Python/maths/trapezoidal_rule.py at master · manmita/Python · GitHub

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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()
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"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 1:
"extended trapezoidal rule"

"""


defmethod_1(boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h= (boundary[1] -boundary[0]) /steps
a=boundary[0]
b=boundary[1]
x_i=make_points(a, b, h)
y=0.0
y+= (h/2.0) *f(a)
foriinx_i:
# print(i)
y+=h*f(i)
y+= (h/2.0) *f(b)
returny


defmake_points(a, b, h):
x=a+h
whilex< (b-h):
yieldx
x=x+h


deff(x): # enter your function here
y= (x-0) * (x-0)
returny


defmain():
a=0.0# Lower bound of integration
b=1.0# Upper bound of integration
steps=10.0# define number of steps or resolution
boundary= [a, b] # define boundary of integration
y=method_1(boundary, steps)
print(f"y = {y}")


if__name__=="__main__":
main()