def test_rbf_epsilon_none_collinear():
# Check that collinear points in one dimension doesn't cause an error
# due to epsilon = 0
x = [1, 2, 3]
y = [4, 4, 4]
z = [5, 6, 7]
rbf = Rbf(x, y, z, epsilon=None)
assert_(rbf.epsilon > 0)
def check_rbf1d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (1D)
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=function)
yi = rbf(x)
assert_array_almost_equal(y, yi)
assert_almost_equal(rbf(float(x[0])), y[0])
def test_function_is_callable():
"""Check that the Rbf class can be constructed with function=callable."""
x = linspace(0, 10, 9)
y = sin(x)
linfunc = lambda x: x
rbf = Rbf(x, y, function=linfunc)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_default_construction():
# Check that the Rbf class can be constructed with the default
# multiquadric basis function. Regression test for ticket #1228.
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def check_rbf2d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (2D).
x = random.rand(50, 1) * 4 - 2
y = random.rand(50, 1) * 4 - 2
z = x * exp(-x**2 - 1j * y**2)
rbf = Rbf(x, y, z, epsilon=2, function=function)
zi = rbf(x, y)
zi.shape = x.shape
assert_array_almost_equal(z, zi)
def check_rbf1d_regularity(function, atol):
# Check that the Rbf function approximates a smooth function well away
# from the nodes.
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=function)
xi = linspace(0, 10, 100)
yi = rbf(xi)
msg = "abs-diff: %f" % abs(yi - sin(xi)).max()
assert_(allclose(yi, sin(xi), atol=atol), msg)
def check_rbf3d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (3D).
x = random.rand(50, 1) * 4 - 2
y = random.rand(50, 1) * 4 - 2
z = random.rand(50, 1) * 4 - 2
d = x * exp(-x**2 - y**2)
rbf = Rbf(x, y, z, d, epsilon=2, function=function)
di = rbf(x, y, z)
di.shape = x.shape
assert_array_almost_equal(di, d)
def check_2drbf1d_interpolation(function):
# Check that the 2-dim Rbf function interpolates through the nodes (1D)
x = linspace(0, 10, 9)
y0 = sin(x)
y1 = cos(x)
y = np.vstack([y0, y1]).T
rbf = Rbf(x, y, function=function, mode='N-D')
yi = rbf(x)
assert_array_almost_equal(y, yi)
assert_almost_equal(rbf(float(x[0])), y[0])
def check_2drbf2d_interpolation(function):
# Check that the 2-dim Rbf function interpolates through the nodes (2D).
x = random.rand(50, ) * 4 - 2
y = random.rand(50, ) * 4 - 2
z0 = x * exp(-x**2 - 1j * y**2)
z1 = y * exp(-y**2 - 1j * x**2)
z = np.vstack([z0, z1]).T
rbf = Rbf(x, y, z, epsilon=2, function=function, mode='N-D')
zi = rbf(x, y)
zi.shape = z.shape
assert_array_almost_equal(z, zi)
def test_two_arg_function_is_callable():
# Check that the Rbf class can be constructed with a two argument
# function=callable.
def _func(self, r):
return self.epsilon + r
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=_func)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def check_2drbf1d_regularity(function, atol):
# Check that the 2-dim Rbf function approximates a smooth function well away
# from the nodes.
x = linspace(0, 10, 9)
y0 = sin(x)
y1 = cos(x)
y = np.vstack([y0, y1]).T
rbf = Rbf(x, y, function=function, mode='N-D')
xi = linspace(0, 10, 100)
yi = rbf(xi)
msg = "abs-diff: %f" % abs(yi - np.vstack([sin(xi), cos(xi)]).T).max()
assert_(allclose(yi, np.vstack([sin(xi), cos(xi)]).T, atol=atol), msg)
def check_2drbf3d_interpolation(function):
