def test_isconst(self):
self.assertFalse(self.f0.isconst)
self.assertFalse(self.f1.isconst)
self.assertFalse(self.f2.isconst)
c1 = Chebfun.initfun_fixedlen(lambda x: 0*x+3, 1, [-2,-1,0,1,2,3])
c2 = Chebfun.initfun_fixedlen(lambda x: 0*x-1, 1, [-2,3])
self.assertTrue(c1.isconst)
self.assertTrue(c2.isconst)
def test_isconst(self):
self.assertFalse(self.f0.isconst)
self.assertFalse(self.f1.isconst)
self.assertFalse(self.f2.isconst)
c1 = Chebfun.initfun_fixedlen(lambda x: 0*x+3, 1, [-2,-1,0,1,2,3])
c2 = Chebfun.initfun_fixedlen(lambda x: 0*x-1, 1, [-2,3])
self.assertTrue(c1.isconst)
self.assertTrue(c2.isconst)
def test_initfun_fixedlen_succeeds(self):
self.assertTrue(Chebfun.initfun_fixedlen(self.f, [], [-2,-1,0]).isempty)
# check that providing a vector with None elements calls the
# Tech adaptive constructor
g0 = Chebfun.initfun_adaptive(self.f, [-2,-1,0])
g1 = Chebfun.initfun_fixedlen(self.f, [None,None], [-2,-1,0])
g2 = Chebfun.initfun_fixedlen(self.f, [None,40], [-2,-1,0])
for fun1, fun2 in zip(g1,g0):
self.assertEqual(sum(fun1.coeffs-fun2.coeffs), 0)
self.assertEqual(sum(g2.funs[0].coeffs-g0.funs[0].coeffs), 0)
def test_initfun_fixedlen_succeeds(self):
self.assertTrue(Chebfun.initfun_fixedlen(self.f, [], [-2,-1,0]).isempty)
# check that providing a vector with None elements calls the
# Tech adaptive constructor
g0 = Chebfun.initfun_adaptive(self.f, [-2,-1,0])
g1 = Chebfun.initfun_fixedlen(self.f, [None,None], [-2,-1,0])
g2 = Chebfun.initfun_fixedlen(self.f, [None,40], [-2,-1,0])
for fun1, fun2 in zip(g1,g0):
self.assertEqual(sum(fun1.coeffs-fun2.coeffs), 0)
self.assertEqual(sum(g2.funs[0].coeffs-g0.funs[0].coeffs), 0)
def test_initfun_fixedlen_succeeds(self):
# check providing a vector with None elements calls the
# Tech adaptive constructor
dom = [-2, -1, 0]
g0 = Chebfun.initfun_adaptive(self.f, dom)
g1 = Chebfun.initfun_fixedlen(self.f, [None, None], dom)
g2 = Chebfun.initfun_fixedlen(self.f, [None, 40], dom)
g3 = Chebfun.initfun_fixedlen(self.f, None, dom)
for funA, funB in zip(g1, g0):
self.assertEqual(sum(funA.coeffs - funB.coeffs), 0)
for funA, funB in zip(g3, g0):
self.assertEqual(sum(funA.coeffs - funB.coeffs), 0)
self.assertEqual(sum(g2.funs[0].coeffs - g0.funs[0].coeffs), 0)
def test_initfun_fixedlen_continuous_domain(self):
ff = Chebfun.initfun_fixedlen(self.f, 20, [-2,-1])
self.assertEqual(ff.funs.size, 1)
a, b = ff.breakdata.keys()
fa, fb, = ff.breakdata.values()
self.assertEqual(a,-2)
self.assertEqual(b,-1)
self.assertLessEqual(abs(fa-self.f(-2)), eps)
self.assertLessEqual(abs(fb-self.f(-1)), eps)
def test_initfun_fixedlen_continuous_domain(self):
ff = Chebfun.initfun_fixedlen(self.f, 20, [-2, -1])
self.assertEqual(ff.funs.size, 1)
a, b = ff.breakdata.keys()
fa, fb, = ff.breakdata.values()
self.assertEqual(a, -2)
self.assertEqual(b, -1)
self.assertLessEqual(abs(fa - self.f(-2)), eps)
self.assertLessEqual(abs(fb - self.f(-1)), eps)
def test_initfun_fixedlen_piecewise_domain_1(self):
ff = Chebfun.initfun_fixedlen(self.f, [30,20], [-2,0,1])
self.assertEqual(ff.funs.size, 2)
a, b, c = ff.breakdata.keys()
fa, fb, fc = ff.breakdata.values()
