def test_asinh(self):
import math
self.ftest(math.asinh(0), 0)
self.ftest(math.asinh(1), 0.88137358701954305)
self.ftest(math.asinh(-1), -0.88137358701954305)
assert math.isinf(math.asinh(float("inf")))
def testAsinh(self):
self.assertRaises(TypeError, math.asinh)
self.ftest('asinh(0)', math.asinh(0), 0)
self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
self.assertEqual(math.asinh(INF), INF)
# self.assertEqual(math.asinh(NINF), NINF)
self.assertTrue(math.isnan(math.asinh(NAN)))
def g(p):
x, y, z = p[0], p[1], abs(p[2])
return + x*y*z * asinh(z / (sqrt(x**2 + y**2) + eps)) \
+ y / 6.0 * (3.0 * z**2 - y**2) * asinh(x / (sqrt(y**2 + z**2) + eps)) \
+ x / 6.0 * (3.0 * z**2 - x**2) * asinh(y / (sqrt(x**2 + z**2) + eps)) \
- z**3 / 6.0 * atan(x*y / (z * sqrt(x**2 + y**2 + z**2) + eps)) \
- z * y**2 / 2.0 * atan(x*z / (y * sqrt(x**2 + y**2 + z**2) + eps)) \
- z * x**2 / 2.0 * atan(y*z / (x * sqrt(x**2 + y**2 + z**2) + eps)) \
- x*y * sqrt(x**2 + y**2 + z**2) / 3.0
def tri_angle_side_angle(a1, s, a2): """if the sides go [s,X,Y] with angles a1, a2, on either side of s, this function returns X,Y""" #find the remaining angle S = math.acos(math.sin(a1)*math.sin(a2)*math.cosh(s) - math.cos(a1)*math.cos(a2)) #use the law of sines to get the other sides sin_ratio = math.sinh(s)/math.sin(S) X = math.asinh(sin_ratio*math.sin(a1)) Y = math.asinh(sin_ratio*math.sin(a2)) return X,Y
def coefRAsientoZapRectangularFlexible(l,b):
'''
coefRAsientoZapRectangularFlexible(l,b):
Devuelve el coeficiente R de la expresión del asiento
de una cimentación superficial flexible rectangular de
acuerdo con el apartado 4.8.1 de la Guia de
cimentaciones en obras de carretera, figura 4.10 de la página 113
'''
retv=b*math.asinh(l/float(b))+l*math.asinh(b/float(l))
return(retv)
def acos(x):
_acos_special = [
[3*pi/4+infj, pi+infj, pi+infj, pi-infj, pi-infj, 3*pi/4-infj, nan+infj],
[pi/2+infj, None, None, None, None, pi/2-infj, nan+nanj],
[pi/2+infj, None, None, None, None, pi/2-infj, pi/2+nanj],
[pi/2+infj, None, None, None, None, pi/2-infj, pi/2+nanj],
[pi/2+infj, None, None, None, None, pi/2-infj, nan+nanj],
[pi/4+infj, infj, infj, 0.0-infj, 0.0-infj, pi/4-infj, nan+infj],
[nan+infj, nan+nanj, nan+nanj, nan+nanj, nan+nanj, nan-infj, nan+nanj]
]
z = _make_complex(x)
if not isfinite(z):
return _acos_special[_special_type(z.real)][_special_type(z.imag)]
if abs(z.real) > _LARGE_DOUBLE or abs(z.imag) > _LARGE_DOUBLE:
if z.real < 0:
imag = -math.copysign(math.log(math.hypot(z.real/2, z.imag/2)) +
2 * _LOG_2, z.imag)
else:
imag = math.copysign(math.log(math.hypot(z.real/2, z.imag/2)) +
2 * _LOG_2, -z.imag)
return complex(math.atan2(abs(z.imag), z.real), imag)
s1 = sqrt(complex(1.0 - z.real, -z.imag))
s2 = sqrt(complex(1.0 + z.real, z.imag))
return complex(2 * math.atan2(s1.real, s2.real),
math.asinh(s2.real*s1.imag - s2.imag*s1.real))
def asinh(x):
_asinh_special = [
[-inf-1j*pi/4, complex(-float("inf"), -0.0), complex(-float("inf"), -0.0),
complex(-float("inf"), 0.0), complex(-float("inf"), 0.0), -inf+1j*pi/4, -inf+nanj],
[-inf-1j*pi/2, None, None, None, None, -inf+1j*pi/2, nan+nanj],
[-inf-1j*pi/2, None, None, None, None, -inf+1j*pi/2, nan+nanj],
[inf-1j*pi/2, None, None, None, None, inf+1j*pi/2, nan+nanj],
[inf-1j*pi/2, None, None, None, None, inf+1j*pi/2, nan+nanj],
[inf-1j*pi/4, complex(float("inf"), -0.0), complex(float("inf"), -0.0),
inf, inf, inf+1j*pi/4, inf+nanj],
[inf+nanj, nan+nanj, complex(float("nan"), -0.0), nan, nan+nanj, inf+nanj, nan+nanj]
]
z = _make_complex(x)
if not isfinite(z):
return _asinh_special[_special_type(z.real)][_special_type(z.imag)]
if abs(z.real) > _LARGE_DOUBLE or abs(z.imag) > _LARGE_DOUBLE:
if z.imag >= 0:
real = math.copysign(math.log(math.hypot(z.imag/2, z.real/2)) +
2 * _LOG_2, z.real)
else:
real = -math.copysign(math.log(math.hypot(z.imag/2, z.real/2)) +
2 * _LOG_2, -z.real)
return complex(real, math.atan2(z.imag, abs(z.real)))
s1 = sqrt(complex(1+z.imag, -z.real))
s2 = sqrt(complex(1-z.imag, z.real))
return complex(math.asinh(s1.real*s2.imag-s2.real*s1.imag),
math.atan2(z.imag, s1.real*s2.real - s1.imag*s2.imag))
def acos(x):
"""
Return the arc cosine of x.
There are two branch cuts: One extends right from 1 along the real axis to ∞, continuous from below.
The other extends left from -1 along the real axis to -∞, continuous from above.
"""
ret = _SPECIAL_VALUE(x, _acos_special_values)
if ret is not None:
return ret
if math.fabs(x.real) > _CM_LARGE_DOUBLE or math.fabs(x.imag) > _CM_LARGE_DOUBLE:
# avoid unnecessary overflow for large arguments
_real = math.atan2(math.fabs(x.imag), x.real)
# split into cases to make sure that the branch cut has the
# correct continuity on systems with unsigned zeros
if x.real < 0:
_imag = -math.copysign(math.log(math.hypot(x.real/2., x.imag/2.)) + _M_LN2*2., x.imag);
else:
_imag = math.copysign(math.log(math.hypot(x.real/2., x.imag/2.)) + _M_LN2*2., -x.imag);
else:
s1 = complex(float(1-x.real), -x.imag)
s1 = sqrt(s1)
s2 = complex(1.0+x.real, x.imag)
s2 = sqrt(s2)
_real = 2.0*math.atan2(s1.real, s2.real);
_imag = math.asinh(s2.real*s1.imag - s2.imag*s1.real)
return complex(_real,_imag)
def zeta(self, snu, cnu, dnu, snv, cnv, dnv):
'''
Lee 54.17 but write
atanh(snu * dnv) = asinh(snu * dnv / sqrt(cnu^2 + _mv * snu^2 * snv^2))
atanh(_e * snu / dnv) =
asinh(_e * snu / sqrt(_mu * cnu^2 + _mv * cnv^2))
'''
d1 = math.sqrt(cnu*cnu + self.mv * (snu*snv)**2.0)
d2 = math.sqrt(self.mu * cnu*cnu + self.mv * cnv*cnv)
t1 = snu * dnv
if d1 != 0.0:
t1 /= d1
else:
t1 = self.overflow if snu >= 0.0 else -self.overflow
t2 = self.e * snu
if d2 != 0.0:
t2 = math.sinh(self.e * math.asinh(t2 / d2))
else:
t2 = self.overflow if snu >= 0.0 else -self.overflow
taup = t1 * math.hypot(1.0, t2) - t2 * math.hypot(1.0, t1);
lam = 0.0
if d1 != 0.0 and d2 != 0.0:
lam = math.atan2(dnu*snv, cnu*cnv) - self.e * math.atan2(self.e*cnu*snv, dnu*cnv)
return [taup, lam]
def deg2num(x, y, zoom):
"""Convert longitude, latitude to tile numbers."""
