def _n_Z(Omega, c10, Dt, loc_q, loc_ym, loc_yp, loc_alcc, loc_alss, loc_bsc, loc_bcs):
arg1 = cmath.sqrt(2.0*loc_yp)/2.0/Dt/c10
arg2 = cmath.sqrt(2.0*loc_ym)/2.0/Dt/c10
return ((loc_alcc*cmath.cosh(arg1)*cmath.cosh(arg2) +
loc_alss*cmath.sinh(arg1)*cmath.sinh(arg2) + loc_q)/
(loc_bsc*cmath.sinh(arg1)*cmath.cosh(arg2) +
loc_bcs*cmath.cosh(arg1)*cmath.sinh(arg2)))
def test_cosh(self):
self.assertAlmostEqual(qmath.cosh(self.f1), math.cosh(self.f1))
self.assertAlmostEqual(qmath.cosh(self.c1), cmath.cosh(self.c1))
self.assertAlmostEqual(qmath.cosh(self.c2), cmath.cosh(self.c2))
self.assertAlmostEqual(qmath.cosh(Quat(self.f1)), math.cosh(self.f1))
self.assertAlmostEqual(qmath.cosh(Quat(0, 3)), cmath.cosh(3J))
self.assertAlmostEqual(qmath.cosh(Quat(4, 5)), cmath.cosh(4 + 5J))
self.assertAlmostEqual(qmath.cosh(Quat(0, self.f1)), Quat(math.cos(self.f1)))
def _N11(Omega, c10, j0, Dt, loc_t, loc_ym, loc_yp, loc_gcm, loc_gcp, loc_gsm, loc_gsp):
twoDtc10 = 2.0*Dt*c10
return (2.0*cmath.sqrt(2.0*loc_t)*c10*j0*(cmath.sqrt(loc_ym)*cmath.sinh(cmath.sqrt(2.0*loc_ym)/twoDtc10) -
cmath.sqrt(loc_yp)*cmath.sinh(cmath.sqrt(2.0*loc_yp)/twoDtc10))/
(loc_gcm*cmath.cosh(cmath.sqrt(2.0*loc_ym)/twoDtc10) +
loc_gcp*cmath.cosh(cmath.sqrt(2.0*loc_yp)/twoDtc10) +
loc_gsm*cmath.sinh(cmath.sqrt(2.0*loc_ym)/twoDtc10) +
loc_gsp*cmath.sinh(cmath.sqrt(2.0*loc_yp)/twoDtc10)))
def cosh(c):
"""Compute Cosh using a Taylor expansion
"""
if not isinstance(c,pol): return math.cosh(c)
a0,p=c.separate();
lst=[math.cosh(a0),math.sinh(a0)]
for n in range(2,c.order+1):
lst.append( lst[-2]/n/(n-1))
return phorner(lst,p)
def test_cosh_cc (self):
src_data = [complex(i,i+1) for i in range(-5, 5, 2)]
expected_result = tuple(cmath.cosh(i) for i in src_data)
src = gr.vector_source_c(src_data)
op = gr.transcendental('cosh', 'complex_float')
snk = gr.vector_sink_c()
self.tb.connect(src, op, snk)
self.tb.run()
result = snk.data()
self.assertComplexTuplesAlmostEqual(expected_result, result, places=5)
def cosh(*args, **kw):
arg0 = args[0]
if isinstance(arg0, (int, float, long)):
return _math.cosh(*args,**kw)
elif isinstance(arg0, complex):
return _cmath.cosh(*args,**kw)
elif isinstance(arg0, _sympy.Basic):
return _sympy.cosh(*args,**kw)
else:
return _numpy.cosh(*args,**kw)
def test_complex_functions():
for x in (list(range(10)) + list(range(-10,0))):
for y in (list(range(10)) + list(range(-10,0))):
z = complex(x, y)/4.3 + 0.01j
assert exp(mpc(z)).ae(cmath.exp(z))
assert log(mpc(z)).ae(cmath.log(z))
assert cos(mpc(z)).ae(cmath.cos(z))
assert sin(mpc(z)).ae(cmath.sin(z))
assert tan(mpc(z)).ae(cmath.tan(z))
assert sinh(mpc(z)).ae(cmath.sinh(z))
assert cosh(mpc(z)).ae(cmath.cosh(z))
assert tanh(mpc(z)).ae(cmath.tanh(z))
def oneArgFuncEval(function, value):
# Evaluates functions that take a complex number input
if function == "sin":
return cmath.sin(value)
elif function == "cos":
return cmath.cos(value)
elif function == "tan":
return cmath.tan(value)
elif function == "asin":
return cmath.asin(value)
elif function == "acos":
return cmath.acos(value)
elif function == "atan":
return cmath.atan(value)
elif function == "csc":
return 1.0 / cmath.sin(value)
elif function == "sec":
return 1.0 / cmath.cos(value)
elif function == "cot":
return 1.0 / cmath.tan(value)
elif function == "ln":
return cmath.log(value)
elif function == "sqr":
return cmath.sqrt(value)
elif function == "abs":
return cmath.sqrt((value.real ** 2) + (value.imag ** 2))
elif function == "exp":
return cmath.exp(value)
if function == "sinh":
return cmath.sinh(value)
elif function == "cosh":
return cmath.cosh(value)
elif function == "tanh":
return cmath.tanh(value)
elif function == "asinh":
return cmath.asinh(value)
elif function == "acosh":
return cmath.acosh(value)
elif function == "atanh":
return cmath.atanh(value)
elif function == "ceil":
return math.ceil(value.real) + complex(0, 1) * math.ceil(value.imag)
elif function == "floor":
return math.floor(value.real) + complex(0, 1) * math.floor(value.imag)
elif function == "trunc":
return math.trunc(value.real) + complex(0, 1) * math.trunc(value.imag)
elif function == "fac":
if value.imag == 0 and value < 0 and value.real == int(value.real):
return "Error: The factorial function is not defined on the negative integers."
return gamma(value + 1)
elif function == "log":
return cmath.log10(value)
def setTransmission(self, gl, Z0): ''' gl = l*gamma l = length gamma = a + j*b a - attenuation constant b - phase constant Z0 - characteristic impedance ''' ch = cmath.cosh(gl) sh = cmath.sinh(gl) self.a = np.array( [ [ch, sh*Z0], [sh/Z0, ch] ]); pass
def cosh(x):
"""
Return the hyperbolic cosine of x.
"""
if isinstance(x,ADF):
ad_funcs = list(map(to_auto_diff,[x]))
x = ad_funcs[0].x
########################################
# Nominal value of the constructed ADF:
f = cosh(x)
########################################
variables = ad_funcs[0]._get_variables(ad_funcs)
if not variables or isinstance(f, bool):
return f
########################################
# Calculation of the derivatives with respect to the arguments
# of f (ad_funcs):
lc_wrt_args = [sinh(x)]
qc_wrt_args = [cosh(x)]
cp_wrt_args = 0.0
########################################
# Calculation of the derivative of f with respect to all the
# variables (Variable) involved.
lc_wrt_vars,qc_wrt_vars,cp_wrt_vars = _apply_chain_rule(
ad_funcs,variables,lc_wrt_args,qc_wrt_args,
cp_wrt_args)
# The function now returns an ADF object:
return ADF(f, lc_wrt_vars, qc_wrt_vars, cp_wrt_vars)
else:
# try: # pythonic: fails gracefully when x is not an array-like object
# return [cosh(xi) for xi in x]
# except TypeError:
if x.imag:
return cmath.cosh(x)
else:
return math.cosh(x.real)
def __init__(self, Var_txt, count_plot, name):
self.Var = dict()
for var in Var_txt:
if var[0] == "comp":
self.Var[var[0]] = []
for i in range(1,len(var)):
self.Var[var[0]].append(float(var[i])/100)
else:
self.Var[var[0]] = float(var[1])
self.file_name = name
self.r = self.Var["r"]
self.L = self.Var["L"]
self.C = self.Var["C"]
self.g = self.Var["g"]
self.l = self.Var["l"]
self.V1 = self.Var["V1"]
self.Vb = self.V1
self.Sb = 100e6
self.fp = self.Var["fp"]
self.f = self.Var["f"]
self.prec = self.Var["prec"]
self.w = 2 * cm.pi * self.f
self.count_plot = count_plot
self.U1 = self.V1 / cm.sqrt(3).real
self.Z = (self.r + 1j * self.w * self.L) * self.l
self.Y = (self.g + 1j * self.w * self.C) * self.l
self.Zc = cm.sqrt(self.Z / self.Y)
self.gamal = cm.sqrt(self.Z * self.Y)
self.A = cm.cosh(self.gamal)
self.B = self.Zc * cm.sinh(self.gamal)
self.C = 1 / self.Zc * cm.sinh(self.gamal)
self.D = self.A
self.result = self.calc_Vr(self.A, self.B)
self.result2 = self.compSeM()
self.result3 = self.compSeEx()
#self.ang_pot = self.calc_ang_pot(self.A,self.B,np.array(self.result[0])/3,np.array(self.result[1])/np.sqrt(3))
self.plot_all_Vr()
def do_transfer_function(length,freq,type=3, measure="m"):
'''
Let the transfer function default to type 3;
Allows for easy default change later
Allows for easy 'case-based' changes
'''
'''
Z=impedance/l, Y=admittance/l
Z=R+jwL, Y=G+jwC
Z0=Characteristic Impedence, gamma=propagation constant
Z0=sqrt(Z/Y), gamma=sqrt(Z*Y)
Should Use PyGSL, but start off with cmath
'''
#Length must be in KM
if measure == "m":
length /= 1000
elif measure == "km":
pass
else: raise TypeError('Improper measurement scale used')
w = 2 * pi * freq
#log.debug("Freq=%f,Len=%d",freq,length)
Z = complex(_R(freq),w*_L(freq))
Y = complex(_G(freq),w*_C(freq))
Z0 = cmath.sqrt(Z/Y)
gamma = cmath.sqrt(Z*Y)
gammad=gamma*length
Zs = complex(100,0)
Zl = complex(100,0)
upper = Z0 * ( 1/cmath.cosh(gammad)) #sech=1/cosh
lower = Zs * ( (Z0/Zl) + cmath.tanh(gammad) ) + Z0 * ( 1+ (Z0/Zl)*cmath.tanh(gammad) )
H = upper/lower
H*=H
return cmath.polar(H)[0] #polar returns (abs(h),real(h))
def exp_mat2_full_scalar(X, t, exp_Xt):
s = 0.5 * (X[0,0] + X[1,1])
det_X_minus_sI = (X[0,0]-s) * (X[1,1]-s) - X[0,1] * X[1,0]
q = cmath.sqrt(-det_X_minus_sI)
# we have to distinguish the case q=0 (the other exceptional case t=0 should not occur)
if abs(q) < 1e-15: # q is (numerically) 0
sinh_qt_over_q = t
else:
sinh_qt_over_q = cmath.sinh(q*t) / q
cosh_qt = cmath.cosh(q*t)
cosh_q_t_minus_s_sinh_qt_over_qt = cosh_qt - s*sinh_qt_over_q
exp_st = cmath.exp(s*t)
# abbreviations for the case of exp_Xt referencing the same array as X
E_00 = exp_st * (cosh_q_t_minus_s_sinh_qt_over_qt + sinh_qt_over_q * X[0,0])
E_01 = exp_st * (sinh_qt_over_q * X[0,1])
E_10 = exp_st * (sinh_qt_over_q * X[1,0])
E_11 = exp_st * (cosh_q_t_minus_s_sinh_qt_over_qt + sinh_qt_over_q * X[1,1])
exp_Xt[0,0] = E_00
exp_Xt[0,1] = E_01
exp_Xt[1,0] = E_10
exp_Xt[1,1] = E_11
print('arc sine =', cmath.asin(c))
print('arc cosine =', cmath.acos(c))
print('arc tangent =', cmath.atan(c))
print('sine =', cmath.sin(c))
print('cosine =', cmath.cos(c))
print('tangent =', cmath.tan(c))
# hyperbolic functions
c = 2 + 2j
print('inverse hyperbolic sine =', cmath.asinh(c))
print('inverse hyperbolic cosine =', cmath.acosh(c))
print('inverse hyperbolic tangent =', cmath.atanh(c))
print('hyperbolic sine =', cmath.sinh(c))
print('hyperbolic cosine =', cmath.cosh(c))
print('hyperbolic tangent =', cmath.tanh(c))
# classification functions
print(cmath.isfinite(2 + 2j)) # True
print(cmath.isfinite(cmath.inf + 2j)) # False
print(cmath.isinf(2 + 2j)) # False
print(cmath.isinf(cmath.inf + 2j)) # True
print(cmath.isinf(cmath.nan + 2j)) # False
print(cmath.isnan(2 + 2j)) # False
print(cmath.isnan(cmath.inf + 2j)) # False
print(cmath.isnan(cmath.nan + 2j)) # True
def rpn_calc(input, angle_mode = 0):
global stack
single_arg_funcs = ['exp','sqrt','sin','asin','cos','acos','tan','atan', 'sinh','asinh','cosh','acosh','tanh',
'atanh','!', 'polar']
num, arg, option = parse(input)
#print(num, arg, option)
#print('\n')
if arg == None and (num != None or num != 'Error'):
config.stack.append(num)
history.append('Entered number: ' + str(num) )
return config.stack
# Simple arithmatic-----------------------------------------------------------------------
if option == None and num != None:
if arg not in single_arg_funcs:
last = config.stack.pop()
if arg == '+':
try:
result = Decimal(last) + Decimal(num)
hist = str(last) + '+' + str(num) + '=' + str(result)
except TypeError:
result = last + num
hist = str(last) + '+' + str(num) + '=' + str(result)
if arg == '-':
try:
result = Decimal(last) - Decimal(num)
hist = str(last) + '-' + str(num) + '=' + str(result)
except TypeError:
result = last - num
hist = str(last) + '-' + str(num) + '=' + str(result)
if arg == '*':
try:
result = Decimal(last) * Decimal(num)
hist = str(last) + '*' + str(num) + '=' + str(result)
except TypeError:
result = last * num
hist = str(last) + '*' + str(num) + '=' + str(result)
if arg == '/':
try:
result = Decimal(last) / Decimal(num)
hist = str(last) + '/' + str(num) + '=' + str(result)
except TypeError:
result = last / num
hist = str(last) + '/' + str(num) + '=' + str(result)
if arg == '**':
try:
result = pow(Decimal(last), Decimal(num) )
hist = str(last) + '**' + str(num) + '=' + str(result)
except TypeError:
result = last ** num
hist = str(last) + '**' + str(num) + '=' + str(result)
if arg == 'rt':
try:
result = root(Decimal(last), Decimal(num) )
hist = str(last) + 'raised to 1 over ' + str(num) + '=' + str(result)
except TypeError:
result = root(last + num)
hist = str(last) + 'raised to 1 over ' + str(num) + '=' + str(result)
if arg == '%':
try:
result = Decimal(last) % Decimal(num)
hist = str(last) + '%' + str(num) + '=' + str(result)
except TypeError:
result = last % num
hist = str(last) + '%' + str(num) + '=' + str(result)
if arg == '!':
try:
result = Decimal(math.factorial(num))
hist = str(num) + '!' + '=' + str(result)
except TypeError:
result = math.factorial(num)
hist = str(num) + '!' + '=' + str(result)
if arg == 'exp':
try:
result = math.exp(Decimal(num))
hist = str(num) + 'exp' + '=' + str(result)
except ValueError:
result = cmath.exp(Decimal(num))
hist = str(num) + 'exp' + '=' + str(result)
