def cheb_sum(x):
s = p0()*SP.eval_chebyt(0,x) +\
p1()*SP.eval_chebyt(1,x) +\
p2()*SP.eval_chebyt(2,x) +\
p3()*SP.eval_chebyt(3,x) +\
p4()*SP.eval_chebyt(4,x)
return s
def cheb_one_pressure(alpha, tlim, plim, temps, pressure):
""" Calculates T,P-dependent rate constants [k(T,P)]s using
a Chebyshev functional expression, at a given pressure,
across several temperatures.
"""
tmin, tmax = tlim
pmin, pmax = plim
alpha_nrows, alpha_ncols = alpha.shape
ktps = np.zeros(len(temps))
for i, temp in enumerate(temps):
ctemp = ((2.0 * temp**(-1) - tmin**(-1) - tmax**(-1)) /
(tmax**(-1) - tmin**(-1)))
cpress = (
(2.0 * np.log10(pressure) - np.log10(pmin) - np.log10(pmax)) /
(np.log10(pmax) - np.log10(pmin)))
logktp = 0.0
for j in range(alpha_nrows):
for k in range(alpha_ncols):
logktp += (alpha[j][k] * eval_chebyt(j, ctemp) *
eval_chebyt(k, cpress))
ktps[i] = 10**(logktp)
return ktps
def cheby_band(w, w1, w2, N, ripple=1, scale=0.95):
"""
Simple Chebyshev Type I bandpass filter function in wavelength space.
Parameters
----------
w : astropy.units.Quantity
Wavelength
w1 : astropy.units.Quantity
Wavelength of short wavelength edge of bandpass
w2 : astropy.units.Quantity
Wavelength of long wavelength edge of bandpass
N : int
Order of the Chebyshev function
ripple : float, optional
Scaling to apply to the ripple of the Chebyshev function, default
1.0
scale : float, optional
Scaling to apply to the transmission of the Chebyshev function,
default 0.95
Returns
-------
transmission : astropy.units.Quantity
Filter transmission at wavelength `w`.
"""
# Bandpass implemented as low pass and high pass in series
w = ensure_unit(w, u.nm)
g1 = 1 / np.sqrt(1 + ripple**2 * eval_chebyt(N, (w1/w).to(u.dimensionless_unscaled).value)**2)
g2 = 1 / np.sqrt(1 + ripple**2 * eval_chebyt(N, (w/w2).to(u.dimensionless_unscaled).value)**2)
return scale * g1 * g2
def Em_cheb_der(x):
s = np.sign(cheb_sum(x))
return 2.*s*np.array([\
SP.eval_chebyt(0,x) ,\
SP.eval_chebyt(1,x) ,\
SP.eval_chebyt(2,x) ,\
SP.eval_chebyt(3,x) ,\
SP.eval_chebyt(4,x) ])
def test_chebyshev():
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
assert allTrue
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
assert allTrue
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
assert allTrue
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
assert allTrue
def cheby_band(w, w1, w2, N, ripple=1, peak=0.95):
"""
Simple Chebyshev Type I bandpass filter function in wavelength space
To be more realistic this should definitely include cone angle effect
but at f/5.34 (Space Eye focal ratio) that is pretty insignficant
"""
# Bandpass implemented as low pass and high pass in series
g1 = 1 / np.sqrt(1 + ripple**2 * eval_chebyt(N, (
w1 / w).to(u.dimensionless_unscaled).value)**2)
g2 = 1 / np.sqrt(1 + ripple**2 * eval_chebyt(N, (
w / w2).to(u.dimensionless_unscaled).value)**2)
return peak * g1 * g2
def chebyshev_one_pressure(alpha, tmin, tmax, pmin, pmax, temps, pressure):
""" Calculates T,P-dependent rate constants [k(T,P)]s using
a Chebyshev functional expression, at a given pressure,
across several temperatures.