# Check that the 2-dim Rbf function interpolates through the nodes (3D).
x = random.rand(50, ) * 4 - 2
y = random.rand(50, ) * 4 - 2
z = random.rand(50, ) * 4 - 2
d0 = x * exp(-x**2 - y**2)
d1 = y * exp(-y**2 - x**2)
d = np.vstack([d0, d1]).T
rbf = Rbf(x, y, z, d, epsilon=2, function=function, mode='N-D')
di = rbf(x, y, z)
di.shape = d.shape
assert_array_almost_equal(di, d)
def check_rbf1d_interpolation(function):
"""Check that the Rbf function interpolates throught the nodes (1D)"""
olderr = np.seterr(all="ignore")
try:
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=function)
yi = rbf(x)
assert_array_almost_equal(y, yi)
assert_almost_equal(rbf(float(x[0])), y[0])
finally:
np.seterr(**olderr)
def _rbf(self, Is, Cs, smooth=0.00005):
rbf_list = []
for ci in xrange(3):
rbf_list.append(Rbf(Is, Cs[:, ci], smooth=smooth))
def f(Is_new):
Cs_new = np.zeros((len(Is_new), Cs.shape[1]))
for ci in xrange(3):
Cs_new[:, ci] = rbf_list[ci](Is_new)
return Cs_new
return f
def check_rbf2d_interpolation(function):
"""Check that the Rbf function interpolates throught the nodes (2D)"""
olderr = np.seterr(all="ignore")
try:
x = random.rand(50, 1) * 4 - 2
y = random.rand(50, 1) * 4 - 2
z = x * exp(-x**2 - 1j * y**2)
rbf = Rbf(x, y, z, epsilon=2, function=function)
zi = rbf(x, y)
zi.shape = x.shape
assert_array_almost_equal(z, zi)
finally:
np.seterr(**olderr)
def bilateralNormalSmoothing(image, normal):
sigma_xy = 1.0
xy = positionFeatures(image) / sigma_xy
Lab = LabFeatures(image)
foreground = foreGroundFeatures(image)
N = normal[:, :, :3].reshape(-1, 3)
LabxyN = np.concatenate((Lab, xy, N), axis=1)[foreground, :]
sigma_L = 1.0
LabxyN[:, 0] = LabxyN[:, 0] / sigma_L
LabxyN_sparse = shuffle(LabxyN, random_state=0)[:100]
N_smooth = np.array(N)
smooth = 10.0
f_x = np.vstack((LabxyN_sparse[:, :5].T, LabxyN_sparse[:, 5]))
f_y = np.vstack((LabxyN_sparse[:, :5].T, LabxyN_sparse[:, 6]))
f_z = np.vstack((LabxyN_sparse[:, :5].T, LabxyN_sparse[:, 7]))
Nx_rbf = Rbf(*(f_x), function='linear', smooth=smooth)
Ny_rbf = Rbf(*(f_y), function='linear', smooth=smooth)
Nz_rbf = Rbf(*(f_z), function='linear', smooth=smooth)
Labxy = LabxyN[:, :5]
#Lab_smooth[:, 0] = L_rbf(Labxy[:, 0], Labxy[:, 1], Labxy[:, 2], Labxy[:, 3], Labxy[:, 4])
N_smooth[foreground, 0] = Nx_rbf(*(Labxy.T))
N_smooth[foreground, 1] = Ny_rbf(*(Labxy.T))
N_smooth[foreground, 2] = Nz_rbf(*(Labxy.T))
h, w = image.shape[:2]
N_smooth = N_smooth.reshape((h, w, 3))
N_smooth = normalizeImage(N_smooth)
return N_smooth
def check_rbf1d_stability(function):
# Check that the Rbf function with default epsilon is not subject
# to overshoot. Regression for issue #4523.
#
# Generate some data (fixed random seed hence deterministic)
np.random.seed(1234)
x = np.linspace(0, 10, 50)
z = x + 4.0 * np.random.randn(len(x))
rbf = Rbf(x, z, function=function)
xi = np.linspace(0, 10, 1000)
yi = rbf(xi)
# subtract the linear trend and make sure there no spikes
assert_(np.abs(yi - xi).max() / np.abs(z - x).max() < 1.1)
def check_rbf1d_regularity(function, atol):
"""Check that the Rbf function approximates a smooth function well away
from the nodes."""
