def derivativeTester(fun, der, n, tol):
ff = Chebtech2.initfun_fixedlen(fun, n)
gg = Chebtech2.initfun_fixedlen(der, max(n-1,1))
def tester(self):
absdiff = infnorm(ff.diff().coeffs - gg.coeffs)
self.assertLessEqual(absdiff, tol)
return tester
def derivativeTester(fun, der, n, tol):
ff = Chebtech2.initfun_fixedlen(fun, n)
gg = Chebtech2.initfun_fixedlen(der, max(n-1,1))
def tester(self):
absdiff = infnorm(ff.diff().coeffs - gg.coeffs)
self.assertLessEqual(absdiff, tol)
return tester
def indefiniteIntegralTester(fun, dfn, n, tol):
ff = Chebtech2.initfun_fixedlen(fun, n)
gg = Chebtech2.initfun_fixedlen(dfn, n+1)
coeffs = gg.coeffs
coeffs[0] = coeffs[0] - dfn(np.array([-1]))
def tester(self):
absdiff = infnorm(ff.cumsum().coeffs - coeffs)
self.assertLessEqual(absdiff, tol)
return tester
def indefiniteIntegralTester(fun, dfn, n, tol):
ff = Chebtech2.initfun_fixedlen(fun, n)
gg = Chebtech2.initfun_fixedlen(dfn, n+1)
coeffs = gg.coeffs
coeffs[0] = coeffs[0] - dfn(np.array([-1]))
def tester(self):
absdiff = infnorm(ff.cumsum().coeffs - coeffs)
self.assertLessEqual(absdiff, tol)
return tester
def binaryOpTester(f, g, binop, nf, ng):
ff = Chebtech2.initfun_fixedlen(f, nf)
gg = Chebtech2.initfun_fixedlen(g, ng)
FG = lambda x: binop(f(x),g(x))
fg = binop(ff, gg)
def tester(self):
vscl = max([ff.vscale, gg.vscale])
lscl = max([ff.size, gg.size])
self.assertLessEqual(infnorm(fg(self.xx)-FG(self.xx)), 3*vscl*lscl*eps)
if binop is operator.mul:
# check simplify is not being called in __mul__
self.assertEqual(fg.size, ff.size+gg.size-1)
return tester
def binaryOpTester(f, g, binop, nf, ng):
ff = Chebtech2.initfun_fixedlen(f, nf)
gg = Chebtech2.initfun_fixedlen(g, ng)
FG = lambda x: binop(f(x),g(x))
fg = binop(ff, gg)
def tester(self):
vscl = max([ff.vscale, gg.vscale])
lscl = max([ff.size, gg.size])
self.assertLessEqual(infnorm(fg(self.xx)-FG(self.xx)), 3*vscl*lscl*eps)
if binop is operator.mul:
# check simplify is not being called in __mul__
self.assertEqual(fg.size, ff.size+gg.size-1)
return tester
def unaryOpTester(unaryop, f, nf):
ff = Chebtech2.initfun_fixedlen(f, nf)
gg = lambda x: unaryop(f(x))
GG = unaryop(ff)
def tester(self):
self.assertLessEqual(infnorm(gg(self.xx)-GG(self.xx)), 4e1*eps)
return tester
def unaryOpTester(unaryop, f, nf):
ff = Chebtech2.initfun_fixedlen(f, nf)
gg = lambda x: unaryop(f(x))
GG = unaryop(ff)
def tester(self):
self.assertLessEqual(infnorm(gg(self.xx)-GG(self.xx)), 4e1*eps)
return tester
def fixedlenTester(fun, n):
ff = Chebtech2.initfun_fixedlen(fun, n)
def tester(self):
self.assertEquals(ff.size, n)
return tester
def test__add__negself(self):
xx = self.xx
for (fun, funlen, _) in testfunctions:
chebtech = Chebtech2.initfun_fixedlen(fun, funlen)
chebzero = chebtech - chebtech
self.assertTrue(chebzero.isconst)
self.assertEqual(infnorm(chebzero(xx)), 0)
def test_truediv_empty(self):
for (fun, funlen, _) in testfunctions:
chebtech = Chebtech2.initfun_fixedlen(fun, funlen)
self.assertTrue(operator.truediv(self.emptyfun,chebtech).isempty)
self.assertTrue(operator.truediv(chebtech,self.emptyfun).isempty)