except TypeError:
result = cmath.exp(num)
hist = str(num) + 'exp' + '=' + str(result)
if arg == 'sqrt':
try:
result = math.sqrt(Decimal(num))
hist = str(num) + 'sqrt' + '=' + str(result)
except ValueError:
result = cmath.sqrt(Decimal(num))
hist = str(num) + 'sqrt' + '=' + str(result)
except TypeError:
result = cmath.sqrt(num)
hist = str(num) + 'sqrt' + '=' + str(result)
if arg == 'log':
try:
result = math.log10(Decimal(num))
hist = str(num) + 'log10' + '=' + str(result)
except ValueError:
result = cmath.log10(Decimal(num))
hist = str(num) + 'log10' + '=' + str(result)
except TypeError:
result = cmath.log10(num)
hist = str(num) + 'log10' + '=' + str(result)
#=================================
if arg == 'ln':
try:
result = math.log(Decimal(num))
hist = str(num) + 'ln' + '=' + str(result)
except ValueError:
result = cmath.log(Decimal(num))
hist = str(num) + 'ln' + '=' + str(result)
except TypeError:
result = cmath.log(num)
hist = str(num) + 'ln' + '=' + str(result)
#--------TRIG--------------------------------
if arg == 'sin':
if angle_mode == 1:
try:
result = math.sin(Decimal(num))
hist = 'sin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.sin(num)
hist = 'sin' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.sin(math.radians(Decimal(num)))
hist = 'sin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.sin(num)
hist = 'sin' + str(num) + '=' + str(result)
if arg == 'cos':
if angle_mode == 1:
try:
result = math.cos(Decimal(num))
hist = 'cos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.cos(num)
hist = 'cos' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.cos(math.radians(Decimal(num)))
hist = 'cos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.cos(num)
hist = 'cos' + str(num) + '=' + str(result)
if arg == 'tan':
if angle_mode == 1:
try:
result = math.tan(Decimal(num))
hist = 'tan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.tan(num)
hist = 'tan' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.tan(math.radians(Decimal(num)))
hist = 'tan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.tan(num)
hist = 'tan' + str(num) + '=' + str(result)
if arg == 'asin':
if angle_mode == 1:
try:
result = math.asin(Decimal(num))
hist = 'asin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.asin(num)
hist = 'asin' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.asin(math.radians(Decimal(num)))
hist = 'asin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.asin(num)
hist = 'asin' + str(num) + '=' + str(result)
if arg == 'acos':
if angle_mode == 1:
try:
result = math.acos(Decimal(num))
hist = 'acos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.acos(num)
hist = 'acos' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.acos(math.radians(Decimal(num)))
hist = 'acos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.acos(num)
hist = 'acos' + str(num) + '=' + str(result)
if arg == 'atan':
if angle_mode == 1:
try:
result = math.atan(Decimal(num))
hist = 'atan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.atan(num)
hist = 'atan' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.atan(math.radians(Decimal(num)))
hist = 'atan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.atan(num)
hist = 'atan' + str(num) + '=' + str(result)
if arg == 'sinh':
try:
result = math.sinh(Decimal(num))
hist = 'sinh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.sinh(num)
hist = 'sinh' + str(num) + '=' + str(result)
if arg == 'cosh':
try:
result = math.cosh(Decimal(num))
hist = 'cosh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.cosh(num)
hist = 'cosh' + str(num) + '=' + str(result)
if arg == 'tanh':
try:
result = math.tanh(Decimal(num))
hist = 'tanh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.tanh(num)
hist = 'tanh' + str(num) + '=' + str(result)
if arg == 'asinh':
try:
result = math.asinh(Decimal(num))
hist = 'asinh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.asinh(num)
hist = 'asinh' + str(num) + '=' + str(result)
if arg == 'acosh':
try:
result = math.acosh(Decimal(num))
hist = 'acosh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.acosh(num)
hist = 'acosh' + str(num) + '=' + str(result)
if arg == 'atanh':
try:
result = math.atanh(Decimal(num))
hist = 'atanh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.atanh(num)
hist = 'atanh' + str(num) + '=' + str(result)
if arg == 'rect': #continue here....
try:
result = rect(last, num)
hist = 'Convert ' + str(last) + ',' + str(num) + ' to rectangular coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to rectangular coords. No result.'
if arg == 'polar':
try:
result = polar(num)
hist = 'Convert ' + str(num) + ' to polar coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to polar coords. No result.'
config.stack.append(result)
history.append(hist)
return config.stack
#=======================================================================================================================
#----Only argument passed-----------------------------------------------------------------------------------------------
#=======================================================================================================================
elif option == None and num == None:
last = config.stack.pop()
if arg not in single_arg_funcs:
try:
n_minus1 = config.stack.pop()
except IndexError:
try:
config.stack.append(Decimal(last))
except TypeError:
config.stack.append(last)
except TypeError:
config.stack.append(last)
except Exception as e:
return 'Error'
if arg == '+':
try:
result = Decimal(n_minus1) + Decimal(last)
hist = str(n_minus1) + '+' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 + last
hist = str(n_minus1) + '+' + str(last) + '=' + str(result)
if arg == '-':
try:
result = Decimal(n_minus1) - Decimal(last)
hist = str(n_minus1) + '-' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 - last
hist = str(n_minus1) + '-' + str(last) + '=' + str(result)
if arg == '*':
try:
result = Decimal(n_minus1) * Decimal(last)
hist = str(n_minus1) + '*' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 * last
hist = str(n_minus1) + '*' + str(last) + '=' + str(result)
if arg == '/':
try:
result = Decimal(n_minus1) / Decimal(last)
hist = str(n_minus1) + '/' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 / last
hist = str(n_minus1) + '/' + str(last) + '=' + str(result)
if arg == '!':
try:
result = Decimal(math.factorial(last))
hist = str(last) + '!' '=' + str(result)
except TypeError:
result = math.factorial(last)
hist = str(last) + '!' '=' + str(result)
except OverflowError:
config.stack.append(last)
hist = str('Factorial overflow error, no result.')
return 'Error'
if arg == '**':
try:
result = pow(Decimal(last), Decimal(last))
hist = str(n_minus1) + '**' + str(last) + '=' + str(result)
except TypeError:
result = last ** last
hist = str(n_minus1) + '**' + str(last) + '=' + str(result)
if arg == 'log':
try:
result = math.log10(Decimal(last))
hist = str(last) +'log10' + '=' + str(result)
except ValueError:
result = cmath.log10(Decimal(last))
hist = str(last) +'log10' + '=' + str(result)
except TypeError:
result = cmath.log10(last)
hist = str(last) +'log10' + '=' + str(result)
if arg == 'ln':
try:
result = math.log(Decimal(last))
hist = str(last) +'ln' + '=' + str(result)
except ValueError:
result = cmath.log(Decimal(last))
hist = str(last) +'ln' + '=' + str(result)
except TypeError:
result = cmath.log(last)
hist = str(last) +'ln' + '=' + str(result)
if arg == 'rt':
try:
result = root(Decimal(last), Decimal(n_minus1))
hist = str(n_minus1) + 'root' + str(last) + '=' + str(result)
except TypeError:
result = root(last), (n_minus1)
hist = str(n_minus1) + 'root' + str(last) + '=' + str(result)
if arg == 'exp':
try:
result = math.exp(Decimal(last))
hist = str(last) +'exp' + '=' + str(result)
except TypeError:
result = cmath.exp(last)
hist = str(last) +'exp' + '=' + str(result)
if arg == 'sqrt':
try:
result = math.sqrt(Decimal(last))
hist = 'Square root of ' + str(last) + '=' + str(result)
except ValueError:
result = cmath.sqrt(Decimal(last))
hist = 'Square root of ' + str(last) + '=' + str(result)
except TypeError:
result = cmath.sqrt(last)
hist = 'Square root of ' + str(last) + '=' + str(result)
#----------Trig----------------------------------------
#--------TRIG--------------------------------
if arg == 'sin':
if angle_mode == 1:
try:
result = math.sin(Decimal(last))
hist = 'sin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.sin(last)
hist = 'sin' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.sin(math.radians(Decimal(last)))
hist = 'sin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.sin(last)
hist = 'sin' + str(last) + '=' + str(result)
if arg == 'cos':
if angle_mode == 1:
try:
result = math.cos(Decimal(last))
hist = 'cos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.cos(last)
hist = 'cos' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.cos(math.radians(Decimal(last)))
hist = 'cos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.cos(last)
hist = 'cos' + str(last) + '=' + str(result)
if arg == 'tan':
if angle_mode == 1:
try:
result = math.tan(Decimal(last))
hist = 'tan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.tan(last)
hist = 'tan' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.tan(math.radians(Decimal(last)))
hist = 'tan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.tan(last)
hist = 'tan' + str(last) + '=' + str(result)
if arg == 'asin':
if angle_mode == 1:
try:
result = math.asin(Decimal(last))
hist = 'asin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.asin(last)
hist = 'asin' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.asin(math.radians(Decimal(last)))
hist = 'asin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.asin(last)
hist = 'asin' + str(last) + '=' + str(result)
if arg == 'acos':
if angle_mode == 1:
try:
result = math.acos(Decimal(last))
hist = 'acos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.acos(last)
hist = 'acos' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.acos(math.radians(Decimal(last)))
hist = 'acos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.acos(last)
hist = 'acos' + str(last) + '=' + str(result)
if arg == 'atan':
if angle_mode == 1:
try:
result = math.atan(Decimal(last))
hist = 'atan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.atan(last)
hist = 'atan' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.atan(math.radians(Decimal(last)))
hist = 'atan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.atan(last)
hist = 'atan' + str(last) + '=' + str(result)
if arg == 'sinh':
try:
result = math.sinh(Decimal(last))
hist = 'sinh' + str(last) + '=' + str(result)
except TypeError:
result = math.sinh(last)
hist = 'sinh' + str(last) + '=' + str(result)
if arg == 'cosh':
try:
result = math.cosh(Decimal(last))
hist = 'cosh' + str(last) + '=' + str(result)
except TypeError:
result = math.cosh(last)
hist = 'cosh' + str(last) + '=' + str(result)
if arg == 'tanh':
try:
result = math.tanh(Decimal(last))
hist = 'tanh' + str(last) + '=' + str(result)
except TypeError:
result = math.tanh(last)
hist = 'tanh' + str(last) + '=' + str(result)
if arg == 'asinh':
try:
result = math.asinh(Decimal(last))
hist = 'asinh' + str(last) + '=' + str(result)
except TypeError:
result = math.asinh(last)
hist = 'asinh' + str(last) + '=' + str(result)
if arg == 'acosh':
try:
result = math.acosh(Decimal(last))
hist = 'acosh' + str(last) + '=' + str(result)
except TypeError:
result = math.acosh(last)
hist = 'acosh' + str(last) + '=' + str(result)
if arg == 'atanh':
try:
result = math.atanh(Decimal(last))
hist = 'atanh' + str(last) + '=' + str(result)
except TypeError:
result = math.atanh(last)
hist = 'atanh' + str(last) + '=' + str(result)
if arg == 'rect': #continue here....
try:
result = rect(n_minus1, last)
hist = 'Convert ' + str(n_minus1) + ',' + str(last) + ' to rectangular coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to rectangular coords. No result.'
