def test_minimum_multipiece(self):
x = chebfun('x', np.linspace(-2,3,11))
y = chebfun(2, x.domain)
g = (x**y).minimum(1.5)
t = np.linspace(-2,3,2001)
f = lambda x: np.minimum(x**2,1.5)
self.assertLessEqual(infnorm(f(t)-g(t)), 1e1*eps)
def test_minimum_multipiece(self):
x = chebfun('x', np.linspace(-2, 3, 11))
y = chebfun(2, x.domain)
g = (x**y).minimum(1.5)
t = np.linspace(-2, 3, 2001)
f = lambda x: np.minimum(x**2, 1.5)
self.assertLessEqual(infnorm(f(t) - g(t)), 1e1 * eps)
def test_simplify(self):
dom = np.linspace(-2, 1.5, 13)
f = chebfun(cos, dom, 70).simplify()
g = chebfun(cos, dom)
self.assertEquals(f.domain, g.domain)
for n, fun in enumerate(f):
# we allow one degree of freedom difference
# TODO: check this
self.assertLessEqual(fun.size - g.funs[n].size, 1)
def test_simplify(self):
dom = np.linspace(-2,1.5,13)
f = chebfun(cos, dom, 70).simplify()
g = chebfun(cos, dom)
self.assertEquals(f.domain, g.domain)
for n, fun in enumerate(f):
# we allow one degree of freedom difference
# TODO: check this
self.assertLessEqual(fun.size-g.funs[n].size, 1)
def test_restrict(self):
dom1 = Domain(np.linspace(-2,1.5,13))
dom2 = Domain(np.linspace(-1.7,0.93,17))
dom3 = dom1.merge(dom2).restrict(dom2)
f = chebfun(cos, dom1).restrict(dom2)
g = chebfun(cos, dom3)
self.assertEquals(f.domain, g.domain)
for n, fun in enumerate(f):
# we allow two degrees of freedom difference either way
# TODO: once standard chop is fixed, may be able to reduce 4 to 0
self.assertLessEqual(fun.size-g.funs[n].size, 4)
def test_restrict(self):
dom1 = Domain(np.linspace(-2, 1.5, 13))
dom2 = Domain(np.linspace(-1.7, 0.93, 17))
dom3 = dom1.merge(dom2).restrict(dom2)
f = chebfun(cos, dom1).restrict(dom2)
g = chebfun(cos, dom3)
self.assertEquals(f.domain, g.domain)
for n, fun in enumerate(f):
# we allow two degrees of freedom difference either way
# TODO: once standard chop is fixed, may be able to reduce 4 to 0
self.assertLessEqual(fun.size - g.funs[n].size, 4)
def test_roots_cache(self):
# check that a _cache property is created containing the stored roots
ff = chebfun(sin, np.linspace(-10, 10, 13))
self.assertFalse(hasattr(ff, '_cache'))
ff.roots()
self.assertTrue(hasattr(ff, '_cache'))
self.assertTrue(ff.roots.__name__ in ff._cache.keys())
def test_roots_cache(self):
# check that a _cache property is created containing the stored roots
ff = chebfun(sin, np.linspace(-10,10,13))
self.assertFalse(hasattr(ff, '_cache'))
ff.roots()
self.assertTrue(hasattr(ff, '_cache'))
self.assertTrue(ff.roots.__name__ in ff._cache.keys())
def domainBreakOpTester(domainBreakOp, f, g, dom, tol):
xx = np.linspace(dom[0],dom[-1],1001)
ff = chebfun(f, dom)
gg = chebfun(g, dom)
# convert constant g to to callable
if isinstance(g, (int, float)):
ffgg = domainBreakOp(f(xx), g)
else:
ffgg = domainBreakOp(f(xx), g(xx))
fg = getattr(ff, domainBreakOp.__name__)(gg)
def tester(self):
vscl = max([ff.vscale, gg.vscale])
hscl = max([ff.hscale, gg.hscale])
lscl = max([fun.size for fun in np.append(ff.funs, gg.funs)])
self.assertLessEqual(infnorm(fg(xx)-ffgg), vscl*hscl*lscl*tol)
return tester
def test_chebfun_alphanum_char(self):
n = 100
d = np.array([-2, 0, 1])
f1 = chebfun('x')
f2 = chebfun('y', d)
f3 = chebfun('z', n=n)
f4 = chebfun('a', d, n)
# check domains
self.assertTrue(f1.domain == DefaultPrefs.domain)
self.assertTrue(f2.domain == d)
self.assertTrue(f3.domain == DefaultPrefs.domain)
self.assertTrue(f4.domain == d)
