def test_polyvander(self):
# check for 1d x
x = np.arange(3)
v = poly.polyvander(x, 3)
assert_(v.shape == (3, 4))
for i in range(4):
coef = [0] * i + [1]
assert_almost_equal(v[..., i], poly.polyval(x, coef))
# check for 2d x
x = np.array([[1, 2], [3, 4], [5, 6]])
v = poly.polyvander(x, 3)
assert_(v.shape == (3, 2, 4))
for i in range(4):
coef = [0] * i + [1]
assert_almost_equal(v[..., i], poly.polyval(x, coef))
def test_lagval(self):
#check empty input
assert_equal(lag.lagval([], [1]).size, 0)
#check normal input)
x = np.linspace(-1, 1)
y = [polyval(x, c) for c in Llist]
for i in range(7):
msg = "At i=%d" % i
tgt = y[i]
res = lag.lagval(x, [0] * i + [1])
assert_almost_equal(res, tgt, err_msg=msg)
#check that shape is preserved
for i in range(3):
dims = [2] * i
x = np.zeros(dims)
assert_equal(lag.lagval(x, [1]).shape, dims)
assert_equal(lag.lagval(x, [1, 0]).shape, dims)
assert_equal(lag.lagval(x, [1, 0, 0]).shape, dims)
def test_polyval(self):
#check empty input
assert_equal(poly.polyval([], [1]).size, 0)
#check normal input)
x = np.linspace(-1, 1)
y = [x**i for i in range(5)]
for i in range(5):
tgt = y[i]
res = poly.polyval(x, [0] * i + [1])
assert_almost_equal(res, tgt)
tgt = x * (x**2 - 1)
res = poly.polyval(x, [0, -1, 0, 1])
assert_almost_equal(res, tgt)
#check that shape is preserved
for i in range(3):
dims = [2] * i
x = np.zeros(dims)
assert_equal(poly.polyval(x, [1]).shape, dims)
assert_equal(poly.polyval(x, [1, 0]).shape, dims)
assert_equal(poly.polyval(x, [1, 0, 0]).shape, dims)
class TestEvaluation(object):
# coefficients of 1 + 2*x + 3*x**2
c1d = np.array([9., -14., 6.])
c2d = np.einsum('i,j->ij', c1d, c1d)
c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d)
# some random values in [-1, 1)
x = np.random.random((3, 5)) * 2 - 1
y = polyval(x, [1., 2., 3.])
def test_lagval(self):
#check empty input
assert_equal(lag.lagval([], [1]).size, 0)
#check normal input)
x = np.linspace(-1, 1)
y = [polyval(x, c) for c in Llist]
for i in range(7):
msg = "At i=%d" % i
tgt = y[i]
res = lag.lagval(x, [0] * i + [1])
assert_almost_equal(res, tgt, err_msg=msg)
#check that shape is preserved
for i in range(3):
dims = [2] * i
x = np.zeros(dims)
assert_equal(lag.lagval(x, [1]).shape, dims)
assert_equal(lag.lagval(x, [1, 0]).shape, dims)
assert_equal(lag.lagval(x, [1, 0, 0]).shape, dims)
def test_lagval2d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test exceptions
assert_raises(ValueError, lag.lagval2d, x1, x2[:2], self.c2d)
#test values
tgt = y1 * y2
res = lag.lagval2d(x1, x2, self.c2d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.lagval2d(z, z, self.c2d)
assert_(res.shape == (2, 3))
def test_lagval3d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test exceptions
assert_raises(ValueError, lag.lagval3d, x1, x2, x3[:2], self.c3d)
#test values
tgt = y1 * y2 * y3
res = lag.lagval3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.lagval3d(z, z, z, self.c3d)
assert_(res.shape == (2, 3))
def test_laggrid2d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test values
tgt = np.einsum('i,j->ij', y1, y2)
res = lag.laggrid2d(x1, x2, self.c2d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.laggrid2d(z, z, self.c2d)
