def draw(self, canvas):
gx, gy, gz = canvas.grid(samples=10, sparse=False)
start = time.time()
points = poly.polyval3d(gx, gy, gz, self.c)
thorus = numpy.around(points) == 0
print("--- %s seconds ---" % (time.time() - start,))
canvas.setgrid(thorus, downsample=True)
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_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 create_random_poly(embedding_size=256, coefficients=None, dim=3):
"""
Create a polynomial embedding of the RGB vectors.
If the coefficients are given then it is that polynomial, if not - some uniformly random
polynomial is chosen, such that each variable is up to the given 'dim' degree
:param coefficients: a 4D array, such that the 3D array coefficients[i] contains the
coefficients of the 3D polynomial of the i-th coordinate of
the 3D function (from (R,G,B) to another 3D space).
:param dim: maximal power of the variables in the polynomial.
i.e. if the dim is 3 than the monomial of the
maximal degree will be x^3 * y^3 * z^3
:return: polynomial mapping of the RGB vectors.
"""
if coefficients is None:
coefficients = np.random.uniform(low=-1,
high=1,
size=(3, dim, dim, dim))
rgb_vectors = create_rgb(embedding_size)
embedding = np.empty_like(rgb_vectors)
for i in range(3):
embedding[:, i] = P.polyval3d(rgb_vectors[:, 0], rgb_vectors[:, 1],
rgb_vectors[:, 2], coefficients[i])
return embedding, coefficients
def draw(self, canvas):
gx, gy, gz = canvas.grid()
c = numpy.zeros((2,2,2))
c[1,0,0] = self.normal[0]
c[0,1,0] = self.normal[1]
c[0,0,1] = self.normal[2]
points = poly.polyval3d(gx, gy, gz, c)
plane = numpy.around(points) == 0
canvas.setgrid(plane)
def newtReconstruct(orders, locations, coeffs,unusedNumPts):
if len(locations.shape)==1:
return np.array(poly.polyval(locations, coeffs))
else:
if locations.shape[1] == 2:
return poly.polyval2d(locations[:,0], locations[:,1], coeffs)
elif locations.shape[1] == 3:
return poly.polyval3d(locations[:,0],locations[:,1],locations[:,2], coeffs)
else:
return genericNewtVal(locations, coeffs)
def test_polyvander3d(self) :
# also tests polyval3d for non-square coefficient array
x1, x2, x3 = self.x
c = np.random.random((2, 3, 4))
van = poly.polyvander3d(x1, x2, x3, [1, 2, 3])
tgt = poly.polyval3d(x1, x2, x3, c)
res = np.dot(van, c.flat)
assert_almost_equal(res, tgt)
# check shape
van = poly.polyvander3d([x1], [x2], [x3], [1, 2, 3])
assert_(van.shape == (1, 5, 24))
def test_polyvander3d(self):
# also tests polyval3d for non-square coefficient array
x1, x2, x3 = self.x
c = np.random.random((2, 3, 4))
van = poly.polyvander3d(x1, x2, x3, [1, 2, 3])
tgt = poly.polyval3d(x1, x2, x3, c)
res = np.dot(van, c.flat)
assert_almost_equal(res, tgt)
# check shape
van = poly.polyvander3d([x1], [x2], [x3], [1, 2, 3])
assert_(van.shape == (1, 5, 24))
def __call__(self, *input_variables):
def ensure_the_type(data):
if isinstance(data, (numpy.number, int, float, numpy.ndarray)):
return data
else:
return numpy.array(data)
if len(input_variables) not in [1, self.variables]:
raise ValueError('Got an unexpected number of input arguments')
if len(input_variables) == 1:
separate = False
inp_vars = ensure_the_type(input_variables[0])
else:
separate = True
inp_vars = [ensure_the_type(entry) for entry in input_variables]
# todo: should we evaluate the viability of the input?
if self.variables == 1:
x = (inp_vars - self._input_offsets[0]) / self._input_scales[0]
value = polynomial.polyval(x, self._numerator_array) / \
polynomial.polyval(x, self._denominator_array)
elif self.variables == 2:
if separate:
x = (inp_vars[0] -
self._input_offsets[0]) / self._input_scales[0]
y = (inp_vars[1] -
self._input_offsets[1]) / self._input_scales[1]
else:
if inp_vars.shape[-1] != 2:
raise ValueError(
'Final dimension of input data ({}) must match the number '
'of variables ({}).'.format(inp_vars.shape,
self.variables))
x = (inp_vars[..., 0] -
self._input_offsets[0]) / self._input_scales[0]
y = (inp_vars[..., 1] -
self._input_offsets[1]) / self._input_scales[1]
value = polynomial.polyval2d(x, y, self._numerator_array) / \
polynomial.polyval2d(x, y, self._denominator_array)
elif self.variables == 3:
if separate:
x = (inp_vars[0] -
self._input_offsets[0]) / self._input_scales[0]
y = (inp_vars[1] -
self._input_offsets[1]) / self._input_scales[1]
z = (inp_vars[2] -
self._input_offsets[2]) / self._input_scales[2]
else:
if inp_vars.shape[-1] != 3:
raise ValueError(
'Final dimension of input data ({}) must match the number '
'of variables ({}).'.format(inp_vars.shape,
self.variables))
x = (inp_vars[..., 0] -
self._input_offsets[0]) / self._input_scales[0]
y = (inp_vars[..., 1] -
self._input_offsets[1]) / self._input_scales[1]
z = (inp_vars[..., 2] -
self._input_offsets[2]) / self._input_scales[2]
value = polynomial.polyval3d(x, y, z, self._numerator_array) / \
polynomial.polyval3d(x, y, z, self._denominator_array)
else:
raise ValueError('More than 3 variables is unsupported')
return value * self._output_scale + self._output_offset
print(coeffs)
print(coeffs_to_array(coeffs, COLOR_POLYN_DEGREE))
c = np.zeros((3, 3, 3, 3))
c[0][1][0][0] = 1
c[1][0][1][0] = 1
c[2][0][0][1] = 1
print(c)
p = coeffs_to_array(c, COLOR_POLYN_DEGREE)
print('P', p)
c = array_to_coeffs(p, COLOR_POLYN_DEGREE)
print('C', c)
raise
d = np.array([[3, 5, 7]], dtype=np.float)
c = np.zeros((3, 3, 3, 3))
c[0][1][0][0] = 1
c[1][0][1][0] = 1
c[2][0][0][1] = 1
print(
poly.polyval3d(d[:, 0], d[:, 1], d[:, 2], c[0]),
poly.polyval3d(d[:, 0], d[:, 1], d[:, 2], c[1]),
poly.polyval3d(d[:, 0], d[:, 1], d[:, 2], c[2]),
)
'''
(4, 2)
y^0 + y^1 + y^2 + y^3
x^1 + x*y + x*y^2 + x*y^3
x^2
'''