def get_error(self, data, model):
(center, diameter, angle) = model
dis = npy.hypot(data[:, 0] - center[0], data[:, 1] - center[1])
theta = npy.arctan2(data[:, 1] - center[1], data[:, 0] - center[0]) - angle
ellipse_radius = npy.hypot(diameter[0] / 2 * npy.cos(theta),
diameter[1] / 2 * npy.sin(theta))
return npy.abs(dis - ellipse_radius)
def _dots_per_unit(self, units):
"""
Return a scale factor for converting from units to pixels
"""
ax = self.ax
if units in ("x", "y", "xy"):
if units == "x":
dx0 = ax.viewLim.width
dx1 = ax.bbox.width
elif units == "y":
dx0 = ax.viewLim.height
dx1 = ax.bbox.height
else: # 'xy' is assumed
dxx0 = ax.viewLim.width
dxx1 = ax.bbox.width
dyy0 = ax.viewLim.height
dyy1 = ax.bbox.height
dx1 = np.hypot(dxx1, dyy1)
dx0 = np.hypot(dxx0, dyy0)
dx = dx1 / dx0
else:
if units == "width":
dx = ax.bbox.width
elif units == "height":
dx = ax.bbox.height
elif units == "dots":
dx = 1.0
elif units == "inches":
dx = ax.figure.dpi
else:
raise ValueError("unrecognized units")
return dx
def zoomToAll(self):
if self.m_nImgs < 1:
return
posA=N.array(self.m_imgPosArr)
sizA=N.array(self.m_imgSizeArr)
a=N.array([N.minimum.reduce(posA),
N.maximum.reduce(posA+sizA),
])
from .all import U
MC = N.array([0.5, 0.5]) # mosaic viewer's center (0.5, 0.5)
a -= MC
hypot = N.array((N.hypot(a[0][0], a[0][1]),
N.hypot(a[1][0], a[1][1])))
theta = N.array((N.arctan2(a[0][1], a[0][0]),
N.arctan2(a[1][1], a[1][0]))) # radians
phi = theta + U.deg2rad(self.m_rot)
mimXY = N.array((hypot[0]*N.cos(phi[0]), hypot[0]*N.sin(phi[0])))
maxXY = N.array((hypot[1]*N.cos(phi[1]), hypot[1]*N.sin(phi[1])))
a = N.array((mimXY, maxXY))
a.sort(0)
if self.m_aspectRatio == -1:
a = N.array(([a[0][0],-a[1][1]],[a[1][0],-a[0][1]]))
self.zoomToRect(x0=a[0][0], y0=a[0][1],
x1=a[-1][0],y1=a[-1][1])
def pix2deg(self, pixel_x, pixel_y, eye_distance_mm):
"""
Stimulus positions (pixel_x,pixel_y) are defined in x and y pixel units,
with the origin (0,0) being at the **center** of the display, as to match
the PsychoPy pix unit coord type.
The pix2deg method is vectorized, meaning that is will perform the
pixel to angle calculations on all elements of the provided pixel
position numpy arrays in one numpy call.
The conversion process can use either a fixed eye to calibration
plane distance, or a numpy array of eye distances passed as
eye_distance_mm. In this case the eye distance array must be the same
length as pixel_x, pixel_y arrays.
"""
eye_dist_mm = self._eye_distance_mm
# if eye_distance_mm is not None:
# eye_dist_mm = eye_distance_mm
x_mm = self.mmpp_x * pixel_x
y_mm = self.mmpp_y * pixel_y
Ah = np.arctan(x_mm, np.hypot(eye_dist_mm, y_mm))
Av = np.arctan(y_mm, np.hypot(eye_dist_mm, x_mm))
return np.rad2deg(Ah), np.rad2deg(Av)
def _dots_per_unit(self, units):
"""
Return a scale factor for converting from units to pixels
"""
ax = self.ax
if units in ('x', 'y', 'xy'):
if units == 'x':
dx0 = ax.viewLim.width
dx1 = ax.bbox.width
elif units == 'y':
dx0 = ax.viewLim.height
dx1 = ax.bbox.height
else: # 'xy' is assumed
dxx0 = ax.viewLim.width
dxx1 = ax.bbox.width
dyy0 = ax.viewLim.height
dyy1 = ax.bbox.height
dx1 = np.hypot(dxx1, dyy1)
dx0 = np.hypot(dxx0, dyy0)
dx = dx1 / dx0
else:
if units == 'width':
dx = ax.bbox.width
elif units == 'height':
dx = ax.bbox.height
elif units == 'dots':
dx = 1.0
elif units == 'inches':
dx = ax.figure.dpi
else:
raise ValueError('unrecognized units')
return dx
def inverse_kepler_2d(xv, m, t):
"""Compute the Keplerian parameters for the osculating orbit.
No partial derivatives are computed (even though it would be much easier)
because you can use the partials for kepler_2d and invert the matrix.
The value of t0 computed is the value within one half-period of t.
"""
mu = G*m
#a_guess = np.hypot(xv[0], xv[1])
h = (xv[0]*xv[3]-xv[1]*xv[2])
r = np.hypot(xv[0], xv[1])
eps2, eps1 = np.array([xv[3], -xv[2]])*h/mu - xv[:2]/r
e = np.hypot(eps1, eps2)
p = h**2/mu
a = p/(1-e**2)
pb = 2*np.pi*(a**3/mu)**(0.5)
om = np.arctan2(eps1, eps2)
true_anomaly = np.arctan2(xv[1], xv[0])-om
eccentric_anomaly = np.arctan2(np.sqrt(1-e**2)*np.sin(true_anomaly),
e+np.cos(true_anomaly))
mean_anomaly = eccentric_anomaly - e*np.sin(eccentric_anomaly)
true_anomaly_0 = -om
eccentric_anomaly_0 = np.arctan2(np.sqrt(1-e**2)*np.sin(true_anomaly_0),
e+np.cos(true_anomaly_0))
mean_anomaly_0 = eccentric_anomaly_0 - e*np.sin(eccentric_anomaly_0)
return Kepler2DParameters(a=a, pb=pb, eps1=eps1, eps2=eps2,
t0=t-(mean_anomaly-mean_anomaly_0)*pb/(2*np.pi))
def getDr(d, IO, type_):
"""Compute distortion with given radial distance."""
# Define radial distance range
xp = np.linspace(0, d, d*50)
yp = 0
# Compute distortion corrections
x0 = IO["x0"]
y0 = IO["y0"]
xbar = xp - x0
ybar = yp - y0
r = np.hypot(xbar, ybar)
if type_ == "symmetric":
k1 = IO["k1"]
k2 = IO["k2"]
k3 = IO["k3"]
dx = xbar * (r**2 * k1 + r**4 * k2 + r**6 * k3)
dy = ybar * (r**2 * k1 + r**4 * k2 + r**6 * k3)
elif type_ == "decentering":
p1 = IO["p1"]
p2 = IO["p2"]
dx = (p1 * (r**2 + 2 * xbar**2) + 2 * p2 * xbar * ybar)
dy = (2 * p1 * xbar * ybar + p2 * (r**2 + 2 * ybar**2))
dr = np.hypot(dx, dy)
return xp, dr
def __init__(self, size=None, n=None):
n = n if n else 256
self.size = size if size else (256, 256)
self.order = len(self.size)
# Generate WAY more numbers than we need
# because we are throwing out all the numbers not inside a unit
# sphere. Something of a hack but statistically speaking
# it should work fine... or crash.
G = (random.uniform(size=2*self.order*n)*2 - 1).reshape(-1, self.order)
# GAH! How do I generalize this?!
#length = hypot(G[:,i] for i in range(self.order))
if self.order == 1:
length = G[:,0]
elif self.order == 2:
length = hypot(G[:,0], G[:,1])
elif self.order == 3:
length = hypot(G[:,0], G[:,1], G[:,2])
self.G = (G[length < 1] / (length[length < 1])[:,newaxis])[:n,]
self.P = arange(n, dtype=int32)
random.shuffle(self.P)
self.idx_ar = indices(2*ones(self.order), dtype=int8).reshape(self.order, -1).T
self.drop = poly1d((-6, 15, -10, 0, 0, 1.0))
def _cart_to_sph(x, y, z):
"""Aux function"""
hypotxy = np.hypot(x, y)
r = np.hypot(hypotxy, z)
elev = np.arctan2(z, hypotxy)
az = np.arctan2(y, x)
return az, elev, r
def plot_winds(m, lat,lon, image, u, v, name, step=16):
m.pcolormesh(lon, lat, image, latlon=True, cmap='gray')
h,w = lat.shape[:2]
y,x = np.mgrid[step/2:h:step,step/2:w:step].reshape(2,-1)
#extract data
u = u[y,x]
v = v[y,x]
lon = lon[y,x]
lat = lat[y,x]
#calculate map positionf lat lons
x,y = m(lon,lat)
# Calculate the orientation of the vectors
x1, y1 = m(lon+u, lat+v)
u_map, v_map = x1-x, y1-y
# Rescale the magnitudes of the vectors...
mag_scale = np.hypot(u_map, v_map) / np.hypot(u, v)
u_map /= mag_scale
v_map /= mag_scale
# Draw barbs
#m.barbs(x,y,u_map,v_map, length=5, color='red')
m.quiver(x,y,u_map,v_map,scale=200, color='red')
# Draw some grid lines for reference
m.drawparallels(np.arange(-90,90,2),labels=[1,1,0,0])
m.drawmeridians(np.arange(0,360,2),labels=[0,0,0,1])
plt.savefig(name,bbox_inches='tight')
plt.close()
def averageNSLSdata (ee, mc, mb, dc, db, n) :
i = ee.size / n # total number of energy points
e = ee[0::n]
# [0,:] is the first energy point
# Reshape to put energy on one axis and readings on the other.
mc.shape = ((i, n))
dc.shape = ((i, n))
mb.shape = ((i, n))
db.shape = ((i, n))
# Average over readings.
mca = np.average (mc, axis=1)
dca = np.average (dc, axis=1)
mba = np.average (mb, axis=1)
dba = np.average (db, axis=1)