assert_(res.shape == (2, 3) * 2)
def test_laggrid3d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test values
tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
res = lag.laggrid3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.laggrid3d(z, z, z, self.c3d)
assert_(res.shape == (2, 3) * 3)
def test_polyfit(self):
def f(x):
return x * (x - 1) * (x - 2)
def f2(x):
return x**4 + x**2 + 1
# Test exceptions
assert_raises(ValueError, poly.polyfit, [1], [1], -1)
assert_raises(TypeError, poly.polyfit, [[1]], [1], 0)
assert_raises(TypeError, poly.polyfit, [], [1], 0)
assert_raises(TypeError, poly.polyfit, [1], [[[1]]], 0)
assert_raises(TypeError, poly.polyfit, [1, 2], [1], 0)
assert_raises(TypeError, poly.polyfit, [1], [1, 2], 0)
assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[[1]])
assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[1, 1])
assert_raises(ValueError, poly.polyfit, [1], [1], [
-1,
])
assert_raises(ValueError, poly.polyfit, [1], [1], [2, -1, 6])
assert_raises(TypeError, poly.polyfit, [1], [1], [])
# Test fit
x = np.linspace(0, 2)
y = f(x)
#
coef3 = poly.polyfit(x, y, 3)
assert_equal(len(coef3), 4)
assert_almost_equal(poly.polyval(x, coef3), y)
coef3 = poly.polyfit(x, y, [0, 1, 2, 3])
assert_equal(len(coef3), 4)
assert_almost_equal(poly.polyval(x, coef3), y)
#
coef4 = poly.polyfit(x, y, 4)
assert_equal(len(coef4), 5)
assert_almost_equal(poly.polyval(x, coef4), y)
coef4 = poly.polyfit(x, y, [0, 1, 2, 3, 4])
assert_equal(len(coef4), 5)
assert_almost_equal(poly.polyval(x, coef4), y)
#
coef2d = poly.polyfit(x, np.array([y, y]).T, 3)
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
coef2d = poly.polyfit(x, np.array([y, y]).T, [0, 1, 2, 3])
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
# test weighting
w = np.zeros_like(x)
yw = y.copy()
w[1::2] = 1
yw[0::2] = 0
wcoef3 = poly.polyfit(x, yw, 3, w=w)
assert_almost_equal(wcoef3, coef3)
wcoef3 = poly.polyfit(x, yw, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef3, coef3)
#
wcoef2d = poly.polyfit(x, np.array([yw, yw]).T, 3, w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
wcoef2d = poly.polyfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
# test scaling with complex values x points whose square
# is zero when summed.
x = [1, 1j, -1, -1j]
assert_almost_equal(poly.polyfit(x, x, 1), [0, 1])
assert_almost_equal(poly.polyfit(x, x, [0, 1]), [0, 1])
# test fitting only even Polyendre polynomials
x = np.linspace(-1, 1)
y = f2(x)
coef1 = poly.polyfit(x, y, 4)
assert_almost_equal(poly.polyval(x, coef1), y)
coef2 = poly.polyfit(x, y, [0, 2, 4])
assert_almost_equal(poly.polyval(x, coef2), y)
assert_almost_equal(coef1, coef2)
def test_polyint(self):
# check exceptions
assert_raises(ValueError, poly.polyint, [0], .5)
assert_raises(ValueError, poly.polyint, [0], -1)
assert_raises(ValueError, poly.polyint, [0], 1, [0, 0])
assert_raises(ValueError, poly.polyint, [0], lbnd=[0])
assert_raises(ValueError, poly.polyint, [0], scl=[0])
assert_raises(ValueError, poly.polyint, [0], axis=.5)
# test integration of zero polynomial
for i in range(2, 5):
