def test_degrees():
assert cos(0*degree) == 1
assert cos(90*degree).ae(0)
assert cos(180*degree).ae(-1)
assert cos(270*degree).ae(0)
assert cos(360*degree).ae(1)
assert sin(0*degree) == 0
assert sin(90*degree).ae(1)
assert sin(180*degree).ae(0)
assert sin(270*degree).ae(-1)
assert sin(360*degree).ae(0)
python类cos()的实例源码
def test_complex_functions():
for x in (list(range(10)) + list(range(-10,0))):
for y in (list(range(10)) + list(range(-10,0))):
z = complex(x, y)/4.3 + 0.01j
assert exp(mpc(z)).ae(cmath.exp(z))
assert log(mpc(z)).ae(cmath.log(z))
assert cos(mpc(z)).ae(cmath.cos(z))
assert sin(mpc(z)).ae(cmath.sin(z))
assert tan(mpc(z)).ae(cmath.tan(z))
assert sinh(mpc(z)).ae(cmath.sinh(z))
assert cosh(mpc(z)).ae(cmath.cosh(z))
assert tanh(mpc(z)).ae(cmath.tanh(z))
def test_complex_inverse_functions():
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def test_mpcfun_real_imag():
mp.dps = 15
x = mpf(0.3)
y = mpf(0.4)
assert exp(mpc(x,0)) == exp(x)
assert exp(mpc(0,y)) == mpc(cos(y),sin(y))
assert cos(mpc(x,0)) == cos(x)
assert sin(mpc(x,0)) == sin(x)
assert cos(mpc(0,y)) == cosh(y)
assert sin(mpc(0,y)) == mpc(0,sinh(y))
assert cospi(mpc(x,0)) == cospi(x)
assert sinpi(mpc(x,0)) == sinpi(x)
assert cospi(mpc(0,y)).ae(cosh(pi*y))
assert sinpi(mpc(0,y)).ae(mpc(0,sinh(pi*y)))
c, s = cospi_sinpi(mpc(x,0))
assert c == cospi(x)
assert s == sinpi(x)
c, s = cospi_sinpi(mpc(0,y))
assert c.ae(cosh(pi*y))
assert s.ae(mpc(0,sinh(pi*y)))
c, s = cos_sin(mpc(x,0))
assert c == cos(x)
assert s == sin(x)
c, s = cos_sin(mpc(0,y))
assert c == cosh(y)
assert s == mpc(0,sinh(y))
def _sinpi_real(x):
if x < 0:
return -_sinpi_real(-x)
n, r = divmod(x, 0.5)
r *= pi
n %= 4
if n == 0: return math.sin(r)
if n == 1: return math.cos(r)
if n == 2: return -math.sin(r)
if n == 3: return -math.cos(r)
def _cospi_real(x):
if x < 0:
x = -x
n, r = divmod(x, 0.5)
r *= pi
n %= 4
if n == 0: return math.cos(r)
if n == 1: return -math.sin(r)
if n == 2: return -math.cos(r)
if n == 3: return math.sin(r)
def _sinpi_complex(z):
if z.real < 0:
return -_sinpi_complex(-z)
n, r = divmod(z.real, 0.5)
z = pi*complex(r, z.imag)
n %= 4
if n == 0: return cmath.sin(z)
if n == 1: return cmath.cos(z)
if n == 2: return -cmath.sin(z)
if n == 3: return -cmath.cos(z)
def _cospi_complex(z):
if z.real < 0:
z = -z
n, r = divmod(z.real, 0.5)
z = pi*complex(r, z.imag)
n %= 4
if n == 0: return cmath.cos(z)
if n == 1: return -cmath.sin(z)
if n == 2: return -cmath.cos(z)
if n == 3: return cmath.sin(z)
def funToVec( tgtfun, low=-1, high=1, steps=40, EqualSpacing=0 ):
'''Compute x,y points from evaluating a target function over an interval (low to high)
at evenly spaces points or with Chebyshev abscissa spacing (default) '''
if EqualSpacing:
h = (0.0+high-low)/steps
xvec = [low+h/2.0+h*i for i in range(steps)]
else:
scale, base = (0.0+high-low)/2.0, (0.0+high+low)/2.0
xvec = [base+scale*math.cos(((2*steps-1-2*i)*math.pi)/(2*steps)) for i in range(steps)]
yvec = map(tgtfun, xvec)
return Mat( [xvec, yvec] )
def test_trig_hyperb_basic():
for x in (range(100) + range(-100,0)):
t = x / 4.1
assert cos(mpf(t)).ae(math.cos(t))
assert sin(mpf(t)).ae(math.sin(t))
assert tan(mpf(t)).ae(math.tan(t))
assert cosh(mpf(t)).ae(math.cosh(t))
assert sinh(mpf(t)).ae(math.sinh(t))
