def generate_integration_tests():
def print_(f, msg):
f.write("\t" + msg + "\n")
integrators_names = {"gauss_kronrod": "gauss_kronrod()",
"simplex": "simplex()", "gauss_legendre": "gauss_legendre()",
"gauss_lobatto": "gauss_lobatto()",
"simplex_steps_1000": "simplex(steps=1000)",
"gauss_legendre_steps_500": "gauss_legendre(steps=500)",
"gauss_lobatto_max_iter_127": "gauss_lobatto(max_number_of_iterations = 255, abs_tolerance = 1.0e-7)",
"gauss_kronrod_check_rel_tolerance": "gauss_kronrod(check_abs_tolerance = False, check_rel_tolerance = True)",
"gauss_kronrod_check_abs_tolerance_check_rel_tolerance": "gauss_kronrod(check_abs_tolerance = True, check_rel_tolerance = True)"
}
fcts_names = ("lambda x:2", "lambda x:x*x", "lambda x:exp(-x*x)",
"lambda x: x*x*x if x > 1 else x-2")
integrators = {'gauss_legendre': gauss_legendre(), 'gauss_lobatto': gauss_lobatto(),
'simplex_steps_1000': simplex(steps=1000), 'simplex': simplex(), 'gauss_kronrod': gauss_kronrod(),
'gauss_legendre_steps_500': gauss_legendre(steps=500),
'gauss_kronrod_check_abs_tolerance_check_rel_tolerance': gauss_kronrod(check_abs_tolerance=True,
check_rel_tolerance=True),
'gauss_lobatto_max_iter_127': gauss_lobatto(max_number_of_iterations=255, abs_tolerance=1.0e-7),
'gauss_kronrod_check_rel_tolerance': gauss_kronrod(check_abs_tolerance=False,
check_rel_tolerance=True)}
fcts = (lambda x: 2, lambda x: x * x, lambda x: exp(-x * x), lambda x: x * x * x if x > 1 else x - 2)
'''
s = []
for int_name, i in integrators_names.items():
s.append("'" + int_name + "':" + i)
print("integrators = {" + ", ".join(s) + "}")
print("fcts = (" + ", ".join(fcts_names) + ")")
'''
integration_boundaries = ((-1.0, 2.0), (0.0, 1.0), (-100.0, 99.0))
file_name = r"/Users/MarcusSteinkamp/Documents/integrator_test_code.txt"
fi = open(file_name, "w")
c = 0
i_fct = 0
for n, i in integrators_names.items():
i_fct = 0
for f in fcts_names:
for l, u in integration_boundaries:
print_(fi, "def test_integrator_" + str(c).zfill(3) + "_" + n + "(self):")
print_(fi, "\tfct = " + f)
print_(fi, "\tintegrator = " + i)
print_(fi, "\tresult = integrator(fct, " + str(l) + ", " + str(u) + ")")
print_(fi, "\tbenchmark = " + "{:18.9f}".format(integrators[n](fcts[i_fct], l, u)))
print_(fi, "\tself.assertAlmostEqual(benchmark, result, 8)")
print_(fi, "")
c = c + 1
i_fct = i_fct + 1
def test_compare_integral_of_density_with_cdf(self):
fct = density_normal_dist
integrator = gauss_kronrod(min_number_of_iterations=15)
l_bound = -1000.0
x_values = [-10.0, -1.3, -0.5, 0.0, 1.3, 5.0, 100.0, 1000.0]
for x in x_values:
integral = integrator(fct, l_bound, x)
cdf_value = cdf_abramowitz_stegun(x)
self.assertAlmostEqual(integral, cdf_value, 4)
def test_integrator_compare(self):
i0 = simplex(steps=5000)
i1 = gauss_kronrod()