# Note that the average might not be best for cases where there
# are outliers. Perhaps a median of some kind?
# Find the standard deviation of detector current measurements.
mcs = np.std (mc, axis=1)
dcs = np.std (dc, axis=1)
mbs = np.std (mb, axis=1)
dbs = np.std (db, axis=1)
ms = np.hypot (mcs, mbs)
ds = np.hypot (dcs, dbs)
return e, mca, mba, ms, dca, dba, ds
def get_bezier_points_at(self, at, grid=256):
at = np.asarray(at)
# The Bezier curve is parameterized by a value t which ranges from 0
# to 1. However, there is a nonlinear relationship between this value
# and arclength. We want to parameterize by t', which measures
# normalized arclength. To do this, we have to calculate the function
# arclength(t), and then invert it.
t = np.linspace(0, 1, grid)
x, y = Bezier(list(zip(self._xp, self._yp)), t).T
x_deltas = np.diff(x)
y_deltas = np.diff(y)
arclength_deltas = np.empty(t.shape)
arclength_deltas[0] = 0
np.hypot(x_deltas, y_deltas, out=arclength_deltas[1:])
arclength = np.cumsum(arclength_deltas)
arclength /= arclength[-1]
# Now (t, arclength) is a LUT describing the t -> arclength mapping
# Invert it to get at -> t
at_t = np.interp(at, arclength, t)
# And finally look up at the Bezier values at at_t
# (Might be quicker to np.interp againts x and y, but eh, doesn't
# really matter.)
return Bezier(list(zip(self._xp, self._yp)), at_t).T
def _cartesian_to_sphere(x, y, z):
"""Transform cartesian coordinates to spherical"""
hypotxy = np.hypot(x, y)
r = np.hypot(hypotxy, z)
elev = np.arctan2(z, hypotxy)
az = np.arctan2(y, x)
return az, elev, r
def go(start, stores, items, price_of_gas, perishable, solved):
if (start, str(sorted(items)), perishable) in solved:
return solved[(start, str(sorted(items)), perishable)]
gas_home = price_of_gas * hypot(0 - start[0], 0 - start[1])
if len(items) == 0:
return gas_home
if start == (0,0):
perishable = 0
costs = list()
if perishable == 1:
costs.append(gas_home + go((0,0), stores, items, price_of_gas, 0, solved))
filtered_stores = [x for x in stores if x[0] == start]
else:
filtered_stores = stores
for i in range(len(items)):
p = perishable
if items[i][-1] == '!':
p = 1
item = items[i][:-1]
else:
item = items[i]
for j in range(len(filtered_stores)):
filtered_items = [x for x in filtered_stores[j][1] if item in x]
if len(filtered_items) == 1:
cost = int(filtered_items[0].split(":")[1])
gas_here = price_of_gas * hypot(start[0] - filtered_stores[j][0][0], start[1] - filtered_stores[j][0][1])
costs.append( cost + gas_here + go(filtered_stores[j][0], stores, [x for x in items if item not in x], price_of_gas, p, solved))
solved[(start,str(sorted(items)),perishable)] = min(costs)
return min(costs)
def cart2sph(x, y, z):
"""Converts cartesian coordinates x, y, z to spherical coordinates az, el, r."""
hxy = _np.hypot(x, y)
r = _np.hypot(hxy, z)
el = _np.arctan2(z, hxy)
az = _np.arctan2(y, x)
return az, el, r
def get_impact_parameters_cpair(cpair,ra0,dec0,cosmo,npoints=1000):
"""Returns the impact parameter between the straight line given by a
cluster-pair and (ra0,dec0), as well as the distance along the
cpair axis to the closest cluster of the pair.
"""
ra1 = cpair['ra1']
dec1 = cpair['dec1']
z1 = cpair['z1']
ra2 = cpair['ra2']
dec2 = cpair['dec2']
z2 = cpair['z2']
zmed = cpair['redshift']
ra_mpc,dec_mpc,sep_mpc,dv = get_line_radec_sepdv(ra1,dec1,z1,ra2,dec2,z2,ra0,dec0,zmed,cosmo,npoints=npoints)
#get hypotenuse
sep = np.hypot(ra_mpc,dec_mpc)
#get minimum distance
sep_min = np.min(sep)
#lets add the distance along the cpair axis to the closest cluster
#find the closest cluster distance first
sep_cl_mpc1 = np.hypot(ra_mpc[0],dec_mpc[0])
sep_cl_mpc2 = np.hypot(ra_mpc[-1],dec_mpc[-1])
sep_cl_mpc = np.min([sep_cl_mpc1.value,sep_cl_mpc2.value])
#then, project along the cluster axis
sep_x_mpc = np.sqrt(sep_cl_mpc**2 - sep_min.value**2)
return sep_min.value, sep_x_mpc
def testProperMotion(self):
"""Test proper motion correction"""
center = make_coord(93.0, -90.0)
loader = LoadIndexedReferenceObjectsTask(butler=self.testButler)
references = loader.loadSkyCircle(center, self.searchRadius, filterName='a').refCat
original = references.copy(True)
# Zero epoch change --> no proper motion correction (except minor numerical effects)
loader.applyProperMotions(references, self.epoch)
self.assertFloatsAlmostEqual(references["coord_ra"], original["coord_ra"], rtol=1.0e-14)
self.assertFloatsAlmostEqual(references["coord_dec"], original["coord_dec"], rtol=1.0e-14)
self.assertFloatsEqual(references["coord_raErr"], original["coord_raErr"])
self.assertFloatsEqual(references["coord_decErr"], original["coord_decErr"])
# One year difference
loader.applyProperMotions(references, self.epoch + 1.0*astropy.units.yr)
self.assertFloatsEqual(references["pm_raErr"], original["pm_raErr"])
self.assertFloatsEqual(references["pm_decErr"], original["pm_decErr"])
for orig, ref in zip(original, references):
self.assertAnglesAlmostEqual(orig.getCoord().separation(ref.getCoord()),
self.properMotionAmt, maxDiff=1.0e-6*lsst.geom.arcseconds)
self.assertAnglesAlmostEqual(orig.getCoord().bearingTo(ref.getCoord()),
self.properMotionDir, maxDiff=1.0e-4*lsst.geom.arcseconds)
predictedRaErr = np.hypot(original["coord_raErr"], original["pm_raErr"])
predictedDecErr = np.hypot(original["coord_decErr"], original["pm_decErr"])
self.assertFloatsAlmostEqual(references["coord_raErr"], predictedRaErr)
self.assertFloatsAlmostEqual(references["coord_decErr"], predictedDecErr)
def get_dH2(lab1, lab2):
"""squared hue difference term occurring in deltaE_cmc and deltaE_ciede94
Despite its name, "dH" is not a simple difference of hue values. We avoid
working directly with the hue value, since differencing angles is
troublesome. The hue term is usually written as:
c1 = sqrt(a1**2 + b1**2)
c2 = sqrt(a2**2 + b2**2)
term = (a1-a2)**2 + (b1-b2)**2 - (c1-c2)**2
dH = sqrt(term)
However, this has poor roundoff properties when a or b is dominant.
Instead, ab is a vector with elements a and b. The same dH term can be
re-written as:
|ab1-ab2|**2 - (|ab1| - |ab2|)**2
and then simplified to:
2*|ab1|*|ab2| - 2*dot(ab1, ab2)
"""
lab1 = np.asarray(lab1)
lab2 = np.asarray(lab2)
a1, b1 = np.rollaxis(lab1, -1)[1:3]
a2, b2 = np.rollaxis(lab2, -1)[1:3]
# magnitude of (a, b) is the chroma
C1 = np.hypot(a1, b1)
C2 = np.hypot(a2, b2)
term = (C1 * C2) - (a1 * a2 + b1 * b2)
return 2 * term
def _cartesian_to_sphere(x, y, z):
"""Convert using old function."""
hypotxy = np.hypot(x, y)
r = np.hypot(hypotxy, z)
elev = np.arctan2(z, hypotxy)
az = np.arctan2(y, x)
return az, elev, r
def inplace_sort(self, points, i=0):
"""Sort the list of points (not actually inplace), starting
at index i.