if arg == 'polar':
try:
result = polar(last)
hist = 'Convert complex value ' + str(last) + ' to rectangular coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to polar coords. No result.'
config.stack.append(result)
history.append(hist)
return config.stack
complexHyp_real = int(
input(
'Enter the real part of the complex number that you want to find the sinh, cosh, or tanh of:'
))
complexHyp_imaginary = int(
input(
'Enter the imaginary part of the complex number that you want to find the sinh, cosh, or tanh of: '
))
complexHyp = complex(complexHyp_real, complexHyp_imaginary)
print('The sinh of ' + str(complexHyp) + ' is ' +
str(cmath.sinh(complexHyp)) + ".")
print("The cosh of " + str(complexHyp) + " is " +
str(cmath.cosh(complexHyp)) + ".")
print("The tanh of " + str(complexHyp) + " is " +
str(cmath.tanh(complexHyp)) + ".")
elif (complexTriginput.lower()).strip() in acceptedComplexArcHyp:
complexArcHype_real = int(
input(
"Enter the real part of the complex number that you want to find the arcsinh, arccosh, or arctanh of: "
))
complexArcHype_imaginary = int(
input(
"Enter the imaginary part of the complex number that you want to find the arcsinh, arcosh, or arctanh of: "
))
complexArcHype = complex(complexArcHype_real,
def Cheb(m, x):
if (abs(x) <= 1):
return math.cos(m * math.acos(x))
else:
return (cmath.cosh(m * cmath.acosh(x))).real
def test_cosh(self):
self.assertAlmostEqual(complex(-6.58066, -7.58155),
cmath.cosh(complex(3, 4)))
def calculate_deflection(system):
# get global variables
[length_left] = length_left_glob.data["length_left"]
[length_right] = length_right_glob.data["length_right"]
[lam] = lam_glob.data["lam"]
A1,A2,A3,A4,B1,B2,B3,B4 = create_matrix_and_calculate_coefficients(system)
y_beam = np.zeros(n_beam, dtype=complex)
if (length_left != 0 and length_right != 0) or (length_left != 0 and system=="Fixed-Free Beam"): # otherwise the beam is not deformed
i = 0
while i < n_beam:
if x_beam[i] <= length_left: # for the subsystem on the left
y_beam[i] = -1*(A1*cm.sin(lam/L*x_beam[i])+A2*cm.cos(lam/L*x_beam[i])+A3*cm.sinh(lam/L*x_beam[i])+A4*cm.cosh(lam/L*x_beam[i]))
else: # for the subsystem on the right
y_beam[i] = -1*(B1*cm.sin(lam/L*(x_beam[i]-length_left))+B2*cm.cos(lam/L*(x_beam[i]-length_left))+B3*cm.sinh(lam/L*(x_beam[i]-length_left))+B4*cm.cosh(lam/L*(x_beam[i]-length_left)))
i+=1
# scales the deflection to a maximum amplitude of 3
max_value = np.amax(np.absolute(y_beam))
y_beam = y_beam * (3/max_value)
beam_coordinates_source.data = dict(x=x_beam,y=y_beam.real)
'cos': lambda x: cmath.cos(x),
'tan': lambda x: cmath.tan(x),
'csc': lambda x: 1/cmath.sin(x),
'sec': lambda x: 1/cmath.cos(x),
'cot': lambda x: 1/cmath.tan(x),
'ln': lambda x: cmath.log(x),
'log': lambda x: cmath.log(x)/cmath.log(10),
'fact': lambda x: factorial(int(x)),
'asin': lambda x: cmath.asin(x),
'acos': lambda x: cmath.acos(x),
'atan': lambda x: cmath.atan(x),
'acsc': lambda x: cmath.asin(1/x),
'asec': lambda x: cmath.acos(1/x),
'acot': lambda x: cmath.atan(1/x),
'sinh': lambda x: cmath.sinh(x),
'cosh': lambda x: cmath.cosh(x),
'tanh': lambda x: cmath.tanh(x),
'csch': lambda x: 1/cmath.sinh(x),
'sech': lambda x: 1/cmath.cosh(x),
'coth': lambda x: 1/cmath.tanh(x),
'asinh': lambda x: cmath.asinh(x),
'acosh': lambda x: cmath.acosh(x),
'atanh': lambda x: cmath.atanh(x),
'acsch': lambda x: cmath.asinh(1/x),
'asech': lambda x: cmath.acosh(1/x),
'acoth': lambda x: cmath.atanh(1/x)
}
def replace_variables(phrase, replacement, var = 'x'):
"""Replaces all instances of a named variable in a phrase with a
replacement, 'x' by default."""
#------------------------------------------------------------------------------ # Hyperbolic functions - real version x = 0.5 assert abs(cosh(x) - math.cosh(x)) < 1e-14 assert abs(sinh(x) - math.sinh(x)) < 1e-14 assert abs(tanh(x) - math.tanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Hyperbolic functions - complex version x = 0.5j assert abs(cosh(x) - cmath.cosh(x)) < 1e-14 assert abs(sinh(x) - cmath.sinh(x)) < 1e-14 assert abs(tanh(x) - cmath.tanh(x)) < 1e-14 assert abs(acosh(x) - cmath.acosh(x)) < 1e-14 assert abs(asinh(x) - cmath.asinh(x)) < 1e-14 assert abs(atanh(x) - cmath.atanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Rounding operations. assert type(round(0.5)) is mpf assert type(round(mpq(1, 2))) is mpf assert type(floor(0.5)) is mpf assert type(ceil(0.5)) is mpf
def UndeformedFBG(self,FBGOriginalWavel,PhotoElasticParam,InitialRefractiveIndex,MeanChangeRefractiveIndex,FringeVisibility,MinBandWidth,MaxBandWidth,SimulationResolution):
"""
Function to Simulate the Undeformed FBG signal
Input:
FBGOriginalWavel: List(Mandatory)
List with the FBG array original wavelength
PhotoElasticParam: float (Mandatory)
Photo-Elastic parameter
InitialRefractiveIndex: float (Mandatory)
Initial effective refractive index (neff)
MeanChangeRefractiveIndex: float (Mandatory)
Mean induced change in the refractive index (dneff)
FringeVisibility: float (Mandatory)
Fringe Visibility (Fv)
MinBandWidth: float (Mandatory)
Light Min. Bandwidth
MaxBandWidth: float (Mandatory)
SimulationResolution: float (Mandatory)
Simulation resolution- Wavelength increment
"""
self.FBGOriginalWavel=FBGOriginalWavel
self.PhotoElasticParam=PhotoElasticParam
self.InitialRefractiveIndex=InitialRefractiveIndex
self.MeanChangeRefractiveIndex=MeanChangeRefractiveIndex
self.FringeVisibility=FringeVisibility
self.MinBandWidth=MinBandWidth
self.MaxBandWidth=MaxBandWidth
self.SimulationResolution=SimulationResolution
#Array with the Original FBG period
self.APFBG=[]
for i in np.arange(0,self.NumberFBG):
self.APFBG.append(self.FBGOriginalWavel[i]*(1-self.MeanChangeRefractiveIndex/self.InitialRefractiveIndex)/(2.0*self.InitialRefractiveIndex))
#Empty Original Reflec spectrum
self.OReflect={}
self.OReflect['wavelength']=[]
self.OReflect['reflec']=[]
#Cycle all the FBG sensors
for i in np.arange(0,self.NumberFBG):
# Wavelength cycle (Here the simulation resolution is used)
for l in np.arange(self.MinBandWidth,self.MaxBandWidth,self.SimulationResolution):
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
M=20.0 #Sections the gratting is divided-- Transfer Matrix
#FBG increment size (nm)
deltz=(self.FBGLength*(10.0**6))/M
for z in np.arange(0,M):
#Sigma Function
sig=2.0*math.pi*self.InitialRefractiveIndex*((1.0/l)-(1.0/(2.0*self.InitialRefractiveIndex*self.APFBG[i])))+(2*math.pi*self.MeanChangeRefractiveIndex/l)
#Kaa Function
kaa=math.pi*self.FringeVisibility*self.MeanChangeRefractiveIndex/l
#Gamma Function
gammab=cmath.sqrt(kaa**2.0-sig**2.0)
#Transfer Matrix Calculation
f11=complex(cmath.cosh(gammab*deltz),-(sig/gammab)*cmath.sinh(gammab*deltz))
f22=complex(cmath.cosh(gammab*deltz),(sig/gammab)*cmath.sinh(gammab*deltz))
f12=complex(0,-(kaa/gammab)*cmath.sinh(gammab*deltz))
f21=complex(0,+(kaa/gammab)*cmath.sinh(gammab*deltz))
#Assemble Transfer Matrix
f1=np.dot(f1,np.matrix([[f11, f12],[ f21, f22]]))
PO=f1[0,0]
NO=f1[1,0]
REF=abs(NO/PO)**2
self.OReflect['wavelength'].append(l)
self.OReflect['reflec'].append(REF)
def p_expression_cosh(t):
'expression : COSH expression'
t[0] = cmath.cosh(t[2])
def p_expression_sech(t):
'expression : SECH expression'
t[0] = 1/cmath.cosh(t[2])
def Heston_cf(self,u):
""" Define a function that computes the characteristic function for variance gamma
"""
sigma = self.sigma
eta0 = self.eta0
kappa = self.kappa
rho = self.rho
theta = self.theta
S0 = self.S0
r = self.r
T = self.T
ii = complex(0,1)
l = cmath.sqrt(sigma**2*(u**2+ii*u)+(kappa-ii*rho*sigma*u)**2)
w = np.exp(ii*u*np.log(S0)+ii*u*(r-0)*T+kappa*theta*T*(kappa-ii*rho*sigma*u)/sigma**2)/(cmath.cosh(l*T/2)+(kappa-ii*rho*sigma*u)/l*cmath.sinh(l*T/2))**(2*kappa*theta/sigma**2)
y = w*np.exp(-(u**2+ii*u)*eta0/(l/cmath.tanh(l*T/2)+kappa-ii*rho*sigma*u))
return y
def mycotanh(z):
return cmath.cosh(z)/cmath.sinh(z)
def cosh(self):
comp_value = cmath.cosh(self.comp_value)
dxr = cmath.sinh(self.comp_value)
comp_unc = self.comp_unc * dxr # if y = coshx than U(y) = U(x)sinhx
return Ucom(comp_value, comp_unc, self.name, self.dep)
def activation(self, x, derive=False):
if derive == True:
i = 1 / (cmath.cosh(x))**2
return i.real
return cmath.tanh(x).real
def NonUniformStrain(self,FBGOriginalWavel,PhotoElasticParam,InitialRefractiveIndex,MeanChangeRefractiveIndex,FringeVisibility,MinBandWidth,MaxBandWidth,SimulationResolution,FBGDirection):
"""
Function to Simulate the FGB Spectrum Considering Non-Uniform Strain
effects
Input:
FBGOriginalWavel: List(Mandatory)
List with the FBG array original wavelength
PhotoElasticParam: float (Mandatory)
Photo-Elastic parameter
InitialRefractiveIndex: float (Mandatory)
Initial effective refractive index (neff)
MeanChangeRefractiveIndex: float (Mandatory)
Mean induced change in the refractive index (dneff)
FringeVisibility: float (Mandatory)
Fringe Visibility (Fv)
MinBandWidth: float (Mandatory)
Light Min. Bandwidth
MaxBandWidth: float (Mandatory)
SimulationResolution: float (Mandatory)
Simulation resolution- Wavelength increment
FBGDirection: int (mandatory)
0-xx 1-yy 2-zz
"""
self.FBGOriginalWavel=FBGOriginalWavel
self.PhotoElasticParam=PhotoElasticParam
self.InitialRefractiveIndex=InitialRefractiveIndex
self.MeanChangeRefractiveIndex=MeanChangeRefractiveIndex
self.FringeVisibility=FringeVisibility
self.MinBandWidth=MinBandWidth
self.MaxBandWidth=MaxBandWidth
self.SimulationResolution=SimulationResolution
self.FBGDirection=FBGDirection
#Array with the original FBG period
self.APFBG=[]
for i in np.arange(0,self.NumberFBG):
self.APFBG.append(self.FBGOriginalWavel[i]/(2.0*self.InitialRefractiveIndex))
#Empty Reflec spectrum -Uniform Strain
self.NUSReflect={}
self.NUSReflect['wavelength']=[]
self.NUSReflect['reflec']=[]
#Cycle all the FBG sensors
for i in np.arange(0,self.NumberFBG):
#Sections the gratting is divided-- Transfer Matrix
M=len(self.FBGArray['FBG'+str(i+1)]['x'])
#FBG increment size (nm)
deltz=(self.FBGLength*(10.0**6))/M
#----Built the grating period chenged by the Non-uniform strain---
FBGperiod=[]
for j in np.arange(0,M):
if self.FBGDirection==0: #FBG longitudinal direction (xx)
FBGperiod.append(self.APFBG[i]*(1+(1-self.PhotoElasticParam)*self.FBGArray['FBG'+str(i+1)]['LE11'][j]))
if self.FBGDirection==1: #FBG longitudinal direction (yy)
FBGperiod.append(self.APFBG[i]*(1+(1-self.PhotoElasticParam)*self.FBGArray['FBG'+str(i+1)]['LE22'][j]))
if self.FBGDirection==2: #FBG longitudinal direction (zz)
FBGperiod.append(self.APFBG[i]*(1+(1-self.PhotoElasticParam)*self.FBGArray['FBG'+str(i+1)]['LE33'][j]))
# Wavelength cycle (Here the simulation resolution is used)
for l in np.arange(self.MinBandWidth,self.MaxBandWidth,self.SimulationResolution):
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
#Cycle-Each FBG increment
for z in np.arange(0,M):
#Sigma Function
sig=2.0*math.pi*self.InitialRefractiveIndex*((1.0/l)-(1.0/(2.0*self.InitialRefractiveIndex*FBGperiod[z])))+(2*math.pi*self.MeanChangeRefractiveIndex/l)
#Kaa Function
kaa=math.pi*self.FringeVisibility*self.MeanChangeRefractiveIndex/l
#Gamma Function
gammab=cmath.sqrt(kaa**2.0-sig**2.0)
#Transfer Matrix Calculation
f11=complex(cmath.cosh(gammab*deltz),-(sig/gammab)*cmath.sinh(gammab*deltz))
f22=complex(cmath.cosh(gammab*deltz),(sig/gammab)*cmath.sinh(gammab*deltz))
