, D):
raise Exception('The given A is not tridiagonal')
# pass to thomas algorithm solver
x = solve_body(a, b, c, dfloat)
return x
def run_target(N, target):
print '== Target', target
vect_discriminant = vectorize([f4(f4, f4, f4), f8(f8, f8, f8)],
target=target)(discriminant)
A, B, C = generate_input(N, dtype=np.float32)
D = np.empty(A.shape, dtype=A.dtype)
ts = time()
D = vect_discriminant(A, B, C)
te = time()
total_time = (te - ts)
print 'Execution time %.4f' % total_time
print 'Throughput %.4f' % (N / total_time)
if '-verify' in sys.argv[1:]:
check_answer(D, A, B, C)
def solve_body(v0, b, g, omega, tol, theta, lamb, M):
'''Projected SOR function. Iterates until errror is less than specified, or M
iterations, whichever comes first.
'''
# set initial guess
err = f8(tol + 1000000) # initial error level
v = v0
# While loop. Main loop exit after M iterations, but has a secondary break
# that stops when the observed error is less than selected tolerance
for k in range(0, M):
v_new = SOR_iter(b, v, g, omega, tol, theta,
lamb) # perform SOR iteration
err = resid(v_new, v) # compute new residual
v = v_new
# second break parameter (under error tolerance)
if err < tol:
break
return v
def solve(v0, b, g, omega, tol, theta, lamb):
'''Wrapper function to use SOR algorithm to solve Ax = b
Parameters
===========
xv: numpy array
First guess for solution
b: numpy array
vector to represent A * w
g: numpy array
vector representing early excercise values
omega: float
relaxation factor
tol: float
error tolerancd for stopping iteration (error for convergence)
theta: float
parameter controlling what discretization method is being used
lamb: float
lambda parameter from option pricing model
'''
# Format dtype of all parameters to numba double precision float
# this helps @njit work correctly
v0 = f8(v0)
b = f8(b)
g = f8(g)
omega = f8(omega)
M = u8(10**6)
tol = f8(tol)
theta = f8(theta)
lamb = f8(lamb)
# call actual SOR algorithm (need the numba dtypes to allow njit compile)
x = solve_body(v0, b, g, omega, tol, theta, lamb, M)
return x
# this is actually a rotation with -rad (use symmetry of sin/cos)
sin_rad = sin(rad)
cos_rad = cos(rad)
return point[0] * cos_rad + point[2] * sin_rad, point[
1], point[2] * cos_rad - point[0] * sin_rad
# @cc.export('coords2cartesian', dtype_3floattuple(f8, f8))
@jit(dtype_3floattuple(f8, f8), nopython=True, cache=True)
def coords2cartesian(lng_rad, lat_rad):
return cos(lng_rad) * cos(lat_rad), sin(lng_rad) * cos(lat_rad), sin(
lat_rad)
# @cc.export('distance_to_point_on_equator', f8(f8, f8, f8))
@jit(f8(f8, f8, f8), nopython=True, cache=True)
def distance_to_point_on_equator(lng_rad, lat_rad, lng_rad_p1):
"""
uses the simplified haversine formula for this special case (lat_p1 = 0)
:param lng_rad: the longitude of the point in radians
:param lat_rad: the latitude of the point
:param lng_rad_p1: the latitude of the point1 on the equator (lat=0)
:return: distance between the point and p1 (lng_rad_p1,0) in km
this is only an approximation since the earth is not a real sphere
"""
# 2* for the distance in rad and * 12742 (mean diameter of earth) for the distance in km
return 12742 * asin(
sqrt(((sin(lat_rad / 2))**2 + cos(lat_rad) * (sin(
(lng_rad - lng_rad_p1) / 2))**2)))
def y_rotate(rad, point):
