def theta(self, eta):
"""The canonical parameter, theta, that
corresponds to the natural parameter, eta."""
assert self._check_shape(eta)
W = 2. * eta[self.k:].reshape((self.k, self.k))
mu = solve(W, eta[:self.k])
return (mu, W)
def linear_solution_bias_estimate(readings):
delta_matrix = delta(readings)
num_sensors = len(delta_matrix)
target_vector = [
sum([delta_matrix[k, i] for i in range(num_sensors) if i != k])
for k in range(num_sensors)
] + [0]
def diagonal(i, j):
if i == j:
return num_sensors - 1
else:
return -1
matrix = [[diagonal(i, j) for i in range(num_sensors)] + [1]
for j in range(num_sensors)] + [[1] * num_sensors + [0]]
return solve(matrix, target_vector)[:num_sensors]
def adapt_whitepoint(src, dst):
""" Compute the adaptation matrix for converting XYZ tristimulus values from
a one standard illuminant to another using the Bradford transform.
This implementation follows the presentation on
http://www.color.org/chadtag.html
The results are cached.
Parameters
----------
src : str
dst : str
The names of the standard illuminants to convert from and to,
respectively. Valid values are the keys of `whitepoints` like 'D65' or
'CIE A'.
Returns
-------
adapt : float array (3, 3)
Matrix-multiply this matrix against XYZ values with the `src` whitepoint
to get XYZ values with the `dst` whitepoint.
"""
# Check the cache first.
key = (src, dst)
if key not in adapt_whitepoint.cache:
bradford = np.array([[0.8951, 0.2664, -0.1614], [-0.7502, 1.7135, 0.0367], [0.0389, -0.0685, 1.0296]])
src_whitepoint = whitepoints[src][-1]
src_rgb = np.dot(bradford, src_whitepoint)
dst_whitepoint = whitepoints[dst][-1]
dst_rgb = np.dot(bradford, dst_whitepoint)
scale = dst_rgb / src_rgb
adapt_whitepoint.cache[key] = solve(bradford, scale[:, np.newaxis] * bradford)
adapt = adapt_whitepoint.cache[key]
return adapt
[0.2434974736455316, 0.8523911562030849, -0.0515994646411065],
[-0.3958579552426224, 1.1655483851630273, 0.0837969419671409],
[0.0, 0.0, 0.6185822095756526],
]
)
xyz_from_lms = inv(lms_from_xyz)
# The transformation from XYZ to the ATD opponent colorspace. These are
# "official" values directly from Guth 1980.
atd_from_xyz = np.array([[0.0, 0.9341, 0.0], [0.7401, -0.6801, -0.1567], [-0.0061, -0.0212, 0.0314]])
xyz_from_atd = inv(atd_from_xyz)
# Now we need to compute the intermediate transformations between LMS and ATD.
# We derive these directly from the other two instead of specifying potentially
# truncated values.
atd_from_lms = solve(lms_from_xyz.T, atd_from_xyz.T).T
lms_from_atd = solve(atd_from_xyz.T, lms_from_xyz.T).T
# XYZ white-point coordinates
# from http://www.aim-dtp.net/aim/technology/cie_xyz/cie_xyz.htm
whitepoints = {
"CIE A": ["Normal incandescent", triwhite(0.4476, 0.4074)],
"CIE B": ["Direct sunlight", triwhite(0.3457, 0.3585)],
"CIE C": ["Average sunlight", triwhite(0.3101, 0.3162)],
"CIE E": ["Normalized reference", triwhite(1.0 / 3, 1.0 / 3)],
"D50": ["Bright tungsten", triwhite(0.3457, 0.3585)],
"D55": ["Cloudy daylight", triwhite(0.3324, 0.3474)],
"D65": ["Daylight", triwhite(0.312713, 0.329016)],
"D75": ["?", triwhite(0.299, 0.3149)],
"D93": ["low-quality old CRT", triwhite(0.2848, 0.2932)],