def run():
def f2(x,y):
return numx.sin(x) / x
sys2 = integrate.gsl_function(f2, None)
def f1(x,y):
return 1 / x
sys1 = integrate.gsl_function(f1, None)
def f3(x,y):
return 1 / -x
sys3 = integrate.gsl_function(f3, None)
w = integrate.workspace(1000000)
cyclew = integrate.workspace(1000000)
table1 = integrate.qawo_table(1, 100, integrate.SINE, 100)
table2 = integrate.qawo_table(-1, 100, integrate.SINE, 100)
# Borders and singualrity for gagp
pts = numx.array((-numx.pi, 0, numx.pi))
flag, result1, error = integrate.qagp(sys2, pts, 1e-8, 1e-8, 100000, w)
flag, result2, error = integrate.qawf(sys1, numx.pi, 1e-8, 100, w,
cyclew, table1)
flag, result3, error = integrate.qawf(sys3, numx.pi, 1e-8, 100, w,
cyclew, table2)
print "Result of integration is :", result1 + result2 + result3
def test_qawf(self):
def f2(x, y):
return Numeric.sin(x) / x
sys2 = integrate.gsl_function(f2, None)
def f1(x, y):
return 1 / x
sys1 = integrate.gsl_function(f1, None)
def f3(x, y):
return 1 / -x
sys3 = integrate.gsl_function(f3, None)
pts = Numeric.array((-Numeric.pi, 0, Numeric.pi))
flag, result1, error = integrate.qagp(sys2, pts, 1e-8, 1e-8, 100000,
self.w)
table1 = integrate.qawo_table(1, 100, integrate.SINE, 100)
cyclew = integrate.workspace(1000000)
flag, result2, error = integrate.qawf(sys1, Numeric.pi, 1e-8, 100,
self.w, cyclew, table1)
table2 = integrate.qawo_table(-1, 100, integrate.SINE, 100)
flag, result3, error = integrate.qawf(sys3, Numeric.pi, 1e-8, 100,
self.w, cyclew, table2)
assert (Numeric.absolute(result1 + result2 + result3 - Numeric.pi) <
1e-8)
def run():
def f2(x, y):
return numx.sin(x) / x
sys2 = integrate.gsl_function(f2, None)
def f1(x, y):
return 1 / x
sys1 = integrate.gsl_function(f1, None)
def f3(x, y):
return 1 / -x
sys3 = integrate.gsl_function(f3, None)
w = integrate.workspace(1000000)
cyclew = integrate.workspace(1000000)
table1 = integrate.qawo_table(1, 100, integrate.SINE, 100)
table2 = integrate.qawo_table(-1, 100, integrate.SINE, 100)
# Borders and singualrity for gagp
pts = numx.array((-numx.pi, 0, numx.pi))
flag, result1, error = integrate.qagp(sys2, pts, 1e-8, 1e-8, 100000, w)
flag, result2, error = integrate.qawf(sys1, numx.pi, 1e-8, 100, w, cyclew,
table1)
flag, result3, error = integrate.qawf(sys3, numx.pi, 1e-8, 100, w, cyclew,
table2)
print "Result of integration is :", result1 + result2 + result3
def test_qagp(self):
def f1(x,y):
return x / x
sys = integrate.gsl_function(f1, None)
pts = Numeric.array((-1, 0, 1))
flag, result, error = integrate.qagp(sys, pts, 1e-8, 1e-8, 100000, self.w)
assert(Numeric.absolute(result - 2.) < 1e-3)
assert(error<1e-8)
def II(x, a, t, method=5):
if method == 0:
sys = integrate.gsl_function(cdf, (a, t))
integral = integrate.qagp(sys, [0., x], 1e-8, 1e-7, 100, w2)
elif method == 2:
integral = quad(cdf_eta, 1e-8, x, args=(a, t))
elif method == 3:
integral = x * cdf_eta(x, a, t) - quad(xpdf, 1e-10, x, args=(a, t))[0]
elif method == 4:
phi = a + 2 * sqrt(t) * erfinv(2. * x - 1.)
integral = x * cdf_phi(phi, a, t) - quad(xr, -12., phi, args=(a, t))[0]
elif method == 5:
phi = a + 2 * sqrt(t) * erfinv(2. * x - 1.)