# y stays the same
# this is actually a rotation with -rad (use symmetry of sin/cos)
sin_rad = sin(rad)
cos_rad = cos(rad)
return point[0] * cos_rad + point[2] * sin_rad, point[1], point[2] * cos_rad - point[0] * sin_rad
# @cc.export('coords2cartesian', dtype_3float_tuple(f8, f8))
@njit(dtype_3float_tuple(f8, f8), cache=True)
def coords2cartesian(lng_rad, lat_rad):
return cos(lng_rad) * cos(lat_rad), sin(lng_rad) * cos(lat_rad), sin(lat_rad)
# @cc.export('distance_to_point_on_equator', f8(f8, f8, f8))
@njit(f8(f8, f8, f8), cache=True)
def distance_to_point_on_equator(lng_rad, lat_rad, lng_rad_p1):
"""
uses the simplified haversine formula for this special case (lat_p1 = 0)
:param lng_rad: the longitude of the point in radians
:param lat_rad: the latitude of the point
:param lng_rad_p1: the latitude of the point1 on the equator (lat=0)
:return: distance between the point and p1 (lng_rad_p1,0) in km
this is only an approximation since the earth is not a real sphere
"""
# 2* for the distance in rad and * 12742 (mean diameter of earth) for the distance in km
return 12742 * asin(sqrt(((sin(lat_rad / 2)) ** 2 + cos(lat_rad) * (sin((lng_rad - lng_rad_p1) / 2)) ** 2)))
# @cc.export('haversine', f8(f8, f8, f8, f8))
@njit(f8(f8, f8, f8, f8), cache=True)
THROTTLE_MID_SPEED = 1400.0
BOOST_ACCELERATION = 991.6667
BREAK_ACCELERATION = 3500.0
MAX_CAR_SPEED = 2300.0
BOOST_CONSUMPTION_RATE = 33.3 # per second
# constants of the acceleration between 0 to 1400 velocity: acceleration = a * velocity + b
a = -(THROTTLE_ACCELERATION_0 -
THROTTLE_ACCELERATION_1400) / THROTTLE_MID_SPEED
b = THROTTLE_ACCELERATION_0
b2 = THROTTLE_ACCELERATION_0 + BOOST_ACCELERATION
fast_jit = jit(f8(f8, f8), nopython=True, fastmath=True, cache=True)
State = namedtuple("State", ["dist", "vel", "boost", "time"])
class VelocityRange:
max_speed = None
use_boost = None
@staticmethod
def distance_traveled(t: float, v0: float) -> float:
raise NotImplementedError
@staticmethod
def velocity_reached(t: float, v0: float) -> float:
raise NotImplementedError
if mean.shape[0] != cov.shape[0]:
raise ValueError("mean and cov must have same length")
L = np.linalg.cholesky(cov)
from numpy.random import standard_normal
z = standard_normal(final_shape).reshape(mean.shape[0],-1)
x = L.dot(z).T
x += mean
x.shape = tuple(final_shape)
return x, L
#@nb.njit(nb.f8[:](nb.f8[:, :], nb.f8[:, :]), nogil=True)
@nb.njit(nb.f8(nb.f8[:, :], nb.f8[:, :]), nogil=True, cache=True)
def poly_line_intersect(poly, line):
# extend_line = True
eps = 1e-6
none = np.inf # np.zeros(1)
v0v1 = poly[1, :] - poly[0, :]
v0v2 = poly[2, :] - poly[0, :]
dir = line[1, :] - line[0, :]
line_len = math.sqrt(np.sum(dir**2))
if line_len < eps:
return none
dir = dir/line_len
pvec = cross3d(dir, v0v2)
@jit(Tuple((f8[::1], i8))(f8, f8, f8, f8, f8, f8[::1], f8[::1]), nopython=True)
def calc_host_propensity_vectors(TAU_H, B_H, D_H, K_H, dtBac, c, dtVec):
birthPropVec = (1 + B_H * c) / TAU_H
deathPropVec = (1 - D_H * c) * c.size / (K_H * TAU_H)
totPropVec = np.concatenate((birthPropVec, deathPropVec))
cumulPropVec = totPropVec.cumsum()
# calc number of required time steps
(dtHost, numSubStep) = calc_dynamic_timestep(cumulPropVec[-1], dtVec,
dtBac)
# calc probVec
cumulPropVec *= dtHost
return (cumulPropVec, numSubStep)
