def test_hermefromroots(self):
res = herme.hermefromroots([])
assert_almost_equal(trim(res), [1])
for i in range(1, 5):
roots = np.cos(np.linspace(-np.pi, 0, 2 * i + 1)[1::2])
pol = herme.hermefromroots(roots)
res = herme.hermeval(roots, pol)
tgt = 0
assert_(len(pol) == i + 1)
assert_almost_equal(herme.herme2poly(pol)[-1], 1)
assert_almost_equal(res, tgt)
def test_hermefromroots(self) :
res = herme.hermefromroots([])
assert_almost_equal(trim(res), [1])
for i in range(1,5) :
roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2])
pol = herme.hermefromroots(roots)
res = herme.hermeval(roots, pol)
tgt = 0
assert_(len(pol) == i + 1)
assert_almost_equal(herme.herme2poly(pol)[-1], 1)
assert_almost_equal(res, tgt)
def test_herme2poly(self):
for i in range(10):
assert_almost_equal(herme.herme2poly([0] * i + [1]), Helist[i])
def test_hermeint(self):
# check exceptions
assert_raises(TypeError, herme.hermeint, [0], .5)
assert_raises(ValueError, herme.hermeint, [0], -1)
assert_raises(ValueError, herme.hermeint, [0], 1, [0, 0])
assert_raises(ValueError, herme.hermeint, [0], lbnd=[0])
assert_raises(ValueError, herme.hermeint, [0], scl=[0])
assert_raises(TypeError, herme.hermeint, [0], axis=.5)
# test integration of zero polynomial
for i in range(2, 5):
k = [0] * (i - 2) + [1]
res = herme.hermeint([0], m=i, k=k)
assert_almost_equal(res, [0, 1])
# check single integration with integration constant
for i in range(5):
scl = i + 1
pol = [0] * i + [1]
tgt = [i] + [0] * i + [1 / scl]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i])
res = herme.herme2poly(hermeint)
assert_almost_equal(trim(res), trim(tgt))
# check single integration with integration constant and lbnd
for i in range(5):
scl = i + 1
pol = [0] * i + [1]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i], lbnd=-1)
assert_almost_equal(herme.hermeval(-1, hermeint), i)
# check single integration with integration constant and scaling
for i in range(5):
scl = i + 1
pol = [0] * i + [1]
tgt = [i] + [0] * i + [2 / scl]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i], scl=2)
res = herme.herme2poly(hermeint)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with default k
for i in range(5):
for j in range(2, 5):
pol = [0] * i + [1]
tgt = pol[:]
for k in range(j):
tgt = herme.hermeint(tgt, m=1)
res = herme.hermeint(pol, m=j)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with defined k
for i in range(5):
for j in range(2, 5):
pol = [0] * i + [1]
tgt = pol[:]
for k in range(j):
tgt = herme.hermeint(tgt, m=1, k=[k])
res = herme.hermeint(pol, m=j, k=list(range(j)))
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with lbnd
for i in range(5):
for j in range(2, 5):
pol = [0] * i + [1]
tgt = pol[:]
for k in range(j):
tgt = herme.hermeint(tgt, m=1, k=[k], lbnd=-1)
res = herme.hermeint(pol, m=j, k=list(range(j)), lbnd=-1)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with scaling
for i in range(5):
for j in range(2, 5):
pol = [0] * i + [1]
tgt = pol[:]
for k in range(j):
tgt = herme.hermeint(tgt, m=1, k=[k], scl=2)
res = herme.hermeint(pol, m=j, k=list(range(j)), scl=2)
assert_almost_equal(trim(res), trim(tgt))
def test_herme2poly(self) :
for i in range(10) :
assert_almost_equal(herme.herme2poly([0]*i + [1]), Helist[i])
def test_hermeint(self) :
# check exceptions
assert_raises(ValueError, herme.hermeint, [0], .5)
assert_raises(ValueError, herme.hermeint, [0], -1)
assert_raises(ValueError, herme.hermeint, [0], 1, [0,0])
# test integration of zero polynomial
for i in range(2, 5):
k = [0]*(i - 2) + [1]
res = herme.hermeint([0], m=i, k=k)
assert_almost_equal(res, [0, 1])
# check single integration with integration constant
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [1/scl]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i])
res = herme.herme2poly(hermeint)
assert_almost_equal(trim(res), trim(tgt))
# check single integration with integration constant and lbnd
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i], lbnd=-1)
assert_almost_equal(herme.hermeval(-1, hermeint), i)
# check single integration with integration constant and scaling
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [2/scl]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i], scl=2)
res = herme.herme2poly(hermeint)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with default k
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = herme.hermeint(tgt, m=1)
res = herme.hermeint(pol, m=j)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with defined k
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = herme.hermeint(tgt, m=1, k=[k])
res = herme.hermeint(pol, m=j, k=range(j))
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with lbnd
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = herme.hermeint(tgt, m=1, k=[k], lbnd=-1)
res = herme.hermeint(pol, m=j, k=range(j), lbnd=-1)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with scaling
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = herme.hermeint(tgt, m=1, k=[k], scl=2)
res = herme.hermeint(pol, m=j, k=range(j), scl=2)
assert_almost_equal(trim(res), trim(tgt))
def toPolynomial(self, projection):
return hermite_e.herme2poly(projection.coef)