:param alpha: Chebyshev coefficient matrix
:type alpha: numpy.ndarray
:param tmin: minimum temperature Chebyshev model is defined
:type tmin: float
:param tmax: maximum temperature Chebyshev model is defined
:type tmax: float
:param pmin: minimum pressure Chebyshev model is defined
:type pmin: float
:param pmax: maximum pressure Chebyshev model is defined
:type pmax: float
:param temps: Temps used to calculate high- and low-k(T)s
:type temps: numpy.ndarray
:param pressure: Pressure used to calculate k(T,P)s
:type pressure: float
:return ktps: Set of k(T,P)s at given pressure
:rtype numpy.ndarray
"""
alpha_nrows, alpha_ncols = alpha.shape
ktps = np.zeros(len(temps))
for i, temp in enumerate(temps):
ctemp = (
(2.0 * 1/temp - 1/tmin - 1/tmax) /
(1/tmax - 1/tmin)
)
cpress = (
(2.0 * np.log10(pressure) - np.log10(pmin) - np.log10(pmax)) /
(np.log10(pmax) - np.log10(pmin))
)
logktp = 0.0
for j in range(alpha_nrows):
for k in range(alpha_ncols):
logktp += (
alpha[j][k] *
eval_chebyt(j, ctemp) *
eval_chebyt(k, cpress)
)
ktps[i] = 10**(logktp)
return ktps
def evaluate_basis(self, x, i=0, output_array=None):
x = np.atleast_1d(x)
if output_array is None:
output_array = np.zeros(x.shape)
#output_array[:] = np.cos(i*np.arccos(x))
output_array[:] = eval_chebyt(i, x)
return output_array
def test_chebyshev_matrices(self):
# test that it works on matrices too
key = jax.random.PRNGKey(0)
xx = jax.random.normal(key, shape=(5, 10))
for i in range(10):
poly0 = chebyshev.eval_chebyt(i, xx)
poly1 = special.eval_chebyt(i, xx)
np.testing.assert_allclose(poly0, poly1, rtol=1E-4)
def test_chebyshev():
if NumCpp.NO_USE_BOOST:
return
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Scaler(order, x)
assert np.round(valuePy,
DECIMALS_ROUND) == np.round(valueCpp, DECIMALS_ROUND)
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Array(order, cArray)
assert np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND))
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Scaler(order, x)
assert np.round(valuePy,
DECIMALS_ROUND) == np.round(valueCpp, DECIMALS_ROUND)
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Array(order, cArray)
assert np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND))
def evaluate(cheby1d, x):
""" チェビシェフ辞書にxの値を代入した結果を評価する．
引数:
cheby1d 評価対象のチェビシェフ辞書．
x xの値．floatを想定（多分sympy値でも動く）．
返り値:
floatまたはsympy値型の評価結果．
"""
return sum(eval_chebyt(i, x) * v for i, v in cheby1d.items())
def approx_weights(self):
"""
Returns the weights of the Chebyshev regression using Chebyshev
polynomials up to 'order'. Number of approximation nodes = gridsize.
Returns an array of order + 1 floats.
"""
theta = np.zeros(self.order + 1)
theta[0] = np.mean(self.func_vals)
for j in range(1, self.order + 1):
tj = eval_chebyt(j, self.roots)
theta[j] = (2.0 / self.gridsize) * np.sum(tj * self.func_vals)
return theta
def chebyshev_basis_2D(x, y, n):
a = np.array([])
b = np.array([])
for i in range(n + 1):
for j in range(n + 1):
if (i + j) < (n + 1):
a = np.append(a, i)
b = np.append(b, j)
A = np.zeros((len(x), len(a)))
xx = x.copy() - x.min()
xx /= xx.max() / 2
xx -= 1
yy = y.copy() - y.min()
yy /= yy.max() / 2
yy -= 1
for i in range(len(a)):
A[:, i] = special.eval_chebyt(a[i], xx) * special.eval_chebyt(b[i], yy)
return A
def __call__(self, eval_grid):
"""
Evaluate the approximation at the points in array eval_grid.
Returns an array of floats.
"""
z_vec = self.to_regular(eval_grid)
j = np.array(range(self.order + 1), dtype=int)
K = len(z_vec)
vals = np.empty(K)
for k in range(K):
y = np.sum(self.theta * eval_chebyt(j, z_vec[k]))
vals[k] = y
return np.array(vals)
def chebyshev_rate_constants(temps, pressure, alpha, tmin, tmax, pmin, pmax):
""" computes the rate constants using the chebyshev polynomials
"""
alpha_nrows, alpha_ncols = alpha.shape
ktps = np.zeros(len(temps))
for i, temp in enumerate(temps):
ctemp = ((2.0 * temp**(-1) - tmin**(-1) - tmax**(-1)) /
(tmax**(-1) - tmin**(-1)))
cpress = (
(2.0 * np.log10(pressure) - np.log10(pmin) - np.log10(pmax)) /
(np.log10(pmax) - np.log10(pmin)))
logktp = 0.0
for j in range(alpha_nrows):
for k in range(alpha_ncols):
logktp += (alpha[j][k] * eval_chebyt(j, ctemp) *
eval_chebyt(k, cpress))
ktps[i] = 10**(logktp)
return ktps
def value_at_a_point(x, An):
"""Evaluates a spectral function at a given spectral point given
the value of the Spectral Coordinate and the set of Spectral Coefficients of the Function."""