# get composition of host parent that will give birth
@jit(f8(f8[::1], f8[::1], i8), nopython=True)
def host_create_offspring(c, d, id_group):
# draw offspring composition
fracPar = c[id_group] / (c[id_group] + d[id_group])
return fracPar
# update host dynamics while keeping microbial dynamics fixed
@jit(
Tuple((f8[::1], f8[::1], f8[::1], i8))(f8[::1], f8[::1], f8[::1], f8[::1],
i8, f8, f8, f8[:, ::1], i8))
def update_host(CVec, DVec, AgeVec, cumulPropVec, numSubStep, n0, sigma,
rndMat, ridx):
# init vectors that keep track of changes in host
numGroup = CVec.size
cNewTemp = np.zeros(numSubStep)
smally2 = y2 // 3
largey2 = smally2 if y2 == smally2 * 3 else smally2 + 1
largez1 = z1 // 3
smallz1 = largez1 if z1 == largez1 * 3 else largez1 + 1
smallz2 = z2 // 3
largez2 = smallz2 if z2 == smallz2 * 3 else smallz2 + 1
if np.any(roughgrid[smallx1:smallx2, smally1:smally2, smallz1:smallz2]):
return True
if not np.any(roughgrid[largex1:largex2, largey1:largey2,
largez1:largez2]):
return False
return np.any(grid[x1:x2, y1:y2, z1:z2])
@nb.njit(
nb.f8(nb.b1[:, :, :], nb.b1[:, :, :], nb.i8, nb.i8, nb.i8, nb.i8[:, :, :],
nb.f8[:, :], nb.i8))
def useBoostedTree2(grid, roughgrid, anchorx, anchory, direction, btsplits,
btleaves, ntrees):
score = 0.
for tree in range(ntrees):
splitidx = 0
for depth in range(3):
tsplit = btsplits[tree, splitidx]
if direction == 0:
x1 = anchorx + tsplit[0]
x2 = anchorx + tsplit[3]
y1 = anchory + tsplit[1]
y2 = anchory + tsplit[4]
else:
x1 = anchorx + 48 - tsplit[
3] ### change when changing anchor!!!
n = int(n)
fib = [0] * n
fib[1] = 1
for i in range(2, n):
fib[i] = fib[i - 2] + fib[i - 1]
return pd.Series(fib)
@lru_cache(maxsize=None)
def fibratio(n):
n = int(n)
f = fib(n)
return f / f.iat[n - 1]
@jit(f8(f8[:], i8, i8), nopython=True)
def __rci_d__(v, i, p):
sum = 0.0
for j in range(p):
o = 1
k = v[i - j]
for l in range(p):
if k < v[i - l]:
o = o + 1
sum = sum + (j + 1 - o)**2
return sum
@jit(void(f8[:], i8, i8, f8[:]), nopython=True)
def __rci_core__(v, n, p, r):
k = (p * (p**2 - 1))
S01 = S[y1, x0, k]
S10 = S[y0, x1, k]
S11 = S[y1, x1, k]
ustar01 = ustar[y1, x0, k]
ustar11 = ustar[y1, x1, k]
ustar21 = ustar[y1, x2, k]
vstar10 = vstar[y0, x1, k]
vstar11 = vstar[y1, x1, k]
vstar12 = vstar[y2, x1, k]
if isnan(S11) == True:
ZonalFlux[j, i, k:] = nan
MeridFlux[j, i, k:] = nan
break
else:
ZonalFlux[j, i, k] = cal_a_GM_Flux(S00, S01, S10, S11, ustar01, ustar11, ustar21, ew_dist)
MeridFlux[j, i, k] = cal_a_GM_Flux(S00, S10, S01, S11, vstar10, vstar11, vstar12, ns_dist)
return ZonalFlux, MeridFlux
@jit(f8(f8, f8, f8, f8, f8, f8, f8, f8))
def cal_a_GM_Flux(S00, S01, S10, S11, U0, U1, U2, dist):
Mt = 60 * 60 * 24 * 30
if any(isnan([S00, S01, S10, S11, U0, U1, U2])) == False:
Flux = -((U2 + U1) * (S10 + S11) / 4.0 - (U1 + U0) * (S01 + S00) / 4.0) / dist * Mt
else:
Flux = nan
return Flux
from compas.numerical.drx.drx_numpy import _beam_data
from compas.numerical.drx.drx_numpy import _create_arrays
# from compas_hpc.geometry import cross_vectors_numba as cross
# from compas_hpc.geometry import dot_vectors_numba as dot
# from compas_hpc.geometry import length_vector_numba as length
from time import time
__all__ = [
'drx_numba',
]
@jit(f8(f8[:]), nogil=True, nopython=True, parallel=False, cache=True)
def length(a):
"""Calculate the length of a vector.