# check lengths of f3 and f4
self.assertEqual(np.sum([fun.size for fun in f3]), n)
self.assertTrue(np.all([fun.size == n for fun in f4]))
def test_chebfun_callable(self):
n = 100
d = np.array([-2, 0, 1])
f1 = chebfun(np.sin)
f2 = chebfun(np.sin, d)
f3 = chebfun(np.sin, n=n)
f4 = chebfun(np.sin, d, n)
# check domains
self.assertTrue(f1.domain == DefaultPrefs.domain)
self.assertTrue(f2.domain == d)
self.assertTrue(f3.domain == DefaultPrefs.domain)
self.assertTrue(f4.domain == d)
# check lengths of f3 and f4
self.assertEqual(f3.funs[0].size, n)
self.assertTrue(np.all([fun.size == n for fun in f4]))
def test_chebfun_alphanum_char(self):
n = 100
d = np.array([-2,0,1])
f1 = chebfun('x')
f2 = chebfun('y', d)
f3 = chebfun('z', n=n)
f4 = chebfun('a', d, n)
# check domains
self.assertTrue(f1.domain==DefaultPrefs.domain)
self.assertTrue(f2.domain==d)
self.assertTrue(f3.domain==DefaultPrefs.domain)
self.assertTrue(f4.domain==d)
# check lengths of f3 and f4
self.assertEqual(np.sum([fun.size for fun in f3]), n)
self.assertTrue(np.all([fun.size==n for fun in f4]))
def domainBreakOpTester(domainBreakOp, f, g, dom, tol):
a, b = dom
xx = linspace(a,b,1001)
ff = chebfun(f, dom)
gg = chebfun(g, dom)
# convert constant g to to callable
if isinstance(g, (int, float)):
ffgg = domainBreakOp(f(xx), g)
else:
ffgg = domainBreakOp(f(xx), g(xx))
fg = getattr(ff, domainBreakOp.__name__)(gg)
def tester(self):
vscl = max([ff.vscale, gg.vscale])
hscl = max([ff.hscale, gg.hscale])
lscl = max([fun.size for fun in append(ff.funs, gg.funs)])
self.assertLessEqual(infnorm(fg(xx)-ffgg), vscl*hscl*lscl*tol)
return tester
def test_chebfun_callable(self):
n = 100
d = np.array([-2,0,1])
f1 = chebfun(np.sin)
f2 = chebfun(np.sin, d)
f3 = chebfun(np.sin, n=n)
f4 = chebfun(np.sin, d, n)
# check domains
self.assertTrue(f1.domain==DefaultPrefs.domain)
self.assertTrue(f2.domain==d)
self.assertTrue(f3.domain==DefaultPrefs.domain)
self.assertTrue(f4.domain==d)
# check lengths of f3 and f4
self.assertEqual(f3.funs[0].size, n)
self.assertTrue(np.all([fun.size==n for fun in f4]))
def test_chebfun_float_arg(self):
d = np.array([-2,0,1])
f1 = chebfun(3.14)
f2 = chebfun('3.14')
f3 = chebfun(2.72, d)
f4 = chebfun('2.72', d)
# check domains
self.assertTrue(f1.domain==DefaultPrefs.domain)
self.assertTrue(f2.domain==DefaultPrefs.domain)
self.assertTrue(f3.domain==d)
self.assertTrue(f4.domain==d)
# check all are constant
self.assertTrue(f1.isconst)
self.assertTrue(f2.isconst)
self.assertTrue(f3.isconst)
self.assertTrue(f4.isconst)
def test_chebfun_float_arg(self):
d = np.array([-2, 0, 1])
f1 = chebfun(3.14)
f2 = chebfun('3.14')
f3 = chebfun(2.72, d)
f4 = chebfun('2.72', d)
# check domains
self.assertTrue(f1.domain == DefaultPrefs.domain)
self.assertTrue(f2.domain == DefaultPrefs.domain)
self.assertTrue(f3.domain == d)
self.assertTrue(f4.domain == d)
# check all are constant
self.assertTrue(f1.isconst)
self.assertTrue(f2.isconst)
self.assertTrue(f3.isconst)
self.assertTrue(f4.isconst)
def test_from_chebfun(self):
ff = chebfun(lambda x: np.cos(x), np.linspace(-10, 10, 11))
Domain.from_chebfun(ff)
def test_chebfun_null_args(self):
self.assertTrue(chebfun().isempty)
def setUp(self):
self.f0 = chebfun(np.sin, [-2, 0, 1])
self.f1 = pickle.loads(pickle.dumps(self.f0))
def test_from_chebfun(self):
ff = chebfun(lambda x: np.cos(x), np.linspace(-10,10,11))
Domain.from_chebfun(ff)
def test_chebfun_null_args(self):
self.assertTrue(chebfun().isempty)