assert tanh(mpf(t)).ae(math.tanh(t))
assert sin(1+1j).ae(cmath.sin(1+1j))
assert sin(-4-3.6j).ae(cmath.sin(-4-3.6j))
assert cos(1+1j).ae(cmath.cos(1+1j))
assert cos(-4-3.6j).ae(cmath.cos(-4-3.6j))
def test_degrees():
assert cos(0*degree) == 1
assert cos(90*degree).ae(0)
assert cos(180*degree).ae(-1)
assert cos(270*degree).ae(0)
assert cos(360*degree).ae(1)
assert sin(0*degree) == 0
assert sin(90*degree).ae(1)
assert sin(180*degree).ae(0)
assert sin(270*degree).ae(-1)
assert sin(360*degree).ae(0)
def test_complex_functions():
for x in (range(10) + range(-10,0)):
for y in (range(10) + range(-10,0)):
z = complex(x, y)/4.3 + 0.01j
assert exp(mpc(z)).ae(cmath.exp(z))
assert log(mpc(z)).ae(cmath.log(z))
assert cos(mpc(z)).ae(cmath.cos(z))
assert sin(mpc(z)).ae(cmath.sin(z))
assert tan(mpc(z)).ae(cmath.tan(z))
assert sinh(mpc(z)).ae(cmath.sinh(z))
assert cosh(mpc(z)).ae(cmath.cosh(z))
assert tanh(mpc(z)).ae(cmath.tanh(z))
def test_complex_inverse_functions():
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def _sinpi_real(x):
if x < 0:
return -_sinpi_real(-x)
n, r = divmod(x, 0.5)
r *= pi
n %= 4
if n == 0: return math.sin(r)
if n == 1: return math.cos(r)
if n == 2: return -math.sin(r)
if n == 3: return -math.cos(r)
def _cospi_real(x):
if x < 0:
x = -x
n, r = divmod(x, 0.5)
r *= pi
n %= 4
if n == 0: return math.cos(r)
if n == 1: return -math.sin(r)
if n == 2: return -math.cos(r)
if n == 3: return math.sin(r)
def _sinpi_complex(z):
if z.real < 0:
return -_sinpi_complex(-z)
n, r = divmod(z.real, 0.5)
z = pi*complex(r, z.imag)
n %= 4
if n == 0: return cmath.sin(z)
if n == 1: return cmath.cos(z)
if n == 2: return -cmath.sin(z)
if n == 3: return -cmath.cos(z)
def _cospi_complex(z):
if z.real < 0:
z = -z
n, r = divmod(z.real, 0.5)
z = pi*complex(r, z.imag)
n %= 4
if n == 0: return cmath.cos(z)
if n == 1: return -cmath.sin(z)
if n == 2: return -cmath.cos(z)
if n == 3: return cmath.sin(z)
def test_cospi_sinpi():
assert sinpi(0) == 0
assert sinpi(0.5) == 1
assert sinpi(1) == 0
assert sinpi(1.5) == -1
assert sinpi(2) == 0
assert sinpi(2.5) == 1
assert sinpi(-0.5) == -1
assert cospi(0) == 1
assert cospi(0.5) == 0
assert cospi(1) == -1
assert cospi(1.5) == 0
assert cospi(2) == 1
assert cospi(2.5) == 0
assert cospi(-0.5) == 0
assert cospi(100000000000.25).ae(sqrt(2)/2)
a = cospi(2+3j)
assert a.real.ae(cos((2+3j)*pi).real)
assert a.imag == 0
b = sinpi(2+3j)
assert b.imag.ae(sin((2+3j)*pi).imag)
assert b.real == 0
mp.dps = 35
x1 = mpf(10000) - mpf('1e-15')
x2 = mpf(10000) + mpf('1e-15')
x3 = mpf(10000.5) - mpf('1e-15')
x4 = mpf(10000.5) + mpf('1e-15')
x5 = mpf(10001) - mpf('1e-15')
x6 = mpf(10001) + mpf('1e-15')
x7 = mpf(10001.5) - mpf('1e-15')
x8 = mpf(10001.5) + mpf('1e-15')
mp.dps = 15
M = 10**15
assert (sinpi(x1)*M).ae(-pi)
assert (sinpi(x2)*M).ae(pi)
assert (cospi(x3)*M).ae(pi)
assert (cospi(x4)*M).ae(-pi)
assert (sinpi(x5)*M).ae(pi)
assert (sinpi(x6)*M).ae(-pi)
assert (cospi(x7)*M).ae(-pi)
assert (cospi(x8)*M).ae(pi)
assert 0.999 < cospi(x1, rounding='d') < 1
assert 0.999 < cospi(x2, rounding='d') < 1
assert 0.999 < sinpi(x3, rounding='d') < 1
assert 0.999 < sinpi(x4, rounding='d') < 1
assert -1 < cospi(x5, rounding='d') < -0.999
assert -1 < cospi(x6, rounding='d') < -0.999
assert -1 < sinpi(x7, rounding='d') < -0.999