xmerc = math.radians(x)
ymerc = math.asinh(math.tan(math.radians(y)))
xtile = int((1 + xmerc/math.pi) / 2 * 2**zoom)
ytile = int((1 - ymerc/math.pi) / 2 * 2**zoom)
return xtile, ytile
def arclen_grad_x0y0ddd(x0, y0, d, dd, low, high): """arclen_grad_x0y0ddd(x0, y0, d, dd, low, high) -> (alpha, beta, gamma) Where arc = Catenary.from_x0y0ddd(x0, y0, d, dd).arc_length(low, high), (D[arc, x0], D[arc, d], D[arc, dd]) """ # gA = Sqrt[1 + d^2] / dd; # gxm = x0 - Sqrt[1 + d^2] ArcSinh[d]/dd; # gym = y0 - (1 + d^2)/dd; # arc = gA Sinh[(high - gxm)/gA] - gA Sinh[(low - gxm)/gA]; f1 = lambda func, bound: func(dd * (bound - x0)/(1 + d**2)**0.5 + math.asinh(d)) term = f1(math.sinh, high) - f1(math.sinh, low) term *= (1 + d**2)**0.5 # D[arc, x0] alpha = f1(math.cosh, low) - f1(math.cosh, high) # D[arc, d] beta = (1 + d**2 + d * dd * (x0 - high)) * f1(math.cosh, high) beta -= (1 + d * (d - dd * low + dd * x0)) * f1(math.cosh, low) beta += d * term beta /= (1 + d**2.0) * dd # D[arc, dd] gamma = dd * (high - x0) * f1(math.cosh, high) gamma += dd * (x0 - low) * f1(math.cosh, low) gamma -= term gamma /= dd**2.0 return alpha, beta, gamma
def pmuboost3d(jets, met, lep):
mw = 80.385
wwwtlv = ROOT.TLorentzVector(1e-9,1e-9,1e-9,1e-9)
mettlv = ROOT.TLorentzVector(1e-9,1e-9,1e-9,1e-9)
leptlv = ROOT.TLorentzVector(1e-9,1e-9,1e-9,1e-9)
for jet in jets:
# if(e.jetPt[ij] > 30.):
tlvaux = ROOT.TLorentzVector(1e-9,1e-9,1e-9,1e-9)
tlvaux.SetPtEtaPhiM(jet['pt'],0.,jet['phi'],0.)
wwwtlv -= tlvaux
mettlv.SetPtEtaPhiM(met['pt'],0.,met['phi'],0.)
leptlv.SetPtEtaPhiM(lep['pt'],lep['eta'],lep['phi'], 0.)
# leptlv.SetPtEtaPhiM(e.muPt[0],e.muEta[0],e.muPhi[0],0.)
# calculate eta(W) estimate; take the + solution
ptl = (wwwtlv - mettlv).Pt()
ptn = mettlv.Pt()
ptw = wwwtlv.Pt()
etal = leptlv.Eta()
A = (mw*mw + ptw*ptw - ptl*ptl - ptn*ptn) / (2.*ptl*ptn)
if(A<1.): A=1.
etaw = asinh((ptl*sinh(etal)+ptn*sinh(etal+acosh(A)))/ptw)
if(abs(etaw)>10.): etaw=10*etaw/abs(etaw) # avoid too large values
wwwtlv.SetPtEtaPhiM(wwwtlv.Pt(),etaw,wwwtlv.Phi(),mw)
# calulate boosted lepton momentum
beta = wwwtlv.BoostVector()
leptlv.Boost(-beta)
return leptlv.P()
def compute(self, plug, data):
# Check if output value is connected
if plug == self.aOutputVaue:
# Get input datas
operationTypeHandle = data.inputValue(self.aOperationType)
operationType = operationTypeHandle.asInt()
inputValueHandle = data.inputValue(self.aInputValue)
inputValue = inputValueHandle.asFloat()
# Math Sinus
outputValue = 0
if operationType == 0:
outputValue = math.asin(inputValue)
if operationType == 1:
outputValue = math.sin(inputValue)
if operationType == 2:
outputValue = math.asinh(inputValue)
if operationType == 3:
outputValue = math.sinh(inputValue)
# Output Value
output_data = data.outputValue(self.aOutputVaue)
output_data.setFloat(outputValue)
# Clean plug
data.setClean(plug)
def test_funcs_multi(self):
pi = math.pi
# sin family
self.assertQuantity(data.sin(Quantity( (0,pi/2), (2,2))), (0,1), (2,0))
self.assertQuantity(data.sinh(Quantity((0,1), (2,2))), (0, math.sinh(1)), (2, math.cosh(1)*2))
self.assertQuantity(data.asin(Quantity((0,0.5), (2,2))), (0,math.asin(0.5)), (2,2/math.sqrt(1-0.5**2)))
self.assertQuantity(data.asinh(Quantity((0,1), (2,2))), (0,math.asinh(1)), (2,2/math.sqrt(1+1**2)))
# cos family
self.assertQuantity(data.cos(Quantity((0,pi/2), (2,2))), (1,0), (0,-2))
self.assertQuantity(data.cosh(Quantity((0,1), (2,2))), (1,math.cosh(1)), (0,math.sinh(1)*2))
self.assertQuantity(data.acos(Quantity((0,0.5), (2,2))), (math.acos(0),math.acos(0.5)), (-2,-2/math.sqrt(1-0.5**2)))
self.assertQuantity(data.acosh(Quantity((2,3), (2,2))), (math.acosh(2), math.acosh(3)), (2/math.sqrt(2**2-1),2/math.sqrt(3**2-1)))
# tan family
self.assertQuantity(data.tan(Quantity((0,1), (2,2))), (0,math.tan(1)), (2,2/math.cos(1)**2))
self.assertQuantity(data.tanh(Quantity((0,1), (2,2))), (0,math.tanh(1)), (2,2/math.cosh(1)**2))
self.assertQuantity(data.atan(Quantity((0,1), (2,2))), (0, math.atan(1)), (2,2/(1+1**2)))
self.assertQuantity(data.atan2(Quantity((0,1), (2,2)), Quantity((1,1), (0,0))), (0,math.atan(1)), (2,2/(1+1**2)))
self.assertQuantity(data.atanh(Quantity((0,0.5), (2,2))), (0,math.atanh(0.5)), (2,2/(1-0.5**2)))
#misc
self.assertQuantity(data.sqrt(Quantity((1,4), (2,2))), (1,2), (1,1/2))
self.assertQuantity(data.exp(Quantity((1,4), (2,2))), (math.e, math.e**4), (2 * math.e,2*math.e**4))
self.assertQuantity(data.log(Quantity((1,4), (2,2))), (0, math.log(4)), (2,1/2))
def test_arcsinh(self):
import math
from _numpypy import arcsinh
for v in [float('inf'), float('-inf'), 1.0, math.e]:
assert math.asinh(v) == arcsinh(v)
assert math.isnan(arcsinh(float("nan")))
def test_arcsinh(self):
import math
from numpypy import arcsinh, inf
for v in [inf, -inf, 1.0, math.e]:
assert math.asinh(v) == arcsinh(v)
assert math.isnan(arcsinh(float("nan")))
def test_acosh(self):
import math
self.ftest(math.acosh(1), 0)
self.ftest(math.acosh(2), 1.3169578969248168)
assert math.isinf(math.asinh(float("inf")))
raises(ValueError, math.acosh, 0)
def chebyshev1(cutoff_frequency, ripple, order, highpass):
"""A helper function for creating the transfer function of a Chebyshev Type 1 filter.