Parameters
----------
a : array
XYZ components of the vector.
Returns
-------
float: The length of the vector.
"""
return sqrt(a[0]**2 + a[1]**2 + a[2]**2)
@njit(f8[:](f8[:], f8[:]))
def update_state(x, c_params):
μ_c, ρ, ϕ_z, v, d, ϕ_σ = c_params
z, σ = x
# update state
σ2 = v * σ**2 + d + ϕ_σ * randn()
σ = np.sqrt(max(σ2, 0))
z = ρ * z + ϕ_z * σ * randn()
return np.array((z, σ))
@njit(f8(f8[:], f8[:], f8[:]))
def eval_kappa(x, y, c_params):
"""
Computes kappa_{t+1} given z_t and sigma_t
"""
μ_c, ρ, ϕ_z, v, d, ϕ_σ = c_params
z, σ = x
return μ_c + z + σ * randn()
def by_function_factory(by, parallelization_flag=False):
"""
Produces functions that compute the stability test value Lambda
via Monte Carlo.
SPLIT_CHOICE_all_max = 2
PRED_CHOICE_majority = 1
PRED_CHOICE_pure_majority = 2
PRED_CHOICE_majority_general = 3
PRED_CHOICE_pure_majority_general = 4
N = 100
def time_ms(f):
f() #warm start
return " %0.6f ms" % (1000.0 * (timeit.timeit(f, number=N) / float(N)))
@njit(f8(u4, u4[:]), cache=True) #,inline='always')
def gini(total, counts):
if (total > 0):
s = 0.0
for c_i in counts:
prob = c_i / total
s += prob * prob
return 1.0 - s
else:
return 0.0
@njit(nogil=True, fastmath=True, cache=False)
def unique_counts(inp):
'''
Finds the unique classes in an input array of class labels
import numpy as np
import numba
from numba import f8, void
"""
Functions operating on 2-Dimensional vectors.
"""
# TODO: Normal, Tangent
@numba.vectorize([f8(f8)])
def wrap_to_pi(rad):
"""
Wraps angles in rad in radians, to the interval [−pi pi].
Pi maps to pi and −pi maps to −pi. (In general, odd, positive multiples of
pi map to pi and odd, negative multiples of pi map to −pi.)
[Matlab](http://se.mathworks.com/help/map/ref/wraptopi.html)
:param rad: Angle in radians.
:return: Angle in [-pi, pi].
"""
rad_ = rad % (2 * np.pi)
if rad < 0 and rad_ == np.pi:
# negative multiples of pi map to −pi
return -np.pi
elif rad_ > np.pi:
return rad_ - (2 * np.pi)
else:
return rad_
for i in range(n):
for l in range(i):
val = 0
for j in range(m):
val += M[j] * C[j, i] * C[j, l]
H[i, l] = val
d = np.empty((1, n))
for i in range(n):
val = 0
for j in range(m):
val += M[j] * C[j, i] * C[j, i]
d[0, i] = val
return H, d, g.T, f
@nb.jit(nb.f8(nb.f8[:, :], nb.f8[:]))
def function_values(C, x):
eCx = exp(dot(C, x))
f = sum(log1p(eCx))
return f
def shrinkage(a, kappa):
return maximum(0, a - kappa) - maximum(0, -a - kappa)
def l1_OLS(A, b, lam, x, z):
return 0.5 * sum((A.dot(x) - b)**2) + lam * np.norm(z, 1)
def lasso_admm_cholesky(A, rho):
@njit(void(f8[:,:],u4,u4,f8,b1[:]))
def split__(array, length, dim, threshold, res):
for i in range(length):
if array[i, dim] <= threshold:
res[i] = True
@jit(b1[:](f8[:,:],u4,f8))
def split(array, dim, threshold):
length = len(array)
res = np.zeros((length), dtype=bool)
split__(array, length, dim, threshold, res)
return res
@njit(f8(f8[:,:],f8[:],f8[:]))
def calc_bbox_growth(data, node_min_d, node_max_d):
"""
Calculate the difference in linear dimension between the
current node, and the incoming data. Roughly, this means
calculating how much the bounding box would have to grow
to accommodate all the new points, in each dimension, and
then summing across these dimensions.