f12=complex(0,-(kaa/gammab)*cmath.sinh(gammab*deltz))
f21=complex(0,+(kaa/gammab)*cmath.sinh(gammab*deltz))
#Assemble Transfer Matrix
f1=np.dot(f1,np.matrix([[f11, f12],[ f21, f22]]))
#Add to the Reflection file
PO=f1[0,0]
NO=f1[1,0]
REF=abs(NO/PO)**2
self.NUSReflect['wavelength'].append(l)
self.NUSReflect['reflec'].append(REF)
def calculate_amp_and_phase():
# get global variables
[length_left] = length_left_glob.data["length_left"]
[length_right] = length_right_glob.data["length_right"]
[lam] = lam_glob.data["lam"]
[EI] = EI_glob.data["EI"]
y_amp = np.zeros(n_r, dtype=complex)
if (length_left != 0 and length_right != 0 and float(lfa_coordinates_source.data['x'][0]) != 0 and float(lfa_coordinates_source.data['x'][0]) != L) or (system_select.value=="Fixed-Free Beam" and float(lfa_coordinates_source.data['x'][0]) != 0 and length_left != 0): # otherwise the amplitude is zero for every excitation frequency
j = 0.04
i = 0
while j < max_r:
lam_temp = calculate_lambda(system_select.value, j, EI) # calculates lambda for every frequency ratio
lam_glob.data = dict(lam=[lam_temp])
A1,A2,A3,A4,B1,B2,B3,B4 = create_matrix_and_calculate_coefficients(system_select.value)
if lfa_coordinates_source.data['x'][0] <= length_left: # for the subsystem on the left
y_amp[i] = -1*EI/(F*(L**3))*(A1*cm.sin(lam_temp/L*lfa_coordinates_source.data['x'][0])+A2*cm.cos(lam_temp/L*lfa_coordinates_source.data['x'][0])
+A3*cm.sinh(lam_temp/L*lfa_coordinates_source.data['x'][0])+A4*cm.cosh(lam_temp/L*lfa_coordinates_source.data['x'][0]))
else: # for the subsystem on the right
y_amp[i] = -1*EI/(F*(L**3))*(B1*cm.sin(lam_temp/L*(lfa_coordinates_source.data['x'][0]-length_left))+B2*cm.cos(lam_temp/L*(lfa_coordinates_source.data['x'][0]-length_left))
+B3*cm.sinh(lam_temp/L*(lfa_coordinates_source.data['x'][0]-length_left))+B4*cm.cosh(lam_temp/L*(lfa_coordinates_source.data['x'][0]-length_left)))
j+=0.02
i+=1
for i in range(0,n_r):
if slider_damping.value == 0:
y_phase[i] = cm.phase(y_amp[i]) # calculate the phase angle for every exitation frequency ratio
else:
y_phase[i] = -cm.phase(y_amp[i])
y_amp[i] = abs(y_amp[i]) # calculate the absolute value
# update plotting variables
amp_coordinates_source.data['y'] = y_amp.real
phase_coordinates_source.data['y'] = y_phase
lam_glob.data = dict(lam=[lam])
def mycotanh(z):
return cmath.cosh(z) / cmath.sinh(z)
def test_cosh(self):
self.assertAlmostEqual(complex(-6.58066, -7.58155),
cmath.cosh(complex(3, 4)))
def dA1dsigm(theta, u, t):
return (u**2 * 1j * u) * t / 2 * dddsigm(theta, u) * cm.cosh(
de(theta, u) * t / 2)
def TransverseStrain(self,FBGOriginalWavel,PhotoElasticParam,InitialRefractiveIndex,MeanChangeRefractiveIndex,FringeVisibility,MinBandWidth,MaxBandWidth,SimulationResolution,FBGDirection,DirectionalRefractiveP11,DirectionalRefractiveP12,YoungsModule,PoissionsCoefficient):
"""
Function to Simulate the FGB Spectrum Considering Uniform longitudinal strain
and transverse Stress
Input:
FBGOriginalWavel: List(Mandatory)
List with the FBG array original wavelength
PhotoElasticParam: float (Mandatory)
Photo-Elastic parameter
InitialRefractiveIndex: float (Mandatory)
Initial effective refractive index (neff)
MeanChangeRefractiveIndex: float (Mandatory)
Mean induced change in the refractive index (dneff)
FringeVisibility: float (Mandatory)
Fringe Visibility (Fv)
MinBandWidth: float (Mandatory)
Light Min. Bandwidth
MaxBandWidth: float (Mandatory)
SimulationResolution: float (Mandatory)
Simulation resolution- Wavelength increment
FBGDirection: int (mandatory)
0-xx 1-yy 2-zz
DirectionalRefractiveP11: float (Mandatory)
Directional Photo-elastic coeffic
DirectionalRefractiveP12: float (Mandatory)
Directional Photo-elastic coefficient
YoungsModule: float (Mandatory)
Optical Fibre Young's Module
PoissionsCoefficient: float (Mandatory)
Optical Fibre Poisson Ration
"""
self.FBGOriginalWavel=FBGOriginalWavel
self.PhotoElasticParam=PhotoElasticParam
self.InitialRefractiveIndex=InitialRefractiveIndex
self.MeanChangeRefractiveIndex=MeanChangeRefractiveIndex
self.FringeVisibility=FringeVisibility
self.MinBandWidth=MinBandWidth
self.MaxBandWidth=MaxBandWidth
self.SimulationResolution=SimulationResolution
self.FBGDirection=FBGDirection
self.DirectionalRefractiveP11=DirectionalRefractiveP11
self.DirectionalRefractiveP12=DirectionalRefractiveP12
self.YoungsModule=YoungsModule/10**6 #Change to MPA
self.PoissionsCoefficient=PoissionsCoefficient
#Array with the FBG period- Longitudinal Strain
self.APFBG=[]
for i in np.arange(0,self.NumberFBG):
if self.FBGDirection==0: #FBG longitudinal direction (xx)
TempMeanFBG=np.mean(self.FBGArray['FBG'+str(i+1)]['LE11'] )#Strain average
TempnewWavelength=self.FBGOriginalWavel[i]*(1+(1-self.PhotoElasticParam)*TempMeanFBG) #weavelength at uniform strain
self.APFBG.append(TempnewWavelength/(2.0*self.InitialRefractiveIndex)) # Grating period at strain state
if self.FBGDirection==1: #FBG longitudinal direction (yy)
TempMeanFBG=np.mean(self.FBGArray['FBG'+str(i+1)]['LE22'] )#Strain average
TempnewWavelength=self.FBGOriginalWavel[i]*(1+(1-self.PhotoElasticParam)*TempMeanFBG) #weavelength at uniform strain
self.APFBG.append(TempnewWavelength/(2.0*self.InitialRefractiveIndex)) # Grating period at strain state
if self.FBGDirection==2: #FBG longitudinal direction (zz)
TempMeanFBG=np.mean(self.FBGArray['FBG'+str(i+1)]['LE33'] )#Strain average
TempnewWavelength=self.FBGOriginalWavel[i]*(1+(1-self.PhotoElasticParam)*TempMeanFBG) #weavelength at uniform strain
self.APFBG.append(TempnewWavelength/(2.0*self.InitialRefractiveIndex)) # Grating period at strain state
#Empty Reflec spectrum- Two waves
self.TSYReflect={}#Y wave
self.TSYReflect['wavelength']=[]
self.TSYReflect['reflec']=[]
self.TSZReflect={}#Z wave
self.TSZReflect['wavelength']=[]
self.TSZReflect['reflec']=[]
#Cycle all the FBG sensors
for i in np.arange(0,self.NumberFBG):
#Sections the gratting is divided-- Transfer Matrix
M=len(self.FBGArray['FBG'+str(i+1)]['x'])
#FBG increment size (nm)
deltz=(self.FBGLength*(10.0**6))/M
#Build a List with the change in the refractive index DeltaNEffY
self.Dneffy=[]
self.Dneffz=[]
for j in np.arange(0,M):
if self.FBGDirection==0: #FBG longitudinal direction (xx)
DirecX='S11'
DirecY='S22'
DirecZ='S33'
self.Dneffy.append(-(self.InitialRefractiveIndex**3.0)/(2*self.YoungsModule)
*((self.DirectionalRefractiveP11-2*self.PoissionsCoefficient*self.DirectionalRefractiveP12)*self.FBGArray['FBG'+str(i+1)][DirecY][j]
+((1-self.PoissionsCoefficient)*self.DirectionalRefractiveP12-self.PoissionsCoefficient*self.DirectionalRefractiveP11)
*(self.FBGArray['FBG'+str(i+1)][DirecZ][j]+self.FBGArray['FBG'+str(i+1)][DirecX][j])))
self.Dneffz.append(-(self.InitialRefractiveIndex**3.0)/(2*self.YoungsModule)
*((self.DirectionalRefractiveP11-2*self.PoissionsCoefficient*self.DirectionalRefractiveP12)*self.FBGArray['FBG'+str(i+1)][DirecZ][j]
+((1-self.PoissionsCoefficient)*self.DirectionalRefractiveP12-self.PoissionsCoefficient*self.DirectionalRefractiveP11)
*(self.FBGArray['FBG'+str(i+1)][DirecY][j]+self.FBGArray['FBG'+str(i+1)][DirecX][j])))
if self.FBGDirection==1: #FBG longitudinal direction (yy)
DirecX='S22'
DirecY='S11' #need to be negative
DirecZ='S33'
self.Dneffy.append(-(self.InitialRefractiveIndex**3.0)/(2*self.YoungsModule)
*((self.DirectionalRefractiveP11-2*self.PoissionsCoefficient*self.DirectionalRefractiveP12)*(-self.FBGArray['FBG'+str(i+1)][DirecY][j])
+((1-self.PoissionsCoefficient)*self.DirectionalRefractiveP12-self.PoissionsCoefficient*self.DirectionalRefractiveP11)
*(self.FBGArray['FBG'+str(i+1)][DirecZ][j]+self.FBGArray['FBG'+str(i+1)][DirecX][j])))
self.Dneffz.append(-(self.InitialRefractiveIndex**3.0)/(2*self.YoungsModule)
*((self.DirectionalRefractiveP11-2*self.PoissionsCoefficient*self.DirectionalRefractiveP12)*self.FBGArray['FBG'+str(i+1)][DirecZ][j]
+((1-self.PoissionsCoefficient)*self.DirectionalRefractiveP12-self.PoissionsCoefficient*self.DirectionalRefractiveP11)
*(-self.FBGArray['FBG'+str(i+1)][DirecY][j]+self.FBGArray['FBG'+str(i+1)][DirecX][j])))
if self.FBGDirection==2: #FBG longitudinal direction (zz)
DirecX='S33'
DirecY='S22'
DirecZ='S11'#Negative
self.Dneffy.append(-(self.InitialRefractiveIndex**3.0)/(2*self.YoungsModule)
*((self.DirectionalRefractiveP11-2*self.PoissionsCoefficient*self.DirectionalRefractiveP12)*self.FBGArray['FBG'+str(i+1)][DirecY][j]
+((1-self.PoissionsCoefficient)*self.DirectionalRefractiveP12-self.PoissionsCoefficient*self.DirectionalRefractiveP11)
*(-self.FBGArray['FBG'+str(i+1)][DirecZ][j]+self.FBGArray['FBG'+str(i+1)][DirecX][j])))
self.Dneffz.append(-(self.InitialRefractiveIndex**3.0)/(2*self.YoungsModule)
*((self.DirectionalRefractiveP11-2*self.PoissionsCoefficient*self.DirectionalRefractiveP12)*(-self.FBGArray['FBG'+str(i+1)][DirecZ][j])
+((1-self.PoissionsCoefficient)*self.DirectionalRefractiveP12-self.PoissionsCoefficient*self.DirectionalRefractiveP11)
*(self.FBGArray['FBG'+str(i+1)][DirecY][j]+self.FBGArray['FBG'+str(i+1)][DirecX][j])))
# Wavelength cycle (Here the simulation resolution is used)
#YWave
for l in np.arange(self.MinBandWidth,self.MaxBandWidth,self.SimulationResolution):
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
#Cycle-Each FBG increment
for z in np.arange(0,M):
#Sigma Function
sig=2.0*math.pi*(self.InitialRefractiveIndex+self.Dneffy[z])*((1.0/l)-(1.0/(2.0*(self.InitialRefractiveIndex+self.Dneffy[z])*self.APFBG[i])))+(2*math.pi*self.MeanChangeRefractiveIndex/l)
#Kaa Function
kaa=math.pi*self.FringeVisibility*self.MeanChangeRefractiveIndex/l
#Gamma Function
gammab=cmath.sqrt(kaa**2.0-sig**2.0)
#Transfer Matrix Calculation
f11=complex(cmath.cosh(gammab*deltz),-(sig/gammab)*cmath.sinh(gammab*deltz))
f22=complex(cmath.cosh(gammab*deltz),(sig/gammab)*cmath.sinh(gammab*deltz))
f12=complex(0,-(kaa/gammab)*cmath.sinh(gammab*deltz))
f21=complex(0,+(kaa/gammab)*cmath.sinh(gammab*deltz))
#Assemble Transfer Matrix
f1=np.dot(f1,np.matrix([[f11, f12],[ f21, f22]]))
#Add to the Reflection file- YWave
PO=f1[0,0]
NO=f1[1,0]
REF=abs(NO/PO)**2
self.TSYReflect['wavelength'].append(l) #Output File
self.TSYReflect['reflec'].append(REF) #Output File
#ZWave
for l in np.arange(self.MinBandWidth,self.MaxBandWidth,self.SimulationResolution):
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
#Cycle-Each FBG increment
for z in np.arange(0,M):
#Sigma Function
sig=2.0*math.pi*(self.InitialRefractiveIndex+self.Dneffz[z])*((1.0/l)-(1.0/(2.0*(self.InitialRefractiveIndex+self.Dneffz[z])*self.APFBG[i])))+(2*math.pi*self.MeanChangeRefractiveIndex/l)
#Kaa Function
kaa=math.pi*self.FringeVisibility*self.MeanChangeRefractiveIndex/l
#Gamma Function
gammab=cmath.sqrt(kaa**2.0-sig**2.0)
#Transfer Matrix Calculation
f11=complex(cmath.cosh(gammab*deltz),-(sig/gammab)*cmath.sinh(gammab*deltz))
f22=complex(cmath.cosh(gammab*deltz),(sig/gammab)*cmath.sinh(gammab*deltz))
f12=complex(0,-(kaa/gammab)*cmath.sinh(gammab*deltz))
f21=complex(0,+(kaa/gammab)*cmath.sinh(gammab*deltz))
#Assemble Transfer Matrix
f1=np.dot(f1,np.matrix([[f11, f12],[ f21, f22]]))
#Add to the Reflection file- YWave
PO=f1[0,0]
NO=f1[1,0]
REF=abs(NO/PO)**2
self.TSZReflect['wavelength'].append(l) #Output File
self.TSZReflect['reflec'].append(REF) #Output File
Power and Log Functions
The cmath() module provides some useful functions for logarithmic
and power operations.
