def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def cache_angles(tile_size=500):
half_size = float(tile_size - 1) / 2
get_zp = lambda x, y: arccos(1 / sqrt(x**2 + y**2 + 1))
get_zm = lambda x, y: arccos(-1 / sqrt(x**2 + y**2 + 1))
get_xypm = lambda x, y: arccos(y / sqrt(x**2 + y**2 + 1))
get_phi = lambda x, y: arctan(float(y) / x)
cache = {
'zp': np.zeros((tile_size, tile_size, ), dtype=np.float),
'zm': np.zeros((tile_size, tile_size, ), dtype=np.float),
'xypm': np.zeros((tile_size, tile_size, ), dtype=np.float),
'phi': np.zeros((tile_size, tile_size, ), dtype=np.float)
}
print 'Perform cache angles...'
for tile_y in xrange(tile_size):
y = float(tile_y) / half_size - 1
for tile_x in xrange(tile_size):
x = float(tile_x) / half_size - 1
cache['zp'][tile_y, tile_x] = get_zp(x, y)
cache['zm'][tile_y, tile_x] = get_zm(x, y)
cache['xypm'][tile_y, tile_x] = get_xypm(x, y)
if x != 0:
cache['phi'][tile_y, tile_x] = get_phi(x, y)
# print 'cache for: [{}, {}] -> [{},{}]'.format(tile_y, tile_x, y, x)
return cache
def para():
import numpy as np
import scipy as sp
N = 10000000
f = lambda x: arctan(x) / (x**2 + x * sin(x)) # 要求积分的函数
f = sp.vectorize(f)
xs = np.array([random() for _ in range(N)]) # 生成N个积分区间（0，1）的数据
fs = f(xs)
mean = fs.mean()
print(mean)
var = fs.var()
print(var)
def compute_pitch_and_inputs_flatness_simple(e_and_derivatives,
lambda_and_derivatives):
e = e_and_derivatives[0]
de1 = e_and_derivatives[1]
de2 = e_and_derivatives[2]
de3 = e_and_derivatives[3]
de4 = e_and_derivatives[4]
l = lambda_and_derivatives[0]
dl1 = lambda_and_derivatives[1]
dl2 = lambda_and_derivatives[2]
dl3 = lambda_and_derivatives[3]
dl4 = lambda_and_derivatives[4]
b = L3 * Jl * dl2
c = L4 * cos(e)
d = Je * de2 - L2 * cos(e)
a = b * c / d
db1 = L3 * Jl * dl3
db2 = L3 * Jl * dl4
dc1 = -L4 * sin(e) * de1
dc2 = -L4 * (cos(e) * de1**2 + sin(e) * de2)
dd1 = Je * de3 + L2 * sin(e) * de1
dd2 = Je * de4 + L2 * (cos(e) * de1**2 + sin(e) * de2)
f = db1 * c * d
g = dc1 * d + c * dd1
h = c * c * d * d
da1 = (f - b * g) / h
df1 = db2 * c * d + db1 * g
dg1 = dc2 * d + 2 * dc1 * dd1 + c * dd2
dh1 = 2 * c * dc1 * d**2 + 2 * c**2 * d * dd1
da2 = ((df1 - (db1 * g + b * dg1)) * h - (f - b * g) * dh1) / h**2
p = arctan(a)
dp1 = da1 / (1 + a**2)
dp2 = (da2 * (1 + a**2) - 2 * a * da1**2) / (1 + a**2)**2
Vs = ((Jl * dl2 / (L4 * cos(e)))**2 +
((Je * de2 - L2 * cos(e)) / L3)**2)**(1 / 2)
Vd = Jp * dp2 / L1
Vf = (Vs + Vd) / 2
Vb = (Vs - Vd) / 2
return np.array([p, dp1, dp2]), np.array([Vf, Vb])
def calc_PA(self) :
"""Calculates the telescope PA. requires LST to be either a field or
previously calculated array
Outputs an array of PA values for each time in radians.
This requires the fields Ra = 'CRVAL2', Dec = 'CRVAL3' and 'DATE-OBS'
to be set.