# Estimating the Number of Spectral Coefficients/Collocation Points:
N = An.size - 1
# Initializing the value
value_at_point = 0.0
# Adding the contribution of each Spectral Mode:
for ns in range(0, N + 1):
# Value of the n-th Chebyshev Polynomial at the given spectral coordinate:
T_nn_x = special.eval_chebyt(ns, x)
value_at_point += An[ns] * T_nn_x
return value_at_point
def _eval_numpy_(self, n, x):
"""
Evaluate ``self`` using numpy.
EXAMPLES::
sage: import numpy
sage: z = numpy.array([1,2])
sage: z2 = numpy.array([[1,2],[1,2]])
sage: z3 = numpy.array([1,2,3.])
sage: chebyshev_T(1,z)
array([ 1., 2.])
sage: chebyshev_T(1,z2)
array([[ 1., 2.],
[ 1., 2.]])
sage: chebyshev_T(1,z3)
array([ 1., 2., 3.])
sage: chebyshev_T(z,0.1)
array([ 0.1 , -0.98])
"""
from scipy.special import eval_chebyt
return eval_chebyt(n, x)
def _eval_numpy_(self, n, x):
"""
Evaluate ``self`` using numpy.
EXAMPLES::
sage: import numpy
sage: z = numpy.array([1,2])
sage: z2 = numpy.array([[1,2],[1,2]])
sage: z3 = numpy.array([1,2,3.])
sage: chebyshev_T(1,z)
array([ 1., 2.])
sage: chebyshev_T(1,z2)
array([[ 1., 2.],
[ 1., 2.]])
sage: chebyshev_T(1,z3)
array([ 1., 2., 3.])
sage: chebyshev_T(z,0.1)
array([ 0.1 , -0.98])
"""
from scipy.special import eval_chebyt
return eval_chebyt(n, x)
def eval_basis(ind, x):
result = 1
for i in range(self.dim):
coord = (x[i] - self.center[i]) / (self.h / 2)
result *= eval_chebyt(ind[i], coord)
return result
def ceb2(x):
return spec.eval_chebyt(p, x / 95)
def approx_integral(i):
"""
Approximates the integral by taking the mean value
of n sample points
"""
return sum(eval_chebyt(i, 2. * xj - 1.) for xj in x) / n
def T(j,u,N,x1,x2):
m = get_slope_intercept(x1,x2)[0]
b = get_slope_intercept(x1,x2)[1]
return eval_chebyt(j,m*u+b)
q1 = q2
q2 = q3
moments = np.mean(G, axis=0)
inputs = np.insert(moments, 0, 1)
pickle.dump(inputs, open('chebyshevmoments' + str(K), "wb"))
#% compute Chebyshev polynomial
x = np.linspace(gmin, gmax, gridlength)
v = np.diff(x)
v = np.append(v, 0)
n = len(inputs)
chebarray = np.zeros((n, int(gridlength)))
for i1 in range(0, n):
q = (special.eval_chebyt(i1, x, out=None))
chebarray[i1, :] = q
typec = 'chebyshev'
#% MaxEnt Algorithm
entr = []
momnum = []
sharpness = (1e-3)
#% store datas
#Y = np.zeros((m,int(gridlength)))
MaxEntdistri = np.zeros((m, int(gridlength)))
MaxEntCoefficient = []
Xbound = np.zeros(m)
Prediction = np.zeros(m)
def cons(alpha):
j = 1 + np.dot(alpha, chebarray[:-(n - m)])
q = np.exp(-j)
u = sum(q * ((special.eval_chebyt(alpha, x, out=None))) * v)
return u
def eval_basis(ind, x):
result = 1
for i in range(self.dim):
coord = (x[i] - self.center[i])/(self.h/2)
result *= eval_chebyt(ind[i], coord)
return result
# -*- coding: utf-8 -*-
import os
import scipy
from scipy.special import airy, jn, eval_chebyt, eval_legendre
subplot(2, 2, 3)
x = linspace(-1, 1)
for i in range(6):
plot(x, eval_chebyt(i, x))
title("Chebyshev polynomials of the first kind")
os.system("pause")
def test_chebyt_int(self):
assert_mpmath_equal(lambda n, x: sc.eval_chebyt(int(n), x),
_exception_to_nan(lambda n, x: mpmath.chebyt(n, x, **HYPERKW)),
[IntArg(), Arg()],
n=2000)
def mesanaceb(x, y):
return spec.eval_chebyt(p1, x / 200) * spec.eval_chebyt(p2, y / 200)
def kfit(temps, ktp_dct, tdeg=6, pdeg=4, a_conv_factor=1):
""" Fits T,P-dependent rate constants [k(T,P)]s to a
a Chebyshev functional expression.