assert -1 < sinpi(x8, rounding='d') < -0.999
assert (sinpi(1e-15)*M).ae(pi)
assert (sinpi(-1e-15)*M).ae(-pi)
assert cospi(1e-15) == 1
assert cospi(1e-15, rounding='d') < 1
def test_cospi_sinpi():
assert sinpi(0) == 0
assert sinpi(0.5) == 1
assert sinpi(1) == 0
assert sinpi(1.5) == -1
assert sinpi(2) == 0
assert sinpi(2.5) == 1
assert sinpi(-0.5) == -1
assert cospi(0) == 1
assert cospi(0.5) == 0
assert cospi(1) == -1
assert cospi(1.5) == 0
assert cospi(2) == 1
assert cospi(2.5) == 0
assert cospi(-0.5) == 0
assert cospi(100000000000.25).ae(sqrt(2)/2)
a = cospi(2+3j)
assert a.real.ae(cos((2+3j)*pi).real)
assert a.imag == 0
b = sinpi(2+3j)
assert b.imag.ae(sin((2+3j)*pi).imag)
assert b.real == 0
mp.dps = 35
x1 = mpf(10000) - mpf('1e-15')
x2 = mpf(10000) + mpf('1e-15')
x3 = mpf(10000.5) - mpf('1e-15')
x4 = mpf(10000.5) + mpf('1e-15')
x5 = mpf(10001) - mpf('1e-15')
x6 = mpf(10001) + mpf('1e-15')
x7 = mpf(10001.5) - mpf('1e-15')
x8 = mpf(10001.5) + mpf('1e-15')
mp.dps = 15
M = 10**15
assert (sinpi(x1)*M).ae(-pi)
assert (sinpi(x2)*M).ae(pi)
assert (cospi(x3)*M).ae(pi)
assert (cospi(x4)*M).ae(-pi)
assert (sinpi(x5)*M).ae(pi)
assert (sinpi(x6)*M).ae(-pi)
assert (cospi(x7)*M).ae(-pi)
assert (cospi(x8)*M).ae(pi)
assert 0.999 < cospi(x1, rounding='d') < 1
assert 0.999 < cospi(x2, rounding='d') < 1
assert 0.999 < sinpi(x3, rounding='d') < 1
assert 0.999 < sinpi(x4, rounding='d') < 1
assert -1 < cospi(x5, rounding='d') < -0.999
assert -1 < cospi(x6, rounding='d') < -0.999
assert -1 < sinpi(x7, rounding='d') < -0.999
assert -1 < sinpi(x8, rounding='d') < -0.999
assert (sinpi(1e-15)*M).ae(pi)
assert (sinpi(-1e-15)*M).ae(-pi)
assert cospi(1e-15) == 1
assert cospi(1e-15, rounding='d') < 1
def test_cospi_sinpi():
assert sinpi(0) == 0
assert sinpi(0.5) == 1
assert sinpi(1) == 0
assert sinpi(1.5) == -1
assert sinpi(2) == 0
assert sinpi(2.5) == 1
assert sinpi(-0.5) == -1
assert cospi(0) == 1
assert cospi(0.5) == 0
assert cospi(1) == -1
assert cospi(1.5) == 0
assert cospi(2) == 1
assert cospi(2.5) == 0
assert cospi(-0.5) == 0
assert cospi(100000000000.25).ae(sqrt(2)/2)
a = cospi(2+3j)
assert a.real.ae(cos((2+3j)*pi).real)
assert a.imag == 0
b = sinpi(2+3j)
assert b.imag.ae(sin((2+3j)*pi).imag)
assert b.real == 0
mp.dps = 35
x1 = mpf(10000) - mpf('1e-15')
x2 = mpf(10000) + mpf('1e-15')
x3 = mpf(10000.5) - mpf('1e-15')
x4 = mpf(10000.5) + mpf('1e-15')
x5 = mpf(10001) - mpf('1e-15')
x6 = mpf(10001) + mpf('1e-15')
x7 = mpf(10001.5) - mpf('1e-15')
x8 = mpf(10001.5) + mpf('1e-15')
mp.dps = 15
M = 10**15
assert (sinpi(x1)*M).ae(-pi)
assert (sinpi(x2)*M).ae(pi)
assert (cospi(x3)*M).ae(pi)
assert (cospi(x4)*M).ae(-pi)
assert (sinpi(x5)*M).ae(pi)
assert (sinpi(x6)*M).ae(-pi)
assert (cospi(x7)*M).ae(-pi)
assert (cospi(x8)*M).ae(pi)
assert 0.999 < cospi(x1, rounding='d') < 1
assert 0.999 < cospi(x2, rounding='d') < 1
assert 0.999 < sinpi(x3, rounding='d') < 1
assert 0.999 < sinpi(x4, rounding='d') < 1
assert -1 < cospi(x5, rounding='d') < -0.999
assert -1 < cospi(x6, rounding='d') < -0.999
assert -1 < sinpi(x7, rounding='d') < -0.999
assert -1 < sinpi(x8, rounding='d') < -0.999
assert (sinpi(1e-15)*M).ae(pi)
assert (sinpi(-1e-15)*M).ae(-pi)
assert cospi(1e-15) == 1
assert cospi(1e-15, rounding='d') < 1