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=function)
xi = linspace(0, 10, 100)
yi = rbf(xi)
#import matplotlib.pyplot as plt
#plt.figure()
#plt.plot(x, y, 'o', xi, sin(xi), ':', xi, yi, '-')
#plt.title(function)
#plt.show()
msg = "abs-diff: %f" % abs(yi - sin(xi)).max()
assert allclose(yi, sin(xi), atol=atol), msg
def main_compress():
x = np.linspace(1, 32, (32 * 5) / 4)
y = np.random.rand((32 * 5) / 4)
#y = np.sin(x)
tck = splrep(x, y, k=3)
rbf_adj = Rbf(x, y, function='gaussian')
x2 = np.linspace(2, 33, 32)
y2 = splev(x2, tck)
y2_rbf = rbf_adj(x2)
print(y2)
print(y2_rbf)
# y2 has shape 32
plt.subplot(311)
plt.plot(x, y)
plt.subplot(312)
#plt.plot(x2, y[8:8+16], 'r-', x2, y2, 'g--')
plt.plot(x2, y2, 'go-')
#plt.plot(x2,y2)
plt.subplot(313)
plt.plot(x2, y2_rbf, 'ro-')
plt.show()
def local_implementation(sigma, img_name):
# -----------------------------------------------------------------------------
# local implementation
fig2 = pl.figure(figsize=(20, 5))
draw = fig2.add_subplot(111)
draw.set_title("Radial Basis Function Interpolation")
draw.set_ylim([-2, 4])
draw.set_xlim([-0.5, 20.5])
draw.plot(x, y, 'bo', label="data", markersize=8)
draw.plot(x, y, 'r', label="linear")
weights = interpolation_rbf(xs, x, y, sigma)
bimes = get_ys(xs, x, weights, sigma)
draw.plot(xs,
bimes,
'orange',
linewidth=3,
label=r"$sigma$={}, own".format(sigma))
rbf = Rbf(x, y, function='gaussian', epsilon=0.5)
bim = rbf(xs)
draw.plot(xs,
bim,
'black',
linewidth=1.1,
label=r"$sigma$={}, Scipy".format(sigma))
draw.legend(bbox_to_anchor=(0., 1.02, 1., .102),
loc=3,
ncol=6,
mode="expand",
borderaxespad=0.0)
draw.plot()
pl.savefig(img_name, bbox_inches='tight')
pl.show()
def get_all_seq_augmentations_4(X, frame, win_size, num_augmentations=32):
'''
Do data augmentation on the given frame in the h5fname for a given
win_size. This is different than `get_all_seq_augmentations` since it
returns fixed number of augmentations for all window sizes.
K:number of augmentations in total. This uses a different algorithm to
generate augmentations i.e. it involves both compression and expansion
of given signal.
'''
K = num_augmentations
speed_up = [1.125, 1.25, 1.375]
all_win_sizes = [int(round(win_size * x)) for x in speed_up]
points_per_win_size = {
# 16:[2, 3, 3], 32:[2, 3, 3], 64:[2, 3, 3]
16: [1, 1, 2],
32: [1, 1, 2],
64: [1, 1, 2]
}
org_win_size = win_size
all_aug = np.zeros((K, X.shape[1], org_win_size))
for feat_idx in range(X.shape[1]):
all_aug_idx = 0
win_idx = 0
for win_size in all_win_sizes:
start_f = int(frame - org_win_size / 2)
end_f = start_f + org_win_size
start_ext_f = int(frame - win_size / 2.0)
end_ext_f = start_ext_f + win_size
X_org = X[start_f:end_f, :]
X_ext, can_compress = None, False
if start_ext_f >= 0 and end_ext_f < X.shape[0]:
can_compress = True
X_ext = X[start_ext_f:end_ext_f]
else:
can_compress = True
X_ext = X[start_ext_f:, :]
# Loop through all the different feature values used from openface
# signal
# Loop through all window sizes (for now we just have 1 win_size)
y = X_org[:, feat_idx]
x = np.linspace(1, org_win_size, org_win_size)