:param cutoff_frequency: the cutoff frequency of the filter in Hz
:param ripple: the allowed passband ripple in dB
:param order: the filter order as an integer
:param highpass: True, if a lowpass-to-highpass-transformation shall be done, False otherwise
"""
k = frequency_scaling(cutoff_frequency=cutoff_frequency, highpass=highpass)
k2 = k ** 2
factors = []
# precompute coefficients
g = math.asinh(1.0 / math.sqrt(10.0 ** (abs(ripple) / 10.0) - 1.0)) / order
sinhg = math.sinh(g)
cosh2g = math.cosh(g) ** 2
# generate the transfer function
if order % 2 == 0:
pb2o = math.pi / (2 * order)
for i in range(1, order // 2 + 1):
b2 = 1.0 / (cosh2g - (math.cos((2 * i - 1) * pb2o) ** 2))
b1 = 2.0 * b2 * sinhg * math.cos((2 * i - 1) * pb2o)
factors.append(Chebyshev1Filter.Polynomial((b2 * k2, b1 * k, 1.0)))
else:
pbo = math.pi / order
b1 = 1.0 / sinhg
factors.append(Chebyshev1Filter.Polynomial((b1 * k, 1.0)))
for i in range(2, (order + 1) // 2 + 1):
b2 = 1.0 / (cosh2g - (math.cos((i - 1) * pbo) ** 2))
b1 = 2.0 * b2 * sinhg * math.cos((i - 1) * pbo)
factors.append(Chebyshev1Filter.Polynomial((b2 * k2, b1 * k, 1.0)))
return ~Chebyshev1Filter.Product(factors=factors, transform=highpass)
def zetainv(self, taup, lam):
psi = math.asinh(taup)
scal = 1.0 / math.hypot(1.0, taup);
(u, v, flag) = self.zetainv0(psi, lam)
if flag:
return [u, v]
stol2 = self.tolerance2 / max(psi, 1.0)**2.0
# min iterations = 2, max iterations = 6; mean = 4.0
trip = 0
for i in range(100):
(snu, cnu, dnu, ph) = ellipj(u, self.mu)
(snv, cnv, dnv, ph) = ellipj(v, self.mv)
(tau1, lam1) = self.zeta(snu, cnu, dnu, snv, cnv, dnv);
(du1, dv1) = self.dwdzeta(snu, cnu, dnu, snv, cnv, dnv)
tau1 -= taup; lam1 -= lam;
tau1 *= scal;
delu = tau1 * du1 - lam1 * dv1
delv = tau1 * dv1 + lam1 * du1
u -= delu; v -= delv;
if trip > 0:
break;
delw2 = delu*delu + delv*delv;
if delw2 < stol2 :
trip += 1
return [u, v]
def eccentric_anomaly(self, time):
"""Eccentric anomaly at a given time (s)"""
M = self.mean_anomaly(time)
e = self.eccentricity
if e < 1: # M = E - e sin E
M %= (2*math.pi)
# sin(E) = E -> M = (1 - e) E
if abs(M) < 2**-26:
return M / (1 - e)
return analysis.newton_raphson(
x_0=math.pi,
f=lambda E: E - e*math.sin(E) - M,
f_prime=lambda E: 1 - e*math.cos(E),
)
else: # M = e sinh E - E
# sinh(E) = E -> M = (e - 1) E
if abs(M) < 2**-26:
return M / (e - 1)
return analysis.newton_raphson(
x_0=math.asinh(M),
f=lambda E: e*math.sinh(E) - E - M,
f_prime=lambda E: e*math.cosh(E) - 1,
)
def hyperbolic_fun_cal(inp_val1, opn_type):
oprn_dic = {
'1': 'inverse hyperbolic cosine of x', '2':'inverse hyperbolic sine of x',
'3':' inverse hyperbolic tangent of x', '4':'hyperbolic cosine of x',
'5':'hyperbolic sine of x', '6':'hyperbolic tangent of x'}
if int(opn_type) == 1:
output = math.acosh(float(inp_val1))
return str(output)
if int(opn_type) == 2:
output = math.asinh(float(inp_val1))
return str(output)
if int(opn_type) == 3:
output = math.atanh(float(inp_val1))
return str(output)
if int(opn_type) == 4:
output = math.cosh(float(inp_val1))
return str(output)
if int(opn_type) == 5:
output = math.sinh(float(inp_val1))
return str(output)
if int(opn_type) == 6:
output = math.tanh(float(inp_val1))
return str(output)
else:
return "Invalid Operation"
def sinh_effective_mass_errors(self, dt, fast=True, period=None):
if fast: logging.info("sinh emass computed fast method")
T = self.period_check(period)
jkasv = self.jackknife_average_sub_vev()
jkemass = {}
for cfg in self.configs:
asvc = jkasv[cfg]
emass = {}
for t in self.times[dt:-dt]:
if t in self.emass_skip_times:
emass[t] = 0.0
continue
try:
guess = (1.0 / float(dt))*math.asinh((asvc[t+dt] + asvc[t-dt])/(2.0*asvc[t]))
if fast:
emass[t] = guess
else:
emass[t] = newton.newton_sinh_for_m(t,t+dt,asvc, guess, T)
except ValueError:
#logging.debug("invalid argument to log, setting to zero")
emass[t] = 0.0
except ZeroDivisionError:
logging.debug("div by zero, setting to zero")
emass[t] = 0.0
except KeyError:
logging.error("index out of range")
jkemass[cfg] = emass
jkemassobj = configtimeobj.Cfgtimeobj.fromDataDict(jkemass)
effmass_dt = self.sinh_effective_mass(dt, fast=fast, period=T)
return {t: jackknife.errorbars(effmass_dt[t], jkemassobj.get(time=t))
for t in self.times[dt:-dt]}
def calculateLockTime(self, radius):
scanRes = self.ship.getModifiedItemAttr("scanResolution")
if scanRes is not None and scanRes > 0:
# Yes, this function returns time in seconds, not miliseconds.
# 40,000 is indeed the correct constant here.
return min(40000 / scanRes / asinh(radius)**2, 30*60)
else:
return self.ship.getModifiedItemAttr("scanSpeed") / 1000.0
def get_x_by_s(self, x0, s): """get_x_by_s(self, x0, s) -> x Gives x such that self.arc_length(x0, x) == s. """ s += self.arc_length_indef(x0) x = self.xm + self.a * math.asinh(s / self.a) return x
def asinh(space, d):
""" asinh - Inverse hyperbolic sine """
try:
return space.wrap(math.asinh(d))
except OverflowError:
return space.wrap(rfloat.INFINITY)
except ValueError:
return space.wrap(rfloat.NAN)
def _getxy(self, coords, zoom):
n = 2**zoom
lat = coords[1] * pi / 180.0
lon = coords[0] * pi / 180.0
yp = math.asinh(math.tan(lat))
x = int(floor((1 + (lon / pi)) / 2 * n))
y = int(floor((1 - (yp / pi)) / 2 * n))
return x, y
def calculateMprime(k):
"""
Wyznacza odległość m' od środka cięgna do miejsca osiągnięcia ekstremum
przez funkcję zwisu
:param k:
:return:
"""
return k * math.asinh(SPAD_B / SPAN_A)
def from_x0y0ddd(x0, y0, d, dd):
"""from_x0y0ddd(x0, y0, d, dd) -> Catenary
The returned catenary passes through the given point with derivative d, and second derivative dd.
