def _trigpats():
global _trigpat
a, b, c = symbols('a b c', cls=Wild)
d = Wild('d', commutative=False)
# for the simplifications like sinh/cosh -> tanh:
# DO NOT REORDER THE FIRST 14 since these are assumed to be in this
# order in _match_div_rewrite.
matchers_division = (
(a*sin(b)**c/cos(b)**c, a*tan(b)**c, sin(b), cos(b)),
(a*tan(b)**c*cos(b)**c, a*sin(b)**c, sin(b), cos(b)),
(a*cot(b)**c*sin(b)**c, a*cos(b)**c, sin(b), cos(b)),
(a*tan(b)**c/sin(b)**c, a/cos(b)**c, sin(b), cos(b)),
(a*cot(b)**c/cos(b)**c, a/sin(b)**c, sin(b), cos(b)),
(a*cot(b)**c*tan(b)**c, a, sin(b), cos(b)),
(a*(cos(b) + 1)**c*(cos(b) - 1)**c,
a*(-sin(b)**2)**c, cos(b) + 1, cos(b) - 1),
(a*(sin(b) + 1)**c*(sin(b) - 1)**c,
a*(-cos(b)**2)**c, sin(b) + 1, sin(b) - 1),
(a*sinh(b)**c/cosh(b)**c, a*tanh(b)**c, S.One, S.One),
(a*tanh(b)**c*cosh(b)**c, a*sinh(b)**c, S.One, S.One),
(a*coth(b)**c*sinh(b)**c, a*cosh(b)**c, S.One, S.One),
(a*tanh(b)**c/sinh(b)**c, a/cosh(b)**c, S.One, S.One),
(a*coth(b)**c/cosh(b)**c, a/sinh(b)**c, S.One, S.One),
(a*coth(b)**c*tanh(b)**c, a, S.One, S.One),
(c*(tanh(a) + tanh(b))/(1 + tanh(a)*tanh(b)),
tanh(a + b)*c, S.One, S.One),
)
matchers_add = (
(c*sin(a)*cos(b) + c*cos(a)*sin(b) + d, sin(a + b)*c + d),
(c*cos(a)*cos(b) - c*sin(a)*sin(b) + d, cos(a + b)*c + d),
(c*sin(a)*cos(b) - c*cos(a)*sin(b) + d, sin(a - b)*c + d),
(c*cos(a)*cos(b) + c*sin(a)*sin(b) + d, cos(a - b)*c + d),
(c*sinh(a)*cosh(b) + c*sinh(b)*cosh(a) + d, sinh(a + b)*c + d),
(c*cosh(a)*cosh(b) + c*sinh(a)*sinh(b) + d, cosh(a + b)*c + d),
)
# for cos(x)**2 + sin(x)**2 -> 1
matchers_identity = (
(a*sin(b)**2, a - a*cos(b)**2),
(a*tan(b)**2, a*(1/cos(b))**2 - a),
(a*cot(b)**2, a*(1/sin(b))**2 - a),
(a*sin(b + c), a*(sin(b)*cos(c) + sin(c)*cos(b))),
(a*cos(b + c), a*(cos(b)*cos(c) - sin(b)*sin(c))),
(a*tan(b + c), a*((tan(b) + tan(c))/(1 - tan(b)*tan(c)))),
(a*sinh(b)**2, a*cosh(b)**2 - a),
(a*tanh(b)**2, a - a*(1/cosh(b))**2),
(a*coth(b)**2, a + a*(1/sinh(b))**2),
(a*sinh(b + c), a*(sinh(b)*cosh(c) + sinh(c)*cosh(b))),
(a*cosh(b + c), a*(cosh(b)*cosh(c) + sinh(b)*sinh(c))),
(a*tanh(b + c), a*((tanh(b) + tanh(c))/(1 + tanh(b)*tanh(c)))),
)
# Reduce any lingering artifacts, such as sin(x)**2 changing
# to 1-cos(x)**2 when sin(x)**2 was "simpler"
artifacts = (
(a - a*cos(b)**2 + c, a*sin(b)**2 + c, cos),
(a - a*(1/cos(b))**2 + c, -a*tan(b)**2 + c, cos),
(a - a*(1/sin(b))**2 + c, -a*cot(b)**2 + c, sin),
(a - a*cosh(b)**2 + c, -a*sinh(b)**2 + c, cosh),
(a - a*(1/cosh(b))**2 + c, a*tanh(b)**2 + c, cosh),
(a + a*(1/sinh(b))**2 + c, a*coth(b)**2 + c, sinh),
