def test_hermfromroots(self) :
res = herm.hermfromroots([])
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 = herm.hermfromroots(roots)
res = herm.hermval(roots, pol)
tgt = 0
assert_(len(pol) == i + 1)
assert_almost_equal(herm.herm2poly(pol)[-1], 1)
assert_almost_equal(res, tgt)
def test_herm2poly(self) :
for i in range(10) :
assert_almost_equal(herm.herm2poly([0]*i + [1]), Hlist[i])
def test_herm2poly(self):
for i in range(10):
assert_almost_equal(herm.herm2poly([0]*i + [1]), Hlist[i])
def test_hermint(self) :
# check exceptions
assert_raises(ValueError, herm.hermint, [0], .5)
assert_raises(ValueError, herm.hermint, [0], -1)
assert_raises(ValueError, herm.hermint, [0], 1, [0,0])
# test integration of zero polynomial
for i in range(2, 5):
k = [0]*(i - 2) + [1]
res = herm.hermint([0], m=i, k=k)
assert_almost_equal(res, [0, .5])
# check single integration with integration constant
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [1/scl]
hermpol = herm.poly2herm(pol)
hermint = herm.hermint(hermpol, m=1, k=[i])
res = herm.herm2poly(hermint)
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]
hermpol = herm.poly2herm(pol)
hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1)
assert_almost_equal(herm.hermval(-1, hermint), 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]
hermpol = herm.poly2herm(pol)
hermint = herm.hermint(hermpol, m=1, k=[i], scl=2)
res = herm.herm2poly(hermint)
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 = herm.hermint(tgt, m=1)
res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k])
res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k], lbnd=-1)
res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k], scl=2)
res = herm.hermint(pol, m=j, k=list(range(j)), scl=2)
assert_almost_equal(trim(res), trim(tgt))
def test_hermint(self):
# check exceptions
assert_raises(ValueError, herm.hermint, [0], .5)
assert_raises(ValueError, herm.hermint, [0], -1)
assert_raises(ValueError, herm.hermint, [0], 1, [0, 0])
# test integration of zero polynomial
for i in range(2, 5):
k = [0]*(i - 2) + [1]
res = herm.hermint([0], m=i, k=k)
assert_almost_equal(res, [0, .5])
# check single integration with integration constant
for i in range(5):
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [1/scl]
hermpol = herm.poly2herm(pol)
hermint = herm.hermint(hermpol, m=1, k=[i])
res = herm.herm2poly(hermint)
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]
hermpol = herm.poly2herm(pol)
hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1)
assert_almost_equal(herm.hermval(-1, hermint), 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]
hermpol = herm.poly2herm(pol)
hermint = herm.hermint(hermpol, m=1, k=[i], scl=2)
res = herm.herm2poly(hermint)
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 = herm.hermint(tgt, m=1)
res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k])
res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k], lbnd=-1)
res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k], scl=2)
res = herm.hermint(pol, m=j, k=list(range(j)), scl=2)
assert_almost_equal(trim(res), trim(tgt))