"""
# FullSimplify[Solve[catenary == y0 && D[catenary, x] == d && D[catenary, {x, 2}] == dd, {xm, ym, a}, Reals]]
a = (1 + d**2)**0.5 / dd
xm = x0 - (1 + d**2)**0.5 * math.asinh(d) / dd
ym = y0 - (1 + d**2.0) / dd
return Catenary(xm, ym, a)
def calculateM(k):
"""
Wylicza wielkość mimośrodu m [m] na podstawie parametru
lini zwisu k [m]
:param k: parametr lini zwisu [m]
:return: wartośc mimośrodu [m]
"""
m = k * math.asinh(SPAD_B / (2 * k * math.sinh(SPAN_A / (2 * k))))
return m
def tileXY(latitude, longitude, zoom): x = longitude * math.pi / 180.0; y = math.asinh(math.tan(latitude * math.pi / 180.0)) # In Google Maps projected sphere is the square [-pi..pi]x[-pi..pi] # This square is then divided on (2^zoom)x(2^zoom) tiles. Tile # coordinates are counting from upper left corner of the grid. x = (x / math.pi / 2.0 + 0.5) * 2**zoom y = (-y/ math.pi / 2.0 + 0.5) * 2**zoom return (int(x), int(y))
# of dimension [Nx columns] by [Ny rows]
u = np.zeros([Ny, Nx])
v = np.zeros([Ny, Nx])
# u is a 2D array of nondimensional x-velocities at all spatial locations
# v is a 2D array of nondimensional y-velocities at all spatial locations
# %% Apply boundary conditions to u matrix
# Set u(x, 0) to be 0 from no-slip boundary condition
u[0, :] = 0 # Set 0th row, all columns to be 0
# Set u(x, 1) to be 1 from Dirichlet boundary condition
u[-1, :] = 1 # Set last row, all columns to be 1
# Set u(0, eta) to starting profile
etaY1 = asinh(
1 * sinh(s) / yMax) / s # Determine eta value corresponding to y = 1
for n in range(len(y)):
# u(0, y <= 1) = sin(pi*y/2)
if eta[n] <= etaY1:
u[n, 0] = sin(pi * y[n] / 2)
# u(0, y > 1) = 1
elif y[n] > etaY1:
u[n, 0] = 1
# %% Apply boundary condition to v matrix
# Set v(x, eta=0) to be 0 from impermeable wall condition
v[0, :] = 0
# %% Loop over each x-step
for i in range(len(x) - 1):
# Set up matrix and RHS "b" matrix (knowns)
def ejecutar(self, ts = None):
if self.parametro2 != None: # 2 PARAMETROS
nodoSyn1 = self.parametro1.ejecutar(ts)
if isinstance(nodoSyn1 , ErrorReport):
return nodoSyn1
nodoSyn2 = self.parametro2.ejecutar(ts)
if isinstance(nodoSyn2 , ErrorReport):
return nodoSyn2
if isinstance(nodoSyn1 , ExpresionNumero) and isinstance(nodoSyn2 , ExpresionNumero):
if self.funcion == "ATAN2":
rads = math.atan2(nodoSyn1.val,nodoSyn2.val)
return ExpresionNumero(rads,self.getTipo(rads),self.linea)
if self.funcion == "ATAN2D":
rads = math.atan2(nodoSyn1.val,nodoSyn2.val)
grados = (rads * 180/math.pi)
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
if self.funcion == "DIV":
izq = nodoSyn1.val
der = nodoSyn2.val
if der == 0:
return ErrorReport('semantico', 'error DIVISION entre 0' ,self.linea)
valor = izq/der
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="GCD":
valor = math.gcd(nodoSyn1.val , nodoSyn2.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="MOD":
try:
valor = (nodoSyn1.val % nodoSyn2.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except:
return ErrorReport('semantico', 'error en MODULO' ,self.linea)
if self.funcion =="POWER":
try:
valor = (nodoSyn1.val ** nodoSyn2.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except:
return ErrorReport('semantico', 'error en MODULO' ,self.linea)
if self.funcion =="ROUND":
valor = round(nodoSyn1.val , nodoSyn2.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion == "TRUNC":
if self.getTipo(nodoSyn2.val) != TIPO_DE_DATO.ENTERO:
return ErrorReport('semantico', 'error en Metodo TRUNC el segundo parametro tiene que ser un entero' ,self.linea)
cadenaInt = str(nodoSyn1.val)
numero_truncado = ''
indice = 0
decimalesAdjuntados = 0
for i in range(len(cadenaInt)):
if cadenaInt[i] == '.':
numero_truncado += cadenaInt[i]
indice = i
break
else:
numero_truncado += cadenaInt[i]
indice+=1
while(decimalesAdjuntados < nodoSyn2.val):
if indice < len(cadenaInt):
numero_truncado += cadenaInt[indice]
else:
numero_truncado += '0'
indice+=1
decimalesAdjuntados+=1
valor = float(numero_truncado)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
else:
return ErrorReport('semantico', 'error de tipo, se esperaba un ENTERO O DECIMAL' ,self.linea)
elif self.parametro1 != None: # 1 PARAMETRO
if isinstance(self.parametro1,list):
if self.funcion =="WIDTH_BUCKET":
return self.metodo_width_bucket(self.parametro1,ts)
nodoSyn1 = self.parametro1.ejecutar(ts)
if isinstance(nodoSyn1 , ErrorReport):
return nodoSyn1
if isinstance(nodoSyn1 , ExpresionNumero): # decimales y eneteros
if self.funcion == "ACOS": # RADIANEES
if nodoSyn1.val > 1 or nodoSyn1.val < 1:
return ErrorReport('semantico', 'Error en ACOS ,el parametro debe estar entre -1 y 1' ,self.linea)
return ExpresionNumero(math.acos(nodoSyn1.val),self.getTipo(nodoSyn1.val),self.linea)
if self.funcion == "ACOSD": # GRADOS
if nodoSyn1.val > 1 or nodoSyn1.val < 1:
return ErrorReport('semantico', 'Error en ACOSD , el parametro debe estar entre -1 y 1' ,self.linea)
rads = math.acos(nodoSyn1.val)
grados = (rads * 180/math.pi)
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
if self.funcion == "ASIN":
if nodoSyn1.val > 1 or nodoSyn1.val < 1:
return ErrorReport('semantico', 'Error en ASIN ,el parametro debe estar entre -1 y 1' ,self.linea)
valor = math.asin(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion == "ASIND":
if nodoSyn1.val > 1 or nodoSyn1.val < 1:
return ErrorReport('semantico', 'Error en ASIND ,el parametro debe estar entre -1 y 1' ,self.linea)
rads = math.asin(nodoSyn1.val)
grados = (rads * 180/math.pi)
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
if self.funcion == "ATAN":
try:
rads = math.atan(nodoSyn1.val)
return ExpresionNumero(rads,self.getTipo(rads),self.linea)
except:
return ErrorReport('semantico', 'Error en ATAN por el valor del parametro ' ,self.linea)
if self.funcion == "ATAND":
try:
rads = math.atan(nodoSyn1.val)
grados = (rads * 180/math.pi)
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
except:
return ErrorReport('semantico', 'Error en ATAND por el valor del parametro ' ,self.linea)
if self.funcion == "COS":
valor = math.cos(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion == "COSD":
rads = math.cos(nodoSyn1.val)
grados = (rads * 180/math.pi)
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
if self.funcion == "COT":
tangente=math.tan(nodoSyn1.val)
if tangente == 0:
