text: """Test inter-conversion of different polynomial classes.
  
  This tests the convert and cast methods of all the polynomial classes.
  
  """
  from __future__ import division, absolute_import, print_function
  
  import operator as op
  from numbers import Number
  
  import numpy as np
  from numpy.polynomial import (
      Polynomial, Legendre, Chebyshev, Laguerre, Hermite, HermiteE)
  from numpy.testing import (
      assert_almost_equal, assert_raises, assert_equal, assert_,
      run_module_suite)
  from numpy.compat import long
  
  
  classes = (
      Polynomial, Legendre, Chebyshev, Laguerre,
      Hermite, HermiteE)
  
  
  def test_class_methods():
      for Poly1 in classes:
          for Poly2 in classes:
              yield check_conversion, Poly1, Poly2
              yield check_cast, Poly1, Poly2
      for Poly in classes:
          yield check_call, Poly
          yield check_identity, Poly
          yield check_basis, Poly
          yield check_fromroots, Poly
          yield check_fit, Poly
          yield check_equal, Poly
          yield check_not_equal, Poly
          yield check_add, Poly
          yield check_sub, Poly
          yield check_mul, Poly
          yield check_floordiv, Poly
          yield check_truediv, Poly
          yield check_mod, Poly
          yield check_divmod, Poly
          yield check_pow, Poly
          yield check_integ, Poly
          yield check_deriv, Poly
          yield check_roots, Poly
          yield check_linspace, Poly
          yield check_mapparms, Poly
          yield check_degree, Poly
          yield check_copy, Poly
          yield check_cutdeg, Poly
          yield check_truncate, Poly
          yield check_trim, Poly
          yield check_ufunc_override, Poly
  
  
  #
  # helper functions
  #
  random = np.random.random
  
  
  def assert_poly_almost_equal(p1, p2, msg=""):
      try:
          assert_(np.all(p1.domain == p2.domain))
          assert_(np.all(p1.window == p2.window))
          assert_almost_equal(p1.coef, p2.coef)
      except AssertionError:
          msg = "Result: %s\nTarget: %s", (p1, p2)
          raise AssertionError(msg)
  
  
  #
  # conversion methods that depend on two classes
  #
  
  
  def check_conversion(Poly1, Poly2):
      x = np.linspace(0, 1, 10)
      coef = random((3,))
  
      d1 = Poly1.domain + random((2,))*.25
      w1 = Poly1.window + random((2,))*.25
      p1 = Poly1(coef, domain=d1, window=w1)
  
      d2 = Poly2.domain + random((2,))*.25
      w2 = Poly2.window + random((2,))*.25
      p2 = p1.convert(kind=Poly2, domain=d2, window=w2)
  
      assert_almost_equal(p2.domain, d2)
      assert_almost_equal(p2.window, w2)
      assert_almost_equal(p2(x), p1(x))
  
  
  def check_cast(Poly1, Poly2):
      x = np.linspace(0, 1, 10)
      coef = random((3,))
  
      d1 = Poly1.domain + random((2,))*.25
      w1 = Poly1.window + random((2,))*.25
      p1 = Poly1(coef, domain=d1, window=w1)
  
      d2 = Poly2.domain + random((2,))*.25
      w2 = Poly2.window + random((2,))*.25
      p2 = Poly2.cast(p1, domain=d2, window=w2)
  
      assert_almost_equal(p2.domain, d2)
      assert_almost_equal(p2.window, w2)
      assert_almost_equal(p2(x), p1(x))
  
  
  #
  # methods that depend on one class
  #
  
  
  def check_identity(Poly):
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      x = np.linspace(d[0], d[1], 11)
      p = Poly.identity(domain=d, window=w)
      assert_equal(p.domain, d)
      assert_equal(p.window, w)
      assert_almost_equal(p(x), x)
  
  
  def check_basis(Poly):
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      p = Poly.basis(5, domain=d, window=w)
      assert_equal(p.domain, d)
      assert_equal(p.window, w)
      assert_equal(p.coef, [0]*5 + [1])
  
  
  def check_fromroots(Poly):
      # check that requested roots are zeros of a polynomial
      # of correct degree, domain, and window.
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      r = random((5,))
      p1 = Poly.fromroots(r, domain=d, window=w)
      assert_equal(p1.degree(), len(r))
      assert_equal(p1.domain, d)
      assert_equal(p1.window, w)
      assert_almost_equal(p1(r), 0)
  