integral = x / 2. * (1. + erf(phi / sqrt(2. * (1. - 2. * t)))) - quad(xr, -Inf, phi, args=(a, t))[0]
return integral
def II(x, a, t, method=5):
if method == 0:
sys = integrate.gsl_function(cdf, (a, t))
integral = integrate.qagp(sys, [0., x], 1e-8, 1e-7, 100, w2)
elif method == 2:
integral = quad(cdf_eta, 1e-8, x, args=(a, t))
elif method == 3:
integral = x * cdf_eta(x, a, t) - quad(xpdf, 1e-10, x, args=(a, t))[0]
elif method == 4:
phi = a + 2 * sqrt(t) * erfinv(2. * x - 1.)
integral = x * cdf_phi(phi, a, t) - quad(xr, -12., phi, args=(a, t))[0]
elif method == 5:
phi = a + 2 * sqrt(t) * erfinv(2. * x - 1.)
integral = x / 2. * (1. + erf(phi / sqrt(2. * (1. - 2. * t)))) - quad(
xr, -Inf, phi, args=(a, t))[0]
return integral
def test_qawf(self):
def f2(x,y):
return Numeric.sin(x) / x
sys2 = integrate.gsl_function(f2, None)
def f1(x,y):
return 1 / x
sys1 = integrate.gsl_function(f1, None)
def f3(x,y):
return 1 / -x
sys3 = integrate.gsl_function(f3, None)
pts = Numeric.array((-Numeric.pi, 0, Numeric.pi))
flag, result1, error = integrate.qagp(sys2, pts, 1e-8, 1e-8, 100000, self.w)
table1 = integrate.qawo_table(1, 100, integrate.SINE, 100)
cyclew = integrate.workspace(1000000)
flag, result2, error = integrate.qawf(sys1, Numeric.pi, 1e-8, 100, self.w, cyclew, table1)
table2 = integrate.qawo_table(-1, 100, integrate.SINE, 100)
flag, result3, error = integrate.qawf(sys3, Numeric.pi, 1e-8, 100, self.w, cyclew, table2)
assert(Numeric.absolute(result1+result2+result3 - Numeric.pi) < 1e-8)
return xx * r(phi, a, t)
def X(phi, a, t):
return 0.5 * (1 + erf((phi - a) / 2. / sqrt(t)))
def phi(x, a, t):
return a + 2 * sqrt(t) * erfinv(2 * x - 1)
def integrand(phi, a, t):
sr = sqrt(1. - 2. * t)
x = 0.5 * (1 + erf((sr * phi - a) / sqrt(1. - sr * sr) / sqrt(2.)))
return x * x * exp(- phi * phi / 2.)
def cdf(x, (a, t)):
sys = integrate.gsl_function(pdf, (a, t))
flag, result, error = integrate.qagp(sys, [0., x], 1e-8, 1e-7, 100, w1)
return result
def cdf_eta(x, a, t):
return quad(pdf, 1e-10, x, args=(a, t))[0]
def cdf_phi(x, a, t):
return quad(r, -12., x, args=(a, t))[0]
def II(x, a, t, method=5):
if method == 0:
sys = integrate.gsl_function(cdf, (a, t))
integral = integrate.qagp(sys, [0., x], 1e-8, 1e-7, 100, w2)
elif method == 2:
integral = quad(cdf_eta, 1e-8, x, args=(a, t))
elif method == 3:
return 0.5 * (1 + erf((phi - a) / 2. / sqrt(t)))
def phi(x, a, t):
return a + 2 * sqrt(t) * erfinv(2 * x - 1)
def integrand(phi, a, t):
sr = sqrt(1. - 2. * t)
x = 0.5 * (1 + erf((sr * phi - a) / sqrt(1. - sr * sr) / sqrt(2.)))
return x * x * exp(-phi * phi / 2.)
def cdf(x, (a, t)):
sys = integrate.gsl_function(pdf, (a, t))
flag, result, error = integrate.qagp(sys, [0., x], 1e-8, 1e-7, 100, w1)
return result
def cdf_eta(x, a, t):
return quad(pdf, 1e-10, x, args=(a, t))[0]
def cdf_phi(x, a, t):
return quad(r, -12., x, args=(a, t))[0]
def II(x, a, t, method=5):
if method == 0:
sys = integrate.gsl_function(cdf, (a, t))
integral = integrate.qagp(sys, [0., x], 1e-8, 1e-7, 100, w2)