"""
p_ = points
N = len(points)
sorted_points = []
while True:
# get the current point
point = p_[i]
# finish if next point is outside the solution triangle
if not self.insolutiontriangle(point):
break
# add the current point to the sorted points
sorted_points.append(point)
# finish if exhausted points
if len(sorted_points) == N:
break
# remove the current point from the points to consider
nonzero = np.hypot(*(p_ - point).T).nonzero()
p_ = p_[nonzero]
# find the index of the nearest point to the current point
distances = np.hypot(*(p_ - point).T)
i = distances.argmin()
return np.array(sorted_points)
def position_angle(xc,yc,x1,y1,x2,y2):
# Compute the position angle (in radians, with respect to north) between three points in pixel space
'''
Points are:
- xc,yc: x,y center of bending angle
- x1,y1: x,y center of 1st component
- x2,y2: x,y center of 2nd component
'''
r1 = np.array([x1,y1])
r2 = np.array([x2,y2])
center = np.array([xc,yc])
r12sum = (r1-center) + (r2-center)
r12len = np.hypot(r12sum[0],r12sum[1])
north = np.array([0,1])
northlen = np.hypot(north[0],north[1])
alpha = np.arccos(np.dot(r12sum,north) / (r12len*northlen))
# Measure CCW from north
if r12sum[0] > 0.:
alpha = 2*np.pi - alpha
return alpha
def edgedist(pixel, shape=(512,512)):
x = pixel[0]
y= pixel[1]
circumference = 2.0*shape[0] + 2.0*shape[1]
totaldist = np.sum([np.hypot(x-a, y-b) for a in range(shape[0]) for b in [0,shape[1]]])
totaldist2 = np.sum([np.hypot(x-a, y-b) for a in [0,shape[0]] for b in range(shape[1])])
return (totaldist + totaldist2) / circumference, circumference
def format_coord(self, xd, yd):
"""
Given the 2D view coordinates attempt to guess a 3D coordinate.
Looks for the nearest edge to the point and then assumes that
the point is at the same z location as the nearest point on the edge.
"""
if self.M is None:
return ''
if self.button_pressed == 1:
return 'azimuth=%d deg, elevation=%d deg ' % (self.azim, self.elev)
p = (xd, yd)
edges = self.tunit_edges()
ldists = [(proj3d.line2d_seg_dist(p0, p1, p), i) for \
i, (p0, p1) in enumerate(edges)]
ldists.sort()
edgei = ldists[0][1]
p0, p1 = edges[edgei]
x0, y0, z0 = p0
x1, y1, z1 = p1
d0 = np.hypot(x0-xd, y0-yd)
d1 = np.hypot(x1-xd, y1-yd)
dt = d0+d1
z = d1/dt * z0 + d0/dt * z1
x, y, z = proj3d.inv_transform(xd, yd, z, self.M)
xs = self.format_xdata(x)
ys = self.format_ydata(y)
zs = self.format_ydata(z)
return 'x=%s, y=%s, z=%s' % (xs, ys, zs)
def sky2pix_ellipse(self, pos, a, b, pa):
"""
Convert an ellipse from sky to pixel corrds
a/b vectors are calculated at an origin pos=(ra,dec)
All input parameters are in degrees
Output parameters are:
x,y - the x,y pixels corresponding to the ra/dec position
sx, sy - the major minor axes (FWHM) in pixels
theta - the position angle in degrees
:param pos: [ra,dec] of the ellipse center
:param a: major axis
:param b: minor axis
:param pa: position angle
:return: x, y, sx, sy, theta
"""
ra, dec = pos
x, y = self.sky2pix(pos)
x_off, y_off = self.sky2pix(translate(ra, dec, a, pa))
sx = np.hypot((x - x_off),(y - y_off))
theta = np.arctan2((y_off - y), (x_off - x))
x_off, y_off = self.sky2pix(translate(ra, dec, b, pa-90))
sy = np.hypot((x - x_off), (y - y_off))
theta2 = np.arctan2((y_off - y), (x_off - x)) - np.pi/2
# The a/b vectors are perpendicular in sky space, but not always in pixel space
# so we have to account for this by calculating the angle between the two vectors
# and modifying the minor axis length
defect = theta - theta2
sy *= abs(np.cos(defect))
return x, y, sx, sy, np.degrees(theta)
def get_plotsense_dict(file, NTOP=None, NANTS=None):
antpos = np.loadtxt(file)
if NANTS is None:
NANTS = antpos.shape[0]
bl_gps = {}
for i in xrange(NANTS-1):
a1pos = antpos[i]
for j in xrange(i+1,NANTS):
a2pos = antpos[j]
blx, bly, blz = a2pos-a1pos
has_entry = False
for key in bl_gps.keys():
if np.hypot(key[0]-blx, key[1]-bly) < 1:
has_entry = True
bl_gps[key] = bl_gps.get(key, []) + [(i,j)]
break
if not has_entry:
bl_gps[(blx, bly)] = [(i,j)]
n_unique = len(bl_gps.keys())
n_total = NANTS*(NANTS-1)/2
print "Found %d classes among %d total baselines" % (n_unique, n_total)
print "Sorting dictionary"
sorted_keys = sorted(bl_gps.keys(), key=lambda x: np.hypot(*x))
if NTOP is None:
NTOP = n_unique
key_pool = np.arange(NTOP)
top_dict = {}
for i, key in enumerate(sorted_keys[:NTOP]):
mult = len(bl_gps[key])
label = str(bl_gps[key][0][0])+'_'+str(bl_gps[key][0][1])
top_dict[label] = ((key[0], key[1], 0.), mult) #dict[example_bl] = ((blx, bly, blz), multiplicity)
return top_dict, bl_gps
def pack_fnl(data):
"""Pack fnl array to fnl struct."""
# Minimal input control
assert isinstance(data, np.ndarray)
assert data.ndim == 2 and data.shape[1] == FNLMeta.nb_columns
# Pack fnl
fnl = FNLData()
fnl.id = data[:, FNLMeta.nl_id_col]
fnl.eos = data[:, FNLMeta.eos_id_col]
fnl.x = data[:, FNLMeta.x_col]
fnl.y = data[:, FNLMeta.y_col]
fnl.z = data[:, FNLMeta.z_col]
fnl.vx = data[:, FNLMeta.vx_col]
fnl.vy = data[:, FNLMeta.vy_col]
fnl.vz = data[:, FNLMeta.vz_col]
fnl.m = data[:, FNLMeta.m_col]
fnl.rho = data[:, FNLMeta.rho_col]
fnl.P = data[:, FNLMeta.P_col]
fnl.T = data[:, FNLMeta.T_col]
fnl.U = data[:, FNLMeta.U_col]
fnl.hmin = data[:, FNLMeta.hmin_col]
fnl.hmax = data[:, FNLMeta.hmax_col]
fnl.nbNodes = len(data)
fnl.r = np.hypot(fnl.x, np.hypot(fnl.y, fnl.z))
# Return
return fnl
def norm_dist(src1, src2):
"""
Calculate the normalised distance between two sources.
Sources are elliptical Gaussians.
The normalised distance is calculated as the GCD distance between the centers,
divided by quadrature sum of the radius of each ellipse along a line joining the two ellipses.
For ellipses that touch at a single point, the normalized distance will be 1/sqrt(2).
Parameters
----------
src1, src2 : object
The two positions to compare. Objects must have the following parameters: (ra, dec, a, b, pa).
Returns
-------
dist: float
The normalised distance.
"""
if np.all(src1 == src2):