      # check that polynomial is monic
      pdom = Polynomial.domain
      pwin = Polynomial.window
      p2 = Polynomial.cast(p1, domain=pdom, window=pwin)
      assert_almost_equal(p2.coef[-1], 1)
  
  
  def check_fit(Poly):
  
      def f(x):
          return x*(x - 1)*(x - 2)
      x = np.linspace(0, 3)
      y = f(x)
  
      # check default value of domain and window
      p = Poly.fit(x, y, 3)
      assert_almost_equal(p.domain, [0, 3])
      assert_almost_equal(p(x), y)
      assert_equal(p.degree(), 3)
  
      # check with given domains and window
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      p = Poly.fit(x, y, 3, domain=d, window=w)
      assert_almost_equal(p(x), y)
      assert_almost_equal(p.domain, d)
      assert_almost_equal(p.window, w)
      p = Poly.fit(x, y, [0, 1, 2, 3], domain=d, window=w)
      assert_almost_equal(p(x), y)
      assert_almost_equal(p.domain, d)
      assert_almost_equal(p.window, w)
  
      # check with class domain default
      p = Poly.fit(x, y, 3, [])
      assert_equal(p.domain, Poly.domain)
      assert_equal(p.window, Poly.window)
      p = Poly.fit(x, y, [0, 1, 2, 3], [])
      assert_equal(p.domain, Poly.domain)
      assert_equal(p.window, Poly.window)
  
      # check that fit accepts weights.
      w = np.zeros_like(x)
      z = y + random(y.shape)*.25
      w[::2] = 1
      p1 = Poly.fit(x[::2], z[::2], 3)
      p2 = Poly.fit(x, z, 3, w=w)
      p3 = Poly.fit(x, z, [0, 1, 2, 3], w=w)
      assert_almost_equal(p1(x), p2(x))
      assert_almost_equal(p2(x), p3(x))
  
  
  def check_equal(Poly):
      p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3])
      p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3])
      p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3])
      p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2])
      assert_(p1 == p1)
      assert_(not p1 == p2)
      assert_(not p1 == p3)
      assert_(not p1 == p4)
  
  
  def check_not_equal(Poly):
      p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3])
      p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3])
      p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3])
      p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2])
      assert_(not p1 != p1)
      assert_(p1 != p2)
      assert_(p1 != p3)
      assert_(p1 != p4)
  
  
  def check_add(Poly):
      # This checks commutation, not numerical correctness
      c1 = list(random((4,)) + .5)
      c2 = list(random((3,)) + .5)
      p1 = Poly(c1)
      p2 = Poly(c2)
      p3 = p1 + p2
      assert_poly_almost_equal(p2 + p1, p3)
      assert_poly_almost_equal(p1 + c2, p3)
      assert_poly_almost_equal(c2 + p1, p3)
      assert_poly_almost_equal(p1 + tuple(c2), p3)
      assert_poly_almost_equal(tuple(c2) + p1, p3)
      assert_poly_almost_equal(p1 + np.array(c2), p3)
      assert_poly_almost_equal(np.array(c2) + p1, p3)
      assert_raises(TypeError, op.add, p1, Poly([0], domain=Poly.domain + 1))
      assert_raises(TypeError, op.add, p1, Poly([0], window=Poly.window + 1))
      if Poly is Polynomial:
          assert_raises(TypeError, op.add, p1, Chebyshev([0]))
      else:
          assert_raises(TypeError, op.add, p1, Polynomial([0]))
  
  
  def check_sub(Poly):
      # This checks commutation, not numerical correctness
      c1 = list(random((4,)) + .5)
      c2 = list(random((3,)) + .5)
      p1 = Poly(c1)
      p2 = Poly(c2)
      p3 = p1 - p2
      assert_poly_almost_equal(p2 - p1, -p3)
      assert_poly_almost_equal(p1 - c2, p3)
      assert_poly_almost_equal(c2 - p1, -p3)
      assert_poly_almost_equal(p1 - tuple(c2), p3)
      assert_poly_almost_equal(tuple(c2) - p1, -p3)
      assert_poly_almost_equal(p1 - np.array(c2), p3)
      assert_poly_almost_equal(np.array(c2) - p1, -p3)
      assert_raises(TypeError, op.sub, p1, Poly([0], domain=Poly.domain + 1))
      assert_raises(TypeError, op.sub, p1, Poly([0], window=Poly.window + 1))
      if Poly is Polynomial:
          assert_raises(TypeError, op.sub, p1, Chebyshev([0]))
      else:
          assert_raises(TypeError, op.sub, p1, Polynomial([0]))
  