# same as above but with noncommutative prefactor
(a*d - a*d*cos(b)**2 + c, a*d*sin(b)**2 + c, cos),
(a*d - a*d*(1/cos(b))**2 + c, -a*d*tan(b)**2 + c, cos),
(a*d - a*d*(1/sin(b))**2 + c, -a*d*cot(b)**2 + c, sin),
(a*d - a*d*cosh(b)**2 + c, -a*d*sinh(b)**2 + c, cosh),
(a*d - a*d*(1/cosh(b))**2 + c, a*d*tanh(b)**2 + c, cosh),
(a*d + a*d*(1/sinh(b))**2 + c, a*d*coth(b)**2 + c, sinh),
)
_trigpat = (a, b, c, d, matchers_division, matchers_add,
matchers_identity, artifacts)
return _trigpat
D=[]
d = []
D1=[]
d1 = []
n = 2*10**-6
L = 100*10**-9
W = 80*10**-9
a = 3*10**-2
s1 = W/ (2*n)
y1 = (L+(W/2)) / (2*n)
x0 = 0.015
r0 = 2*x0
s2 = r0 / n
y0 = (x0 / n)/1000000
print x0, y0, y1
A = ((W/n)**2) *(sp.kv(0, s1)+(math.pi / 2)*sp.kv(1,s1)*coth(y1))
B = ((W/n)**2) *(sp.iv(0, s1)+(math.pi / 2)*sp.iv(1,s1)*coth(y1))
print A, B
def t1(t):
return (t**-1)*sp.kv(0, s2)
def t2(t):
return (t**-1)*sp.iv(0, s2)
print t2
temp = integrate.quad(t1, s1, s2)
Fk2 = (math.pi**-2) * np.array(temp[:0])
temp1 = integrate.quad(t2, s1, s2)
FI2 = (math.pi**-2) * np.array(temp1[:0])
print Fk2 , FI2
r1 = 0.0
while r1 < y1:
C0 = sp.kv(0,s2)*(1 + (A*FI2)-(B*Fk2))/A
def _trigpats():
global _trigpat
a, b, c = symbols('a b c', cls=Wild)
d = Wild('d', commutative=False)
# for the simplifications like sinh/cosh -> tanh:
# DO NOT REORDER THE FIRST 14 since these are assumed to be in this
# order in _match_div_rewrite.
matchers_division = (
(a * sin(b)**c / cos(b)**c, a * tan(b)**c, sin(b), cos(b)),
(a * tan(b)**c * cos(b)**c, a * sin(b)**c, sin(b), cos(b)),
(a * cot(b)**c * sin(b)**c, a * cos(b)**c, sin(b), cos(b)),
(a * tan(b)**c / sin(b)**c, a / cos(b)**c, sin(b), cos(b)),
(a * cot(b)**c / cos(b)**c, a / sin(b)**c, sin(b), cos(b)),
(a * cot(b)**c * tan(b)**c, a, sin(b), cos(b)),
(a * (cos(b) + 1)**c * (cos(b) - 1)**c, a * (-sin(b)**2)**c,
cos(b) + 1, cos(b) - 1),
(a * (sin(b) + 1)**c * (sin(b) - 1)**c, a * (-cos(b)**2)**c,
sin(b) + 1, sin(b) - 1),
(a * sinh(b)**c / cosh(b)**c, a * tanh(b)**c, S.One, S.One),
(a * tanh(b)**c * cosh(b)**c, a * sinh(b)**c, S.One, S.One),
(a * coth(b)**c * sinh(b)**c, a * cosh(b)**c, S.One, S.One),
(a * tanh(b)**c / sinh(b)**c, a / cosh(b)**c, S.One, S.One),
(a * coth(b)**c / cosh(b)**c, a / sinh(b)**c, S.One, S.One),
(a * coth(b)**c * tanh(b)**c, a, S.One, S.One),
(c * (tanh(a) + tanh(b)) / (1 + tanh(a) * tanh(b)), tanh(a + b) * c,
S.One, S.One),
)
matchers_add = (
(c * sin(a) * cos(b) + c * cos(a) * sin(b) + d, sin(a + b) * c + d),
(c * cos(a) * cos(b) - c * sin(a) * sin(b) + d, cos(a + b) * c + d),