"""
c = 1+2j
print('e^c = ', cmath.exp(c))
print('log2(c) = ', cmath.log(c,2))
print('log10(c) = ', cmath.log10(c))
print('sqrt(c) = ', cmath.sqrt(c))
"""
Trigonometric Functions
"""
c = 2+4j
print('arc sine value:\n ', cmath.asin(c))
print('arc cosine value:\n ', cmath.acos(c))
print('arc tangent value:\n ', cmath.atan(c))
print('sine value:\n ', cmath.sin(c))
print('cosine value:\n ', cmath.cos(c))
print('tangent value:\n ', cmath.tan(c))
"""
Hyperbolic Functions
"""
c = 2+4j
print('Inverse hyperbolic sine value: \n', cmath.asinh(c))
print('Inverse hyperbolic cosine value: \n', cmath.acosh(c))
print('Inverse hyperbolic tangent value: \n', cmath.atanh(c))
print('Inverse sine value: \n', cmath.sinh(c))
print('Inverse cosine value: \n', cmath.cosh(c))
print('Inverse tangent value: \n', cmath.tanh(c))
def dA1drho(theta, u, t):
return -1j * u * (u**2 + 1j * u) * t * xi(theta, u) * theta[4] / (
2 * de(theta, u)) * cm.cosh(de(theta, u) * t / 2)
def COSH(df, price='Close'):
"""
Hyperbolic Cosine
Returns: list of floats = jhta.COSH(df, price='Close')
"""
return [cmath.cosh(df[price][i]).real for i in range(len(df[price]))]
def dA2drho(theta, u, t):
return -theta[4] * 1j * u * (2 + t * xi(theta, u)) / (
2 * de(theta, u)) * (xi(theta, u) * cm.cosh(de(theta, u) * t / 2) +
de(theta, u) * cm.sinh(de(theta, u) * t / 2))
def compute_zx_polar(Z0, L, q, x):
'''computes the polar represntation of Zx (equation 2.8 in Gals thesis)
'''
ZX = Z0 * cmath.cosh(q * (L - x)) / cmath.cosh(q * L)
ZX = cmath.polar(ZX)
return ZX
def cosh(a, b):
result = a**2 + b**2
return cmath.cosh(result) + 1.6j
def Intergration (self,u):
sigma = self.sigma
eta = self.eta
kappa = self.kappa
rho = self.rho
theta = self.theta
S0 = self.S0
r = self.r
T = self.T
ii = complex(0,1)
l = cmath.sqrt( sigma ** 2 * ( u ** 2 + ii * u ) + ( kappa - ii * rho * sigma * u) ** 2)
w = np.exp(ii * u * np.log(S0) + ii * u * (r - 0) * T + kappa * theta * T * (kappa - ii * rho * sigma * u)/ sigma ** 2)/(cmath.cosh(l * T/2) + (kappa - ii * rho * sigma * u) / l * cmath.sinh(l * T/2)) ** (2 * kappa * theta/sigma**2)
E = w * np.exp(-(u ** 2 + ii * u) * eta/( l / cmath.tanh( l * T/2) + kappa - ii * rho * sigma * u))
return E
def cosh(a):
return (cmath.cosh(a) if (a.__class__ == mpc) else math.cosh(a))
print('arc sine =', cmath.asin(c))
print('arc cosine =', cmath.acos(c))
print('arc tangent =', cmath.atan(c))
print('sine =', cmath.sin(c))
print('cosine =', cmath.cos(c))
print('tangent =', cmath.tan(c))
# hyperbolic functions
c = 2 + 2j
print('inverse hyperbolic sine =', cmath.asinh(c))
print('inverse hyperbolic cosine =', cmath.acosh(c))
print('inverse hyperbolic tangent =', cmath.atanh(c))
print('hyperbolic sine =', cmath.sinh(c))
print('hyperbolic cosine =', cmath.cosh(c))
print('hyperbolic tangent =', cmath.tanh(c))
# classification functions
print(cmath.isfinite(2 + 2j)) # True
print(cmath.isfinite(cmath.inf + 2j)) # False
print(cmath.isinf(2 + 2j)) # False
print(cmath.isinf(cmath.inf + 2j)) # True
print(cmath.isinf(cmath.nan + 2j)) # False
print(cmath.isnan(2 + 2j)) # False
print(cmath.isnan(cmath.inf + 2j)) # False
print(cmath.isnan(cmath.nan + 2j)) # True
print(cmath.isclose(2 + 2j, 2.01 + 1.9j, rel_tol=0.05)) # True
def cos_impl(z):
"""cmath.cos(z) = cmath.cosh(z j)"""
return cmath.cosh(complex(-z.imag, z.real))
def calculations(parameters):
#Receving the input parameters from the user_input function
system = parameters["system"]
phase_spacing_sym = parameters['phase_spacing_sym']
a1 = parameters["a1"]
b1 = parameters["b1"]
c1 = parameters["c1"]
no_sub_conductors = parameters["no_subconductors"]
sub_cond_spacing = parameters["sub_cond_spacing"]
no_strands = parameters["no_strands"]
d = parameters["diameter"]
length = parameters["length_of_line"]
model = parameters["model"]
resistance = parameters["resistance"]
freq = parameters["freq"]
nom_volt = parameters["nom_volt"]
power_rec = parameters["load"]
pf = parameters["pf"]
#Receiving End Voltage
VR = nom_volt / math.sqrt(3)
#Calculating radius---r
a = 3
b = -3
c = 1 - no_strands
# calculate the discriminant
di = (b**2) - (4 * a * c)
# find two solutions
sol1 = (-b - cmath.sqrt(di)) / (2 * a)
sol2 = (-b + cmath.sqrt(di)) / (2 * a)
if (sol1.real >= sol2.real):
n = sol1.real
else:
n = sol2.real
D = (2 * n - 1) * d
r = D / 2
# Inductance---L
if (system == 1):
if (no_sub_conductors == 2):
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / (math.pow(r, 1) * math.exp(
-1 / 4) * math.pow(sub_cond_spacing, 1))
q = math.pow(i, 1 / h)
print(q)
elif (no_sub_conductors == 3):
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / math.pow(
r * math.pow(sub_cond_spacing, 2) * math.exp(-1 / 4), 3)
q = math.pow(i, 1 / h)
print(q)
elif (no_sub_conductors == 4):
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / math.pow(
r * math.pow(sub_cond_spacing, 3) * math.exp(-1 / 4) *
math.sqrt(2), 4)
q = math.pow(i, 1 / h)
else:
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / math.pow(
r * math.exp(-1 / 4) * math.pow(sub_cond_spacing, 5) * 6, 6)
q = math.pow(i, 1 / h)
else:
if (no_sub_conductors == 2):
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.exp(-1 / (4 * no_sub_conductors)) * math.pow(
r, 1 / no_sub_conductors) * math.pow(sub_cond_spacing,
1 / no_sub_conductors)
q = h / i
elif (no_sub_conductors == 3):
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(r * math.pow(sub_cond_spacing, 2) * math.exp(-1 / 4),
1 / no_sub_conductors)
q = h / i
elif (no_sub_conductors == 4):
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(
math.sqrt(2) * r * math.pow(sub_cond_spacing, 3) *
math.exp(-1 / 4), 1 / no_sub_conductors)
q = h / i
else:
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(
6 * r * math.pow(sub_cond_spacing, 5) * math.exp(-1 / 4),
1 / no_sub_conductors)
q = h / i
L = 2 * math.pow(10, -4) * math.log(q)
#Capacitance---Cap
if (model == 1):
Cap = 0
else:
if (system == 1):
if (no_sub_conductors == 2):
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / (
math.pow(r, 1) * math.pow(sub_cond_spacing, 1))
q = math.pow(i, 1 / h)
print(q)
elif (no_sub_conductors == 3):
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / math.pow(
r * math.pow(sub_cond_spacing, 2), 3)
q = math.pow(i, 1 / h)
print(q)
elif (no_sub_conductors == 4):
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / math.pow(
r * math.pow(sub_cond_spacing, 3) * math.sqrt(2), 4)
q = math.pow(i, 1 / h)
else:
h = math.pow(no_sub_conductors, 2)
i = math.pow(phase_spacing_sym, 6) / math.pow(
r * math.pow(sub_cond_spacing, 5) * 6, 6)
q = math.pow(i, 1 / h)
else:
if (no_sub_conductors == 2):
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(r, 1 / no_sub_conductors) * math.pow(
sub_cond_spacing, 1 / no_sub_conductors)
q = h / i
elif (no_sub_conductors == 3):
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(r * math.pow(sub_cond_spacing, 2),
1 / no_sub_conductors)
q = h / i
elif (no_sub_conductors == 4):
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(
math.sqrt(2) * r * math.pow(sub_cond_spacing, 3),
1 / no_sub_conductors)
q = h / i
else:
h = math.pow(a1 * b1 * c1, 1 / 3)
i = math.pow(6 * r * math.pow(sub_cond_spacing, 5),
1 / no_sub_conductors)
q = h / i
Cap = 2 * math.pi * 8.84 * math.pow(10, -9) / math.log(q)
# Inductive Reactance---XL
XL = 2 * math.pi * freq * L * length
#Capacitive Reactance---XC
if (model == 1):
XC = "infinite"
else:
XC = 1 / (2 * math.pi * freq * Cap * length)
# ABCD paramters
if (model == 1):
Y = 0
else:
Y = complex(0, 1 / XC)
Z = complex(resistance * length, XL)
if (model == 1):
A = 1
B = Z
C = Y
D = 1
elif (model == 2):
A = 1 + Y * Z / 2
B = Z
C = Y * (1 + Y * Z / 4)
D = 1 + Y * Z / 2
else:
A = cmath.cosh(cmath.sqrt(Y * Z))
B = cmath.sqrt(Z / Y) * cmath.sinh(cmath.sqrt(Y * Z))
C = cmath.sqrt(Y / Z) * cmath.sinh(cmath.sqrt(Y * Z))
D = cmath.cosh(cmath.sqrt(Y * Z))
# Sending end line voltage---VS
# Receving end current---IR
IR = power_rec * math.pow(10, 6) / (pf * VR * 3)
VS = (A * VR + IR * B)
#charging current---IC
if (model == 1):
IC = 0
elif (model == 2):
IC1 = VS * Y / 2
IC2 = VR * Y / 2
IC = IC1 + IC2
else:
IC = C * VR
# Sending end line Current----IS
IS = C * VR + D * IR
#Voltage Regulation---volt_reg
if (model == 1):
volt_reg = (abs(VS) - abs(VR)) * 100 / abs(VR)
else:
volt_reg = (abs(VS / A) - abs(VR)) * 100 / abs(VR)
#Power loss---power_loss
power_loss = 3 * IR.real * IR.real * resistance * length
#Transmission Efficiency---eff
eff = power_rec * 100 / (power_rec + power_loss * math.pow(10, -6))
#Angles
angle_1 = cmath.phase(A) #alpha
angle_2 = cmath.phase(B) #beta
# Sending end circle
x = -abs(A) * abs(VS / 1000) * abs(
VS / 1000) * math.cos(angle_2 - angle_1) / abs(B)
y = abs(A) * abs(VS / 1000) * abs(
VS / 1000) * math.sin(angle_2 - angle_1) / abs(B)
rad_1 = abs(VS / 1000) * abs(VR / 1000) / abs(B)
centre_1 = complex(x, y)
fig, ax = plt.subplots()
ax.set(xlim=(-5 * rad_1, 5 * rad_1), ylim=(-5 * rad_1, 5 * rad_1))
a_circle = plt.Circle((x, y), rad_1)
ax.add_artist(a_circle)
plt.title('Sending End Circle', fontsize=12)
plt.ylabel("Apparent Power")
plt.xlabel("Real Power")
plt.text(
100, 200, 'Centre= %s\n Radius = %s\n' %