return ErrorReport('semantico', 'Error en COT por el valor del parametro ' ,self.linea)
cot = 1 / tangente
return ExpresionNumero(cot,self.getTipo(cot),self.linea)
if self.funcion == "COTD":
tangente=math.tan(nodoSyn1.val)
if tangente == 0:
return ErrorReport('semantico', 'Error en COTD por el valor del parametro ' ,self.linea)
cot =math.degrees(1 / tangente)
return ExpresionNumero(cot,self.getTipo(cot),self.linea)
if self.funcion == "SIN":
radianes=math.sin(nodoSyn1.val)
return ExpresionNumero(radianes,self.getTipo(radianes),self.linea)
if self.funcion == "SIND":
grados=math.degrees(math.sin(nodoSyn1.val))
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
if self.funcion == "TAN":
try:
radianes=math.tan(nodoSyn1.val)
return ExpresionNumero(radianes,self.getTipo(radianes),self.linea)
except:
return ErrorReport('semantico', 'Error en TAN por el valor del parametro ' ,self.linea)
if self.funcion == "TAND":
try:
grados=math.degrees(math.tan(nodoSyn1.val))
return ExpresionNumero(grados,self.getTipo(grados),self.linea)
except:
return ErrorReport('semantico', 'Error en TAND por el valor del parametro ' ,self.linea)
if self.funcion == "COSH":
try:
valor=math.cosh(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except:
return ErrorReport('semantico', 'Error en COSH por el valor del parametro ' ,self.linea)
if self.funcion == "SINH":
try:
valor=math.sinh(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except:
return ErrorReport('semantico', 'Error en SINH por el valor del parametro ' ,self.linea)
if self.funcion == "TANH":
try:
valor=math.tanh(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except:
return ErrorReport('semantico', 'Error en TANH por el valor del parametro ' ,self.linea)
if self.funcion == "ACOSH":
if nodoSyn1.val < 1:
return ErrorReport('semantico', 'Error en ACOSH, el parametro debe de ser mayor o igual a 1 ' ,self.linea)
valor=math.acosh(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion == "ASINH":
valor=math.asinh(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion == "ATANH":
if nodoSyn1.val > 0.99 or nodoSyn1.val < -0.99:
return ErrorReport('semantico', 'Error en ATANH, el parametro debe estar entre 0.99 y -0.99 ' ,self.linea)
valor=math.atanh(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
#_________________________________ fin de trigonometricas
if self.funcion == "ABS":
valor=math.fabs(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion == "CBRT": #RAIZ CUBICA SOLO PARA ENTREROS
if (nodoSyn1.val) < 0 :
return ErrorReport('semantico', 'error SQRT solo recibe enteros POSITIVOS :D' ,self.linea)
if (nodoSyn1.val % 1) == 0:
valor = nodoSyn1.val**(1/3)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
else:
return ErrorReport('semantico', 'error CBRT solo recibe enteros, NO decimales' ,self.linea)
if self.funcion =="CEIL" or self.funcion == "CEILING":
valor = math.ceil(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="DEGREES":
valor = math.degrees(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="FACTORIAL":
valor = math.factorial(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="FLOOR":# POR SI VIENE EN UN INSERT
valor = math.floor(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="LN":
try:
valor = math.log(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except :
return ErrorReport('semantico', 'error en el paramtro de LN' ,self.linea)
if self.funcion =="LOG":
try:
valor = math.log10(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except :
return ErrorReport('semantico', 'error en el paramtro de LOG' ,self.linea)
if self.funcion =="EXP":
try:
valor = math.exp(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
except :
return ErrorReport('semantico', 'error en el paramtro de EXP' ,self.linea)
if self.funcion =="RADIANS":
valor = math.radians(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="ROUND":
valor = round(nodoSyn1.val)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
if self.funcion =="SIGN":
if nodoSyn1.val > 0:
valor = 1
return ExpresionNumero(valor,TIPO_DE_DATO.ENTERO,self.linea)
if nodoSyn1.val < 0:
valor = -1
return ExpresionNumero(valor,TIPO_DE_DATO.ENTERO,self.linea)
else:
return ErrorReport('semantico', 'error en funcion SING , EL 0 no tiene signo ' ,self.linea)
if self.funcion == "SQRT":
if (nodoSyn1.val) < 0 :
return ErrorReport('semantico', 'error SQRT solo recibe enteros POSITIVOS' ,self.linea)
if (nodoSyn1.val % 1) == 0:
valor = nodoSyn1.val**(1/2)
return ExpresionNumero(valor,self.getTipo(valor),self.linea)
else:
return ErrorReport('semantico', 'error SQRT solo recibe enteros, NO decimales' ,self.linea)
if self.funcion == "TRUNC":
valor = math.trunc(nodoSyn1.val)
return ExpresionNumero(valor,TIPO_DE_DATO.ENTERO,self.linea)
else:
return ErrorReport('semantico', 'error de tipo, se esperaba un ENTERO O DECIMAL' ,self.linea)
else:# SIN PARAMETROS
if self.funcion == 'PI':
return ExpresionNumero(math.pi,TIPO_DE_DATO.DECIMAL,self.linea)
elif self.funcion == "RANDOM":
valor = random.choice((1,0))
return ExpresionNumero(valor,TIPO_DE_DATO.ENTERO,self.linea)
def asinh(x):
return math.asinh(x)
def ExactSolution(xL):
Term1 = m.sqrt((xL - L)**2 + 1) - xL * m.asinh(xL - L) # z = L
Term2 = m.sqrt((xL - 0)**2 + 1) - xL * m.asinh(xL - 0) # z = 0
return Term1 - Term2
import math x = math.pi a = math.acos(x) b = math.acosh(x) c = math.asin(x) d = math.asinh(x) e = math.atan(x) f = math.atan2(x, a) g = math.atanh(x) h = math.ceil(x) i = math.copysign(x, f) j = math.cos(x) k = math.cosh(x) l = math.degrees(x) m = math.erf(x) n = math.erfc(x) o = math.exp(x) p = math.expm1(x) q = math.fabs(x) r = math.factorial(math.floor(x)) s = math.fmod(x, n) t, u = math.frexp(x) v = math.fsum([a, b, c, d]) w = math.gamma(x) gcd = math.gcd(r, u) y = math.hypot(x, a) z = math.isclose(x, y) aa = math.isclose(x, y) ab = math.isfinite(x)
def get_dist_pct(self, pct):
# calculate inverse of dist fn
val_inv = math.asinh(self.nonlinearity * pct) / self.factor
val = min(max(float(val_inv), 0.0), 1.0)
return val
def _intSecAtan(x):
# In : sympy.integrate(sp.sec(sp.atan(x)))
# Out: x*sqrt(x**2 + 1)/2 + asinh(x)/2
return x * math.sqrt(x**2 + 1) / 2 + math.asinh(x) / 2
def math_asinh(A, B):
i = cuda.grid(1)
B[i] = math.asinh(A[i])