return 0
dist = gcd(src1.ra, src1.dec, src2.ra, src2.dec) # degrees
# the angle between the ellipse centers
phi = bear(src1.ra, src1.dec, src2.ra, src2.dec) # Degrees
# Calculate the radius of each ellipse along a line that joins their centers.
r1 = src1.a*src1.b / np.hypot(src1.a * np.sin(np.radians(phi - src1.pa)),
src1.b * np.cos(np.radians(phi - src1.pa)))
r2 = src2.a*src2.b / np.hypot(src2.a * np.sin(np.radians(180 + phi - src2.pa)),
src2.b * np.cos(np.radians(180 + phi - src2.pa)))
R = dist / (np.hypot(r1, r2) / 3600)
return R
def bending_angle(xc,yc,x1,y1,x2,y2):
# Compute the bending angle (in radians) between three points in pixel space
'''
Points are:
- xc,yc: x,y center of IR counterpart
- x1,y1: x,y center of 1st radio lobe
- x2,y2: x,y center of 2nd radio lobe
'''
r1 = np.array([x1,y1])
r2 = np.array([x2,y2])
center = np.array([xc,yc])
r1diff = r1-center
r2diff = r2-center
r1len = np.hypot(r1diff[0],r1diff[1])
r2len = np.hypot(r2diff[0],r2diff[1])
alpha = np.arccos(np.dot(r1diff,r2diff) / (r1len*r2len))
return alpha
def plateASTundo(ast, p, q):
""" Map gnomonic coordinates to theta, phi. """
M = ast.M
# Calculate beta and gamma
bet = np.arcsin(np.hypot(p, q))
gam = np.arctan2(q, p)
if bet > np.pi:
return False
# Init vector v
v = np.zeros(3)
v[0] = np.sin(bet)*np.cos(gam)
v[1] = np.sin(bet)*np.sin(gam)
v[2] = np.cos(bet)
# Calculate vector u
u = np.zeros(3)
u[0] = M[0,0]*v[0] + M[0,1]*v[1] + M[0,2]*v[2]
u[1] = M[1,0]*v[0] + M[1,1]*v[1] + M[1,2]*v[2]
u[2] = M[2,0]*v[0] + M[2,1]*v[1] + M[2,2]*v[2]
# Convert to theta, phi
th = np.arctan2(np.hypot(u[0], u[1]), u[2])
phi = np.arctan2(u[1], u[0])
return th, phi
def solve_for_nearest( px,py,rx,ry ):
dpx = polyder(px)
dpy = polyder(py)
cp = polymul( dpx, px ) + polymul( dpy, py )
cp = polyadd( cp, -rx*dpx )
cp = polyadd( cp, -ry*dpy )
t = roots(cp)
t = real(t[isreal(t)])
t = t[ (t>=0) * (t<=1) ]
##tt = linspace(0,1,100)
##from pylab import plot
##plot( polyval(px,tt), polyval(py,tt), 'k', hold = 0 )
##plot( [rx],[ry], 'r.' )
##plot( polyval(px,t[isreal(t)*(real(t)>=0)*(real(t)<=1)]),
## polyval(py,t[isreal(t)*(real(t)>=0)*(real(t)<=1)]), 'o' )
##pdb.set_trace()
if len(t):
if len(t) == 1:
return t[0]
else:
ux = polyval( px, t )
uy = polyval( py, t )
d = hypot( ux - rx, uy - ry )
return t[ d==d.min() ][0]
else:
t = array([0.0,1.0])
ux = polyval( px, t )
uy = polyval( py, t )
d = hypot( ux - rx, uy - ry )
if d[0] < d[1]:
return 0.0
else:
return 1.0
def center_distance(self, bubble, bubbles):
return np.hypot(bubble[0] - bubbles[:, 0],
bubble[1] - bubbles[:, 1])
def align_face(filepath, predictor):
"""
:param filepath: str
:return: PIL Image
"""
lm = get_landmark(filepath, predictor)
lm_chin = lm[0: 17] # left-right
lm_eyebrow_left = lm[17: 22] # left-right
lm_eyebrow_right = lm[22: 27] # left-right
lm_nose = lm[27: 31] # top-down
lm_nostrils = lm[31: 36] # top-down
lm_eye_left = lm[36: 42] # left-clockwise
lm_eye_right = lm[42: 48] # left-clockwise
lm_mouth_outer = lm[48: 60] # left-clockwise
lm_mouth_inner = lm[60: 68] # left-clockwise
# Calculate auxiliary vectors.
eye_left = np.mean(lm_eye_left, axis=0)
eye_right = np.mean(lm_eye_right, axis=0)
eye_avg = (eye_left + eye_right) * 0.5
eye_to_eye = eye_right - eye_left
mouth_left = lm_mouth_outer[0]
mouth_right = lm_mouth_outer[6]
mouth_avg = (mouth_left + mouth_right) * 0.5
eye_to_mouth = mouth_avg - eye_avg
# Choose oriented crop rectangle.
x = eye_to_eye - np.flipud(eye_to_mouth) * [-1, 1]
x /= np.hypot(*x)
x *= max(np.hypot(*eye_to_eye) * 2.0, np.hypot(*eye_to_mouth) * 1.8)
y = np.flipud(x) * [-1, 1]
c = eye_avg + eye_to_mouth * 0.1
quad = np.stack([c - x - y, c - x + y, c + x + y, c + x - y])
qsize = np.hypot(*x) * 2
# read image
img = PIL.Image.open(filepath)
output_size = 112
transform_size = 112
enable_padding = True
# Shrink.
shrink = int(np.floor(qsize / output_size * 0.5))
if shrink > 1:
rsize = (int(np.rint(float(img.size[0]) / shrink)), int(np.rint(float(img.size[1]) / shrink)))
img = img.resize(rsize, PIL.Image.ANTIALIAS)
quad /= shrink
qsize /= shrink
# Crop.
border = max(int(np.rint(qsize * 0.1)), 3)
crop = (int(np.floor(min(quad[:, 0]))), int(np.floor(min(quad[:, 1]))), int(np.ceil(max(quad[:, 0]))),
int(np.ceil(max(quad[:, 1]))))
crop = (max(crop[0] - border, 0), max(crop[1] - border, 0), min(crop[2] + border, img.size[0]),
min(crop[3] + border, img.size[1]))
if crop[2] - crop[0] < img.size[0] or crop[3] - crop[1] < img.size[1]:
img = img.crop(crop)
quad -= crop[0:2]
# Pad.
pad = (int(np.floor(min(quad[:, 0]))), int(np.floor(min(quad[:, 1]))), int(np.ceil(max(quad[:, 0]))),
int(np.ceil(max(quad[:, 1]))))
pad = (max(-pad[0] + border, 0), max(-pad[1] + border, 0), max(pad[2] - img.size[0] + border, 0),
max(pad[3] - img.size[1] + border, 0))
if enable_padding and max(pad) > border - 4:
pad = np.maximum(pad, int(np.rint(qsize * 0.3)))
img = np.pad(np.float32(img), ((pad[1], pad[3]), (pad[0], pad[2]), (0, 0)), 'reflect')
h, w, _ = img.shape
y, x, _ = np.ogrid[:h, :w, :1]
mask = np.maximum(1.0 - np.minimum(np.float32(x) / pad[0], np.float32(w - 1 - x) / pad[2]),
1.0 - np.minimum(np.float32(y) / pad[1], np.float32(h - 1 - y) / pad[3]))
blur = qsize * 0.02
img += (scipy.ndimage.gaussian_filter(img, [blur, blur, 0]) - img) * np.clip(mask * 3.0 + 1.0, 0.0, 1.0)
img += (np.median(img, axis=(0, 1)) - img) * np.clip(mask, 0.0, 1.0)
img = PIL.Image.fromarray(np.uint8(np.clip(np.rint(img), 0, 255)), 'RGB')
quad += pad[:2]
# Transform.
img = img.transform((transform_size, transform_size), PIL.Image.QUAD, (quad + 0.5).flatten(), PIL.Image.BILINEAR)
if output_size < transform_size:
img = img.resize((output_size, output_size), PIL.Image.ANTIALIAS)
# Save aligned image.
return img
def run(self):
mode = self.mode
if mode not in ('zone', 'both', 'full'):
self.log.error("Unlnowm mode '%s' . Allowed: [zone|full|both]",
mode)
return -1
recipe = self.recipe
# self.log.debug(recipe)
zone = np.array(recipe.get('zone'))
products = recipe['products']
if mode in ('zone', 'both') and zone is None:
self.log.error('No zone info in recipe')
return -1
sigma_avg_names = recipe['channels'].get('sigma_avg', [])
sigma_names = recipe['channels'].get('sigma', [])
sigma_vv_names = recipe['channels'].get('sigmaVV', [])
sigma_vh_names = recipe['channels'].get('sigmaVH', [])
coh_avg_names = recipe['channels'].get('coh_avg', [])
coh_names = recipe['channels'].get('coh', [])
coh_vv_names = recipe['channels'].get('cohVV', [])
coh_vh_names = recipe['channels'].get('cohVH', [])
channel_names = sigma_names + sigma_avg_names + sigma_vv_names + sigma_vh_names + coh_names + coh_avg_names + coh_vv_names + coh_vh_names
full_shape, _ = self.envi.read_header(channel_names[0])
self.log.info({'full shape:': full_shape})
# zone = [[0, 0], [full_shape[0], full_shape[1]]]
if zone is not None:
zone_shape = (zone[1][0] - zone[0][0], zone[1][1] - zone[0][1])
self.log.info({'Zone': zone, 'Shape': full_shape})
nproducts = (
(len(sigma_names) if 'sigma' in products else 0) +
(1 if 'sigma_avg' in products else 0) +
(len(sigma_vv_names) if 'sigma_hypot' in products else 0) +
(len(sigma_vv_names) if 'sigma_pol' in products else 0) +
(len(coh_names) if 'coh' in products else 0) +
(1 if 'coh_avg' in products else 0) +
(len(coh_vv_names) if 'coh_hypot' in products else 0) +
(len(coh_vv_names) if 'coh_pol' in products else 0))
if mode in ('zone', 'both'):
tnsr_zone = np.empty((zone_shape[0], zone_shape[1], nproducts),
dtype=np.float32)
bd_zone = np.zeros((zone_shape[0], zone_shape[1]), dtype=np.bool)
if mode in ('full', 'both'):
tnsr_full = np.empty((full_shape[0], full_shape[1], nproducts),
dtype=np.float32)
bd_full = np.zeros((full_shape[0], full_shape[1]), dtype=np.bool)
product_index = 0
if ('sigma' in products):
params = products['sigma']
for sn in sigma_names:
self.log.debug('sigma %s', sn)
s = self.envi.load(sn)[0]
if mode == 'zone':
s = s[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
bad_data = (s < 1e-6) | (s > 10) | (s < 1e-6) | (s > 10)
s = np.clip(s, 1e-6, 10)
s = np.log10(s)
fix_pixels(s, bad_data)
s = anisotropic_diffusion(s,
params[0],
params[1],
0.2,
option=1)
if mode == 'zone':
tnsr_zone[..., product_index] = s
product_index += 1
bd_zone |= bad_data
elif mode == 'full':
tnsr_full[..., product_index] = s
product_index += 1
bd_full |= bad_data
elif mode == 'both':
tnsr_full[..., product_index] = s
tnsr_zone[..., product_index] = s[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