("{:g}".format(centre_1), "{:.3f}".format(rad_1)))
#Receving end circle
x1 = -abs(A) * abs(VR / 1000) * abs(
VR / 1000) * math.cos(angle_2 - angle_1) / abs(B)
y1 = -abs(A) * abs(VR / 1000) * abs(
VR / 1000) * math.sin(angle_2 - angle_1) / abs(B)
rad_2 = abs(VS / 1000) * abs(VR / 1000) / abs(B)
centre_2 = complex(x1, y1)
fig, ax_1 = plt.subplots()
ax_1.set(xlim=(-5 * rad_2, 5 * rad_2), ylim=(-5 * rad_2, 5 * rad_2))
b_circle = plt.Circle((x1, y1), rad_2, color='r')
ax_1.add_artist(b_circle)
plt.title('Receving End Circle', fontsize=12)
plt.ylabel("Apparent Power")
plt.xlabel("Real Power")
plt.text(
100, 200, 'Centre= %s\n Radius = %s\n' %
("{:g}".format(centre_2), "{:.3f}".format(rad_2)))
plt.show()
#Dictionary to pass values to output function
features = {
"Inductance": L,
"Capacitance": Cap,
"XL": XL,
"XC": XC,
"IC": IC,
"A": A,
"B": B,
"C": C,
"D": D,
"VS": VS,
"IS": IS,
"volt_reg": volt_reg,
"power_loss": power_loss,
"eff": eff,
"centre_1": centre_1,
"rad_1": rad_1,
"centre_2": centre_2,
"rad_2": rad_2,
"model": model
}
return features
def cos_impl(z):
"""cmath.cos(z) = cmath.cosh(z j)"""
return cmath.cosh(complex(-z.imag, z.real))
def profileCalc(EkmanDepth_array, EkmanDepth_back, delta_array, frVelCpx_array, frVelCpx_back,
stratPar_array, stratPar_back, SBLHeight_array, roughLength_m_array, roughLength_m_back,
roughLength_h, roughLength_h_back, tempSurf, tempTop, temp_array, tempSurf_back,
tempScale_array, tempScale_back, windCpx_back_array, geostrWindCpx, dpar,
alpha_array, corPar, angle, epsilon, M, MODB):
CHARNOCKCONST = 0.018
GRAVITYACC = 9.8
OMEGA = 7.29e-5
VONKARMANCONST = 0.41
BETA = GRAVITYACC / 300
N = 50
zmax = max(max([x * 2 for x in EkmanDepth_array]), EkmanDepth_back)
hmax = zmax
hmin = 1
dlnz = math.log(hmax / hmin) / (N - 1)
J = 0
wind_prof = [[] for x in xrange(0, len(delta_array), 2)]
temp_prof = [[] for x in xrange(0, len(delta_array), 2)]
z_array = [[] for x in xrange(0, len(delta_array), 2)]
for i in xrange(0, len(delta_array), 2):
d = dpar[i] - epsilon
frVel = abs(frVelCpx_array[i])
lambInv = VONKARMANCONST * frVel / (EkmanDepth_array[i] * corPar)
profileFunc_m = profileFunc_momentum_Calc(lambInv, epsilon, stratPar_array[i])
u_h = frVelCpx_array[i] / VONKARMANCONST * (math.log(SBLHeight_array[i] / roughLength_m_array[i]) - profileFunc_m)
wind_prof_back = []
temp_prof_back = []
z = []
for indx in xrange(N):
z.append(hmin * math.exp(dlnz * indx))
if z[indx] <= epsilon * EkmanDepth_back:
stratPar = stratPar_back * z[indx] / (epsilon * EkmanDepth_back)
tmpLambInv = VONKARMANCONST * abs(frVelCpx_back) / (EkmanDepth_back * corPar)
profileFunc_m = profileFunc_momentum_Calc(tmpLambInv, epsilon, stratPar)
profileFunc_h = profileFunc_heat_Calc(tmpLambInv, epsilon, stratPar)
wind_prof_back.append(frVelCpx_back / VONKARMANCONST *
(math.log(z[indx] / roughLength_m_back) - profileFunc_m))
temp_prof_back.append(tempSurf_back + tempScale_back / VONKARMANCONST *
(math.log(z[indx] / roughLength_h_back) - profileFunc_h))
else:
dmax = M - epsilon
ksi = (z[indx] - epsilon * EkmanDepth_back) / (EkmanDepth_back * dmax)
tmpKsi = ksi
ksi = min(1, ksi)
coeff = (1 - 1j) * cmath.sinh((1 + 1j) * dmax * (1 - ksi)) / cmath.cosh((1 + 1j) * dmax)
wind_prof_back.append(geostrWindCpx - 1. / lambdaCalc(epsilon, stratPar_back) *
frVelCpx_back / VONKARMANCONST * coeff)
temp_prof_back.append(tempTop - 2. / lambdaCalc(epsilon, stratPar_back) *
tempScale_back / VONKARMANCONST * dmax * (1 - tmpKsi))
if z[indx] <= delta_array[i]:
if z[indx] <= SBLHeight_array[i]:
stratPar = stratPar_array[i] * z[indx] / SBLHeight_array[i]
profileFunc_m = profileFunc_momentum_Calc(lambInv, epsilon, stratPar)
profileFunc_h = profileFunc_heat_Calc(lambInv, epsilon, stratPar)
wind_prof[J].append(frVelCpx_array[i] / VONKARMANCONST *
(math.log(z[indx] / roughLength_m_array[i]) - profileFunc_m))
temp_prof[J].append(tempSurf + tempScale_array[i] / VONKARMANCONST *
(math.log(z[indx] / roughLength_h) - profileFunc_h))
else:
ksi = (z[indx] - SBLHeight_array[i]) / (delta_array[i] - SBLHeight_array[i])
tmpKsi = ksi
tmpKsi = ksi
ksi = min(1, ksi)
heatFlux = - frVel * tempScale_array[i]
alpha = alpha_array[i]
coeff1 = (1 - 1j) * cmath.sinh((1 + 1j) * d * (1 - ksi)) / cmath.cosh((1 + 1j) * d)
coeff2 = heatFlux * (1 - ksi)
tmpCoeff2 = 0
coeff3 = heatFlux * (1 - ksi)
coeff4 = BETA * d ** 2 / (corPar * abs(geostrWindCpx) * math.cos(angle) * (alpha + 1j * d ** 2))
coeff4 *= (coeff2 - tmpCoeff2)
coeff4 *= MODB
coeff5 = (windCpx_back_array[i] - geostrWindCpx) * \
cmath.cosh((1 + 1j) * d * ksi) / cmath.cosh((1 + 1j) * d)
wind_prof[J].append(geostrWindCpx - lambInv * frVelCpx_array[i] / VONKARMANCONST * coeff1\
+ coeff4 +coeff5)
temp_prof[J].append(temp_array[i] + 2. * lambInv * d * coeff3 / (frVel * VONKARMANCONST))
else:
wind_prof[J].append(wind_prof_back[indx])
temp_prof[J].append(temp_prof_back[indx])
z_array[J].append(z[indx])
J += 1
return wind_prof, temp_prof, z_array, wind_prof_back, temp_prof_back
def UndeformedFBG(self, SimulationResolution, MinBandWidth, MaxBandWidth,
InitialRefractiveIndex, MeanChangeRefractiveIndex,
FringeVisibility, DirectionalRefractiveP11,
DirectionalRefractiveP12, PoissonsCoefficient,
FBGOriginalWavel):
"""
Parameters
----------
SimulationResolution: float (Mandatory)
Simulation resolution- Wavelength increment
MinBandWidth: float (Mandatory)
Light Min. Bandwidth
MaxBandWidth: float (Mandatory)
Light Max. Bandwidth
InitialRefractiveIndex: float (Mandatory)
Initial effective refractive index (neff)
MeanChangeRefractiveIndex: float (Mandatory)
Mean induced change in the refractive index (dneff)
FringeVisibility: float (Mandatory)
Fringe Visibility (FV)
DirectionalRefractiveP11 : float (Mandatory)
Pockel’s normal photoelastic constant
DirectionalRefractiveP12 : float (Mandatory)
Pockel’s shear photoelastic constant
PoissonsCoefficient : float (Mandatory)
Poisson's Coefficient of fiber
FBGOriginalWavel: array (Mandatory)
Original wavelengths of FBG regions
Returns
-------
None.
"""
self.SimulationResolution = SimulationResolution
self.MinBandWidth = MinBandWidth
self.MaxBandWidth = MaxBandWidth
self.InitialRefractiveIndex = InitialRefractiveIndex
self.MeanChangeRefractiveIndex = MeanChangeRefractiveIndex
self.FringeVisibility = FringeVisibility
self.DirectionalRefractiveP11 = DirectionalRefractiveP11
self.DirectionalRefractiveP12 = DirectionalRefractiveP12
self.PoissonsCoefficient = PoissonsCoefficient
self.FBGOriginalWavel = FBGOriginalWavel
#Array with the Original FBG period
self.APFBG = []
for i in np.arange(0, self.NumberFBG):
self.APFBG.append(self.FBGOriginalWavel[i] /
(2.0 * self.InitialRefractiveIndex))
#Empty Original Reflec spectrum
self.OReflect = {}
self.OReflect['wavelength'] = []
self.OReflect['reflec'] = []
#Cycle all the FBG sensors
for i in np.arange(0, self.NumberFBG):
# Wavelength cycle (Here the simulation resolution is used)
for l in np.arange(self.MinBandWidth, self.MaxBandWidth,
self.SimulationResolution):
#print("---------- WAVELENGTH: "+str(l))
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
M = 20.0 #Sections the gratting is divided-- Transfer Matrix
#FBG increment size (nm)
deltz = (self.FBGLength * (10.0**6)) / M
for z in np.arange(0, M):
#Sigma Function
sig = 2.0 * math.pi * self.InitialRefractiveIndex * (
(1.0 / l) -
(1.0 /
(2.0 * self.InitialRefractiveIndex * self.APFBG[i]))
) + (2 * math.pi * self.MeanChangeRefractiveIndex / l)
#print("Sigma: "+str(sig))
#print("Lamb: "+str((2.0*self.InitialRefractiveIndex*self.APFBG[i])))
#Kaa Function
kaa = math.pi * self.FringeVisibility * self.MeanChangeRefractiveIndex / l
#print("Kaa: "+str(kaa))
#Gamma Function
gammab = cmath.sqrt(kaa**2.0 - sig**2.0)
#print("Gammab: "+str(gammab))
#Transfer Matrix Calculation
f11 = complex(cmath.cosh(gammab * deltz),
-(sig / gammab) * cmath.sinh(gammab * deltz))
f22 = complex(cmath.cosh(gammab * deltz),
(sig / gammab) * cmath.sinh(gammab * deltz))
f12 = complex(0,
-(kaa / gammab) * cmath.sinh(gammab * deltz))
f21 = complex(0,
+(kaa / gammab) * cmath.sinh(gammab * deltz))
#print("TM: "+str(gammab))
#Assemble Transfer Matrix
f1 = np.dot(f1, np.matrix([[f11, f12], [f21, f22]]))
#print("Transfer Matrix "+str(z)+": "+str(f1))
PO = f1[0, 0]
NO = f1[1, 0]
REF = abs(NO / PO)**2
#print("Reflectivity "+str(REF))
self.OReflect['wavelength'].append(l)
self.OReflect['reflec'].append(REF)
print(self.OReflect['wavelength'][0:15])
print(self.OReflect['reflec'][0:15])
def DeformedFBG(self, SimulationResolution, MinBandWidth, MaxBandWidth,
AmbientTemperature, InitialRefractiveIndex,
MeanChangeRefractiveIndex, FringeVisibility,
DirectionalRefractiveP11, DirectionalRefractiveP12,
YoungsModule, PoissonsCoefficient, ThermoOptic, StrainType,
StressType, EmulateTemperature,
FiberThermalExpansionCoefficient,
HostThermalExpansionCoefficient, FBGOriginalWavel):
"""
Parameters
----------
SimulationResolution: float (Mandatory)
Simulation resolution- Wavelength increment
MinBandWidth: float (Mandatory)
Light Min. Bandwidth
MaxBandWidth: float (Mandatory)
Light Max. Bandwidth
AmbientTemperature : float (Mandatory)
Base in which our reference temperature is set.