"""
n_rows, n_cols = data.shape
total = 0
for j in range(n_cols):
# Keep track of maximum extension required for lower
# and upper bound, respectively, in this dimension
l_extension = 0
import numpy as np
from numba import njit, b1, i1, i8, f8
from numba.types import UniTuple
@njit(f8(i8, i8, f8, f8, b1[:, :], b1[:, :], f8[:, :], b1), cache=True)
def signals_order_func_np(i, col, run_cash, run_shares, entries, exits, volume,
accumulate):
"""Order function to buy/sell based on signals."""
if run_shares > 0:
if entries[i, col] and not exits[i, col]:
if accumulate:
return volume[i, col]
elif not entries[i, col] and exits[i, col]:
return -volume[i, col]
else:
if entries[i, col] and not exits[i, col]:
return volume[i, col]
elif not entries[i, col] and exits[i, col]:
if accumulate:
return -volume[i, col]
return 0.
@njit(f8(i8, i8, f8, f8, f8[:, :], b1), cache=True)
def orders_order_func_np(i, col, run_cash, run_shares, orders, is_target):
"""Buy/sell the amount of shares specified by orders."""
if is_target:
return orders[i, col] - run_shares
else:
return orders[i, col]
Raises:
RebinError: for the following cases:
old: └┴┴┴┴┘
new: └┴┴┴┘
old: └┴┴┴┴┘
new: └┴┴┴┘
"""
if (in_edges[..., -1] <= out_edges[..., 0]).any():
raise RebinError("Input edges are all smaller than output edges")
if (in_edges[..., 0] >= out_edges[..., -1]).any():
raise RebinError("Input edges are all larger than output edges")
@nb.vectorize([nb.f8(nb.f8, nb.f8, nb.f8, nb.f8)], nopython=True)
def _linear_offset(slope, cts, low, high):
"""
Calculate the offset of the linear approximation of slope when splitting
counts between bins.
Args:
slope:
cts: counts within the bin
low: lower bin edge energy
high: higher bin edge energy
Returns:
the offset
"""
if np.abs(slope) < 1e-6:
if axis == 0:
b = array([0., 0., 0.])
for i in prange(m):
b[0] += a[i, 0]
b[1] += a[i, 1]
b[2] += a[i, 2]
elif axis == 1:
b = np.zeros(m)
for i in prange(m):
b[i] += a[i, 0] + a[i, 1] + a[i, 2]
return b
@jit(f8(f8[:]), nogil=True, nopython=True, parallel=True)
def norm_vector_numba(a):
""" Calculate the L2 norm or length of a vector.
Parameters
----------
a (array): XYZ components of the vector.
Returns
-------
float: The L2 norm of the vector.
"""
return sqrt(a[0]**2 + a[1]**2 + a[2]**2)
@jit(f8[:](f8[:, :]), nogil=True, nopython=True, parallel=False)
# this is actually a rotation with -rad (use symmetry of sin/cos)
sin_rad = sin(rad)
cos_rad = cos(rad)
return point[0] * cos_rad + point[2] * sin_rad, point[
1], point[2] * cos_rad - point[0] * sin_rad
# @cc.export('coords2cartesian', dtype_3float_tuple(f8, f8))
@njit(dtype_3float_tuple(f8, f8), cache=True)
def coords2cartesian(lng_rad, lat_rad):
return cos(lng_rad) * cos(lat_rad), sin(lng_rad) * cos(lat_rad), sin(
lat_rad)
# @cc.export('distance_to_point_on_equator', f8(f8, f8, f8))
@njit(f8(f8, f8, f8), cache=True)
def distance_to_point_on_equator(lng_rad, lat_rad, lng_rad_p1):
"""
uses the simplified haversine formula for this special case (lat_p1 = 0)
:param lng_rad: the longitude of the point in radians
:param lat_rad: the latitude of the point
:param lng_rad_p1: the latitude of the point1 on the equator (lat=0)
:return: distance between the point and p1 (lng_rad_p1,0) in km
this is only an approximation since the earth is not a real sphere
"""
# 2* for the distance in rad and * 12742 (mean diameter of earth) for the distance in km
return 12742 * asin(
sqrt(((sin(lat_rad / 2))**2 + cos(lat_rad) * (sin(
(lng_rad - lng_rad_p1) / 2))**2)))
tmp = 1 + 4 * ((alpha - theta2) / fwhm)**2
return 1 / tmp
def pseudo_voigt(theta2, alpha, fwhm, eta):
"""
Original Pseudo-Voigt function for profiling peaks
- Thompson, D. E. Cox & J. B. Hastings (1986).