product_index += 1
bd_full |= bad_data
bd_zone |= bad_data[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
if ('sigma_avg' in products):
params = products['sigma_avg']
if mode in ('zone', 'both'):
savg_zone = np.zeros(zone_shape, dtype=np.float32)
if mode in ('full', 'both'):
savg_full = np.zeros(full_shape, dtype=np.float32)
for sn in sigma_avg_names:
self.log.debug("sigma_avg %s", sn)
s = self.envi.load(sn)[0]
if mode == 'zone':
s = s[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
bad_data = (s < 1e-6) | (s > 10) | (s < 1e-6) | (s > 10)
s = np.clip(s, 1e-6, 10)
s = np.log10(s)
fix_pixels(s, bad_data)
if mode == 'zone':
savg_zone += s
bd_zone |= bad_data
elif mode == 'full':
savg_full += s
bd_full |= bad_data
elif mode == 'both':
savg_full += s
savg_zone += s[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
bd_full |= bad_data
bd_zone |= bad_data[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
if mode in ('zone', 'both'):
tnsr_zone[..., product_index] = anisotropic_diffusion(
savg_zone / len(sigma_avg_names),
params[0],
params[1],
0.2,
option=1)
if mode in ('full', 'both'):
tnsr_full[..., product_index] = anisotropic_diffusion(
savg_full / len(sigma_avg_names),
params[0],
params[1],
0.2,
option=1)
product_index += 1
if ('sigma_hypot' in products) or ('sigma_pol' in products):
if 'sigma_hypot' in products:
params = products['sigma_hypot']
else:
params = products['sigma_pol']
for svvn, svhn in zip(sigma_vv_names, sigma_vh_names):
self.log.debug({'svvn': svvn, 'svhn': svhn})
svv = self.envi.load(svvn)[0]
svh = self.envi.load(svhn)[0]
if mode == 'zone':
svv = svv[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
svh = svh[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
bad_data = (svv < 1e-6) | (svv > 10) | (svh < 1e-6) | (svh >
10)
svh = np.clip(svh, 1e-6, 10)
sv = np.clip(np.hypot(svv, svh), 1e-6, 10)
svpol = None
if 'sigma_pol' in products:
svpol = np.arcsin(svh / sv)
fix_pixels(svpol, bad_data)
svpol = gaussian_filter(svpol, params[2])
svpol = anisotropic_diffusion(svpol,
params[3],
params[4],
0.2,
option=1)
svv = None
svh = None
sv = np.log10(sv)
fix_pixels(sv, bad_data)
sv = anisotropic_diffusion(sv,
params[0],
params[1],
0.2,
option=1)
if mode == 'zone':
if 'sigma_hypot' in products:
tnsr_zone[..., product_index] = sv
product_index += 1
if 'sigma_pol' in products:
tnsr_zone[..., product_index] = svpol
product_index += 1
bd_zone |= bad_data
elif mode == 'full':
if 'sigma_hypot' in products:
tnsr_full[..., product_index] = sv
product_index += 1
if 'sigma_pol' in products:
tnsr_full[..., product_index] = svpol
product_index += 1
bd_full |= bad_data
elif mode == 'both':
if 'sigma_hypot' in products:
tnsr_full[..., product_index] = sv
tnsr_zone[...,
product_index] = sv[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
product_index += 1
if 'sigma_pol' in products:
tnsr_full[..., product_index] = svpol
tnsr_zone[...,
product_index] = svpol[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
product_index += 1
bd_full |= bad_data
bd_zone |= bad_data[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
if ('coh' in products):
params = products['coh']
for cn in coh_names:
self.log.debug('coh %s', cn)
c = self.envi.load(cn)[0]
if mode == 'zone':
c = c[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
bad_data = (c < 0) | (c > 1) | (c < 0) | (c > 1)
c = np.clip(c, 0, 1)
fix_pixels(c, bad_data)
c = anisotropic_diffusion(c,
params[0],
params[1],
0.2,
option=1)
if mode == 'zone':
tnsr_zone[..., product_index] = c
product_index += 1
bd_zone |= bad_data
elif mode == 'full':
tnsr_full[..., product_index] = c
product_index += 1
bd_full |= bad_data
elif mode == 'both':
tnsr_full[..., product_index] = c
tnsr_zone[..., product_index] = c[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
product_index += 1
bd_full |= bad_data
bd_zone |= bad_data[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
if ('coh_avg' in products):
if mode in ('zone', 'both'):
cavg_zone = np.zeros(zone_shape, dtype=np.float32)
if mode in ('full', 'both'):
cavg_full = np.zeros(full_shape, dtype=np.float32)
params = products['coh_avg']
for cn in coh_avg_names:
self.log.debug("coh_avg %s", cn)
c = self.envi.load(cn)[0]
if mode == 'zone':
c = c[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
bad_data = (c < 0) | (c > 1) | (c < 0) | (c > 1)
c = np.clip(c, 0, 1)
fix_pixels(c, bad_data)
if mode == 'zone':
cavg_zone += c
bd_zone |= bad_data
elif mode == 'full':
cavg_full += c
bd_full |= bad_data
elif mode == 'both':
cavg_full += c
cavg_zone += c[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
bd_full |= bad_data
bd_zone |= bad_data[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
if mode in ('zone', 'both'):
tnsr_zone[..., product_index] = anisotropic_diffusion(
cavg_zone / len(coh_avg_names),
params[0],
params[1],
0.2,
option=1)
if mode in ('full', 'both'):
tnsr_full[..., product_index] = anisotropic_diffusion(
cavg_full / len(coh_avg_names),
params[0],
params[1],
0.2,
option=1)
product_index += 1
if ('coh_hypot' in products) or ('coh_pol' in products):
if 'coh_hypot' in products:
params = products['coh_hypot']
else:
params = products['coh_pol']
for cvvn, cvhn in zip(coh_vv_names, coh_vh_names):
self.log.debug({'cvvn': cvvn, 'cvhn': cvhn})
cvv = self.envi.load(cvvn)[0]
cvh = self.envi.load(cvhn)[0]
if mode == 'zone':
cvv = cvv[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
cvh = cvh[zone[0][0]:zone[1][0], zone[0][1]:zone[1][1]]
bad_data = (cvv < 0) | (cvv > 1) | (cvh < 0) | (cvh > 1)
cvh = np.clip(cvh, 0, 1)
cv = np.clip(np.hypot(cvv, cvh), 0, 2)
cvpol = None
if 'coh_pol' in products:
cvpol = np.arcsin(cvh / cv)
fix_pixels(cvpol, bad_data)
cvpol = gaussian_filter(cvpol, params[2])
cvpol = anisotropic_diffusion(cvpol,
params[3],
params[4],
0.2,
option=1)
cvv = None
cvh = None
fix_pixels(cv, bad_data)
cv = anisotropic_diffusion(cv,
params[0],
params[1],
0.2,
option=1)
if mode == 'zone':
if 'coh_hypot' in products:
tnsr_zone[..., product_index] = cv
product_index += 1
if 'coh_pol' in products:
tnsr_zone[..., product_index] = cvpol
product_index += 1
bd_zone |= bad_data
elif mode == 'full':
if 'coh_hypot' in products:
tnsr_full[..., product_index] = cv
product_index += 1
if 'coh_pol' in products:
tnsr_full[..., product_index] = cvpol
product_index += 1
bd_full |= bad_data
elif mode == 'both':
if 'coh_hypot' in products:
tnsr_full[..., product_index] = cv
tnsr_zone[...,
product_index] = cv[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
product_index += 1
if 'coh_pol' in products:
tnsr_full[..., product_index] = cvpol
tnsr_zone[...,
product_index] = cvpol[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
product_index += 1
bd_full |= bad_data
bd_zone |= bad_data[zone[0][0]:zone[1][0],
zone[0][1]:zone[1][1]]
if not os.path.exists(self.WORKDIR):
os.makedirs(self.WORKDIR)
self.log.debug("Saving tnsr and bd into %s", self.WORKDIR)
if mode in ('zone', 'both'):
np.save(self.WORKDIR + 'tnsr_zone.npy', tnsr_zone)
np.save(self.WORKDIR + 'bd_zone.npy', bd_zone)
if mode in ('full', 'both'):
np.save(self.WORKDIR + 'tnsr_full.npy', tnsr_full)
np.save(self.WORKDIR + 'bd_full.npy', bd_full)
self.log.info('tensors processed')
# system("say 'assembling complete'")
return 0
def reverseUnitCycleKernel(rad, size): #TO USE WITH AI
rx, ry = size/2, size/2
x, y = np.indices((size, size))
return ((np.hypot(rx - x, ry - y) - rad) > 0.5).astype(int)
def getBracketingIndices(evalColRow, cr):
"""
Get the indices of `evalColRow` that bracket `cr`
This is a special function used by TessPrf
This function encapsulates some fairly knotty bookkeeping. Unless something
is broken you probably want to leave this function well alone
Inputs
--------
evalColRow
(3d np array) See discussion below
cr
(2 element np array) The column and row to be bracketed
Returns
----------
A 4x2 numpy array. Each row represents the indices into
`evalColRow[,,:]` representing the 4 points in `evalColRow`
that bracket the location represented by evalColRow
Note
-----
The model prf is evaluated on a regular grid across the CCD. Each
grid point can be represented in two coordinate systems; the
CCD pixel coordinates (this PRF is evaluated at col,row=24,36,
and a grid Index (this is the second grid location in column, and
the third in row). `evalColRow` encodes a mapping from one coord sys
to the other.