# __truediv__
self.assertTrue((self.emptyfun/chebtech).isempty)
self.assertTrue((chebtech/self.emptyfun).isempty)
def test_truediv_empty(self):
for (fun, funlen, _) in testfunctions:
chebtech = Chebtech2.initfun_fixedlen(fun, funlen)
self.assertTrue(truediv(self.emptyfun, chebtech).isempty)
self.assertTrue(truediv(chebtech, self.emptyfun).isempty)
# __truediv__
self.assertTrue((self.emptyfun / chebtech).isempty)
self.assertTrue((chebtech / self.emptyfun).isempty)
def definiteIntegralTester(fun, n, vscale):
ff = Chebtech2.initfun_fixedlen(fun, n)
def tester(self):
absdiff = abs(ff.vscale - vscale)
self.assertLessEqual(absdiff, .1 * vscale)
return tester
def definiteIntegralTester(fun, n, integral, tol):
ff = Chebtech2.initfun_fixedlen(fun, n)
def tester(self):
absdiff = abs(ff.sum() - integral)
self.assertLessEqual(absdiff, tol)
return tester
def test_rpow_const(self):
xx = self.xx
for (fun, funlen) in [(np.sin, 15), (np.exp,15)]:
for c in (1, 2):
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
g = lambda x: c ** fun(x)
gg = c ** techfun
tol = 2e1 * eps * abs(c)
self.assertLessEqual(infnorm(g(xx)-gg(xx)), tol)
def test_pow_const(self):
xx = self.xx
for (fun, funlen) in [(np.sin, 15), (np.exp,15)]:
for c in (1, 2):
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
f = lambda x: fun(x) ** c
ff = techfun ** c
tol = 2e1 * eps * abs(c)
self.assertLessEqual(infnorm(f(xx)-ff(xx)), tol)
def test_rpow_const(self):
xx = self.xx
for (fun, funlen) in [(np.sin, 15), (np.exp,15)]:
for c in (1, 2):
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
g = lambda x: c ** fun(x)
gg = c ** techfun
tol = 2e1 * eps * abs(c)
self.assertLessEqual(infnorm(g(xx)-gg(xx)), tol)
def test_pow_const(self):
xx = self.xx
for (fun, funlen) in [(np.sin, 15), (np.exp,15)]:
for c in (1, 2):
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
f = lambda x: fun(x) ** c
ff = techfun ** c
tol = 2e1 * eps * abs(c)
self.assertLessEqual(infnorm(f(xx)-ff(xx)), tol)
def test__add__radd__constant(self):
xx = self.xx
for (fun, funlen, _) in testfunctions:
for const in (-1, 1, 10, -1e5):
f = lambda x: const + fun(x)
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
f1 = const + techfun
f2 = techfun + const
tol = 5e1 * eps * abs(const)
self.assertLessEqual(infnorm(f(xx) - f1(xx)), tol)
self.assertLessEqual(infnorm(f(xx) - f2(xx)), tol)
def test__add__radd__constant(self):
xx = self.xx
for (fun, funlen, _) in testfunctions:
for const in (-1, 1, 10, -1e5):
f = lambda x: const + fun(x)
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
f1 = const + techfun
f2 = techfun + const
tol = 5e1 * eps * abs(const)
self.assertLessEqual(infnorm(f(xx)-f1(xx)), tol)
self.assertLessEqual(infnorm(f(xx)-f2(xx)), tol)
def test__mul__rmul__constant(self):
xx = self.xx
for (fun, funlen, _) in testfunctions:
for const in (-1, 1, 10, -1e5):
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
f = lambda x: const * fun(x)
g = lambda x: fun(x) * const
ff = const * techfun
gg = techfun * const
tol = 5e1 * eps * abs(const)
self.assertLessEqual(infnorm(f(xx)-ff(xx)), tol)
self.assertLessEqual(infnorm(g(xx)-gg(xx)), tol)
