mirror of
https://github.com/stevenrobertson/cuburn.git
synced 2025-02-05 11:40:04 -05:00
105 lines
3.4 KiB
Python
105 lines
3.4 KiB
Python
import numpy as np
|
|
|
|
# The maximum number of coeffecients that will ever be retained on the device
|
|
FWIDTH = 15
|
|
|
|
# The number of points on either side of the center in one dimension
|
|
F2 = int(FWIDTH/2)
|
|
|
|
# The maximum size of any one coeffecient to be retained
|
|
COEFF_EPS = 0.0001
|
|
|
|
dists2d = np.fromfunction(lambda i, j: np.hypot(i-F2, j-F2), (FWIDTH, FWIDTH))
|
|
dists = dists2d.flatten()
|
|
|
|
# A flam3 estimator radius corresponds to a Gaussian filter with a standard
|
|
# deviation of 1/3 the radius. We choose 13 as an arbitrary upper bound for the
|
|
# max filter radius. The filter should reject larger radii.
|
|
MAX_SD = 13 / 3.
|
|
|
|
# The minimum estimator radius can be set as low as 0, but below a certain
|
|
# radius only one coeffecient is retained. Since things get unstable near 0,
|
|
# we explicitly set a minimum threshold below which no coeffecients are
|
|
# retained.
|
|
MIN_SD = np.sqrt(-1 / (2 * np.log(COEFF_EPS)))
|
|
|
|
# Using two predicated three-term approximations is much more accurate than
|
|
# using a very large number of terms, due to nonlinear behavior at low SD.
|
|
# Everything above this SD uses one approximation; below, another.
|
|
SPLIT_SD = 0.75
|
|
|
|
# The lower endpoints are undershot by this proportion to reduce error
|
|
UNDERSHOOT = 0.98
|
|
|
|
sds_hi = np.linspace(SPLIT_SD * UNDERSHOOT, MAX_SD, num=1000)
|
|
sds_lo = np.linspace(MIN_SD * UNDERSHOOT, SPLIT_SD, num=1000)
|
|
|
|
print 'At MIN_SD = %g, these are the coeffs:' % MIN_SD
|
|
print np.exp(dists2d**2 / (-2 * MIN_SD ** 2))
|
|
|
|
def eval_sds(sds, name, nterms):
|
|
# Calculate the filter sums at each coordinate
|
|
sums = []
|
|
for sd in sds:
|
|
coeffs = np.exp(dists**2 / (-2 * sd ** 2))
|
|
# Note that this sum is the sum of all coordinates, though it should
|
|
# actually be the result of the polynomial approximation. We could do
|
|
# a feedback loop to improve accuracy, but I don't think the difference
|
|
# is worth worrying about.
|
|
sum = np.sum(coeffs)
|
|
sums.append(np.sum(filter(lambda v: v / sum > COEFF_EPS, coeffs)))
|
|
print 'Evaluating %s:' % name
|
|
poly, resid, rank, sing, rcond = np.polyfit(sds, sums, nterms, full=True)
|
|
print 'Fit for %s:' % name, poly, resid, rank, sing, rcond
|
|
return sums, poly
|
|
|
|
import matplotlib.pyplot as plt
|
|
|
|
sums_hi, poly_hi = eval_sds(sds_hi, 'hi', 8)
|
|
sums_lo, poly_lo = eval_sds(sds_lo, 'lo', 7)
|
|
|
|
num_undershoots = len(filter(lambda v: v < SPLIT_SD, sds_hi))
|
|
sds_hi = sds_hi[num_undershoots:]
|
|
sums_hi = sums_hi[num_undershoots:]
|
|
|
|
num_undershoots = len(filter(lambda v: v < MIN_SD, sds_lo))
|
|
sds_lo = sds_lo[num_undershoots:]
|
|
sums_lo = sums_lo[num_undershoots:]
|
|
|
|
polyf_hi = np.float32(poly_hi)
|
|
vals_hi = np.polyval(polyf_hi, sds_hi)
|
|
polyf_lo = np.float32(poly_lo)
|
|
vals_lo = np.polyval(polyf_lo, sds_lo)
|
|
|
|
def print_filt(filts):
|
|
print ' filtsum = %4.8ff;' % filts[0]
|
|
for f in filts[1:]:
|
|
print ' filtsum = filtsum * sd + % 16.8ff;' % f
|
|
|
|
print '\n\nFor your convenience:'
|
|
print '#define MIN_SD %.8f' % MIN_SD
|
|
print '#define MAX_SD %.8f' % MAX_SD
|
|
print 'if (sd < %g) {' % SPLIT_SD
|
|
print_filt(polyf_lo)
|
|
print '} else {'
|
|
print_filt(polyf_hi)
|
|
print '}'
|
|
|
|
sds = np.concatenate([sds_lo, sds_hi])
|
|
sums = np.concatenate([sums_lo, sums_hi])
|
|
vals = np.concatenate([vals_lo, vals_hi])
|
|
|
|
fig = plt.figure()
|
|
ax = fig.add_subplot(1,1,1)
|
|
ax.plot(sds, sums)
|
|
ax.plot(sds, vals)
|
|
ax.set_xlabel('stdev')
|
|
ax.set_ylabel('filter sum')
|
|
|
|
ax = ax.twinx()
|
|
ax.plot(sds, [abs((s-v)/v) for s, v in zip(sums, vals)])
|
|
ax.set_ylabel('rel err')
|
|
|
|
plt.show()
|
|
|