InitialRefractiveIndex: float (Mandatory)
Initial effective refractive index (neff)
MeanChangeRefractiveIndex: float (Mandatory)
Mean induced change in the refractive index (dneff)
FringeVisibility: float (Mandatory)
Fringe Visibility (FV)
DirectionalRefractiveP11 : float (Mandatory)
Pockel’s normal photoelastic constant
DirectionalRefractiveP12 : float (Mandatory)
Pockel’s shear photoelastic constant
YoungsModule : float (Mandatory)
Young's modulus of fiber
PoissonsCoefficient : float (Mandatory)
Poisson's Coefficient of fiber
ThermoOptic : float (Mandatory)
Thermo optic coefficient of fiber
StrainType : int (Mandatory)
0 for none, 1 for uniform, 2 for non-uniform
StressType : int (Mandatory)
0 for none, 1 for included
EmulateTemperature : float (Mandatory)
Theoretical emulated temperature of fiber
FiberThermalExpansionCoefficient : float (Mandatory)
Thermal expansion coefficient of fiber material
HostThermalExpansionCoefficient : float (Mandatory)
Thermal expansion coefficient of host material
FBGOriginalWavel: array (Mandatory)
Original wavelengths of FBG regions
Returns
-------
None.
"""
self.SimulationResolution = SimulationResolution
self.MinBandWidth = MinBandWidth
self.MaxBandWidth = MaxBandWidth
self.AmbientTemperature = AmbientTemperature
self.InitialRefractiveIndex = InitialRefractiveIndex
self.MeanChangeRefractiveIndex = MeanChangeRefractiveIndex
self.FringeVisibility = FringeVisibility
self.DirectionalRefractiveP11 = DirectionalRefractiveP11
self.DirectionalRefractiveP12 = DirectionalRefractiveP12
self.YoungsModule = YoungsModule
self.PoissonsCoefficient = PoissonsCoefficient
self.ThermoOptic = ThermoOptic
self.EmulateTemperature = EmulateTemperature
self.FiberThermalExpansionCoefficient = FiberThermalExpansionCoefficient
self.HostThermalExpansionCoefficient = HostThermalExpansionCoefficient
self.FBGOriginalWavel = FBGOriginalWavel
#Calculate photoelastic coef from directional coefs.
self.PhotoElasticParam = (self.InitialRefractiveIndex**2 / 2) * (
self.DirectionalRefractiveP12 - self.PoissonsCoefficient *
(self.DirectionalRefractiveP11 - self.DirectionalRefractiveP12))
#Determine if we need to emulate a theoretical temperature value
if self.EmulateTemperature != -1.0:
for i in np.arange(0, self.NumberFBG):
for j in range(len(self.FBGArray['FBG' + str(i + 1)]['T'])):
self.FBGArray['FBG' +
str(i + 1)]['T'][j] = self.EmulateTemperature
print(self.FBGArray['FBG' + str(i + 1)]['T'][0:5])
#Array with the original FBG periods
self.APFBG = []
for i in np.arange(0, self.NumberFBG):
self.APFBG.append(self.FBGOriginalWavel[i] /
(2.0 * self.InitialRefractiveIndex))
#Empty Reflec spectrum- Two waves (individual contributions to account for any transverse stress)
self.YReflect = {} #Y wave
self.YReflect['wavelength'] = []
self.YReflect['reflec'] = []
self.ZReflect = {} #Z wave
self.ZReflect['wavelength'] = []
self.ZReflect['reflec'] = []
#Empty Reflec spectrum- Composite wave of Y and Z contributions
self.DReflect = {} #Composite wave
self.DReflect['wavelength'] = []
self.DReflect['reflec'] = []
#Cycle all the FBG sensors
for i in np.arange(0, self.NumberFBG):
#Sections the gratting is divided-- Transfer Matrix
M = len(self.FBGArray['FBG' + str(i + 1)]['x'])
#FBG increment size (nm)
deltz = (self.FBGLength * (10.0**6)) / M
#--- STRAIN ---
FBGperiod = []
if StrainType == 0:
#--- Case of "no longitudinal strain" ---
for j in np.arange(0, M):
FBGperiod.append(self.APFBG[i])
elif StrainType == 1:
#--- Case of "uniform longitudinal strain" ---
StrainMeanFBG = np.mean(
self.FBGArray['FBG' + str(i + 1)]
['LE11']) #Strain average over FBG region
TempMeanFBG = np.mean(
self.FBGArray['FBG' + str(i + 1)]
['T']) #Temperature average over FBG region
TempnewWavelength = self.FBGOriginalWavel[i] * (
1 + (1 - self.PhotoElasticParam) * StrainMeanFBG +
(self.FiberThermalExpansionCoefficient +
(1 - self.PhotoElasticParam) *
(self.HostThermalExpansionCoefficient - self.
FiberThermalExpansionCoefficient) + self.ThermoOptic) *
(TempMeanFBG - self.AmbientTemperature)
) #weavelength at uniform strain and temperature
for j in np.arange(0, M):
FBGperiod.append(
TempnewWavelength /
(2.0 * self.InitialRefractiveIndex)) # Grating period
else:
#--- Case of "non-uniform longitudinal strain" build the grating period changed ---
for j in np.arange(0, M):
TempnewWavelength = self.FBGOriginalWavel[i] * (
1 + (1 - self.PhotoElasticParam) *
self.FBGArray['FBG' + str(i + 1)]['LE11'][j] +
(self.FiberThermalExpansionCoefficient +
(1 - self.PhotoElasticParam) *
(self.HostThermalExpansionCoefficient -
self.FiberThermalExpansionCoefficient) +
self.ThermoOptic) *
(self.FBGArray['FBG' + str(i + 1)]['T'][j] -
self.AmbientTemperature)
) #weavelength at nonuniform strain and temperature
#print(self.FBGArray['FBG'+str(i+1)]['T'][0]-self.AmbientTemperature)
FBGperiod.append(
TempnewWavelength /
(2.0 * self.InitialRefractiveIndex)) # Grating period
#--- STRESS ---
#Build a List with the change in the refractive index DeltaNEffY
self.Dneffy = []
self.Dneffz = []
if StressType == 0:
#--- Case of "no transverse stress" ---
for j in np.arange(0, M):
self.Dneffy.append(0)
self.Dneffz.append(0)
else:
#--- Case of "included transverse stress" ---
for j in np.arange(0, M):
DirecX = 'S11'
DirecY = 'S22'
DirecZ = 'S33'
self.Dneffy.append(
-(self.InitialRefractiveIndex**3.0) /
(2 * self.YoungsModule) *
((self.DirectionalRefractiveP11 -
2 * self.PoissonsCoefficient *
self.DirectionalRefractiveP12) *
self.FBGArray['FBG' + str(i + 1)][DirecY][j] +
((1 - self.PoissonsCoefficient) * self.
DirectionalRefractiveP12 - self.PoissonsCoefficient *
self.DirectionalRefractiveP11) *
(self.FBGArray['FBG' + str(i + 1)][DirecZ][j] +
self.FBGArray['FBG' + str(i + 1)][DirecX][j])))
self.Dneffz.append(
-(self.InitialRefractiveIndex**3.0) /
(2 * self.YoungsModule) *
((self.DirectionalRefractiveP11 -
2 * self.PoissonsCoefficient *
self.DirectionalRefractiveP12) *
self.FBGArray['FBG' + str(i + 1)][DirecZ][j] +
((1 - self.PoissonsCoefficient) * self.
DirectionalRefractiveP12 - self.PoissonsCoefficient *
self.DirectionalRefractiveP11) *
(self.FBGArray['FBG' + str(i + 1)][DirecY][j] +
self.FBGArray['FBG' + str(i + 1)][DirecX][j])))
#--- SIMULATION ---
#YWave
for l in np.arange(
self.MinBandWidth, self.MaxBandWidth,
self.SimulationResolution
): # Wavelength cycle (Here the simulation resolution is used)
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
#Cycle-Each FBG increment
for z in np.arange(0, M):
#Sigma Function
sig = 2.0 * math.pi * (
self.InitialRefractiveIndex + self.Dneffy[z]) * (
(1.0 / l) -
(1.0 /
(2.0 *
(self.InitialRefractiveIndex + self.Dneffy[z]) *
FBGperiod[z]))) + (
2 * math.pi *
self.MeanChangeRefractiveIndex / l)
#Kaa Function
kaa = math.pi * self.FringeVisibility * self.MeanChangeRefractiveIndex / l
#Gamma Function
gammab = cmath.sqrt(kaa**2.0 - sig**2.0)
#Transfer Matrix Calculation
f11 = complex(cmath.cosh(gammab * deltz),
-(sig / gammab) * cmath.sinh(gammab * deltz))
f22 = complex(cmath.cosh(gammab * deltz),
(sig / gammab) * cmath.sinh(gammab * deltz))
f12 = complex(0,
-(kaa / gammab) * cmath.sinh(gammab * deltz))
f21 = complex(0,
+(kaa / gammab) * cmath.sinh(gammab * deltz))
#Assemble Transfer Matrix
f1 = np.dot(f1, np.matrix([[f11, f12], [f21, f22]]))
#Add to the Reflection file- YWave
PO = f1[0, 0]
NO = f1[1, 0]
REF = abs(NO / PO)**2
self.YReflect['wavelength'].append(l) #Output File
self.YReflect['reflec'].append(REF) #Output File
#ZWave
for l in np.arange(self.MinBandWidth, self.MaxBandWidth,
self.SimulationResolution):
f1 = np.matrix('1 0; 0 1') #empty transfer matrix
#Cycle-Each FBG increment
for z in np.arange(0, M):
#Sigma Function
sig = 2.0 * math.pi * (
self.InitialRefractiveIndex + self.Dneffz[z]) * (
(1.0 / l) -
(1.0 /
(2.0 *
(self.InitialRefractiveIndex + self.Dneffz[z]) *
FBGperiod[z]))) + (
2 * math.pi *
self.MeanChangeRefractiveIndex / l)
#Kaa Function
kaa = math.pi * self.FringeVisibility * self.MeanChangeRefractiveIndex / l
#Gamma Function
gammab = cmath.sqrt(kaa**2.0 - sig**2.0)
#Transfer Matrix Calculation
f11 = complex(cmath.cosh(gammab * deltz),
-(sig / gammab) * cmath.sinh(gammab * deltz))
f22 = complex(cmath.cosh(gammab * deltz),
(sig / gammab) * cmath.sinh(gammab * deltz))
f12 = complex(0,
-(kaa / gammab) * cmath.sinh(gammab * deltz))
f21 = complex(0,
+(kaa / gammab) * cmath.sinh(gammab * deltz))
#Assemble Transfer Matrix
f1 = np.dot(f1, np.matrix([[f11, f12], [f21, f22]]))
#Add to the Reflection file- YWave
PO = f1[0, 0]
NO = f1[1, 0]
REF = abs(NO / PO)**2
self.ZReflect['wavelength'].append(l) #Output File
self.ZReflect['reflec'].append(REF) #Output File
#Halve the amplitude of each of the y and z waves, then sum to find composite wave.
self.DReflect['wavelength'] = self.YReflect['wavelength']
self.YReflect['reflec'] = np.divide(self.YReflect['reflec'], 2.0)
self.ZReflect['reflec'] = np.divide(self.ZReflect['reflec'], 2.0)
self.DReflect['reflec'] = np.add(self.YReflect['reflec'],
self.ZReflect['reflec'])
def Coth(x): return cmath.cosh(x)/cmath.sinh(x)
def __new__(cls, argument):
if isinstance(argument, (RealValue, Zero)):
return FloatValue(math.cosh(float(argument)))
if isinstance(argument, (ComplexValue)):
return ComplexValue(cmath.cosh(complex(argument)))
return MathFunction.__new__(cls)
def fit(lines_seriestab, file_prefix, sparky_peaklist, OS):