self.assertEqual(a,-2)
self.assertEqual(b, 0)
self.assertEqual(c, 1)
self.assertLessEqual(abs(fa-self.f(-2)), 3*eps)
self.assertLessEqual(abs(fb-self.f( 0)), 3*eps)
self.assertLessEqual(abs(fc-self.f( 1)), 6*eps)
def test_initfun_fixedlen_piecewise_domain_1(self):
ff = Chebfun.initfun_fixedlen(self.f, [30, 20], [-2, 0, 1])
self.assertEqual(ff.funs.size, 2)
a, b, c = ff.breakdata.keys()
fa, fb, fc = ff.breakdata.values()
self.assertEqual(a, -2)
self.assertEqual(b, 0)
self.assertEqual(c, 1)
self.assertLessEqual(abs(fa - self.f(-2)), 3 * eps)
self.assertLessEqual(abs(fb - self.f(0)), 3 * eps)
self.assertLessEqual(abs(fc - self.f(1)), 6 * eps)
def test_x_property(self):
_doms = (
np.linspace(-1,1,2),
np.linspace(-1,1,11),
np.linspace(-9.3,-3.2,22),
)
for _dom in _doms:
f = Chebfun.initfun_fixedlen(sin, 1000, _dom)
x = f.x
a, b = x.support
pts = np.linspace(a, b, 1001)
tol = eps * f.hscale
self.assertLessEqual(infnorm(x(pts)-pts), tol)
def test_x_property(self):
_doms = (
np.linspace(-1, 1, 2),
np.linspace(-1, 1, 11),
np.linspace(-9.3, -3.2, 22),
)
for _dom in _doms:
f = Chebfun.initfun_fixedlen(sin, 1000, _dom)
x = f.x
a, b = x.support
pts = np.linspace(a, b, 1001)
tol = eps * f.hscale
self.assertLessEqual(infnorm(x(pts) - pts), tol)
def test_restrict_(self):
# test a variety of domains with breaks
doms = [(-4,4), (-4,0,4), (-2,-1, 0.3, 1, 2.5)]
for dom in doms:
ff = Chebfun.initfun_fixedlen(cos, 25, domain=dom)
# define some arbitrary subdomains
yy = np.linspace(dom[0], dom[-1], 11)
subdoms = [yy, yy[2:7], yy[::2]]
for subdom in subdoms:
xx = np.linspace(subdom[0], subdom[-1], 1001)
gg = ff._restrict(subdom)
vscl = ff.vscale
hscl = ff.hscale
lscl = max([fun.size for fun in ff])
tol = vscl*hscl*lscl*eps
# sample the restricted function and comapre with original
self.assertLessEqual(infnorm(ff(xx)-gg(xx)), tol)
# check there are at least as many funs as subdom elements
self.assertGreaterEqual(len(gg.funs), len(subdom)-1)
for fun in gg:
# chec each fun has length 25
self.assertEqual(fun.size, 25)
def test_restrict_(self):
# test a variety of domains with breaks
doms = [(-4, 4), (-4, 0, 4), (-2, -1, 0.3, 1, 2.5)]
for dom in doms:
ff = Chebfun.initfun_fixedlen(cos, 25, domain=dom)
# define some arbitrary subdomains
yy = np.linspace(dom[0], dom[-1], 11)
subdoms = [yy, yy[2:7], yy[::2]]
for subdom in subdoms:
xx = np.linspace(subdom[0], subdom[-1], 1001)
gg = ff._restrict(subdom)
vscl = ff.vscale
hscl = ff.hscale
lscl = max([fun.size for fun in ff])
tol = vscl * hscl * lscl * eps
# sample the restricted function and comapre with original
self.assertLessEqual(infnorm(ff(xx) - gg(xx)), tol)
# check there are at least as many funs as subdom elements
self.assertGreaterEqual(len(gg.funs), len(subdom) - 1)
for fun in gg:
# chec each fun has length 25
self.assertEqual(fun.size, 25)
def _initfun(f, domain, n):
if n is None:
return Chebfun.initfun_adaptive(f, domain)
else:
return Chebfun.initfun_fixedlen(f, n, domain)
def test_initfun_fixedlen_empty_domain(self):
f = Chebfun.initfun_fixedlen(self.f, n=10, domain=[])
self.assertTrue(f.isempty)