# expansion augmentation
# increase interpolation scale by 2 times. This will calculate the
# interpolating signal at the half values i.e. 1.5, 2.5 etc.
x2 = np.linspace(1, org_win_size, win_size)
# range(2) since we do 2 kinds of interpolation for now.
for j in range(2):
if j == 0:
# Cubic interpolation
tck = splrep(x, y, k=3)
y2 = splev(x2, tck)
else:
rbf_adj = Rbf(x, y, function='gaussian')
y2 = rbf_adj(x2)
if np.abs(np.mean(y) - np.mean(y2)) > 100:
assert (False)
num_interpolations = points_per_win_size[org_win_size][win_idx]
if win_size - org_win_size == num_interpolations:
for i in range(win_size - org_win_size):
all_aug[all_aug_idx,
feat_idx, :] = y2[i:i + org_win_size]
all_aug_idx = all_aug_idx + 1
else:
for i in range(num_interpolations):
idx = np.random.randint(0, win_size - org_win_size)
all_aug[all_aug_idx,
feat_idx, :] = y2[idx:idx + org_win_size]
all_aug_idx = all_aug_idx + 1
assert (can_compress)
# compression augmentation
if can_compress:
y = X_ext[:, feat_idx]
x = np.linspace(1, win_size, win_size)
tck = splrep(x, y, k=3)
rbf_adj = Rbf(x, y, function='gaussian')
num_interpolations = points_per_win_size[org_win_size][win_idx]
assert (win_size - org_win_size >= num_interpolations)
for i in range(num_interpolations):
x2 = np.linspace(1 + i, win_size, org_win_size)
y2_cubic = splev(x2, tck)
# For egocentric videos the mean change is a lot greater than 100px
# easily. But for static camera case it is ok.
if np.abs(np.mean(y) - np.mean(y2_cubic)) > 500:
print("NOTE!! Very high mean difference during interpolation. " \
"Most likely some value is inf. Frame# {}".format(
frame))
all_aug[all_aug_idx, feat_idx, :] = y2_cubic
all_aug_idx = all_aug_idx + 1
y2_rbf = rbf_adj(x2)
if np.abs(np.mean(y) - np.mean(y2_rbf)) > 500:
print("NOTE!! Very high mean difference during interpolation. " \
"Most likely some value is inf. Frame# {}".format(
frame))
all_aug[all_aug_idx, feat_idx, :] = y2_rbf
all_aug_idx = all_aug_idx + 1
win_idx = win_idx + 1
assert (all_aug_idx == K)
return all_aug
import os, PySide2 dirname = os.path.dirname(PySide2.__file__) plugin_path = os.path.join(dirname, 'plugins', 'platforms') os.environ['QT_QPA_PLATFORM_PLUGIN_PATH'] = plugin_path import numpy as np import pylab as pl from mpl_toolkits.mplot3d import Axes3D from scipy.interpolate.rbf import Rbf # 3 维数据点 x, y = np.mgrid[-np.pi / 2:np.pi / 2:5j, -np.pi / 2:np.pi / 2:5j] z = np.cos(np.sqrt(x**2 + y**2)) fig = pl.figure(figsize=(12, 6)) ax = fig.gca(projection="3d") ax.scatter(x, y, z) # 3 维RBF插值 zz = Rbf(x, y, z) xx, yy = np.mgrid[-np.pi / 2:np.pi / 2:50j, -np.pi / 2:np.pi / 2:50j] fig = pl.figure(figsize=(12, 6)) ax = fig.gca(projection="3d") ax.plot_surface(xx, yy, zz(xx, yy), rstride=1, cstride=1, cmap=pl.cm.jet) pl.show()
def test_rbf_epsilon_none():
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, epsilon=None)
import numpy as np
from scipy.interpolate.rbf import Rbf
import pyfits
import pymc
""" Interpolation functions for intrinsic magnitudes """
siess = pyfits.getdata("siess_isochrones.fits", 1) # Siess et al. (2000)
# Interpolation is performed using linear Radial Basis Functions
siess_Mr = Rbf(siess.field("logMass"), siess.field("logAge"),