"""
L = lorentzian(theta2, alpha, fwhm)
G = gaussian(theta2, alpha, fwhm)
return eta * L + (1 - eta) * G
@nb.njit(nb.f8(nb.f8[:], nb.f8[:], nb.f8, nb.i8, nb.f8[:], nb.f8[:]))
def similarity_calculate(r, w, d, Npts, fy, gy):
"""
Compute the similarity between the pair of spectra f, g
"""
xCorrfg_w, aCorrff_w, aCorrgg_w = 0, 0, 0
for r0, w0 in zip(r, w):
Corrfg, Corrff, Corrgg = 0, 0, 0
shift = int(r0 / d)
for i in range(Npts):
if 0 <= i + shift <= Npts - 1:
Corrfg += fy[i] * gy[i + shift] * d
Corrff += fy[i] * fy[i + shift] * d
Corrgg += gy[i] * gy[i + shift] * d
"""Evacuation related functions"""
import numba
import numpy as np
from numba.typing.typeof import typeof
from crowddynamics.core.geom2D import line_intersect
from crowddynamics.core.sensory_region import is_obstacle_between_points
from crowddynamics.core.structures import obstacle_type_linear
from crowddynamics.core.vector2D import length
from numba import i8, f8, optional
from crowddynamics.simulation.agents import NO_TARGET
@numba.jit(f8(f8, f8, optional(f8), f8), nopython=True, nogil=True, cache=True)
def narrow_exit_capacity(d_door, d_agent, d_layer=None, coeff=1.0):
r"""
Capacity estimation :math:`\beta` of unidirectional flow through narrow
bottleneck. Capacity of the bottleneck increases in stepwise manner.
Estimation 1
Simple estimation
.. math::
\beta_{simple} = c \left \lfloor \frac{d_{door}}{d_{agent}} \right \rfloor
Estimation 2
More sophisticated estimation [Hoogendoorn2005a]_, [Seyfried2007a]_
.. math::
\beta_{hoogen} = c \left \lfloor \frac{d_{door} - (d_{agent} - d_{layer})}{d_{layer}} \right \rfloor,\quad d_{door} \geq d_{agent}
import numba
from numba import f8
import numpy as np
from scipy.spatial.qhull import Delaunay
from shapely.geometry import Polygon, Point
@numba.jit(f8(f8[:], f8[:], f8[:]), nopython=True, nogil=True)
def triangle_area(a, b, c):
return np.abs(a[0] * (b[1] - c[1]) +
b[0] * (c[1] - a[1]) +
c[0] * (a[1] - b[1])) / 2
@numba.jit(f8[:](f8[:], f8[:], f8[:]), nopython=True, nogil=True)
def random_sample_triangle(a, b, c):
"""
Uniform sampling of a triangle
------------------------------
Generate uniform random sample from a triangle defined by points A, B
and C [1]_, [2]_. Point inside the triangle is given
.. math::
P = (1 - \sqrt{r_1}) A + (\sqrt{r_1} (1 - r_2)) B + (r_2 \sqrt{r_1}) C,
where random variables are
.. math::
r_1, r_2 \sim \mathcal{U}(0, 1)
References
Monte Carlo based computation of the test value, SSY model, with active
truncation.
Unfortunately this file replicates a huge amount of code from
ssy_monte_carlo_test.py. This is purely for reasons of efficiency, and the
limits of what can and can't be done with current versions of Numba.