The zeroth dimension of `evalColRow` encodes the column of the grid
location (e.g. 2 in the example above). The first dimension
encodes row of the grid location (3 in the example), the second
dimension encodes whether the value represents CCD column
(`evalColRow[:,:,0]`) or CCD row (`evalColRow[:,:,1]`). The
value at each array element represents the CCD position (either
column or row).
The return value of this function is a list of the 4 grid locations
that bracket the input `cr` in column and row (below left, below right,
above left, above right)
Example
---------
`evalColRow` consists of 4 points at which the model prf is evalulated
.. code-block:: python
a[0,0,0] = 45
a[0,0,1] = 1 #Zeroth prf evalulated at (col, row) = (45,1)
a[0,1,0] = 45
a[0,1,1] = 128
a[1,0,0] = 183
a[1,0,1] = 1
a[1,1,0] = 183
a[1,1,1] = 128
cr = (45, 45) #Somewhere in the middle
The return value is
.. code-block:: python
[ [0,0], [1,0], [1,0], [1,1] ]
Because these are the indices that bracket the input col,row
"""
tmp = (evalColRow - cr)
dist = np.hypot(tmp[:,:,0], tmp[:,:,1])
wh = np.unravel_index( np.argmin(dist), dist.shape)
nearestEval = evalColRow[wh]
delta = cr - nearestEval
#Find the 3 other evaluations of the PRF that bracket (col, row)
tmp = []
if delta[0] >= 0 and delta[1] >= 0: #A
tmp.append( wh )
tmp.append( wh + np.array((+1, +0)) )
tmp.append( wh + np.array((+0, +1)) )
tmp.append( wh + np.array((+1, +1)) )
elif delta[0] < 0 and delta[1] >= 0: #S
tmp.append( wh + np.array((-1, +0)) )
tmp.append( wh )
tmp.append( wh + np.array((-1, +1)) )
tmp.append( wh + np.array((+0, +1)) )
elif delta[0] < 0 and delta[1] < 0: #T
tmp.append( wh + np.array((-1, -1)) )
tmp.append( wh + np.array((-0, -1)) )
tmp.append( wh + np.array((-1, +0)) )
tmp.append( wh )
else: #C
tmp.append( wh + np.array((-0, -1)) )
tmp.append( wh + np.array((+1, -1)) )
tmp.append( wh )
tmp.append( wh + np.array((+1, +0)) )
tmp = np.array(tmp)
#Check the order of values is correct
c0 = tmp[:,0]
r0 = tmp[:,1]
assert c0[0] == c0[2]
assert c0[1] == c0[3]
assert r0[0] == r0[1]
assert r0[2] == r0[3]
#Bounds checking
assert np.min(tmp) >= 0
assert np.max(tmp[:,0]) < evalColRow.shape[0]
assert np.max(tmp[:,1]) < evalColRow.shape[1]
return tmp
levels = 15
cset = ax.contourf(X2,
X1,
RESULT_DEPS.T,
levels=levels,
inline=1,
cmap='coolwarm')
cset = ax.contour(X2,
X1,
RESULT_DEPS.T,
levels=levels,
inline=1,
colors='k')
ax.clabel(cset, colors='k', fmt='%2.0f')
M = np.hypot(RESULT_DX, RESULT_DY)
q = ax.quiver(X2__, X1__, -RESULT_DY, RESULT_DX, units='x', scale=120)
ax.scatter(X2__, X1__, color='0.5', s=10)
ax.grid()
plt.ylim(min(X1) - 5, max(X1) + 10)
plt.savefig('DXDYDE.png')
# %% PLOT DE
fig, ax = plt.subplots(num='DEPS')
plt.title('DEPS')
levels = 15
cset = ax.contourf(X2,
X1,
RESULT_DEPS.T,
from scipy import misc import matplotlib.pyplot as plt from scipy import ndimage import numpy as np face = misc.face(gray=True) im = np.zeros((256, 256)) im[64:-64, 64:-64] = 1 facerotated = ndimage.rotate(face, 15, mode="constant") facefiltered = ndimage.gaussian_filter(facerotated, 5) sobelx = ndimage.sobel(im, axis=0, mode="constant") sobely = ndimage.sobel(im, axis=1, mode="constant") sobel = np.hypot(sobelx, sobely) plt.figure() plt.subplot(331) plt.imshow(face, cmap=plt.cm.gray) plt.subplot(332) plt.imshow(facerotated, cmap=plt.cm.gray) plt.subplot(333) plt.imshow(facefiltered, cmap=plt.cm.gray) plt.subplot(335) plt.imshow(sobelx, cmap=plt.cm.gray) plt.subplot(336) plt.imshow(sobely, cmap=plt.cm.gray) plt.subplot(338) plt.imshow(sobel, cmap=plt.cm.gray) plt.show()
def ecef2geodetic_old(x: float,
y: float,
z: float,
ell: Ellipsoid = None,
deg: bool = True) -> Tuple[float, float, float]:
"""
convert ECEF (meters) to geodetic coordinates
input
-----
x,y,z [meters] target ECEF location [0,Infinity)
ell reference ellipsoid
deg degrees input/output (False: radians in/out)
output
------
lat,lon (degrees/radians)
alt (meters)
Algorithm is based on
http://www.astro.uni.torun.pl/~kb/Papers/geod/Geod-BG.htm
This algorithm provides a converging solution to the latitude equation
in terms of the parametric or reduced latitude form (v)
This algorithm provides a uniform solution over all latitudes as it does
not involve division by cos(phi) or sin(phi)
"""
if ell is None:
ell = Ellipsoid()
ea = ell.a
eb = ell.b
rad = hypot(x, y)
# Constant required for Latitude equation
rho = arctan2(eb * z, ea * rad)
# Constant required for latitude equation
c = (ea**2 - eb**2) / hypot(ea * rad, eb * z)
# Starter for the Newtons Iteration Method
vnew = arctan2(ea * z, eb * rad)
# Initializing the parametric latitude
v = 0
for _ in range(5):
v = deepcopy(vnew)
# %% Newtons Method for computing iterations
vnew = v - ((2 * sin(v - rho) - c * sin(2 * v)) /
(2 * (cos(v - rho) - c * cos(2 * v))))
if allclose(v, vnew):
break
# %% Computing latitude from the root of the latitude equation
lat = arctan2(ea * tan(vnew), eb)
# by inspection
lon = arctan2(y, x)
alt = (((rad - ea * cos(vnew)) * cos(lat)) +
((z - eb * sin(vnew)) * sin(lat)))
with np.errstate(invalid='ignore'):
# NOTE: need np.any() to handle scalar and array cases
if np.any((lat < -pi / 2) | (lat > pi / 2)):
raise ValueError('-90 <= lat <= 90')
if np.any((lon < -pi) | (lon > 2 * pi)):
raise ValueError('-180 <= lat <= 360')
if deg:
return degrees(lat), degrees(lon), alt
else:
return lat, lon, alt # radians
selem.astype(np.int) a = np.zeros((7,7), dtype=np.int) a[1:6, 2:5] = 1 print(a) print(ndimage.binary_erosion(a).astype(a.dtype)) print(ndimage.binary_erosion(a, structure=np.ones((5,5))).astype(a.dtype)) # Feature Extraction im = np.zeros((256, 256)) im[64:-64, 64:-64] = 1 im = ndimage.rotate(im, 15, mode='constant') im = ndimage.gaussian_filter(im, 8) plt.imshow(im, cmap=plt.cm.gray) sx = ndimage.sobel(im, axis=0, mode='constant') sy = ndimage.sobel(im, axis=1, mode='constant') sob = np.hypot(sx, sy) plt.imshow(sob) # Segmentation # Histogram-based n = 10 l = 256 im = np.zeros((l, l)) np.random.seed(1) points = l*np.random.random((2, n**2)) im[(points[0]).astype(np.int), (points[1]).astype(np.int)] = 1 im = ndimage.gaussian_filter(im, sigma=l/(4.*n)) mask = (im > im.mean()).astype(np.float) mask += 0.1 * im img = mask + 0.2*np.random.randn(*mask.shape)
q = np.dot(scipy.linalg.inv(innerMat), np.linalg.multi_dot([bPolyMat.T, W, z])) # this is just for visual controlPoints = ConstructControlPoints(q, order) print(controlPoints) # Evaluate it on a grid... startIt = time.time() xx, yy, zz = GenerateSurfaceMesh(pGridsize, controlPoints[:,2], u, v, xDataMin, yDataMin, xDataRange, yDataRange, order) ############## # image filter idea, should pull this to separate class & file sobX = ndimage.sobel(zz, axis=1) sobY = ndimage.sobel(zz, axis=0) sobG = np.hypot(sobX, sobY) sobXX = ndimage.sobel(sobX, axis=1) sobYY = ndimage.sobel(sobY, axis=0) sobXY = ndimage.sobel(sobX, axis=0) hessDet = sobXX * sobYY - sobXY * sobXY # note element-wise multiplication # remove extra pad from computation (maybe need more) cut = 2 sobG = sobG[cut:-cut, cut:-cut] sobXX = sobXX[cut:-cut, cut:-cut] hessDet = hessDet[cut:-cut, cut:-cut] # filter test maskedG = np.zeros(sobG.shape) zDepth = zz.max() - zz.min()
def detect_edges(self, im, thr=0):
sx = ndimage.sobel(im, axis=0, mode='constant')
sy = ndimage.sobel(im, axis=1, mode='constant')
sob = np.hypot(sx, sy)
return sob > thr
def runSim(self):
self.makeModelDirs()
self.getTimeParams()
self.getBrainModelParams()
self.getSeedParams()
for seed, seedParams in enumerate(self.seedsParamsList):
print('\nSeed {}'.format(seed))
self.brainModelParams = copy.copy(seedParams)
self.makeSeedDir(seed)
self.getBrainElementsInitialActivities()