import os, math, cmath
##
## (tau,R2eff)-fit and kex,R2-determ.
##
lines_fit_o = ['#atom Ra Rb ka kb dw\n']
fd = open('%s.gnudata' %(file_prefix),'r')
gnudata = fd.readlines()
fd.close()
## set a list of sums of squares
SS = []
for i in range(len(lines_seriestab)):
if not sparky_peaklist:
ass = assignments_Sparky[peakindexes_NMRPipe[i]]
else:
ass = lines_seriestab[i][58:68].strip()
print 'nonlinear fit for %s' %(ass)
lines_gnuplot_script = ([
'#freqCP = x\n'
'tauCP(x) = 1/(4.*x)\n',
## 'psi(x) = (Ra-Rb-ka+kb)**2-deltaomega**2+4.*ka*kb\n', ## tc
'psi(x) = kex**2-deltaomega**2\n', ## kt
## 'epsilon(x) = 2*deltaomega*(Ra-Rb-ka+kb)\n', ## tc
'epsilon(x) = -2*deltaomega*kex*(2*pA-1)\n', ## kt
## 'Dpos(x) = (1./2.)*( 1+(psi(x)+2*deltaomega**2)/sqrt(psi(x)**2+epsilon(x)**2))\n',
## 'Dneg(x) = (1./2.)*(-1+(psi(x)+2*deltaomega**2)/sqrt(psi(x)**2+epsilon(x)**2))\n',
'Dpos(x) = (1./2.)*( 1+(psi(x)+2*deltaomega**2)/sqrt(psi(x)**2+epsilon(x)**2))\n',
'Dneg(x) = (1./2.)*(-1+(psi(x)+2*deltaomega**2)/sqrt(psi(x)**2+epsilon(x)**2))\n',
'etapos(x) = (tauCP(x)/sqrt(2))*sqrt( psi(x)+sqrt(psi(x)**2+epsilon(x)**2))\n',
'etaneg(x) = (tauCP(x)/sqrt(2))*sqrt(-psi(x)+sqrt(psi(x)**2+epsilon(x)**2))\n',
## 'f(x) = (1./2.)*( Ra+Rb+ka+kb-(1/tauCP(x))*( acosh( Dpos(x)*cosh(etapos(x)) - Dneg(x)*cos(etaneg(x)) ) ) )\n',
'f(x) = R+(1./2.)*( kex-(1/tauCP(x))*( acosh( Dpos(x)*cosh(etapos(x)) - Dneg(x)*cos(etaneg(x)) ) ) )\n',
## 'Ra = 17\n', ## tc
## 'Rb = 23\n', ## tc
## 'ka = 29\n', ## tc
## 'kb = 19\n', ## tc
'kex = 2000\n', ## kt
'pA = 0.9\n', ## kt
'R = 7\n', ## kt
'deltaomega = 1000\n',
## 'fit f(x) "%s.gnudata" using 1:%s via Ra,Rb,ka,kb,deltaomega\n' %(file_prefix, i+2),
'fit f(x) "%s.gnudata" using 1:%s via kex,pA,R,deltaomega\n' %(file_prefix, i+2),
'set terminal png\n',
'set output "%s%s.png"\n' %(file_prefix, i),
'plot [][0:]"%s.gnudata" using 1:%s title "%s", f(x)\n' %(file_prefix, i+2, ass)
])
## write gnuplot script file
fd = open('%s.gnuscript%s' %(file_prefix, i), 'w')
fd.writelines(lines_gnuplot_script)
fd.close()
## execute gnuplot script file and write gnuplot fit log
if OS == 'linux':
os.system('/usr/bin/gnuplot %s.gnuscript%s' %(file_prefix, i))
elif OS == 'windows':
os.system('gnuplot %s.gnuscript%s' %(file_prefix, i))
## remove gnuplot script file
os.remove('%s.gnuscript%s' %(file_prefix, i))
## parse gnuplot fit log
if OS == 'linux':
lines_fit_i = os.popen('tail -n18 fit.log').readlines()
elif OS == 'windows':
fd = open('fit.log','r')
lines_fit_i = fd.readlines()[-18:]
fd.close()
## Ra = float(lines_fit_i[3].split()[2])
## Rb = float(lines_fit_i[4].split()[2])
## ka = float(lines_fit_i[5].split()[2])
## kb = float(lines_fit_i[6].split()[2])
## dw = float(lines_fit_i[7].split()[2])
kex = float(lines_fit_i[5].split()[2])
pA = float(lines_fit_i[6].split()[2])
R = float(lines_fit_i[7].split()[2])
dw = float(lines_fit_i[8].split()[2])
## write parsed fit data to other fit log
## lines_fit_o += ['%10s %6.3f %6.3f %6.3f %6.3f %8.3f\n' %(ass, Ra, Rb, ka, kb, dw)]
lines_fit_o += ['%10s %6.3f %6.3f %6.3f %8.3f\n' %(ass, kex, pA, R, dw)]
##
## SS calculation for use in F-test comparing nonlinear and linear fits
##
n = len(gnudata[1:])
deltaomega = dw
sumdiffsq = 0
sumdiff = 0
for line in gnudata[1:]:
x = float(line.split()[0])
y = float(line.split()[i+1])
tauCP = 1/(4.*x)
## psi = (Ra-Rb-ka+kb)**2-deltaomega**2+4.*ka*kb
psi = kex**2-deltaomega**2
## epsilon = 2*deltaomega*(Ra-Rb-ka+kb)
epsilon = -2*deltaomega*kex*(2*pA-1)
Dpos = (1./2.)*( 1+(psi+2*deltaomega**2)/math.sqrt(psi**2+epsilon**2))
Dneg = (1./2.)*(-1+(psi+2*deltaomega**2)/math.sqrt(psi**2+epsilon**2))
etapos = (tauCP/math.sqrt(2))*math.sqrt( psi+math.sqrt(psi**2+epsilon**2))
etaneg = (tauCP/math.sqrt(2))*math.sqrt(-psi+math.sqrt(psi**2+epsilon**2))
## yhat = (1./2.)*( Ra+Rb+ka+kb-(1/tauCP)*( cmath.acosh( Dpos*cmath.cosh(etapos) - Dneg*math.cos(etaneg) ) ) )
yhat = R+(1./2.)*( kex-(1/tauCP)*( cmath.acosh( Dpos*cmath.cosh(etapos) - Dneg*math.cos(etaneg) ) ) )
diff = yhat-y
sumdiff += diff ## abs??
sumdiffsq += diff**2
ss = abs(sumdiffsq-(sumdiff**2)/n)
stop
## append ss calculated for 1 chemical group to list of sums of squares
SS += [ss]
os.remove('fit.log')
fd = open('%s.fit' %(file_prefix), 'w')
fd.writelines(lines_fit_o)
fd.close()
return SS
#------------------------------------------------------------------------------ # Hyperbolic functions - real version x = 0.5 assert abs(cosh(x) - math.cosh(x)) < 1e-14 assert abs(sinh(x) - math.sinh(x)) < 1e-14 assert abs(tanh(x) - math.tanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Hyperbolic functions - complex version x = 0.5j assert abs(cosh(x) - cmath.cosh(x)) < 1e-14 assert abs(sinh(x) - cmath.sinh(x)) < 1e-14 assert abs(tanh(x) - cmath.tanh(x)) < 1e-14 assert abs(acosh(x) - cmath.acosh(x)) < 1e-14 assert abs(asinh(x) - cmath.asinh(x)) < 1e-14 assert abs(atanh(x) - cmath.atanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Rounding operations. assert type(round(0.5)) is mpf assert type(round(mpq(1,2))) is mpf assert type(floor(0.5)) is mpf assert type(ceil(0.5)) is mpf
def cosh(a, b):
result = a**2 + b**2
return cmath.cosh(result) + 1.6j
def cosh_usecase(x):
return cmath.cosh(x)
def calculate_3d_plot_coordinates(system):
# get global variables
[length_left] = length_left_glob.data["length_left"]
[length_right] = length_right_glob.data["length_right"]
[lam] = lam_glob.data["lam"]
[EI] = EI_glob.data["EI"]
xx = xx_all[0]
value_unraveled_all = np.zeros((250,26), dtype=complex)
if (length_left != 0 and length_right != 0) or (length_left != 0 and system=="Fixed-Free Beam"): # otherwise the beam is not deformed
j = 0.04
k = 0
while j <= 10.0:
lam_temp = calculate_lambda(system,j,EI) # calculates lambda for every frequency
lam_glob.data = dict(lam=[lam_temp])
A1,A2,A3,A4,B1,B2,B3,B4 = create_matrix_and_calculate_coefficients(system)
i = 0
while i < 26:
if xx[i] <= length_left: # for the subsystem on the left
value_unraveled_all[k][i] = -1*EI*j*j/(F*(L**3))*(A1*cm.sin(lam_temp/L*xx[i])+A2*cm.cos(lam_temp/L*xx[i])+A3*cm.sinh(lam_temp/L*xx[i])+A4*cm.cosh(lam_temp/L*xx[i]))
else: # for the subsystem on the right
value_unraveled_all[k][i] = -1*EI*j*j/(F*(L**3))*(B1*cm.sin(lam_temp/L*(xx[i]-length_left))+B2*cm.cos(lam_temp/L*(xx[i]-length_left))+B3*cm.sinh(lam_temp/L*(xx[i]-length_left))+B4*cm.cosh(lam_temp/L*(xx[i]-length_left)))
i+=1
k+=1
j = round(j+0.04,2)
zmax = complex(max(value_unraveled_all.ravel().real), 0) # get maximum z value
zmin = complex(min(value_unraveled_all.ravel().real), 0) # get minimum z value
if (zmax.real == 0.0 and zmin.real == 0.0):
zmax = complex(0.05, 0)
zmin = complex(-0.05, 0)
lam_glob.data = dict(lam=[lam])
zmax_glob.data = dict(zmax=[zmax])
zmin_glob.data = dict(zmin=[zmin])
value_unraveled_all_glob.data = dict(value_unraveled_all=value_unraveled_all)
def cosh_usecase(x):
return cmath.cosh(x)
def birefringence_rot(s, chi, lambda_0, n_o, n_e, jones, rng_states,
thread_idx, B, U, U_epar, rand_nums, seed):
if n_o != n_e or chi != 0:
if B[0] == 2.0 and B[1] == 2.0 and B[2] == 2.0:
# rand_num = xoroshiro128p_uniform_float32(rng_states, thread_idx)
rand_num = rand_nums[seed]
theta = cmath.pi * rand_num
# rand_num = xoroshiro128p_uniform_float32(rng_states, thread_idx + 1)
rand_num = rand_nums[seed + 1]
beta0 = cmath.pi * 2 * rand_num
B[0] = cmath.sin(theta).real * cmath.cos(beta0).real
B[1] = cmath.sin(theta).real * cmath.sin(beta0).real
B[2] = cmath.cos(theta).real
theta1 = cuda.local.array(1, float32)
get_theta(B, U, theta1)
Bp = cuda.local.array(3, float32)
temp = B[0] * U[0] + B[1] * U[1] + B[2] * U[2]
Bp[0] = B[0] - U[0] * temp
Bp[1] = B[1] - U[1] * temp
Bp[2] = B[2] - U[2] * temp
temp = cmath.sqrt(Bp[0] * Bp[0] + Bp[1] * Bp[1] + Bp[2] * Bp[2]).real
if temp != 0:
Bp[0] /= temp
Bp[1] /= temp
Bp[2] /= temp
beta = cuda.local.array(1, float32)
get_beta(U_epar, Bp, U, beta)
# temp = n_e * cmath.cos(theta1[0]).real * n_e * cmath.cos(theta1[0]).real
delta_n = n_o * n_e / cmath.sqrt(
n_e * cmath.cos(theta1[0]).real * n_e * cmath.cos(theta1[0]).real +
n_o * cmath.sin(theta1[0]).real * n_o *
cmath.sin(theta1[0]).real).real - n_o
g_o = cmath.pi * delta_n / (lambda_0 * 1e4)
# n_mat = np.array([g_o.j, -g_o.j, -chi, chi])
n_mat = cuda.local.array(4, nb.complex64)
n_mat[0] = g_o * 1j
n_mat[1] = -g_o * 1j
n_mat[2] = -chi
n_mat[3] = chi
Q_n = cmath.sqrt(n_mat[0] * n_mat[0] - n_mat[3] * n_mat[3])
m = cuda.local.array(4, nb.complex64)
m_new = cuda.local.array(4, nb.complex64)
if Q_n != 0:
# todo check which to keep
# m[0] = (n_mat[0] - n_mat[1]) * cmath.sinh(Q_n * s) / (2 * Q_n) + cmath.cosh(Q_n * s)
# m[1] = (n_mat[0] - n_mat[1]) * cmath.sinh(Q_n * s) / (2 * Q_n) + cmath.cosh(Q_n * s)
# m[2] = (n_mat[2]) * cmath.sinh(Q_n * s) / (Q_n)
# m[3] = -m[2]
m[0] = cmath.exp((n_mat[0] + n_mat[1]) / 2 * s) * (
(n_mat[0] - n_mat[1]) * cmath.sinh(Q_n * s) /
(2 * Q_n) + cmath.cosh(Q_n * s))
m[1] = cmath.exp((n_mat[0] + n_mat[1]) / 2 * s) * (
(n_mat[0] - n_mat[1]) * cmath.sinh(Q_n * s) /
(2 * Q_n) + cmath.cosh(Q_n * s))
m[2] = cmath.exp((n_mat[0] + n_mat[1]) / 2 * s) * (
(n_mat[2]) * cmath.sinh(Q_n * s) / (Q_n))
m[3] = cmath.exp((n_mat[0] + n_mat[1]) / 2 * s) * (-m[2])
m_new[0] = m[0] * cmath.cos(beta[0]) + m[2] * cmath.sin(beta[0])
m_new[1] = m[1] * cmath.cos(beta[0]) + m[3] * cmath.sin(beta[0])
m_new[2] = -m[0] * cmath.sin(beta[0]) + m[2] * cmath.cos(beta[0])
m_new[3] = -m[1] * cmath.sin(beta[0]) + m[3] * cmath.cos(beta[0])
jones[thread_idx,
0] = jones[thread_idx, 0] * m_new[0] + jones[thread_idx,
2] * m_new[3]
jones[thread_idx,
1] = jones[thread_idx, 1] * m_new[0] + jones[thread_idx,
3] * m_new[3]
jones[thread_idx,
2] = jones[thread_idx, 0] * m_new[2] + jones[thread_idx,
2] * m_new[1]
jones[thread_idx,
3] = jones[thread_idx, 1] * m_new[2] + jones[thread_idx,
3] * m_new[1]
def coth(x):
return cosh(x)/sinh(x)