siess.field("Mr_iphas"), function="linear")
siess_Mi = Rbf(siess.field("logMass"), siess.field("logAge"),
siess.field("Mi_iphas"), function="linear")
siess_Mj = Rbf(siess.field("logMass"), siess.field("logAge"),
siess.field("Mj"), function="linear")
siess_logR = Rbf(siess.field("logMass"), siess.field("logAge"),
siess.field("logRadius"), function="linear")
""" Functions for magnitude offsets due to emission & exctinction """
sim = pyfits.getdata("simulated_iphas_colours_barentsen2011.fits", 1) # PaperI
# Functions for r'/Ha/i' offsets as a function of colour, extinction and EW
r_offset = Rbf(sim.field("ri_unred"), sim.field("av"), sim.field("logew"),
sim.field("d_r"), function="linear")
ha_offset = Rbf(sim.field("ri_unred"), sim.field("av"), sim.field("logew"),
sim.field("d_ha"), function="linear")
i_offset = Rbf(sim.field("ri_unred"), sim.field("av"), sim.field("logew"),
sim.field("d_i"), function="linear")
# Intrinsic (r'-Ha) colour as a function of intrinsic (r'-i')
intrinsic = (sim.field("av") == 0) & (sim.field("logew") == -1)
rminHa_intrinsic = Rbf(sim.field("ri_unred")[intrinsic],
sim.field("rha")[intrinsic], function="linear")
def makeInterpolation(self, myMethod="sbs", methodVal=None):
# construct the interpolation grids for all coordinate systems
# dictionaries with interpolation grids and coordinate systems
self.interpGrids = {}
self.interpEdges = {}
self.interpValues = {}
self.interpSpline = {}
self.interpRbf = {}
self.interpIDW = {}
self.interpBMedian = {}
self.interpBNentry = {}
self.interpBMAD = {}
self.interpTMean = {}
self.interpTStd = {}
# loop over Coordinate systems
for iCoord in self.coordList:
# build cell-centers for the interpolation grid
ny, ylo, yhi, nx, xlo, xhi = self.gridArray[iCoord]
yGrid, xGrid, yEdge, xEdge = self.makeGrid(ny, ylo, yhi, nx, xlo,
xhi)
self.interpGrids[iCoord] = [xGrid, yGrid]
self.interpEdges[iCoord] = [xEdge, yEdge]
data = self.pointsArray[iCoord]
if self.debugFlag:
print("PointMesh: At ", iCoord, "we have ", data.shape[0],
" points")
npts = data.shape[0]
# check number of points
if npts >= 5:
xData = data[:, 0]
yData = data[:, 1]
zData = data[:, 2]
if myMethod == "sbs":
# SmoothBivariateSpline
if npts > 600:
self.interpSpline[iCoord] = SmoothBivariateSpline(
xData,
yData,
zData,
bbox=[xlo, xhi, ylo, yhi],
kx=4,
ky=4,
s=1.e6)
elif npts >= 100:
self.interpSpline[iCoord] = SmoothBivariateSpline(
xData,
yData,
zData,
bbox=[xlo, xhi, ylo, yhi],
kx=3,
ky=3,
s=1.e6)
elif npts > 9:
self.interpSpline[iCoord] = SmoothBivariateSpline(
xData,
yData,
zData,
bbox=[xlo, xhi, ylo, yhi],
kx=2,
ky=2,
s=1.e6)
else:
self.interpSpline[iCoord] = SmoothBivariateSpline(
xData,
yData,
zData,
bbox=[xlo, xhi, ylo, yhi],
kx=1,
ky=1,
s=1.e7)
self.interpValues[iCoord] = self.interpSpline[iCoord].ev(
xGrid.reshape((ny * nx)), yGrid.reshape(
(ny * nx))).reshape((ny, nx))
elif myMethod == "rbf":
self.interpRbf[iCoord] = Rbf(xData, yData, zData)
self.interpValues[iCoord] = self.interpRbf[iCoord](
xGrid.reshape((ny * nx)), yGrid.reshape(
(ny * nx))).reshape((ny, nx))
elif myMethod == "tmean":