def test__mul__rmul__constant(self):
xx = self.xx
for (fun, funlen, _) in testfunctions:
for const in (-1, 1, 10, -1e5):
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
f = lambda x: const * fun(x)
g = lambda x: fun(x) * const
ff = const * techfun
gg = techfun * const
tol = 5e1 * eps * abs(const)
self.assertLessEqual(infnorm(f(xx) - ff(xx)), tol)
self.assertLessEqual(infnorm(g(xx) - gg(xx)), tol)
def test_truediv_constant(self):
xx = self.xx
for (fun, funlen, hasRoots) in testfunctions:
for const in (-1, 1, 10, -1e5):
tol = eps*abs(const)
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
g = lambda x: fun(x) / const
gg = techfun / const
self.assertLessEqual(infnorm(g(xx)-gg(xx)), 2*gg.size*tol)
# don't do the following test for functions with roots
if not hasRoots:
f = lambda x: const / fun(x)
ff = const / techfun
self.assertLessEqual(infnorm(f(xx)-ff(xx)), 3*ff.size*tol)
def test_truediv_constant(self):
xx = self.xx
for (fun, funlen, hasRoots) in testfunctions:
for const in (-1, 1, 10, -1e5):
tol = eps*abs(const)
techfun = Chebtech2.initfun_fixedlen(fun, funlen)
g = lambda x: fun(x) / const
gg = techfun / const
self.assertLessEqual(infnorm(g(xx)-gg(xx)), 2*gg.size*tol)
# don't do the following test for functions with roots
if not hasRoots:
f = lambda x: const / fun(x)
ff = const / techfun
self.assertLessEqual(infnorm(f(xx)-ff(xx)), 3*ff.size*tol)
def test__mul__rmul__empty(self):
for (fun, funlen, _) in testfunctions:
chebtech = Chebtech2.initfun_fixedlen(fun, funlen)
self.assertTrue((self.emptyfun * chebtech).isempty)
self.assertTrue((chebtech * self.emptyfun).isempty)
def setUp(self):
f = lambda x: sin(3*x) + 5e-1*cos(30*x)
self.f0 = Chebtech2.initfun_fixedlen(f, 100)
self.f1 = Chebtech2.initfun_adaptive(f)
def setUp(self):
f = lambda x: sin(3 * x) + 5e-1 * cos(30 * x)
self.f0 = Chebtech2.initfun_fixedlen(f, 100)
self.f1 = Chebtech2.initfun_adaptive(f)
def setUp(self):
self.ff = Chebtech2.initfun_fixedlen(lambda x: sin(30 * x), 100)
self.xx = -1 + 2 * rand(100)
def definiteIntegralTester(fun, n, integral, tol):
ff = Chebtech2.initfun_fixedlen(fun, n)
def tester(self):
absdiff = abs(ff.sum()-integral)
self.assertLessEqual(absdiff, tol)
return tester
def test__mul__rmul__empty(self):
for (fun, funlen, _) in testfunctions:
chebtech = Chebtech2.initfun_fixedlen(fun, funlen)
self.assertTrue((self.emptyfun*chebtech).isempty)
self.assertTrue((chebtech*self.emptyfun).isempty)
def definiteIntegralTester(fun, n, vscale):
ff = Chebtech2.initfun_fixedlen(fun, n)
def tester(self):
absdiff = abs(ff.vscale-vscale)
self.assertLessEqual(absdiff, .1*vscale)
return tester
def setUp(self):
f = lambda x: sin(3 * x) + 5e-1 * cos(30 * x)
u = lambda x: np.exp(2 * np.pi * 1j * x)
self.f0 = Chebtech2.initfun_fixedlen(f, 100)
self.f1 = Chebtech2.initfun_adaptive(f)
self.f2 = Chebtech2.initfun_adaptive(u)
def setUp(self):
self.ff = Chebtech2.initfun_fixedlen(lambda x: np.sin(30*x), 100)
self.xx = -1 + 2*np.random.rand(100)
def fixedlenTester(fun, n):
ff = Chebtech2.initfun_fixedlen(fun, n)
def tester(self):
self.assertEquals(ff.size, n)
return tester