"""
from numpy.random import randn
from numba import jit, njit, f8, prange
from ssy_model import *
@njit(f8(f8))
def truncated_randn(truncation_val):
y = randn()
if y > truncation_val:
return truncation_val
if y < -truncation_val:
return -truncation_val
return y
@njit(f8[:](f8[:], f8[:], f8))
def update_state(x, c_params, trunc_val):
μ_c, ρ, ϕ_z, σ_bar, ϕ_c, ρ_hz, σ_hz, ρ_hc, σ_hc = c_params
z, h_z, h_c = x
# import glob
from os.path import join
import numpy as np
import os
# import pandas as pd
# from utils.helper_fncs import save_obj, load_obj
# import pickle
from numba import jit, njit
import numba as nb
@njit(nb.f8(nb.u8, nb.u8, nb.u8, nb.u8))
def compute_overlap(xA, xB, yA, yB):
# x,y files, A start, B end
num = yB - yA + xB - xA
den = max(xB, yB) - min(xA, yA)
folap = max(0, num / den - 1)
return folap
@njit(nb.f8(nb.u8, nb.u8, nb.u8, nb.u8))
def compute_intersect(xA, xB, yA, yB):
num = yB - yA + xB - xA
den = max(xB, yB) - min(xA, yA)
intersct = max(num - den, 0)
return intersct
@njit(nb.b1[:](nb.u8[:, :], nb.u8[:, :], nb.f8[:, :], nb.f8))
import numba as nb
from numba import jit, f8, int32,b1
# Fluid Specific Heat
percGly=20
@jit(f8 (f8 ,f8 ),nopython=True)
def fCp(Tref,percglyvol=percGly):
if(Tref>=292):
return 0.6502826505e5 - 0.55296090e8 / Tref + 0.8269255092e2 * percglyvol - 0.8130626690e-1 * percglyvol ** 2 + 0.167409225e11 / Tref ** 2 - 0.180431100e4 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) ** 2 - 0.44220204e7 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) / Tref - 0.16876350e13 / Tref ** 3 - 0.68413806e3 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) ** 3 + 0.52095834e6 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) ** 2 / Tref + 0.54229338e9 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) / Tref ** 2
else:
return (0.2451e6 - 0.25033e4 * Tref + 0.867151e1 * Tref ** 2 - 0.100147e-1 * Tref ** 3) * (0.1560553517e2 - 0.13270e5 / Tref + 0.1984462465e-1 * percglyvol - 0.1951194310e-4 * percglyvol ** 2 + 0.40175e7 / Tref ** 2 - 0.43300e0 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) ** 2 - 0.10612e4 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) / Tref - 0.4050e9 / Tref ** 3 - 0.16418e0 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) ** 3 + 0.12502e3 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) ** 2 / Tref + 0.13014e6 * (0.6336420000e-3 + 0.1107710000e-1 * percglyvol - 0.1089140000e-4 * percglyvol ** 2) / Tref ** 2)
import numpy as np
# import scipy.special as scsp
import numba as nub
# # @nub.autojit(nub.double(nub.double, nub.double, nub.double))
# @nub.autojit()
# def loglike_vonmises(x, params):
# mu = params[0]
# kappa = params[1]
# out = kappa*np.cos(x - mu) - np.log(2.*np.pi) - np.log(scsp.i0(kappa))
# return out
# @nub.autojit(locals={'thetas':nub.double[:], 'datapoint':nub.double[:], 'ATtcB':nub.double, 'sampled_feature_index':nub.int_, 'mean_fixed_contrib':nub.double[:], 'inv_covariance_fixed_contrib':nub.double[:,:]})
@nub.jit(nub.f8(nub.f8, nub.f8[:], nub.f8[:], nub.object_, nub.f8, nub.int_, nub.f8[:], nub.f8[:, :]))
def loglike_fct(new_theta, thetas, datapoint, rn, ATtcB, sampled_feature_index, mean_fixed_contrib, inv_covariance_fixed_contrib):
'''
Compute the loglikelihood of: theta_r | n_tc theta_r' tc
'''
# print 'what?', params, len(params)
# thetas = params[0]
# datapoint = params[1]
# # rn = params[2]
# # theta_mu = params[3]
# # theta_kappa = params[4]
# ATtcB = nub.double(params[5])
# sampled_feature_index = params[6]
# mean_fixed_contrib = params[7]