  
  def check_mul(Poly):
      c1 = list(random((4,)) + .5)
      c2 = list(random((3,)) + .5)
      p1 = Poly(c1)
      p2 = Poly(c2)
      p3 = p1 * p2
      assert_poly_almost_equal(p2 * p1, p3)
      assert_poly_almost_equal(p1 * c2, p3)
      assert_poly_almost_equal(c2 * p1, p3)
      assert_poly_almost_equal(p1 * tuple(c2), p3)
      assert_poly_almost_equal(tuple(c2) * p1, p3)
      assert_poly_almost_equal(p1 * np.array(c2), p3)
      assert_poly_almost_equal(np.array(c2) * p1, p3)
      assert_poly_almost_equal(p1 * 2, p1 * Poly([2]))
      assert_poly_almost_equal(2 * p1, p1 * Poly([2]))
      assert_raises(TypeError, op.mul, p1, Poly([0], domain=Poly.domain + 1))
      assert_raises(TypeError, op.mul, p1, Poly([0], window=Poly.window + 1))
      if Poly is Polynomial:
          assert_raises(TypeError, op.mul, p1, Chebyshev([0]))
      else:
          assert_raises(TypeError, op.mul, p1, Polynomial([0]))
  
  
  def check_floordiv(Poly):
      c1 = list(random((4,)) + .5)
      c2 = list(random((3,)) + .5)
      c3 = list(random((2,)) + .5)
      p1 = Poly(c1)
      p2 = Poly(c2)
      p3 = Poly(c3)
      p4 = p1 * p2 + p3
      c4 = list(p4.coef)
      assert_poly_almost_equal(p4 // p2, p1)
      assert_poly_almost_equal(p4 // c2, p1)
      assert_poly_almost_equal(c4 // p2, p1)
      assert_poly_almost_equal(p4 // tuple(c2), p1)
      assert_poly_almost_equal(tuple(c4) // p2, p1)
      assert_poly_almost_equal(p4 // np.array(c2), p1)
      assert_poly_almost_equal(np.array(c4) // p2, p1)
      assert_poly_almost_equal(2 // p2, Poly([0]))
      assert_poly_almost_equal(p2 // 2, 0.5*p2)
      assert_raises(
          TypeError, op.floordiv, p1, Poly([0], domain=Poly.domain + 1))
      assert_raises(
          TypeError, op.floordiv, p1, Poly([0], window=Poly.window + 1))
      if Poly is Polynomial:
          assert_raises(TypeError, op.floordiv, p1, Chebyshev([0]))
      else:
          assert_raises(TypeError, op.floordiv, p1, Polynomial([0]))
  
  
  def check_truediv(Poly):
      # true division is valid only if the denominator is a Number and
      # not a python bool.
      p1 = Poly([1,2,3])
      p2 = p1 * 5
  
      for stype in np.ScalarType:
          if not issubclass(stype, Number) or issubclass(stype, bool):
              continue
          s = stype(5)
          assert_poly_almost_equal(op.truediv(p2, s), p1)
          assert_raises(TypeError, op.truediv, s, p2)
      for stype in (int, long, float):
          s = stype(5)
          assert_poly_almost_equal(op.truediv(p2, s), p1)
          assert_raises(TypeError, op.truediv, s, p2)
      for stype in [complex]:
          s = stype(5, 0)
          assert_poly_almost_equal(op.truediv(p2, s), p1)
          assert_raises(TypeError, op.truediv, s, p2)
      for s in [tuple(), list(), dict(), bool(), np.array([1])]:
          assert_raises(TypeError, op.truediv, p2, s)
          assert_raises(TypeError, op.truediv, s, p2)
      for ptype in classes:
          assert_raises(TypeError, op.truediv, p2, ptype(1))
  
  
  def check_mod(Poly):
      # This checks commutation, not numerical correctness
      c1 = list(random((4,)) + .5)
      c2 = list(random((3,)) + .5)
      c3 = list(random((2,)) + .5)
      p1 = Poly(c1)
      p2 = Poly(c2)
      p3 = Poly(c3)
      p4 = p1 * p2 + p3
      c4 = list(p4.coef)
      assert_poly_almost_equal(p4 % p2, p3)
      assert_poly_almost_equal(p4 % c2, p3)
      assert_poly_almost_equal(c4 % p2, p3)
      assert_poly_almost_equal(p4 % tuple(c2), p3)
      assert_poly_almost_equal(tuple(c4) % p2, p3)
      assert_poly_almost_equal(p4 % np.array(c2), p3)
      assert_poly_almost_equal(np.array(c4) % p2, p3)
      assert_poly_almost_equal(2 % p2, Poly([2]))
      assert_poly_almost_equal(p2 % 2, Poly([0]))
      assert_raises(TypeError, op.mod, p1, Poly([0], domain=Poly.domain + 1))
      assert_raises(TypeError, op.mod, p1, Poly([0], window=Poly.window + 1))
      if Poly is Polynomial:
          assert_raises(TypeError, op.mod, p1, Chebyshev([0]))
      else:
          assert_raises(TypeError, op.mod, p1, Polynomial([0]))
  