# i2 = gauss_legendre(steps = 1000) # gauss_legendre calculates bad.
i3 = gauss_lobatto()
fct = lambda x: cos(x)
l = 0
u = PI / 2.0
r0 = i0(fct, l, u)
r1 = i1(fct, l, u)
# r2 = i2(fct, l, u)
r3 = i3(fct, l, u)
benchmark = 1.0
self.assertAlmostEqual(r0, benchmark, 6)
self.assertAlmostEqual(r1, benchmark, 6)
self.assertAlmostEqual(r3, benchmark, 6)
def test_integrator_099_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: x * x
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, -1.0, 2.0)
benchmark = 3.0
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_101_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: x * x
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, -100.0, 99.0)
benchmark = 656766.3333333333
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_076_gauss_kronrod_check_abs_tolerance_check_rel_tolerance(self):
fct = lambda x: x * x
integrator = gauss_kronrod(check_abs_tolerance=True, check_rel_tolerance=True)
result = integrator(fct, 0.0, 1.0)
benchmark = 0.333333333333
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_081_gauss_kronrod_check_abs_tolerance_check_rel_tolerance(self):
fct = lambda x: x * x * x if x > 1 else x - 2
integrator = gauss_kronrod(check_abs_tolerance=True, check_rel_tolerance=True)
result = integrator(fct, -1.0, 2.0)
benchmark = -0.263211802191
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_107_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: x * x * x if x > 1 else x - 2
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, -100.0, 99.0)
benchmark = 24009698.44306267
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_051_gauss_kronrod(self):
fct = lambda x: x * x
integrator = gauss_kronrod()
result = integrator(fct, -1.0, 2.0)
benchmark = 3.0
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_057_gauss_kronrod(self):
fct = lambda x: x * x * x if x > 1 else x - 2
integrator = gauss_kronrod()
result = integrator(fct, -1.0, 2.0)
benchmark = -0.263211802191
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_104_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: exp(-x * x)
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, -100.0, 99.0)
benchmark = 1.7724538509055159
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_055_gauss_kronrod(self):
fct = lambda x: exp(-x * x)
integrator = gauss_kronrod()
result = integrator(fct, 0.0, 1.0)
benchmark = 0.746824132812
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_056_gauss_kronrod(self):
fct = lambda x: exp(-x * x)
integrator = gauss_kronrod()
result = integrator(fct, -100.0, 99.0)
benchmark = 1.7724538509055159
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_054_gauss_kronrod(self):
fct = lambda x: exp(-x * x)
integrator = gauss_kronrod()
result = integrator(fct, -1.0, 2.0)
benchmark = 1.62890552357
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_053_gauss_kronrod(self):
fct = lambda x: x * x
integrator = gauss_kronrod()
result = integrator(fct, -100.0, 99.0)
benchmark = 656766.3333333333
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_052_gauss_kronrod(self):
fct = lambda x: x * x
integrator = gauss_kronrod()
result = integrator(fct, 0.0, 1.0)
benchmark = 0.333333333333
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_102_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: exp(-x * x)
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, -1.0, 2.0)
benchmark = 1.62890552357
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_058_gauss_kronrod(self):
fct = lambda x: x * x * x if x > 1 else x - 2
integrator = gauss_kronrod()
result = integrator(fct, 0.0, 1.0)
benchmark = -1.5
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_103_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: exp(-x * x)
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, 0.0, 1.0)
benchmark = 0.746824132812
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_049_gauss_kronrod(self):
fct = lambda x: 2
integrator = gauss_kronrod()
result = integrator(fct, 0.0, 1.0)
benchmark = 2.0
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_106_gauss_kronrod_check_rel_tolerance(self):
fct = lambda x: x * x * x if x > 1 else x - 2
integrator = gauss_kronrod(check_abs_tolerance=False, check_rel_tolerance=True)
result = integrator(fct, 0.0, 1.0)
benchmark = -1.5
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_074_gauss_kronrod_check_abs_tolerance_check_rel_tolerance(self):
fct = lambda x: 2
integrator = gauss_kronrod(check_abs_tolerance=True, check_rel_tolerance=True)
result = integrator(fct, -100.0, 99.0)
benchmark = 398.0
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_059_gauss_kronrod(self):
fct = lambda x: x * x * x if x > 1 else x - 2
integrator = gauss_kronrod()
result = integrator(fct, -100.0, 99.0)
benchmark = 24009698.44306267
self.assertAlmostEqual(benchmark, result, 8)
def test_integrator_050_gauss_kronrod(self):
fct = lambda x: 2
integrator = gauss_kronrod()
result = integrator(fct, -100.0, 99.0)
benchmark = 398.0
self.assertAlmostEqual(benchmark, result, 8)
