def test_hermeder(self):
# check exceptions
assert_raises(ValueError, herme.hermeder, [0], .5)
assert_raises(ValueError, herme.hermeder, [0], -1)
# check that zeroth derivative does nothing
for i in range(5):
tgt = [0]*i + [1]
res = herme.hermeder(tgt, m=0)
assert_equal(trim(res), trim(tgt))
# check that derivation is the inverse of integration
for i in range(5):
for j in range(2, 5):
tgt = [0]*i + [1]
res = herme.hermeder(herme.hermeint(tgt, m=j), m=j)
assert_almost_equal(trim(res), trim(tgt))
# check derivation with scaling
for i in range(5):
for j in range(2, 5):
tgt = [0]*i + [1]
res = herme.hermeder(
herme.hermeint(tgt, m=j, scl=2), m=j, scl=.5)
assert_almost_equal(trim(res), trim(tgt))
def test_hermeder(self):
# check exceptions
assert_raises(TypeError, herme.hermeder, [0], .5)
assert_raises(ValueError, herme.hermeder, [0], -1)
# check that zeroth derivative does nothing
for i in range(5):
tgt = [0] * i + [1]
res = herme.hermeder(tgt, m=0)
assert_equal(trim(res), trim(tgt))
# check that derivation is the inverse of integration
for i in range(5):
for j in range(2, 5):
tgt = [0] * i + [1]
res = herme.hermeder(herme.hermeint(tgt, m=j), m=j)
assert_almost_equal(trim(res), trim(tgt))
# check derivation with scaling
for i in range(5):
for j in range(2, 5):
tgt = [0] * i + [1]
res = herme.hermeder(herme.hermeint(tgt, m=j, scl=2),
m=j,
scl=.5)
assert_almost_equal(trim(res), trim(tgt))
def test_integ(self) :
p = self.p2.integ()
assert_almost_equal(p.coef, herme.hermeint([1,2,3], 1, 0, scl=.5))
p = self.p2.integ(lbnd=0)
assert_almost_equal(p(0), 0)
p = self.p2.integ(1, 1)
assert_almost_equal(p.coef, herme.hermeint([1,2,3], 1, 1, scl=.5))
p = self.p2.integ(2, [1, 2])
assert_almost_equal(p.coef, herme.hermeint([1,2,3], 2, [1,2], scl=.5))
def test_hermeint_axis(self):
# check that axis keyword works
c2d = np.random.random((3, 4))
tgt = np.vstack([herme.hermeint(c) for c in c2d.T]).T
res = herme.hermeint(c2d, axis=0)
assert_almost_equal(res, tgt)
tgt = np.vstack([herme.hermeint(c) for c in c2d])
res = herme.hermeint(c2d, axis=1)
assert_almost_equal(res, tgt)
tgt = np.vstack([herme.hermeint(c, k=3) for c in c2d])
res = herme.hermeint(c2d, k=3, axis=1)
assert_almost_equal(res, tgt)
def test_hermeint_axis(self):
# check that axis keyword works
c2d = np.random.random((3, 4))
tgt = np.vstack([herme.hermeint(c) for c in c2d.T]).T
res = herme.hermeint(c2d, axis=0)
assert_almost_equal(res, tgt)
tgt = np.vstack([herme.hermeint(c) for c in c2d])
res = herme.hermeint(c2d, axis=1)
assert_almost_equal(res, tgt)
tgt = np.vstack([herme.hermeint(c, k=3) for c in c2d])
res = herme.hermeint(c2d, k=3, axis=1)
assert_almost_equal(res, tgt)
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_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))