"""
self.PA = sp.zeros(self.dims[0])
for ii in range(self.dims[0]) :
RA = self.field['CRVAL2'][ii]
DEC = self.field['CRVAL3'][ii]
LST = utils.LSTatGBT(self.field['DATE-OBS'][ii])
H = LST-RA
Latit = 38.0+26.0/60
tanPA = ma.sin(H*sp.pi/180)/(ma.cos(DEC*sp.pi/180)*ma.tan(Latit*sp.pi/180)-ma.sin(DEC*sp.pi/180)*ma.cos(H*sp.pi/180))
self.PA[ii] = ma.arctan(tanPA)
def calc_PA(self):
"""Calculates the telescope PA. requires LST to be either a field or
previously calculated array
Outputs an array of PA values for each time in radians.
This requires the fields Ra = 'CRVAL2', Dec = 'CRVAL3' and 'DATE-OBS'
to be set.
"""
self.PA = sp.zeros(self.dims[0])
for ii in range(self.dims[0]):
RA = self.field['CRVAL2'][ii]
DEC = self.field['CRVAL3'][ii]
LST = utils.LSTatGBT(self.field['DATE-OBS'][ii])
H = LST - RA
Latit = 38.0 + 26.0 / 60
tanPA = ma.sin(H * sp.pi / 180) / (
ma.cos(DEC * sp.pi / 180) * ma.tan(Latit * sp.pi / 180) -
ma.sin(DEC * sp.pi / 180) * ma.cos(H * sp.pi / 180))
self.PA[ii] = ma.arctan(tanPA)
import math
from numpy.ma import arctan
x = math.pi/3
def f(n):
return (-1)**n * (math.pi/3)**(2*n+1) /(2*n+1)
def arctan_n_series(n):
result = 0.0
for i in range(n):
result += f(i)
return result
actual = arctan(x)
n_list = [3, 5, 10, 20]
print("n arctan(pi/3) actual absolute error")
for i in n_list:
temp_arctan = arctan_n_series(i)
abs_error = abs(temp_arctan - actual)
print(str(i) + " " + str(temp_arctan) + " " + str(actual) + " " + str(abs_error))
┃ ☃ ┃
┃ ┳┛ ┗┳ ┃
┃ ┻ ┃
┗━┓ ┏━┛
┃ ┗━━━┓
┃ 神兽保佑 ┣┓
┃ 永无BUG！ ┏┛
┗┓┓┏━┳┓┏┛
┃┫┫ ┃┫┫
┗┻┛ ┗┻┛
"""
from random import uniform
from numpy.ma import mean, arctan, sin, var
N = 10000
f = lambda x: arctan(x) / (x**2 + x * sin(x)) # 要求积分的函数
a, b = 0, 1 # 积分区间
xs = [uniform(a, b) for _ in range(N)] # 从均匀分布uniform(a,answers)生成N个样本
mean = mean([f(x) for x in xs]) # 代入积分函数，用均值去近似期望，因为函数不收敛，所以这个值也不确定
print(mean)
print(var([f(x) for x in xs])) # 由于函数不收敛，方差巨大
def para():
import numpy as np
import scipy as sp
N = 10000000
f = lambda x: arctan(x) / (x**2 + x * sin(x)) # 要求积分的函数
f = sp.vectorize(f)
xs = np.array([random() for _ in range(N)]) # 生成N个积分区间（0，1）的数据
fs = f(xs)
def get_poles_analyze(self, poles):
"""
definition for analyzing by graph poles:
- regulation time
- hesistation
- overshoot
- degree of attenuation
:param poles: mean of poles transmission function
:return: keys for handle changing regulator quality
"""
# ключи для оценки регулирования
key_koleb = 0
key_reg = 0
key_per = 0
degree_max = 0
a = True
counter = 1
print("Полюса плоскости: ")
for i in poles:
if i.real >= 0: # корень в левой полуплоскости
a = False
print("Полюс ", counter, " : ", i)
counter += 1
print("СИСТЕМА НЕ ПРОХОДИТ ПРОВЕРКУ ПО УСТОЙЧИВОСТИ!"