# use the truncated mean for each Coord -- very very simple!!
zstd = stats.tstd(zData)
zmean = stats.tmean(zData)
ztmean = stats.tmean(
zData, (zmean - 3. * zstd, zmean + 3. * zstd))
ztstd = stats.tstd(zData,
(zmean - 3. * zstd, zmean + 3. * zstd))
self.interpTMean[iCoord] = ztmean
self.interpTStd[iCoord] = ztstd
self.interpValues[iCoord] = ztmean * numpy.ones((ny, nx))
elif myMethod == "bmedian":
# use the median for each bin in each Coord
self.interpBMedian[iCoord] = numpy.zeros((ny, nx))
self.interpBNentry[iCoord] = numpy.zeros((ny, nx))
self.interpBMAD[iCoord] = numpy.zeros((ny, nx))
zvalL = []
xbin = numpy.digitize(xData, xEdge[0, :]) - 1
ybin = numpy.digitize(yData, yEdge[:, 0]) - 1
for i in range(nx):
for j in range(ny):
ok = numpy.logical_and.reduce(
(xbin == i, ybin == j))
zHere = zData[ok]
# add nEntry, MAD to the saved variables for the Mesh
nEntry = zHere.shape[0]
if nEntry >= 1:
median_value = numpy.median(zHere)
self.interpBMedian[iCoord][j, i] = median_value
self.interpBNentry[iCoord][j, i] = nEntry
self.interpBMAD[iCoord][j, i] = numpy.median(
numpy.abs(zHere - median_value))
else:
# need to do something better!
self.interpBMedian[iCoord][j, i] = 0.
# fill interpValues, need to match order of locations in xGrid and yGrid
self.interpValues[iCoord] = self.interpBMedian[
iCoord].copy()
elif myMethod == "grid":
Z = griddata((xData, yData), zData, (xGrid.reshape(
(ny * nx)), yGrid.reshape((ny * nx))), "linear")
self.interpValues[iCoord] = Z.reshape(xGrid.shape)
elif myMethod == "idw":
# July 15, 2013 - change to use epsilon=1.0 (mm) to set a cutoff in the distance
# this will make small changes in the results for all Donuts
if methodVal != None:
usekNN = methodVal[0]
useEpsilon = methodVal[1]
else:
usekNN = 4
useEpsilon = 1.0
self.interpIDW[iCoord] = IDWInterp(xData,
yData,
zData,
kNN=usekNN,
epsilon=useEpsilon)
self.interpValues[iCoord] = self.interpIDW[iCoord].ev(
xGrid.reshape((ny * nx)), yGrid.reshape(
(ny * nx))).reshape((ny, nx))
else:
self.interpSpline[iCoord] = None
self.interpValues[iCoord] = numpy.zeros(xGrid.shape)
else:
self.interpTMean[iCoord] = 0.0
self.interpBMedian[iCoord] = None
self.interpBNentry[iCoord] = None
self.interpBMAD[iCoord] = None
self.interpTStd[iCoord] = 0.0
self.interpSpline[iCoord] = None
self.interpRbf[iCoord] = None
self.interpValues[iCoord] = numpy.zeros(xGrid.shape)
percent = 0.1
minX = minX - (maxX - minX) * percent
maxX = maxX + (maxX - minX) * percent
minY = minY - (maxY - minY) * percent
maxY = maxY + (maxY - minY) * percent
#FUNCTIONS = ('multiquadric', 'inverse multiquadric', 'gaussian', 'cubic', 'quintic', 'thin-plate', 'linear')
# 2-d tests - setup scattered data
tiX = np.linspace(minX, maxX, 500)
tiY = np.linspace(minY, maxY, 500)
XI, YI = np.meshgrid(tiX, tiY)
# use RBF
rbf1 = Rbf(x1, y1, z1, epsilon=2)
rbf2 = Rbf(x2, y2, z2, epsilon=2)
ZI1 = rbf1(XI, YI)
ZI2 = rbf2(XI, YI)
#Union of A and B
ZI5 = np.array(ZI1)
for i in range(0, XI.shape[0]):
for j in range(0, YI.shape[0]):
if ZI1[i][j] > ZI2[i][j]:
ZI5[i][j] = ZI2[i][j]
else:
ZI5[i][j] = ZI1[i][j]
#Intersection of A and B
ZI6 = np.array(ZI1)