  
  def check_divmod(Poly):
      # This checks commutation, not numerical correctness
      c1 = list(random((4,)) + .5)
      c2 = list(random((3,)) + .5)
      c3 = list(random((2,)) + .5)
      p1 = Poly(c1)
      p2 = Poly(c2)
      p3 = Poly(c3)
      p4 = p1 * p2 + p3
      c4 = list(p4.coef)
      quo, rem = divmod(p4, p2)
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(p4, c2)
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(c4, p2)
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(p4, tuple(c2))
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(tuple(c4), p2)
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(p4, np.array(c2))
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(np.array(c4), p2)
      assert_poly_almost_equal(quo, p1)
      assert_poly_almost_equal(rem, p3)
      quo, rem = divmod(p2, 2)
      assert_poly_almost_equal(quo, 0.5*p2)
      assert_poly_almost_equal(rem, Poly([0]))
      quo, rem = divmod(2, p2)
      assert_poly_almost_equal(quo, Poly([0]))
      assert_poly_almost_equal(rem, Poly([2]))
      assert_raises(TypeError, divmod, p1, Poly([0], domain=Poly.domain + 1))
      assert_raises(TypeError, divmod, p1, Poly([0], window=Poly.window + 1))
      if Poly is Polynomial:
          assert_raises(TypeError, divmod, p1, Chebyshev([0]))
      else:
          assert_raises(TypeError, divmod, p1, Polynomial([0]))
  
  
  def check_roots(Poly):
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      tgt = np.sort(random((5,)))
      res = np.sort(Poly.fromroots(tgt, domain=d, window=w).roots())
      assert_almost_equal(res, tgt)
      # default domain and window
      res = np.sort(Poly.fromroots(tgt).roots())
      assert_almost_equal(res, tgt)
  
  
  def check_degree(Poly):
      p = Poly.basis(5)
      assert_equal(p.degree(), 5)
  
  
  def check_copy(Poly):
      p1 = Poly.basis(5)
      p2 = p1.copy()
      assert_(p1 == p2)
      assert_(p1 is not p2)
      assert_(p1.coef is not p2.coef)
      assert_(p1.domain is not p2.domain)
      assert_(p1.window is not p2.window)
  
  
  def check_integ(Poly):
      P = Polynomial
      # Check defaults
      p0 = Poly.cast(P([1*2, 2*3, 3*4]))
      p1 = P.cast(p0.integ())
      p2 = P.cast(p0.integ(2))
      assert_poly_almost_equal(p1, P([0, 2, 3, 4]))
      assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1]))
      # Check with k
      p0 = Poly.cast(P([1*2, 2*3, 3*4]))
      p1 = P.cast(p0.integ(k=1))
      p2 = P.cast(p0.integ(2, k=[1, 1]))
      assert_poly_almost_equal(p1, P([1, 2, 3, 4]))
      assert_poly_almost_equal(p2, P([1, 1, 1, 1, 1]))
      # Check with lbnd
      p0 = Poly.cast(P([1*2, 2*3, 3*4]))
      p1 = P.cast(p0.integ(lbnd=1))
      p2 = P.cast(p0.integ(2, lbnd=1))
      assert_poly_almost_equal(p1, P([-9, 2, 3, 4]))
      assert_poly_almost_equal(p2, P([6, -9, 1, 1, 1]))
      # Check scaling
      d = 2*Poly.domain
      p0 = Poly.cast(P([1*2, 2*3, 3*4]), domain=d)
      p1 = P.cast(p0.integ())
      p2 = P.cast(p0.integ(2))
      assert_poly_almost_equal(p1, P([0, 2, 3, 4]))
      assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1]))
  
  
  def check_deriv(Poly):
      # Check that the derivative is the inverse of integration. It is
      # assumes that the integration has been checked elsewhere.
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      p1 = Poly([1, 2, 3], domain=d, window=w)
      p2 = p1.integ(2, k=[1, 2])
      p3 = p1.integ(1, k=[1])
      assert_almost_equal(p2.deriv(1).coef, p3.coef)
      assert_almost_equal(p2.deriv(2).coef, p1.coef)
      # default domain and window
      p1 = Poly([1, 2, 3])
      p2 = p1.integ(2, k=[1, 2])
      p3 = p1.integ(1, k=[1])
      assert_almost_equal(p2.deriv(1).coef, p3.coef)
      assert_almost_equal(p2.deriv(2).coef, p1.coef)
  
