def square_integration(file):
result = 0
n = read_json(file, "number")
start, end = read_json(file, "range")
function = read_json(file, "function")
dx = (end - start) / n
for x in arange(start + dx, end + dx, dx):
pol = polyval(function, x)
result = result + pol
return result * dx
def nm_method():
a, b = read_json("range")
accuracy = read_json("accuracy")
x = read_json("start")
x1 = x - (fun(x) / pfun(x))
while abs(fun(x)) >= accuracy and abs(x1 - x) >= accuracy:
x = x1
x1 = x - (fun(x) / pfun(x))
return x1
def trapeze_integration(file):
result = 0
n = read_json(file, "number")
start, end = read_json(file, "range")
function = read_json(file, "function")
dx = (end - start) / n
for x in arange(start, end, dx):
pol = (polyval(function, x) + polyval(function, x + dx)) / 2
result = result + dx * pol
return result
def monte_carlo_integration(file):
result = 0.0
n = read_json(file, "number")
start, end = read_json(file, "range")
function = read_json(file, "function")
generated_points = np.random.uniform(start, end, n)
# generated_points = [1.5, 2.6, 3.8, 4.5]
for x in generated_points:
result += polyval(function, x)
return result / n * abs(end - start)
def simpson_integration(file):
result = 0.0
n = read_json(file, "number") * 2
start, end = read_json(file, "range")
function = read_json(file, "function")
h = (end - start) / n
for x in arange(start, end, 2 * h):
pol = polyval(function, x) + 4 * polyval(function, x + h) + polyval(
function, x + 2 * h)
result = result + h / 3 * pol
return result
def bisection():
a, b = read_json("range")
accuracy = read_json("accuracy")
x = a + b / 2
while abs(a - b) > accuracy:
if fun(x) == 0:
return x
if fun(x) * fun(a) < 0:
b = x
else:
a = x
x = (a + b) / 2
return x
def fun(x):
y = 0
function = read_json("function")
for i in range(0, len(function)):
y = y + function[i] * (x**(len(function) - 1 - i))
return y
def pfun(x):
y = 0
function = read_json("derivative")
for i in range(0, len(function)):
y = y + function[i] * (x**(len(function) - 1 - i))
return y