:param alpha: Chebyshev coefficient matrix
:type alpha: np.ndarray
:param tdeg: degree of the temp component of Chebyshev polynomial
:type tdeg: int
:param pdeg: degree of the pressure component of Chebyshev polynomial
:type pdeg: int
:param temps: Temps used to calculate high- and low-k(T)s
:type temps: np.ndarray
:param pressure: Pressure used to calculate k(T,P)s
:type pressure: float
:return alpha: alpha fitting coefficients
:rtype np.ndarray
"""
# Get the pressures from the ktp_dct
pressures = tuple(pressure for pressure in ktp_dct.keys()
if pressure != 'high')
# Determine the number and range of temperatures and pressures
tnum, pnum = len(temps), len(pressures)
tmin, tmax = min(temps), max(temps)
pmin, pmax = min(pressures), max(pressures)
# Calculate the reduced temperatures and pressures
tred = []
for temp in temps:
tred.append(
(2.0 * temp**(-1) - tmin**(-1) - tmax**(-1)) /
(tmax**(-1) - tmin**(-1))
)
pred = []
for pressure in pressures:
pred.append(
(2.0 * np.log10(pressure) - np.log10(pmin) - np.log10(pmax)) /
(np.log10(pmax) - np.log10(pmin))
)
# Build a numpy array for the fits
ktps = conv_dct_to_array(ktp_dct, temps, a_conv_factor=a_conv_factor)
# Create matrices for fits
A = np.zeros((tnum * pnum, tdeg * pdeg), np.float64)
b = np.zeros((tnum * pnum), np.float64)
nzero = 0
for t1, T in enumerate(tred):
for p1, P in enumerate(pred):
for t2 in range(tdeg):
for p2 in range(pdeg):
idx1, idx2 = (p1 * tnum + t1), (p2 * tdeg + t2)
A[idx1, idx2] = eval_chebyt(t2, T) * eval_chebyt(p2, P)
if ktps[t1, p1] is not None:
b[idx1] = np.log10(ktps[t1, p1])
else:
b[idx1] = None
nzero += 1
nnonzero = tnum * pnum - nzero
idxp = -1
Ap = np.zeros((nnonzero, tdeg * pdeg), np.float64)
bp = np.zeros((nnonzero), np.float64)
for idx in range(tnum*pnum):
if not np.isnan(b[idx]):
idxp += 1
bp[idxp] = b[idx]
for idx2 in range(tdeg*pdeg):
Ap[idxp,idx2] = A[idx,idx2]
# Perform least-squares fit to get alpha coefficients
theta = np.linalg.lstsq(Ap, bp, rcond=RCOND)[0]
alpha = np.zeros((tdeg, pdeg), np.float64)
for t2 in range(tdeg):
for p2 in range(pdeg):
alpha[t2, p2] = theta[p2 * tdeg + t2]
return alpha, (tmin, tmax), (pmin, pmax)
def test_chebyt_int(self):
assert_mpmath_equal(
lambda n, x: sc.eval_chebyt(int(n), x),
_exception_to_nan(lambda n, x: mpmath.chebyt(n, x, **HYPERKW)),
[IntArg(), Arg()],
n=2000)
def test_chebyshev(self):
xx = jnp.linspace(-5, 5)
for i in range(10):
poly0 = chebyshev.eval_chebyt(i, xx)
poly1 = special.eval_chebyt(i, xx)
np.testing.assert_allclose(poly0, poly1, rtol=1E-5)
def ceb(x):
return spec.eval_chebyt(p, x / 200)
svdo[i] = np.array([(tov[i]) * 0.0010000] * nlat)
svd[i] = np.array([(sv.speed[i]) * 0.0010000] * nlat)
svpo = [svdo[0]]
svp = [svd[0]]
for i in range(1, ndep):
svpo = np.append(svpo, [svdo[i]], axis=0)
svp = np.append(svp, [svd[i]], axis=0)
o0 = np.array([svpo] * nlon)
a0 = np.array([svp] * nlon)
########## com model
svp = [[] for s in range(nlon)]
chet = np.arange(o_chet + 1, dtype=float)
for s in range(nlon):
achet = 0
for c in range(o_chet + 1):
chet[c] = eval_chebyt(c, (s - slon) / slon)
achet = c_chet[c] * chet[c] + achet
achet = achet / d_chet
svc = [[] for i in range(ndep)]
for i in range(0, m_s_dp[0]):
svc[i] = np.array([m_s_km[0] * 0.001 * 0.1 * 0.5 * achet] * nlat)
# svc[i] = np.array([m_s_km[0]*0.001*0.1*(1./float(2*slon))*float(s-slon)] * nlat)
for i in range(m_s_dp[0], m_s_dp[1]):
svc[i] = np.array([m_s_km[1] * 0.001 * 0.1 * 0.5 * achet] * nlat)
# svc[i] = np.array([m_s_km[1]*0.001*0.1*(1./float(2*slon))*float(s-slon)] * nlat)
for i in range(m_s_dp[1], ndep):
svc[i] = np.array([m_s_km[2] * 0.001 * 0.1 * 0.5 * achet] * nlat)
# svc[i] = np.array([m_s_km[2]*0.001*0.1*(1./float(2*slon))*float(s-slon)] * nlat)
svp[s] = [svc[0]]
for i in range(1, ndep):
svp[s] = np.append(svp[s], [svc[i]], axis=0)
def testFunctions():
print(colored('Testing Polynomial functions', 'magenta'))
ORDER_MAX = 5
DECIMALS_ROUND = 7