  
  def check_linspace(Poly):
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      p = Poly([1, 2, 3], domain=d, window=w)
      # check default domain
      xtgt = np.linspace(d[0], d[1], 20)
      ytgt = p(xtgt)
      xres, yres = p.linspace(20)
      assert_almost_equal(xres, xtgt)
      assert_almost_equal(yres, ytgt)
      # check specified domain
      xtgt = np.linspace(0, 2, 20)
      ytgt = p(xtgt)
      xres, yres = p.linspace(20, domain=[0, 2])
      assert_almost_equal(xres, xtgt)
      assert_almost_equal(yres, ytgt)
  
  
  def check_pow(Poly):
      d = Poly.domain + random((2,))*.25
      w = Poly.window + random((2,))*.25
      tgt = Poly([1], domain=d, window=w)
      tst = Poly([1, 2, 3], domain=d, window=w)
      for i in range(5):
          assert_poly_almost_equal(tst**i, tgt)
          tgt = tgt * tst
      # default domain and window
      tgt = Poly([1])
      tst = Poly([1, 2, 3])
      for i in range(5):
          assert_poly_almost_equal(tst**i, tgt)
          tgt = tgt * tst
      # check error for invalid powers
      assert_raises(ValueError, op.pow, tgt, 1.5)
      assert_raises(ValueError, op.pow, tgt, -1)
  
  
  def check_call(Poly):
      P = Polynomial
      d = Poly.domain
      x = np.linspace(d[0], d[1], 11)
  
      # Check defaults
      p = Poly.cast(P([1, 2, 3]))
      tgt = 1 + x*(2 + 3*x)
      res = p(x)
      assert_almost_equal(res, tgt)
  
  
  def check_cutdeg(Poly):
      p = Poly([1, 2, 3])
      assert_raises(ValueError, p.cutdeg, .5)
      assert_raises(ValueError, p.cutdeg, -1)
      assert_equal(len(p.cutdeg(3)), 3)
      assert_equal(len(p.cutdeg(2)), 3)
      assert_equal(len(p.cutdeg(1)), 2)
      assert_equal(len(p.cutdeg(0)), 1)
  
  
  def check_truncate(Poly):
      p = Poly([1, 2, 3])
      assert_raises(ValueError, p.truncate, .5)
      assert_raises(ValueError, p.truncate, 0)
      assert_equal(len(p.truncate(4)), 3)
      assert_equal(len(p.truncate(3)), 3)
      assert_equal(len(p.truncate(2)), 2)
      assert_equal(len(p.truncate(1)), 1)
  
  
  def check_trim(Poly):
      c = [1, 1e-6, 1e-12, 0]
      p = Poly(c)
      assert_equal(p.trim().coef, c[:3])
      assert_equal(p.trim(1e-10).coef, c[:2])
      assert_equal(p.trim(1e-5).coef, c[:1])
  
  
  def check_mapparms(Poly):
      # check with defaults. Should be identity.
      d = Poly.domain
      w = Poly.window
      p = Poly([1], domain=d, window=w)
      assert_almost_equal([0, 1], p.mapparms())
      #
      w = 2*d + 1
      p = Poly([1], domain=d, window=w)
      assert_almost_equal([1, 2], p.mapparms())
  
  
  def check_ufunc_override(Poly):
      p = Poly([1, 2, 3])
      x = np.ones(3)
      assert_raises(TypeError, np.add, p, x)
      assert_raises(TypeError, np.add, x, p)
  
  
  class TestInterpolate(object):
  
      def f(self, x):
          return x * (x - 1) * (x - 2)
  
      def test_raises(self):
          assert_raises(ValueError, Chebyshev.interpolate, self.f, -1)
          assert_raises(TypeError, Chebyshev.interpolate, self.f, 10.)
  
      def test_dimensions(self):
          for deg in range(1, 5):
              assert_(Chebyshev.interpolate(self.f, deg).degree() == deg)
  
      def test_approximation(self):
  
          def powx(x, p):
              return x**p
  
          x = np.linspace(0, 2, 10)
          for deg in range(0, 10):
              for t in range(0, deg + 1):
                  p = Chebyshev.interpolate(powx, deg, domain=[0, 2], args=(t,))
                  assert_almost_equal(p(x), powx(x, t), decimal=12)
  
  
  if __name__ == "__main__":
      run_module_suite()
  