self.integrateBrainElementsActivities()
self.plotBrainElementsActivities()
# self.getHealtySteadyStateMAPE()
# if self.saveData:
# self.saveEvents()
# self.saveBrainElementsActivities()
self.CX = self.y[:, 3].copy()
self.CXHealthyMean = self.CX[self.healtyRange[0] *
100:self.healtyRange[1] * 100].mean()
self.CXHealthyRange = [0, self.CXHealthyMean * 2]
self.efPosHistory = np.zeros([self.nStep, 2])
self.DA = self.y[:, 5].copy()
self.DAHealthyMean = self.DA[self.healtyRange[0] *
100:self.healtyRange[1] * 100].mean()
self.DADamaged1Mean = self.DA[self.damagedRange1[0] *
100:self.damagedRange1[1] *
100].mean()
self.DADamaged2Mean = self.DA[self.damagedRange2[0] *
100:self.damagedRange2[1] *
100].mean()
self.DADamaged3Mean = self.DA[self.damagedRange3[0] *
100:self.damagedRange3[1] *
100].mean()
self.shoulderRange = np.deg2rad(np.array([-60.0, 150.0]))
self.elbowRange = np.deg2rad(np.array([0.0, 180.0]))
self.arm = Arm(self.shoulderRange, self.elbowRange)
self.desiredAngles = np.ones(2) * 0.5
self.Kp1 = 20.0
self.Kd1 = 1.5
self.Kp2 = 10.0
self.Kd2 = 1.0
if self.armPlot == True:
self.simFig = plt.figure("ARM SIMULATION", dpi=300)
self.simPlot = self.simFig.add_subplot(111)
self.simPlot.set_xlim([-1.0, 1.0])
self.simPlot.set_ylim([0.0, 1.0])
self.text1 = plt.figtext(.02,
.72,
"sec = %s" % (0.00),
style='italic',
bbox={'facecolor': 'yellow'})
self.armPlot, = self.simPlot.plot(
[0, self.arm.xElbow, self.arm.xEndEf],
[0, self.arm.yElbow, self.arm.yEndEf],
'k-',
color='black',
linewidth=5)
self.xDesAng = self.arm.L1*np.cos(self.desiredAngles[0]) + \
self.arm.L2*np.cos(self.desiredAngles[0]+self.desiredAngles[1])
self.yDesAng = self.arm.L1*np.sin(self.desiredAngles[0]) + \
self.arm.L2*np.sin(self.desiredAngles[0]+self.desiredAngles[1])
self.desEnd, = self.simPlot.plot([self.xDesAng],
[self.yDesAng],
'o',
color='green',
markersize=10)
for t in range(self.nStep):
self.desiredAngles[0] = utils.changeRange(
self.CX[t], self.CXHealthyRange[0], self.CXHealthyRange[1],
self.shoulderRange[0], self.shoulderRange[1])
self.desiredAngles[1] = utils.changeRange(
self.CX[t], self.CXHealthyRange[0], self.CXHealthyRange[1],
self.elbowRange[0], self.elbowRange[1])
self.Torque = self.arm.PD_controller(
[self.desiredAngles[0], self.desiredAngles[1]], self.Kp1,
self.Kp2, self.Kd1, self.Kd2) # compute torques
self.arm.SolveDirectDynamics(self.Torque[0],
self.Torque[1]) # move the arm
self.efPosHistory[t, :] = np.array(
[self.arm.xEndEf, self.arm.yEndEf])
if self.armPlot and t > self.startArmPlot:
self.text1.set_text("sec = {}".format(t / 100.0))
self.xDesAng = self.arm.L1*np.cos(self.desiredAngles[0]) +\
self.arm.L2*np.cos(self.desiredAngles[0]+self.desiredAngles[1])
self.yDesAng = self.arm.L1*np.sin(self.desiredAngles[0]) +\
self.arm.L2*np.sin(self.desiredAngles[0]+self.desiredAngles[1])
self.desEnd.set_data([self.xDesAng], [self.yDesAng])
self.armPlot.set_data(
[0, self.arm.xElbow, self.arm.xEndEf],
[0, self.arm.yElbow, self.arm.yEndEf])
plt.pause(self.dt)
if self.saveData:
efColNames = ['X', 'Y']
self.efDataFrame = pd.DataFrame(data=self.efPosHistory,
columns=efColNames)
efPath = os.path.join(self.armDir, 'efPos.csv')
self.efDataFrame.to_csv(efPath)
self.efX = self.efPosHistory[:, 0].copy()
self.efY = self.efPosHistory[:, 1].copy()
self.efdX = np.ediff1d(self.efX, to_begin=np.array([0]))
self.efdY = np.ediff1d(self.efY, to_begin=np.array([0]))
self.euclDist = np.hypot(self.efdX, self.efdY)
self.meanPhys, self.stdPhys = \
self.getTremorOscillationAmplitude(self.healtyRange)
if self.modelType == 'DRNDamage':
self.meanDmg1, self.stdDmg1 = \
self.getTremorOscillationAmplitude(self.damagedRange1)
self.meanDmg2, self.stdDmg2 = \
self.getTremorOscillationAmplitude(self.damagedRange2)
self.meanDmg3, self.stdDmg3 = \
self.getTremorOscillationAmplitude(self.damagedRange3)
self.seedTremorData[seed, 0] = self.meanPhys
if self.modelType == 'DRNDamage':
self.seedTremorData[seed, 1] = self.meanDmg1
self.seedTremorData[seed, 2] = self.meanDmg2
self.seedTremorData[seed, 3] = self.meanDmg3
self.seedDA5HTData[seed, 0] = self.DAHealthyMean
self.seedDA5HTData[seed, 1] = self.DADamaged1Mean
self.seedDA5HTData[seed, 2] = self.DADamaged2Mean
self.seedDA5HTData[seed, 3] = self.DADamaged3Mean
self.dataColumns = ['healthy', 'damaged 1', 'damaged 2', 'damaged 3']
self.tremorResults = pd.DataFrame(data=self.seedTremorData,
columns=self.dataColumns)
if self.tremorPlot:
self.healthyLabel = 'HEALTHY'
self.xTicksLabels = [
self.healthyLabel,
'DAMAGE 1',
'DAMAGE 2',
'DAMAGE 3',
]
self.oscillationAmpFig = \
plt.figure(
"oscillation amplitude",
dpi=300
)
self.oscillationAmpPlot = self.oscillationAmpFig.add_subplot(111)
self.oscillationAmpPlot.set_ylabel("Oscillation amplitude (m)",
fontsize=10,
fontweight='bold')
self.oscillationAmpPlot.set_xlabel("DRN Lesion",
fontsize=10,
fontweight='bold')
self.oscillationAmpPlot.set_ylim(0.0, 0.01)
self.oscillationAmpPlot.set_xticks(np.arange(5))
self.oscillationAmpPlot.set_xticklabels(self.xTicksLabels)
self.oscillationAmpPlot.tick_params(axis='both',
which='major',
labelsize=7)
self.oscillationAmpPlot.tick_params(axis='both',
which='minor',
labelsize=7)
self.oscillationAmpPlot.errorbar([0],
self.seedTremorData[:, 0].mean(),
yerr=self.seedTremorData[:,
0].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='solid')
self.oscillationAmpPlot.errorbar([1],
self.seedTremorData[:, 1].mean(),
yerr=self.seedTremorData[:,
1].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='solid')
self.oscillationAmpPlot.errorbar([2],
self.seedTremorData[:, 2].mean(),
yerr=self.seedTremorData[:,
2].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='solid')
self.oscillationAmpPlot.errorbar([3],
self.seedTremorData[:, 3].mean(),
yerr=self.seedTremorData[:,
3].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='solid')
self.oscillationAmpPlot.plot(list(range(4)), [
self.seedTremorData[:, 0].mean(),
self.seedTremorData[:, 1].mean(),
self.seedTremorData[:, 2].mean(),
self.seedTremorData[:, 3].mean()
],
color='black')
if self.saveData:
self.dataColumns = [
'healthy', 'damaged1', 'damaged2', 'damaged3'
]
self.tremorResults = pd.DataFrame(data=self.seedTremorData,
columns=self.dataColumns)
tremorPath = os.path.join(self.modelDir, 'tremors.csv')
self.tremorResults.to_csv(tremorPath)
self.DAConcFig = \
plt.figure(
"DA concentration reduction",
dpi=300
)
self.DAConcPlot = self.DAConcFig.add_subplot(111)
self.DAConcPlot.set_ylabel("DA concentration (nM)",
fontsize=10,
fontweight='bold')
self.DAConcPlot.set_xlabel("DRN Lesion",
fontsize=10,
fontweight='bold')
# self.DAConcPlot.set_ylim(0.0, 3.0)
self.DAConcPlot.set_xticks(np.arange(5))
self.DAConcPlot.set_xticklabels(self.xTicksLabels)
self.DAConcPlot.tick_params(
axis='both',
which='major',
labelsize=7,
# fontweight= 'bold'
)
self.DAConcPlot.tick_params(
axis='both',
which='minor',
labelsize=7,
# fontweight= 'bold'
)
self.DAConcPlot.errorbar([0],
self.seedDA5HTData[:, 0].mean(),
yerr=self.seedDA5HTData[:, 0].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='none')
self.DAConcPlot.errorbar([1],
self.seedDA5HTData[:, 1].mean(),
yerr=self.seedDA5HTData[:, 1].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='none')
self.DAConcPlot.errorbar([2],
self.seedDA5HTData[:, 2].mean(),
yerr=self.seedDA5HTData[:, 2].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='none')
self.DAConcPlot.errorbar([3],
self.seedDA5HTData[:, 3].mean(),
yerr=self.seedDA5HTData[:, 3].std(),
marker='s',
markersize='7',
mec='black',
mfc='white',
ecolor='black',
fmt='',
linestyle='none')
self.DAConcPlot.plot(list(range(4)), [
self.seedDA5HTData[:, 0].mean(), self.seedDA5HTData[:,
1].mean(),
self.seedDA5HTData[:, 2].mean(), self.seedDA5HTData[:,