param_dct["param_1"] + param_dct["param_2"] * 30.0 - param_dct["param_5"], (param_dct["param_1"] + 1) / param_dct["param_2"], math.sqrt(param_dct["param_2"]), math.fmod(param_dct["param_4"], param_dct["param_1"]), math.sin(param_dct["param_7"]), math.cos(param_dct["param_7"]), math.tan(param_dct["param_7"]), math.asin(param_dct["param_7"]), math.acos(param_dct["param_7"]), math.atan(param_dct["param_7"]), math.atan2(param_dct["param_7"], 2.0), math.hypot(3.0, 4.0), math.sinh(param_dct["param_7"]), math.cosh(param_dct["param_7"]), math.tanh(param_dct["param_7"]), math.asinh(param_dct["param_7"]), math.acosh(param_dct["param_2"]), math.atanh(param_dct["param_7"]), math.degrees(math.radians(param_dct["param_7"])), math.log(param_dct["param_3"]), math.log10(param_dct["param_3"]), math.log2(param_dct["param_3"]), math.fabs(param_dct["param_5"]), math.ceil(param_dct["param_5"]), math.floor(param_dct["param_5"]), round(param_dct["param_5"]), math.exp(param_dct["param_1"]), 2.0 * math.e, math.pi + 1, 2.0, param_dct["param_5"] % param_dct["param_6"],
def f_asinh(x: (int, float)):
"""Inverse Hyperbolic Sine"""
return math.asinh(x)
def test_gh1284(self):
import math
self.assertEqual(round(math.asinh(4.),12),round(math.log(math.sqrt(17.)+4.),12))
self.assertEqual(round(math.asinh(.4),12),round(math.log(math.sqrt(1.16)+.4),12))
self.assertEqual(round(math.asinh(-.5),12),round(math.log(math.sqrt(1.25)-.5),12))
self.assertEqual(round(math.asinh(-6.),12),round(math.log(math.sqrt(37.)-6.),12))
def ppf(r, k, l, s, q):
return s * math.asinh(-math.log((math.pow(q, -1 / r) - 1) / k)) + l
def eta(self):
return math.asinh(self.z / math.sqrt(self.x**2 + self.y**2))
def coords2tilexy(lat_deg, lon_deg, zoom):
lat_rad = math.radians(lat_deg)
n = 2.0**zoom
xtile = int((lon_deg + 180.0) / 360.0 * n)
ytile = int((1.0 - math.asinh(math.tan(lat_rad)) / math.pi) / 2.0 * n)
return (xtile, ytile)
def acaSchroeder_scalar(f):
return 7 * math.asinh(f / 650)
def FunctionWithOneParameter(self, funcion, parametros, exp):
if (parametros == 1):
if (funcion == "abs"):
if (exp < 0):
return exp * -1
else:
return exp
elif (funcion == "cbrt"):
return math.pow(exp, 3)
elif (funcion == "ceil"):
return math.ceil(exp)
elif (funcion == "ceiling"):
return math.ceil(exp)
elif (funcion == "degrees"):
return math.degrees(exp)
elif (funcion == "exp"):
return math.exp(exp)
elif (funcion == "factorial"):
return math.factorial(exp)
elif (funcion == "floor"):
return math.floor(exp)
elif (funcion == "ln"):
return math.log(exp)
elif (funcion == "log"):
return math.log10(exp)
elif (funcion == "radians"):
return math.radians(exp)
elif (funcion == "sing"):
if (exp > 0):
return 1
else:
return -1
elif (funcion == "sqrt"):
return math.sqrt(exp)
elif (funcion == "trunc"):
return math.trunc(exp)
elif (funcion == "acos"):
return math.acos(exp)
elif (funcion == "acosd"):
return math.degrees(math.acos(exp))
elif (funcion == "asin"):
return math.asin(exp)
elif (funcion == "asind"):
return math.degrees(math.asin(exp))
elif (funcion == "atan"):
return math.atan(exp)
elif (funcion == "atand"):
return math.degrees(math.atan(exp))
elif (funcion == "cos"):
return math.cos(exp)
elif (funcion == "cosd"):
return math.degrees(math.cos(exp))
elif (funcion == "cot"):
return (1 / math.tan(exp))
elif (funcion == "cotd"):
return math.degrees(1 / math.tan(exp))
elif (funcion == "sin"):
return math.sin(exp)
elif (funcion == "sind"):
return math.degrees(math.sin(exp))
elif (funcion == "sin"):
return math.sin(exp)
elif (funcion == "sind"):
return math.degrees(math.sin(exp))
elif (funcion == "tan"):
return math.tan(exp)
elif (funcion == "tand"):
return math.degrees(math.tan(exp))
elif (funcion == "sinh"):
return math.sinh(exp)
elif (funcion == "cosh"):
return math.cosh(exp)
elif (funcion == "tanh"):
return math.tanh(exp)
elif (funcion == "asinh"):
return math.asinh(exp)
elif (funcion == "acosh"):
return math.acosh(exp)
elif (funcion == "atanh"):
return math.atanh(exp)
elif (funcion == "length"):
leng = len(exp)
return leng
elif (funcion == "md5"):
m = exp
result = hashlib.md5(m.encode())
return result.hexdigest()
elif (funcion == "sha256"):
m = exp
result = hashlib.sha256(m.encode()).hexdigest()
return result
elif (funcion == "convert"):
print("convert")
else:
reporteerrores.append(
Lerrores("Error Semantico",
"La funcion" + funcion + "solo recibe 2 parametros",
0, 0))
return "Error: La funcion: " + funcion + " recibe un parametro"
def run_arcsinh_test():
# for x in [-100000, -1000, -10, -1, 0, 1, 10, 1000, 1000000]:
for x in [-100, -10, -1, 0, 1, 10, 100]:
print("Doing arcsinh({})".format(x))
assert_close(asinh(x), Arcsinh(x), "arcsinh({})".format(x))
def f(p):
x, y, z = abs(p[0]), abs(p[1]), abs(p[2])
return + y / 2.0 * (z**2 - x**2) * asinh(y / (sqrt(x**2 + z**2) + eps)) \
+ z / 2.0 * (y**2 - x**2) * asinh(z / (sqrt(x**2 + y**2) + eps)) \
- x*y*z * atan(y*z / (x * sqrt(x**2 + y**2 + z**2) + eps)) \
+ 1.0 / 6.0 * (2*x**2 - y**2 - z**2) * sqrt(x**2 + y**2 + z**2)
def geo_utm(lat, lon):
a, f = 6378137.0, 1 / 298.257223563 #datum WGS84 and flatening
ko = 0.9996 # UTM scale factor on the central meridian
ns = 'N'
ew = 'E'
# identifying North or South
if lat < 0:
ns = 'S'
lat = abs(lat)
# identifying East or West and calculating meridian centre
if lon < 0:
bo = int(lon / 6) * 6 - 3 # for western
ew = 'W'
else:
bo = int(lon / 6) * 6 + 3 # for eastern
# Converting to radians
λo = radians(bo)
φ = radians(lat)
λ = radians(lon) - λo
#computtion
e = sqrt(f * (2 - f))
n = f / (2 - f)
n2 = n * n
n3 = n2 * n
n4 = n3 * n
n5 = n4 * n
n6 = n5 * n
n7 = n6 * n
n8 = n7 * n
cosλ = cos(λ)
sinλ = sin(λ)
tanλ = tan(λ)
τ = tan(φ)
σ = sinh(e * atanh(e * τ / sqrt(1 + τ * τ)))
τ1 = τ * sqrt(1 + σ * σ) - σ * sqrt(1 + τ * τ)
ξ1 = atan2(τ1, cosλ)
η1 = asinh(sinλ / sqrt(τ1 * τ1 + cosλ * cosλ))
A = a / (1 + n) * (1 + 1 / 4 * n2 + 1 / 64 * n4 + 1 / 256 * n6 +
25 / 16384 * n8)
α1 = 1 / 2 * n - 2 / 3 * n2 + 5 / 16 * n3 + 41 / 180 * n4 - 127 / 288 * n5 + 7891 / 37800 * n6 + 72161 / 387072 * n7 - 18975107 / 50803200 * n8
α2 = 13 / 48 * n2 - 3 / 5 * n3 + 557 / 1440 * n4 + 281 / 630 * n5 - 1983433 / 1935360 * n6 + 13769 / 28800 * n7 + 148003883 / 174182400 * n8
α3 = 61 / 240 * n3 - 103 / 140 * n4 + 15061 / 26880 * n5 + 167603 / 181440 * n6 - 67102379 / 29030400 * n7 + 79682431 / 79833600 * n8
α4 = 49561 / 161280 * n4 - 179 / 168 * n5 + 6601661 / 7257600 * n6 + 97445 / 49896 * n7 + 40176129013 / 7664025600 * n8