print(colored('Testing chebyshev_t_Scaler', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing chebyshev_t_Array', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(colored('Testing chebyshev_u_Scaler', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing chebyshev_u_Array', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(colored('Testing hermite_Scaler', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_hermite(order, x)
valueCpp = NumCpp.hermite_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing hermite_Array', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_hermite(order, x)
valueCpp = NumCpp.hermite_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(colored('Testing laguerre_Scaler1', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_laguerre(order, x)
valueCpp = NumCpp.laguerre_Scaler1(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing laguerre_Array1', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_laguerre(order, x)
valueCpp = NumCpp.laguerre_Array1(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(colored('Testing laguerre_Scaler2', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
degree = np.random.randint(0, 10, [
1,
]).item()
x = np.random.rand(1).item()
valuePy = sp.eval_genlaguerre(degree, order, x)
valueCpp = NumCpp.laguerre_Scaler2(order, degree, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing laguerre_Array2', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
degree = np.random.randint(0, 10, [
1,
]).item()
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_genlaguerre(degree, order, x)
valueCpp = NumCpp.laguerre_Array2(order, degree, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(colored('Testing legendre_p_Scaler1', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_legendre(order, x)
valueCpp = NumCpp.legendre_p_Scaler1(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing legendre_p_Array1', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_legendre(order, x)
valueCpp = NumCpp.legendre_p_Array1(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(colored('Testing legendre_p_Scaler2', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
degree = np.random.randint(order, ORDER_MAX)
valuePy = sp.lpmn(order, degree, x)[0][order, degree]
valueCpp = NumCpp.legendre_p_Scaler2(order, degree, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing legendre_q_Scaler', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.lqn(order, x)[0][order]
valueCpp = NumCpp.legendre_q_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing spherical_harmonic', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
degree = np.random.randint(order, ORDER_MAX)
theta = np.random.rand(1).item() * np.pi * 2
phi = np.random.rand(1).item() * np.pi
valuePy = sp.sph_harm(order, degree, theta, phi)
valueCpp = NumCpp.spherical_harmonic(order, degree, theta, phi)
if (np.round(valuePy.real, DECIMALS_ROUND) != np.round(
valueCpp[0], DECIMALS_ROUND)
or np.round(valuePy.imag, DECIMALS_ROUND) != np.round(
valueCpp[1], DECIMALS_ROUND)):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing spherical_harmonic_r', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
degree = np.random.randint(order, ORDER_MAX)
theta = np.random.rand(1).item() * np.pi * 2
phi = np.random.rand(1).item() * np.pi
valuePy = sp.sph_harm(order, degree, theta, phi)
valueCpp = NumCpp.spherical_harmonic_r(order, degree, theta, phi)
if np.round(valuePy.real, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
print(colored('Testing spherical_harmonic_i', 'cyan'))
allTrue = True
for order in range(ORDER_MAX):
degree = np.random.randint(order, ORDER_MAX)
theta = np.random.rand(1).item() * np.pi * 2
phi = np.random.rand(1).item() * np.pi
valuePy = sp.sph_harm(order, degree, theta, phi)
valueCpp = NumCpp.spherical_harmonic_i(order, degree, theta, phi)
if np.round(valuePy.imag, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
if allTrue:
print(colored('\tPASS', 'green'))
else:
print(colored('\tFAIL', 'red'))
print(f'valuePy = {valuePy}, valueCpp = {valueCpp}')
def reaction(ktp_dct, temps, tdeg=6, pdeg=4, a_conv_factor=1.0):
""" Fits T,P-dependent rate constants [k(T,P)]s to a
a Chebyshev functional expression.
