def swing_int(fun, x0, x1, blocks, points):
"""
use monte carlo to integrate a wildy swinging function at endpoint
# vähän kiire, tämä toimii ja käytetään nyt valmiita
Parameters
----------
fun : functipn
function what to integrate
x0 : double
start point of integration
x1 : double
end point of integration
blocks : int
amount of blocks
points : int
how many points are calculated per block
Returns
-------
double
value of intergral
"""
return monte_carlo_integration(fun, x0, x1, blocks, points)
def calculate_monte_carlo_errors():
# Calculates numerical integral using monte carlo simulation
# and compares the values to analytical answer
correct_integral = 2
errors = []
iteration_amounts = np.linspace(40, 1000, 10, dtype=int)
for iters in iteration_amounts:
integral, dI = monte_carlo_integration(np.sin, 0., np.pi / 2, 10,
iters)
errors.append(2 * dI) # 2SEM
plot_monte_carlo_error(iteration_amounts, errors)
def test_intKolmas():
#wolfram alpha
true = 6.647272079953789849569443469671631160297360492445608431
blocks = np.arange(1,1000,100)
integral_errors = []
for block in blocks:
integral_errors.append(np.abs(monte_carlo_integration(kolmas, 0, 5, block, 1000)[0]- true))
plt.plot(blocks*1000, integral_errors, 'ob', label = r'Int from 0 to 5 $f(x) = exp(sin(x^3)) $ ')
plt.xlabel("number of points")
plt.ylabel("Abs. error")
# plt.xlim(blocks[-1], blocks[0])
plt.title("Integral error")
plt.xscale('log')
plt.yscale('log')
plt.legend(loc = 0)
plt.show()
from num_calculus import monte_carlo_integration
if __name__=="__main__":
def fun(x):
return 3*x**2
x = 0.8
dx = 0.001
der1 = test_first_derivative(fun, x, dx);
print(der1)
der2 = test_second_derivative(fun, x, dx);
print(der2)
def fun2(x):
return np.sin(x)
x0 = 0.9
dx = np.pi/2
n = 100
x2 = np.linspace(x0, dx, n)
I_Riemann = Riemann_sum(fun2, x2, dx, n)
I_trapezoid = trapezoid_sum(fun2, x2, dx, n)
I_Simpson = Simpson_sum(fun2, x2, dx, n)
I, dI = monte_carlo_integration(fun2, 0.0, np.pi/2, 10, 100)
print(I, '+/-', 2*dI)