α5 = 34729 / 80640 * n5 - 3418889 / 1995840 * n6 + 14644087 / 9123840 * n7 + 2605413599 / 622702080 * n8
α6 = 212378941 / 319334400 * n6 - 30705481 / 10378368 * n7 + 175214326799 / 58118860800 * n8
α7 = 1522256789 / 1383782400 * n7 - 16759934899 / 3113510400 * n8
α8 = 1424729850961 / 743921418240 * n8
ξ = ξ1 + α1 * sin(2 * ξ1) * cosh(2 * η1) + α2 * sin(4 * ξ1) * cosh(
4 * η1) + α3 * sin(6 * ξ1) * cosh(6 * η1) + α4 * sin(8 * ξ1) * cosh(
8 * η1) + α5 * sin(10 * ξ1) * cosh(10 * η1) + α6 * sin(
12 * ξ1) * cosh(12 * η1) + α7 * sin(14 * ξ1) * cosh(
14 * η1) + α8 * sin(16 * ξ1) * cosh(16 * η1)
η = η1 + α1 * cos(2 * ξ1) * sinh(2 * η1) + α2 * cos(4 * ξ1) * sinh(
4 * η1) + α3 * cos(6 * ξ1) * sinh(6 * η1) + α4 * cos(8 * ξ1) * sinh(
8 * η1) + α5 * cos(10 * ξ1) * sinh(10 * η1) + α6 * cos(
12 * ξ1) * sinh(12 * η1) + α7 * cos(14 * ξ1) * sinh(
14 * η1) + α8 * cos(16 * ξ1) * sinh(16 * η1)
# UTM Coordinate
x = 500000 + ko * A * η
y = ko * A * ξ
if (ns == 'S'):
y = 10000000 - y
# UTM Meridian Convergency
p1 = 1
q1 = 0
p1 = p1 + 2 * α1 * cos(2 * ξ1) * cosh(2 * η1) + 4 * α2 * cos(
4 * ξ1) * cosh(4 * η1) + 6 * α3 * cos(6 * ξ1) * cosh(
6 * η1) + 8 * α4 * cos(8 * ξ1) * cosh(8 * η1) + 10 * α5 * cos(
10 * ξ1) * cosh(10 * η1) + 12 * α6 * cos(12 * ξ1) * cosh(
12 * η1)
q1 = q1 + 2 * α1 * sin(2 * ξ1) * sinh(2 * η1) + 4 * α2 * sin(
4 * ξ1) * sinh(4 * η1) + 6 * α3 * sin(6 * ξ1) * sinh(
6 * η1) + 8 * α4 * sin(8 * ξ1) * sinh(8 * η1) + 10 * α5 * sin(
10 * ξ1) * sinh(10 * η1) + 12 * α6 * sin(12 * ξ1) * sinh(
12 * η1)
γ1 = atan(τ1 / sqrt(1 + τ1 * τ1) * tanλ)
γ2 = atan2(q1, p1)
γ = degrees(γ1 + γ2)
if ((lon < bo and lat > 0) or (lon > bo and lat < 0)):
γ = -1 * γ
# UTM Scale Factor
sinφ = sin(φ)
k1 = sqrt(1 - e * e * sinφ * sinφ) * sqrt(1 + τ * τ) / sqrt(τ1 * τ1 +
cosλ * cosλ)
k2 = A / a * sqrt(p1 * p1 + q1 * q1)
k = ko * k1 * k2
# UTM Zone Number
zone = round((lon + 180) / 6 + 0.5)
return (x, y, zone, bo, k, γ)
'+': Operator(2, 1, lambda a, b: [a + b]),
'-': Operator(2, 1, lambda a, b: [a - b]),
'^': Operator(2, 1, lambda a, b: [a**b]),
'sin': Operator(1, 1, lambda a: [math.sin(
a)]), #change from (a) to (a*(math.pi/180)) to give answer in degrees
'cos': Operator(1, 1, lambda a: [math.cos(a)]),
'tan': Operator(1, 1, lambda a: [math.tan(a)]),
'sinh': Operator(1, 1, lambda a: [math.sinh(a)]),
'cosh': Operator(1, 1, lambda a: [math.cosh(a)]),
'tanh': Operator(1, 1, lambda a: [math.tanh(a)]),
'exp': Operator(1, 1, lambda a: [math.exp(a)]),
'sqrt': Operator(1, 1, lambda a: [math.sqrt(a)]),
'asin': Operator(1, 1, lambda a: [math.asin(a)]),
'acos': Operator(1, 1, lambda a: [math.acos(a)]),
'atan': Operator(1, 1, lambda a: [math.atan(a)]),
'asinh': Operator(1, 1, lambda a: [math.asinh(a)]),
'acosh': Operator(1, 1, lambda a: [math.acosh(a)]),
'atanh': Operator(1, 1, lambda a: [math.atanh(a)])
}
OPERATORS = set(['+', '-', '*', '/', '(', ')',
'^']) #establish the operators for infix_to_postfix function
OPERATORS_STRING = [
'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'exp', 'sqrt', 'asin', 'acos',
'atan', 'asinh', 'acosh', 'atanh'
] #establish the trigonometric, hyperbolic functions
#PRIORITY --> sets the priority of operations for the 'infix_to_postfix' function, according to the BIDMAS rule
PRIORITY = {
'+': 1,
'-': 1,
'*': 2,
}
output_step = 20
DEM.dt = dt
DEM.sim_params = sim_params
DEM.particles = particles
inv_sinh = 1.0 / sinh(particles["mu_ref"] / particles["a_tilde"])
DEM.particles["inv_sinh_mu_ref"] = inv_sinh
DEM.saved_data = []
DEM.render_mesh()
# DEM.draw_scene(tri=True)
s = np.zeros_like(t)
mu = np.zeros_like(t)
mu_ss = particles["a_tilde"] * asinh(vy_p[0] /
(particles["vc_ref"] * inv_sinh))
for i in range(len(t)):
DEM.t = t[i]
DEM.particles["coords"][1] = x_p[i], y_p[i]
DEM.particles["v"][1] = vx_p[i], vy_p[i]
DEM.check_remesh()
DEM.init_step()
DEM.update_particle_forces()
if i % output_step == 0:
data = {
"particles": copy.deepcopy(DEM.particles),
"contacts": copy.deepcopy(DEM.contacts),
}
DEM.saved_data.append(data)
def asinh(self):
# self.result=False
self.current=math.asinh(float(txtDisplay.get()))
self.expression = "asinh(" + str(txtDisplay.get()) +")=" + str(self.current)
self.display(self.expression)
math.expml(x) # $e ^ x-1$ math.log(x) # xの自然対数 math.log(x, y) # yを底とする xの対数 math.log1p math.log2(x) # 2を底とする xの対数 math.log10(x) # xの常用対数 math.sqrt(x) # xの平方根 math.cos(x) # xの余弦 math.dist(x) # xとxのユークリッド距離 math.hypot(x, y) # xとyのノルム math.sin(x) # xの正弦 math.tan(x) # xの正接 math.degrees(x) # xの角度 math.radians(x) # xのラジアン math.acosh(x) # xの逆双曲線余弦 math.asinh(x) # xの逆双曲線正弦 math.atanh(x) # xの逆双曲線正接 math.cosh(x) # xの双曲線余弦 math.sinh(x) # xの双曲線正弦 math.tanh(x) # xの双曲線正接 math.gamma(x) # xのガンマ関数 math.lgamma(x) # xのガンマ関数の絶対値の自然対数 math.pi # 円周率 math.e # ネイピア数 math.inf # 無限大 math.nan # NaN _マッチする = 'マッチする|含まれる|マッチする' re.search(x, y) # x(正規表現)がyにマッチする 最初の位置 -> int re.match(x, y) # yに x(正規表現)がマッチするかどうか -> bool
def asinh(self):
self.result = False
self.current = math.asinh(float(txtDisplay.get()))
self.display(self.current)
#In this we will see import function import math as mt #importing math to solve complex mathematical operation import random as rd #imporing rand to select value randmoly a=mt.asinh(90) print(a) b=rd.randint(100000,900000) print(b)
def cMathOperations(inputFromUser, outputFromUser):
# TO OPERATE SIMPLE ARITHMETIC OPERATIONS
arithmaticOperations = [float(index) for index in inputFromUser.split(' ')]
if len(arithmaticOperations)>1:
if (sum(arithmaticOperations)==float(outputFromUser)):
f= open("Program.c","w+")
f.write('/*Add this in int main()\n\tfloat variable2;\n\tscanf("%f", &variable2);\n*/\n\n')
f.close
function = 'variable1+variable2'
return str(function)
elif (float(arithmaticOperations[0]-arithmaticOperations[1])==float(outputFromUser)):
f= open("Program.c","w+")
f.write('/*Add this in int main()\n\tfloat variable2;\n\tscanf("%f", &variable2);\n*/\n\n')
f.close
function = 'variable1-variable2'
return str(function)
elif (float(arithmaticOperations[0]*arithmaticOperations[1])==float(outputFromUser)):
f= open("Program.c","w+")
f.write('/*Add this in int main()\n\tfloat variable2;\n\tscanf("%f", &variable2);\n*/\n\n')
f.close
function = 'variable1*variable2'
return str(function)