k = [0] * (i - 2) + [1]
res = poly.polyint([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]
res = poly.polyint(pol, m=1, k=[i])
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]
res = poly.polyint(pol, m=1, k=[i], lbnd=-1)
assert_almost_equal(poly.polyval(-1, res), 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]
res = poly.polyint(pol, m=1, k=[i], scl=2)
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 = poly.polyint(tgt, m=1)
res = poly.polyint(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 = poly.polyint(tgt, m=1, k=[k])
res = poly.polyint(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 = poly.polyint(tgt, m=1, k=[k], lbnd=-1)
res = poly.polyint(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 = poly.polyint(tgt, m=1, k=[k], scl=2)
res = poly.polyint(pol, m=j, k=list(range(j)), scl=2)
assert_almost_equal(trim(res), trim(tgt))
def test_polyvalfromroots(self):
# check exception for broadcasting x values over root array with
# too few dimensions
assert_raises(ValueError,
poly.polyvalfromroots, [1], [1],
tensor=False)
# check empty input
assert_equal(poly.polyvalfromroots([], [1]).size, 0)
assert_(poly.polyvalfromroots([], [1]).shape == (0, ))
# check empty input + multidimensional roots
assert_equal(poly.polyvalfromroots([], [[1] * 5]).size, 0)
assert_(poly.polyvalfromroots([], [[1] * 5]).shape == (5, 0))
# check scalar input
assert_equal(poly.polyvalfromroots(1, 1), 0)
assert_(poly.polyvalfromroots(1, np.ones((3, 3))).shape == (3, ))
# check normal input)
x = np.linspace(-1, 1)
y = [x**i for i in range(5)]
for i in range(1, 5):
tgt = y[i]
res = poly.polyvalfromroots(x, [0] * i)
assert_almost_equal(res, tgt)
tgt = x * (x - 1) * (x + 1)
res = poly.polyvalfromroots(x, [-1, 0, 1])
assert_almost_equal(res, tgt)
# check that shape is preserved
for i in range(3):
dims = [2] * i
x = np.zeros(dims)
assert_equal(poly.polyvalfromroots(x, [1]).shape, dims)
assert_equal(poly.polyvalfromroots(x, [1, 0]).shape, dims)
assert_equal(poly.polyvalfromroots(x, [1, 0, 0]).shape, dims)
# check compatibility with factorization
ptest = [15, 2, -16, -2, 1]
r = poly.polyroots(ptest)
x = np.linspace(-1, 1)
assert_almost_equal(poly.polyval(x, ptest),
poly.polyvalfromroots(x, r))
# check multidimensional arrays of roots and values
# check tensor=False
rshape = (3, 5)
x = np.arange(-3, 2)
r = np.random.randint(-5, 5, size=rshape)
res = poly.polyvalfromroots(x, r, tensor=False)
tgt = np.empty(r.shape[1:])
for ii in range(tgt.size):
tgt[ii] = poly.polyvalfromroots(x[ii], r[:, ii])
assert_equal(res, tgt)
# check tensor=True
x = np.vstack([x, 2 * x])
res = poly.polyvalfromroots(x, r, tensor=True)
tgt = np.empty(r.shape[1:] + x.shape)
for ii in range(r.shape[1]):
for jj in range(x.shape[0]):
tgt[ii, jj, :] = poly.polyvalfromroots(x[jj], r[:, ii])
assert_equal(res, tgt)
class TestEvaluation(object):
# coefficients of 1 + 2*x + 3*x**2
c1d = np.array([1., 2., 3.])
c2d = np.einsum('i,j->ij', c1d, c1d)
c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d)
# some random values in [-1, 1)
x = np.random.random((3, 5)) * 2 - 1
y = poly.polyval(x, [1., 2., 3.])