(c * sin(a) * cos(b) - c * cos(a) * sin(b) + d, sin(a - b) * c + d),
(c * cos(a) * cos(b) + c * sin(a) * sin(b) + d, cos(a - b) * c + d),
(c * sinh(a) * cosh(b) + c * sinh(b) * cosh(a) + d,
sinh(a + b) * c + d),
(c * cosh(a) * cosh(b) + c * sinh(a) * sinh(b) + d,
cosh(a + b) * c + d),
)
# for cos(x)**2 + sin(x)**2 -> 1
matchers_identity = (
(a * sin(b)**2, a - a * cos(b)**2),
(a * tan(b)**2, a * (1 / cos(b))**2 - a),
(a * cot(b)**2, a * (1 / sin(b))**2 - a),
(a * sin(b + c), a * (sin(b) * cos(c) + sin(c) * cos(b))),
(a * cos(b + c), a * (cos(b) * cos(c) - sin(b) * sin(c))),
(a * tan(b + c), a * ((tan(b) + tan(c)) / (1 - tan(b) * tan(c)))),
(a * sinh(b)**2, a * cosh(b)**2 - a),
(a * tanh(b)**2, a - a * (1 / cosh(b))**2),
(a * coth(b)**2, a + a * (1 / sinh(b))**2),
(a * sinh(b + c), a * (sinh(b) * cosh(c) + sinh(c) * cosh(b))),
(a * cosh(b + c), a * (cosh(b) * cosh(c) + sinh(b) * sinh(c))),
(a * tanh(b + c), a * ((tanh(b) + tanh(c)) / (1 + tanh(b) * tanh(c)))),
)
# Reduce any lingering artifacts, such as sin(x)**2 changing
# to 1-cos(x)**2 when sin(x)**2 was "simpler"
artifacts = (
(a - a * cos(b)**2 + c, a * sin(b)**2 + c, cos),
(a - a * (1 / cos(b))**2 + c, -a * tan(b)**2 + c, cos),
(a - a * (1 / sin(b))**2 + c, -a * cot(b)**2 + c, sin),
(a - a * cosh(b)**2 + c, -a * sinh(b)**2 + c, cosh),
(a - a * (1 / cosh(b))**2 + c, a * tanh(b)**2 + c, cosh),
(a + a * (1 / sinh(b))**2 + c, a * coth(b)**2 + c, sinh),
# same as above but with noncommutative prefactor
(a * d - a * d * cos(b)**2 + c, a * d * sin(b)**2 + c, cos),
(a * d - a * d * (1 / cos(b))**2 + c, -a * d * tan(b)**2 + c, cos),
(a * d - a * d * (1 / sin(b))**2 + c, -a * d * cot(b)**2 + c, sin),
(a * d - a * d * cosh(b)**2 + c, -a * d * sinh(b)**2 + c, cosh),
(a * d - a * d * (1 / cosh(b))**2 + c, a * d * tanh(b)**2 + c, cosh),
(a * d + a * d * (1 / sinh(b))**2 + c, a * d * coth(b)**2 + c, sinh),
)
_trigpat = (a, b, c, d, matchers_division, matchers_add, matchers_identity,
artifacts)
return _trigpat
Temp0=[]
D=[]
d = []
D1=[]
d1 = []
n = 2*10**-6
L = 50*10**-6
W = 80*10**-9
a = 3*10**-2
s1 = W/ (2*n)
y1 = (L+(W/2)) / (2*n)
x0 = 0.015
y0 = (x0 / n)/1000000
print x0, y0, y1
g = (2/math.pi)*(sp.kv(0,s1))*(sp.kv(1,s1))**-1
G = (1+g*math.tanh(y1-y0))*(1+g*coth(y1-y0))**-1
print g, G
r1 = 0.0
while r1 < y0:
r1 += 0.0001
j = -1*r1
D.append(r1)
d.append(j)
T = Tc + (Tc - Tb)*G*coth(y0)*coth(y1-y0)*(1-(math.cosh(r1)/math.cosh(y0)))
Temp0.append(T)
print T, r1
r2 = y0
while r2 < y1:
r2 += 0.0001
D1.append(r2)
d1.append(-1*r2)