if not a else "По критерию полюсов система устойчива")
regulation_time = 1.0 / abs(max(poles.real))
print("\nВремя регулирования: " + str(regulation_time))
print("Полученная величина выше оптимальной области регулирования"
if regulation_time > 17 else "Отлично")
if regulation_time > 17:
key_reg = -1
for a in poles:
degree = arctan(abs(a.imag) / abs(a.real))
degree_max = (degree if (a.imag != 0) &
(degree_max < degree) else degree_max)
print("*" * 20, "\n" "Колебательность составляет: " + str(degree_max))
if degree_max >= 1.57:
print("Колебательность выше оптимального диапазона")
key_koleb = -1
overshoot = exp(-pi / degree_max) * 100
print("*" * 20, "\n" "Перерегулирование: " + str(overshoot) + " %")
if overshoot > 27:
print("Полученная величина выше оптимальной области регулирования")
key_per = -1
elif overshoot < 10:
print("Полученная величина ниже оптимальной области регулирования")
key_per = 1
else:
print("Отлично")
degree_of_attenuation = 1 - exp(-2 * pi / degree_max)
print("*" * 20, "\n"
"Степень затухания: " + str(degree_of_attenuation))
plt.title('Graph of poles')
plt.plot()
plt.show()
return [key_koleb, key_reg, key_per]
def compute_pitch_and_inputs_flatness_centripetal(eps_derivs, lamb_derivs):
eps = eps_derivs[0]
deps1 = eps_derivs[1]
deps2 = eps_derivs[2]
deps3 = eps_derivs[3]
deps4 = eps_derivs[4]
lamb = lamb_derivs[0]
dlamb1 = lamb_derivs[1]
dlamb2 = lamb_derivs[2]
dlamb3 = lamb_derivs[3]
dlamb4 = lamb_derivs[4]
p_phi_1 = mc.m_h * mc.d_h**2 + mc.m_h * mc.l_p**2
p_phi_2 = -mc.g * mc.d_h * mc.m_h
p_eps_1 = mc.m_h * (mc.l_h**2 + mc.d_h**2) + mc.m_c * (mc.l_c**2 +
mc.d_c**2)
p_eps_2 = mc.g * (mc.m_c * mc.d_c - mc.m_h * mc.d_h)
p_eps_3 = mc.g * (mc.m_h * mc.l_h - mc.m_c * mc.l_c)
p_lamb_1 = mc.m_h * (mc.l_h**2 + mc.l_p**2) + mc.m_c * mc.l_c**2
A = p_eps_1 * deps2 + mc.mu_eps * deps1 + p_eps_2 * sin(
eps) + p_eps_3 * cos(eps)
B = p_lamb_1 * dlamb2 + mc.mu_lamb * dlamb1
dA1 = p_eps_1 * deps3 + mc.mu_eps * deps2 + p_eps_2 * deps1 * cos(
eps) - p_eps_3 * deps1 * sin(eps)
dB1 = p_lamb_1 * dlamb3 + mc.mu_lamb * dlamb2
dA2 = p_eps_1 * deps4 + mc.mu_eps * deps3 + p_eps_2 * (
deps2 * cos(eps) - deps1**2 * sin(eps)) - p_eps_3 * (
deps2 * sin(eps) + deps1**2 * cos(eps))
dB2 = p_lamb_1 * dlamb4 + mc.mu_lamb * dlamb3
D = dB1 * A * cos(eps) - B * (dA1 * cos(eps) - A * sin(eps) * deps1)
E = (A * cos(eps))**2
dD1 = dB2 * A * cos(eps) - B * (dA2 * cos(eps) -
2 * dA1 * sin(eps) * deps1 - A *
(deps2 * sin(eps) + deps1**2 * cos(eps)))
dE1 = 2 * A * cos(eps) * (dA1 * cos(eps) - A * deps1 * sin(eps))
C = B / (A * cos(eps))
dC1 = D / E
dC2 = (dD1 * E - D * dE1) / E**2
phi = arctan(C)
dphi1 = dC1 / (1 + C**2)
dphi2 = (dC2 * (1 + C**2) - 2 * C * dC1**2) / (1 + C**2)**2
Fs = 1 / mc.l_h * sqrt(A**2 + (B / cos(eps))**2)
Fd = 1 / mc.l_p * (p_phi_1 * dphi2 + p_phi_2 * sin(phi) +
mc.mu_phi * dphi1)
Ff = (Fs + Fd) / 2
Fb = (Fs - Fd) / 2
uf = Fr_inverse(Ff)
ub = Fr_inverse(Fb)
return np.array([phi, dphi1, dphi2]), np.array([uf, ub])