elif (float(arithmaticOperations[0]/arithmaticOperations[1])==float(outputFromUser)) or (float(arithmaticOperations[1]/arithmaticOperations[0])==float(outputFromUser)):
f= open("Program.c","w+")
f.write('/*Add this in int main()\n\tfloat variable2;\n\tscanf("%f", &variable2);\n*/\n\n')
f.close
function = 'variable1/variable2'
return str(function)
elif max(arithmaticOperations[0], arithmaticOperations[1])==float(outputFromUser):
f= open("Program.c","w+")
f.write('/*Add this in int main()\n\tfloat variable2;\n\tscanf("%f", &variable2);\n*/\n\n')
f.close
function = '{ variable1 > variable2 ? variable1:variable2 }'
return str(function)
elif min(arithmaticOperations[0], arithmaticOperations[1])==float(outputFromUser):
f= open("Program.c","w+")
f.write('/*Add this in int main()\n\tfloat variable2;\n\tscanf("%f", &variable2);\n*/\n\n')
f.close
function = '{ variable1 < variable2 ? variable1:variable2 }'
return str(function)
else:
return str('0')
inputFromUser=float(inputFromUser)
outputFromUser=float(outputFromUser)
try:
while True:
if (round(inputFromUser**(access_iter.__next__()), 3)==outputFromUser):
function = 'pow(variable1, '+ str(access_iter.__next__()-1) +')'
return str(function)
except:
pass
access_iter.reset()
try:
while True:
if (round(outputFromUser**(access_iter.__next__()), 3)==inputFromUser):
function = 'pow(variable1, '+ str(float(1/(access_iter.__next__()-1))) +')'
return str(function)
except:
pass
access_iter.reset()
# REMOVE 1 FROM accessNaturalNumbers to operate log
try:
while True:
base=int(logarithmic_iter.__next__())
if (math.log(inputFromUser, base)==outputFromUser):
function = 'log(variable1, '+ str(base) +')'
return str(function)
except:
pass
if(math.floor(inputFromUser)==outputFromUser):
return 'floor(variable1)'
elif(math.ceil(inputFromUser)==outputFromUser):
return 'ceil(variable1)'
elif(abs(inputFromUser)==outputFromUser):
return 'abs(variable1)'
elif(1/inputFromUser==outputFromUser):
return '1/variable1'
elif(round(math.sin(inputFromUser), 2)==outputFromUser):
return 'sin(variable1)'
elif(round(math.cos(inputFromUser), 2)==outputFromUser):
return 'cos(variable1)'
elif(round(math.tan(inputFromUser), 2)==outputFromUser):
return 'tan(variable1)'
elif(round(math.sinh(inputFromUser), 2)==outputFromUser):
return 'sinh(variable1)'
elif(round(math.cosh(inputFromUser), 2)==outputFromUser):
return 'cosh(variable1)'
elif(round(math.tanh(inputFromUser), 2)==outputFromUser):
return 'tanh(variable1)'
elif(round(math.asinh(inputFromUser), 2)==outputFromUser):
return 'asinh(variable1)'
elif(round(math.acosh(inputFromUser), 2)==outputFromUser):
return 'acosh(variable1)'
elif(round(math.atanh(inputFromUser), 2)==outputFromUser):
return 'atanh(variable1)'
else:
return '0'
def modelo(dr):
pi = math.pi
rho_c = 3 * 10**17 #densidad central
m_n = 1.68 * 10**(-27) #masa neutron
h = 6.62 * 10**-34 #constante de planck
c = 5.9 * 10**8 #velocidad luz
G = 6.67 * 10**(-11) #constante universal
M_sun = 1.989 * 10**(30)
p_f = ((3 / (8 * pi)) * (rho_c / m_n))**(1.0 / 3) * h #momento de fermi
x = float(((p_f)) / (m_n * c)) #x
e_c = rho_c * c**2
m = 0.0 #masa inicial
dm = 0
dP = 0
r = 1 #radio inicial
#listas
lista_P = []
lista_E = []
lista_m = []
lista_r = []
E = (((pi * m_n**4 * c**5) / h**3) * ((((x**2) + 1)**0.5 *
(2 * x**3 + x) - math.asinh(x))))
P = ((pi * m_n**4 * c**5) /
(3 * h**3)) * ((((x**2) + 1)**0.5 *
(2 * x**3 - 3 * x) + 3 * math.asinh(x)))
while P > 0:
dP_dr = -(
(G * (E / c**2.0 + P / c**2.0)) *
(m + 4.0 * pi * r**3 * P / c**2.0)) / (r * (r - 2 * G * m / c**2))
dP_dx = (((pi * m_n**4 * c**5) / (3 * h**3)) * ((8 * x**4) /
(x**2 + 1)**0.5))
dx = ((dP_dr) / (dP_dx)) * dr
dP = (((pi * m_n**4 * c**5) / (3 * h**3)) * ((8 * x**4) /
(x**2 + 1)**0.5)) * dx
dE_dx = (((pi * m_n**4 * c**5) / h**3) * ((8 * (x**4 + x**2)) /
(x**2 + 1)**0.5))
dE = (((pi * m_n**4 * c**5) / h**3) * ((8 * (x**4 + x**2)) /
(x**2 + 1)**0.5)) * dx
dm = ((4 * pi * E * r**2) / (c**2)) * dr
x = x + dx
m = m + dm
P = P + dP
r = r + dr
E = E + dE
lista_P.append(P)
lista_m.append(m)
lista_r.append(r)
lista_E.append(E)
return (np.array(lista_P), np.array(lista_m) / M_sun, np.array(lista_r),
np.array(lista_E) / e_c)
def NormalizeColumn(df, formant):
colIndex = range(1, 22)
cols = []
for i in colIndex:
col = formant + '_' + str(i)
cols.append(col)
df[col + '_Z'] = (df[col] - df[formant+ '_mean']) / df[formant+ '_stdev']
print(cols)
F_a = []
F_i = []
F_u = []
Z_a = []
Z_i = []
Z_u = []
for _, row in df.iterrows():
comps = row['Filename'].split('_')
age_gender = int(row['Filename'].split('_')[2])
if not age_gender % 2 == 1: # not male
continue
if not comps[0].startswith('norm'):
continue
if row['Annotation'] == 'a':
AddDataPoint(F_a, Z_a, row, cols)
continue
if row['Annotation'] == 'i':
AddDataPoint(F_i, Z_i, row, cols)
continue
if row['Annotation'] == 'u':
AddDataPoint(F_u, Z_u, row, cols)
continue
F_bar_a = mean(F_a)
F_bar_i = mean(F_i)
F_bar_u = mean(F_u)
F_bar = mean(F_a + F_i + F_u)
Z_bar_a = mean(Z_a)
Z_bar_i = mean(Z_i)
Z_bar_u = mean(Z_u)
Z_bar = mean(Z_a + Z_i + Z_u)
numerator = 0
numerator += abs(F_bar_a - F_bar)
numerator += abs(F_bar_i - F_bar)
numerator += abs(F_bar_u - F_bar)
denominator = 0
denominator = abs(Z_bar_a - Z_bar)
denominator += abs(Z_bar_i - Z_bar)
denominator += abs(Z_bar_u - Z_bar)
R = numerator / denominator
df[formant+'_R'] = R
for col in cols:
df[col + '_p'] = df[col + '_Z'] * df[formant + '_R']
F_p = []
for _, row in df.iterrows():
comps = row['Filename'].split('_')
age_gender = int(row['Filename'].split('_')[2])
if not age_gender % 2 == 1: # not male
continue
if not comps[0].startswith('norm'):
continue
for col in cols:
F_p.append(float(row[col+'_p']))
F_p_bar = mean(F_p)
df[formant+'_bar'] = F_bar
df[formant+'_p_bar'] = F_p_bar
for col in cols:
df[col + '_pp'] = df[col + '_p'] - \
(df[formant + '_p_bar'] - df[formant + '_bar'])
df[col + '_pp_bark'] = df[col+'_pp'].apply(lambda x:7 * math.asinh(x/650))
return df
def deg2num(lat_deg, lon_deg, zoom):
lat_rad = math.radians(lat_deg)
n = 2.0**zoom
xtile = (n / 360) * (lon_deg + 180)
ytile = (n / 2) * (1.0 - math.asinh(math.tan(lat_rad)) / math.pi)
return int(xtile), int(ytile)
def _deg2num(self, lat_deg, lon_deg, zoom):
lat_rad = radians(lat_deg)
n = 2.0**zoom
xtile = (lon_deg + 180.0) / 360.0 * n
ytile = (1.0 - asinh(tan(lat_rad)) / pi) / 2.0 * n
return (xtile, ytile)