:param ktp_dct: k(T,P)s
:type ktp_dct: k(T,P) dictionary
:param temps: Temps used to calculate high- and low-k(T)s
:type temps: np.ndarray
:param tdeg: degree of the temp component of Chebyshev polynomial
:type tdeg: int
:param pdeg: degree of the pressure component of Chebyshev polynomial
:type pdeg: int
:rtype: (np.ndarray, tuple(float), tuple(float))
"""
# Get the pressures from the ktp_dct
pressures = tuple(pressure for pressure in ktp_dct.keys()
if pressure != 'high')
# Determine the number and range of temperatures and pressures
tnum, pnum = len(temps), len(pressures)
tmin, tmax = min(temps), max(temps)
pmin, pmax = min(pressures), max(pressures)
# Calculate the reduced temperatures and pressures
tred = []
for temp in temps:
tred.append(
(2.0 * temp**(-1) - tmin**(-1) - tmax**(-1)) /
(tmax**(-1) - tmin**(-1))
)
pred = []
for pressure in pressures:
pred.append(
(2.0 * np.log10(pressure) - np.log10(pmin) - np.log10(pmax)) /
(np.log10(pmax) - np.log10(pmin))
)
# Build a numpy array for the fits
ktps = conv_dct_to_array(ktp_dct, temps, a_conv_factor=a_conv_factor)
# Create matrices for fits
amat = np.zeros((tnum * pnum, tdeg * pdeg), np.float64)
bvec = np.zeros((tnum * pnum), np.float64)
nzero = 0
for tidx1, temp in enumerate(tred):
for pidx1, press in enumerate(pred):
for tidx2 in range(tdeg):
for pidx2 in range(pdeg):
idx1 = (pidx1 * tnum + tidx1)
idx2 = (pidx2 * tdeg + tidx2)
amat[idx1, idx2] = (
eval_chebyt(tidx2, temp) * eval_chebyt(pidx2, press)
)
if ktps[tidx1, pidx1] is not None:
bvec[idx1] = np.log10(ktps[tidx1, pidx1])
else:
bvec[idx1] = None
nzero += 1
nnonzero = tnum * pnum - nzero
idxp = -1
amatp = np.zeros((nnonzero, tdeg * pdeg), np.float64)
bvecp = np.zeros((nnonzero), np.float64)
for idx in range(tnum*pnum):
if not np.isnan(bvec[idx]):
idxp += 1
bvecp[idxp] = bvec[idx]
for idx2 in range(tdeg*pdeg):
amatp[idxp, idx2] = amat[idx, idx2]
# Perform least-squares fit to get alpha coefficients
theta = np.linalg.lstsq(amatp, bvecp, rcond=RCOND)[0]
alpha = np.zeros((tdeg, pdeg), np.float64)
for tidx2 in range(tdeg):
for pidx2 in range(pdeg):
alpha[tidx2, pidx2] = theta[pidx2 * tdeg + tidx2]
return alpha, (tmin, tmax), (pmin, pmax)
def Tn(n, x):
return np.where(np.asarray(n) >= 0, eval_chebyt(n, x), 0)
import numpy as np
import matplotlib.pyplot as plt
from scipy.special import eval_chebyt
fig = plt.figure()
xvalues = np.linspace(-1, 1, 300)
nmax = 5
for n in range(nmax+1):
yvalues = eval_chebyt(n, xvalues)
plt.plot(xvalues, yvalues)
plt.title('Chebyshev polynomials $T_n(x)$ for $n=0,\\ldots,{}$'.format(nmax))
plt.axhline(0, color='gray')
plt.axvline(0, color='gray')
plt.xlabel('$x$')
plt.ylabel('$T_n(x)$')
print('Displaying graph')
plt.show()