def test_polyval(self):
#check empty input
assert_equal(poly.polyval([], [1]).size, 0)
#check normal input)
x = np.linspace(-1, 1)
y = [x**i for i in range(5)]
for i in range(5):
tgt = y[i]
res = poly.polyval(x, [0] * i + [1])
assert_almost_equal(res, tgt)
tgt = x * (x**2 - 1)
res = poly.polyval(x, [0, -1, 0, 1])
assert_almost_equal(res, tgt)
#check that shape is preserved
for i in range(3):
dims = [2] * i
x = np.zeros(dims)
assert_equal(poly.polyval(x, [1]).shape, dims)
assert_equal(poly.polyval(x, [1, 0]).shape, dims)
assert_equal(poly.polyval(x, [1, 0, 0]).shape, dims)
def test_polyvalfromroots(self):
# check exception for broadcasting x values over root array with
# too few dimensions
assert_raises(ValueError,
poly.polyvalfromroots, [1], [1],
tensor=False)
# check empty input
assert_equal(poly.polyvalfromroots([], [1]).size, 0)
assert_(poly.polyvalfromroots([], [1]).shape == (0, ))
# check empty input + multidimensional roots
assert_equal(poly.polyvalfromroots([], [[1] * 5]).size, 0)
assert_(poly.polyvalfromroots([], [[1] * 5]).shape == (5, 0))
# check scalar input
assert_equal(poly.polyvalfromroots(1, 1), 0)
assert_(poly.polyvalfromroots(1, np.ones((3, 3))).shape == (3, ))
# check normal input)
x = np.linspace(-1, 1)
y = [x**i for i in range(5)]
for i in range(1, 5):
tgt = y[i]
res = poly.polyvalfromroots(x, [0] * i)
assert_almost_equal(res, tgt)
tgt = x * (x - 1) * (x + 1)
res = poly.polyvalfromroots(x, [-1, 0, 1])
assert_almost_equal(res, tgt)
# check that shape is preserved
for i in range(3):
dims = [2] * i
x = np.zeros(dims)
assert_equal(poly.polyvalfromroots(x, [1]).shape, dims)
assert_equal(poly.polyvalfromroots(x, [1, 0]).shape, dims)
assert_equal(poly.polyvalfromroots(x, [1, 0, 0]).shape, dims)
# check compatibility with factorization
ptest = [15, 2, -16, -2, 1]
r = poly.polyroots(ptest)
x = np.linspace(-1, 1)
assert_almost_equal(poly.polyval(x, ptest),
poly.polyvalfromroots(x, r))
# check multidimensional arrays of roots and values
# check tensor=False
rshape = (3, 5)
x = np.arange(-3, 2)
r = np.random.randint(-5, 5, size=rshape)
res = poly.polyvalfromroots(x, r, tensor=False)
tgt = np.empty(r.shape[1:])
for ii in range(tgt.size):
tgt[ii] = poly.polyvalfromroots(x[ii], r[:, ii])
assert_equal(res, tgt)
# check tensor=True
x = np.vstack([x, 2 * x])
res = poly.polyvalfromroots(x, r, tensor=True)
tgt = np.empty(r.shape[1:] + x.shape)
for ii in range(r.shape[1]):
for jj in range(x.shape[0]):
tgt[ii, jj, :] = poly.polyvalfromroots(x[jj], r[:, ii])
assert_equal(res, tgt)
def test_polyval2d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test exceptions
assert_raises(ValueError, poly.polyval2d, x1, x2[:2], self.c2d)
#test values
tgt = y1 * y2
res = poly.polyval2d(x1, x2, self.c2d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = poly.polyval2d(z, z, self.c2d)
assert_(res.shape == (2, 3))
def test_polyval3d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test exceptions
assert_raises(ValueError, poly.polyval3d, x1, x2, x3[:2], self.c3d)
#test values
tgt = y1 * y2 * y3
res = poly.polyval3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = poly.polyval3d(z, z, z, self.c3d)
assert_(res.shape == (2, 3))
def test_polygrid2d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test values
tgt = np.einsum('i,j->ij', y1, y2)
res = poly.polygrid2d(x1, x2, self.c2d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = poly.polygrid2d(z, z, self.c2d)
assert_(res.shape == (2, 3) * 2)
def test_polygrid3d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test values
tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
res = poly.polygrid3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = poly.polygrid3d(z, z, z, self.c3d)
assert_(res.shape == (2, 3) * 3)