def test_sine():
# a sine curve from zero to pi -- should be 2
# with a hundred points, only correct to about 4 figures
result = trapz(math.sin, 0, math.pi, tol=1e-4)
assert isclose(result, 2.0, rel_tol=1e-04)
assert not isclose(result, 2.0, rel_tol=1e-05)
# Try again with higher tol:
result = trapz(math.sin, 0, math.pi, tol=1e-12)
assert isclose(result, 2.0, rel_tol=1e-12)
assert not isclose(result, 2.0, rel_tol=1e-13)
def test_sine():
# a sine curve from zero to pi -- should be 2
# with a hundred points, only correct to about 4 figures
result = trapz(math.sin, 0, math.pi, tol=1e-4)
assert isclose(result, 2.0, rel_tol=1e-04)
assert not isclose(result, 2.0, rel_tol=1e-05)
# Try again with higher tol:
result = trapz(math.sin, 0, math.pi, tol=1e-12)
assert isclose(result, 2.0, rel_tol=1e-12)
assert not isclose(result, 2.0, rel_tol=1e-13)
def test_sine2():
# a sine curve from zero to 2pi -- should be 0.0
# tricky for the convergence!
# need to set an absolute tolerance when comparing to zero
result = trapz(math.sin, 0, 2*math.pi, tol=1e-4)
assert isclose(result, 0.0, abs_tol=1e-04)
# actualy gets a better answer right off the bat:
# Trapezoidal rulw works very well for periodic functions
# The errors cancel out.
# assert not isclose(result, 0.0, abs_tol=1e16)
# try again with a higher tolerance
# using abs_tol to compare with zero
result = trapz(math.sin, 0, 2*math.pi, tol=1e-12)
assert isclose(result, 0.0, abs_tol=1e-12)
def test_sine2():
# a sine curve from zero to 2pi -- should be 0.0
# tricky for the convergence!
# need to set an absolute tolerance when comparing to zero
result = trapz(math.sin, 0, 2 * math.pi, tol=1e-4)
assert isclose(result, 0.0, abs_tol=1e-04)
# actualy gets a better answer right off the bat:
# Trapezoidal rulw works very well for periodic functions
# The errors cancel out.
# assert not isclose(result, 0.0, abs_tol=1e16)
# try again with a higher tolerance
# using abs_tol to compare with zero
result = trapz(math.sin, 0, 2 * math.pi, tol=1e-12)
assert isclose(result, 0.0, abs_tol=1e-12)
def test_sloping_line():
''' a simple linear function '''
def line(x):
return 2 + 3*x
# I got 159.99999999999 rather than 160
# hence the need for isclose()
assert isclose(trapz(line, 2, 10), 160)
m, B = 3, 2
a, b = 0, 5
assert isclose(trapz(line, a, b), 1/2*m*(b**2 - a**2) + B*(b-a))
a, b = 5, 10
assert isclose(trapz(line, a, b), 1/2*m*(b**2 - a**2) + B*(b-a))
a, b = -10, 5
assert isclose(trapz(line, a, b), 1/2*m*(b**2 - a**2) + B*(b-a))
def test_sloping_line():
''' a simple linear function '''
def line(x):
return 2 + 3 * x
# I got 159.99999999999 rather than 160
# hence the need for isclose()
assert isclose(trapz(line, 2, 10), 160)
m, B = 3, 2
a, b = 0, 5
assert isclose(trapz(line, a, b), 1 / 2 * m * (b**2 - a**2) + B * (b - a))
a, b = 5, 10
assert isclose(trapz(line, a, b), 1 / 2 * m * (b**2 - a**2) + B * (b - a))
a, b = -10, 5
assert isclose(trapz(line, a, b), 1 / 2 * m * (b**2 - a**2) + B * (b - a))