3].mean()
],
color='black')
if self.saveData:
self.dataColumns = [
'healthy', 'damaged1', 'damaged2', 'damaged3'
]
self.DAResults = pd.DataFrame(data=self.seedDA5HTData,
columns=self.dataColumns)
DAPath = os.path.join(self.modelDir, 'DAconc.csv')
self.DAResults.to_csv(DAPath)
# fig.savefig('interp_data_cut_%s_%i.png'%(filename.split('.')[0], number))
# Load data
data = np.loadtxt(filename, delimiter=',')
x = data[:, 0]
y = data[:, 1]
z = data[:, 2]
v = data[:, 3]
plt.style.use('./PaperFig_0.8_textwidth.mplstyle')
fig2, ax2 = plt.subplots()
fig3, ax3 = plt.subplots()
for xx, yy in [[250, 0], [0, 0], [-250, 0]]:
distances = np.hypot(x - xx, y - yy)
axon_i = np.where(distances == distances.min())
# Modify xx and yy so that they match the real ones
xx = x[axon_i][0]
yy = y[axon_i][0]
ax2.plot(z[axon_i], v[axon_i], label=r'$x = %i$ ' % xx + r'$\rm \mu m$')
ax3.plot(z[axon_i],
np.abs(v[axon_i]),
label=r'$x = %i$ ' % xx + r'$\rm \mu m$')
ax2.set_xlim(0.2875e4, 0.7125e4)
ax2.set_xlabel(r'$\rm z$' + ' (' + r'$\rm \mu m$' + ')')
ax2.set_ylabel(r'$\rm v_{E}$' + ' (' + r'$\rm mV$' + ')')
# ax2.legend(loc='best', fontsize=8)
def hog(image, orientations=9, pixels_per_cell=(8, 8), cells_per_block=(3, 3),
block_norm='L2-Hys', visualize=False, visualise=None, transform_sqrt=False,
feature_vector=True, multichannel=None):
"""Extract Histogram of Oriented Gradients (HOG) for a given image.
Compute a Histogram of Oriented Gradients (HOG) by
1. (optional) global image normalization
2. computing the gradient image in `row` and `col`
3. computing gradient histograms
4. normalizing across blocks
5. flattening into a feature vector
Parameters
----------
image : (M, N[, C]) ndarray
Input image.
orientations : int, optional
Number of orientation bins.
pixels_per_cell : 2-tuple (int, int), optional
Size (in pixels) of a cell.
cells_per_block : 2-tuple (int, int), optional
Number of cells in each block.
block_norm : str {'L1', 'L1-sqrt', 'L2', 'L2-Hys'}, optional
Block normalization method:
``L1``
Normalization using L1-norm.
``L1-sqrt``
Normalization using L1-norm, followed by square root.
``L2``
Normalization using L2-norm.
``L2-Hys``
Normalization using L2-norm, followed by limiting the
maximum values to 0.2 (`Hys` stands for `hysteresis`) and
renormalization using L2-norm. (default)
For details, see [3]_, [4]_.
visualize : bool, optional
Also return an image of the HOG. For each cell and orientation bin,
the image contains a line segment that is centered at the cell center,
is perpendicular to the midpoint of the range of angles spanned by the
orientation bin, and has intensity proportional to the corresponding
histogram value.
transform_sqrt : bool, optional
Apply power law compression to normalize the image before
processing. DO NOT use this if the image contains negative
values. Also see `notes` section below.
feature_vector : bool, optional
Return the data as a feature vector by calling .ravel() on the result
just before returning.
multichannel : boolean, optional
If True, the last `image` dimension is considered as a color channel,
otherwise as spatial.
Returns
-------
out : (n_blocks_row, n_blocks_col, n_cells_row, n_cells_col, n_orient) ndarray
HOG descriptor for the image. If `feature_vector` is True, a 1D
(flattened) array is returned.
hog_image : (M, N) ndarray, optional
A visualisation of the HOG image. Only provided if `visualize` is True.
References
----------
.. [1] https://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
.. [2] Dalal, N and Triggs, B, Histograms of Oriented Gradients for
Human Detection, IEEE Computer Society Conference on Computer
Vision and Pattern Recognition 2005 San Diego, CA, USA,
https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf,
:DOI:`10.1109/CVPR.2005.177`
.. [3] Lowe, D.G., Distinctive image features from scale-invatiant
keypoints, International Journal of Computer Vision (2004) 60: 91,
http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf,
:DOI:`10.1023/B:VISI.0000029664.99615.94`
.. [4] Dalal, N, Finding People in Images and Videos,
Human-Computer Interaction [cs.HC], Institut National Polytechnique
de Grenoble - INPG, 2006,
https://tel.archives-ouvertes.fr/tel-00390303/file/NavneetDalalThesis.pdf
Notes
-----
The presented code implements the HOG extraction method from [2]_ with
the following changes: (I) blocks of (3, 3) cells are used ((2, 2) in the
paper; (II) no smoothing within cells (Gaussian spatial window with sigma=8pix
in the paper); (III) L1 block normalization is used (L2-Hys in the paper).
Power law compression, also known as Gamma correction, is used to reduce
the effects of shadowing and illumination variations. The compression makes
the dark regions lighter. When the kwarg `transform_sqrt` is set to
``True``, the function computes the square root of each color channel
and then applies the hog algorithm to the image.
"""
image = np.atleast_2d(image)
if multichannel is None:
multichannel = (image.ndim == 3)
ndim_spatial = image.ndim - 1 if multichannel else image.ndim
if ndim_spatial != 2:
raise ValueError('Only images with 2 spatial dimensions are '
'supported. If using with color/multichannel '
'images, specify `multichannel=True`.')
"""
The first stage applies an optional global image normalization
equalisation that is designed to reduce the influence of illumination
effects. In practice we use gamma (power law) compression, either
computing the square root or the log of each color channel.
Image texture strength is typically proportional to the local surface
illumination so this compression helps to reduce the effects of local
shadowing and illumination variations.
"""
if transform_sqrt:
image = np.sqrt(image)
"""
The second stage computes first order image gradients. These capture
contour, silhouette and some texture information, while providing
further resistance to illumination variations. The locally dominant
color channel is used, which provides color invariance to a large
extent. Variant methods may also include second order image derivatives,
which act as primitive bar detectors - a useful feature for capturing,
e.g. bar like structures in bicycles and limbs in humans.
"""
if image.dtype.kind == 'u':
# convert uint image to float
# to avoid problems with subtracting unsigned numbers
image = image.astype('float')
if multichannel:
g_row_by_ch = np.empty_like(image, dtype=np.double)
g_col_by_ch = np.empty_like(image, dtype=np.double)
g_magn = np.empty_like(image, dtype=np.double)
for idx_ch in range(image.shape[2]):
g_row_by_ch[:, :, idx_ch], g_col_by_ch[:, :, idx_ch] = \
_hog_channel_gradient(image[:, :, idx_ch])
g_magn[:, :, idx_ch] = np.hypot(g_row_by_ch[:, :, idx_ch],
g_col_by_ch[:, :, idx_ch])
# For each pixel select the channel with the highest gradient magnitude
idcs_max = g_magn.argmax(axis=2)
rr, cc = np.meshgrid(np.arange(image.shape[0]),
np.arange(image.shape[1]),
indexing='ij',
sparse=True)
g_row = g_row_by_ch[rr, cc, idcs_max]
g_col = g_col_by_ch[rr, cc, idcs_max]
else:
g_row, g_col = _hog_channel_gradient(image)
"""
The third stage aims to produce an encoding that is sensitive to
local image content while remaining resistant to small changes in
pose or appearance. The adopted method pools gradient orientation
information locally in the same way as the SIFT [Lowe 2004]
feature. The image window is divided into small spatial regions,
called "cells". For each cell we accumulate a local 1-D histogram
of gradient or edge orientations over all the pixels in the
cell. This combined cell-level 1-D histogram forms the basic
"orientation histogram" representation. Each orientation histogram
divides the gradient angle range into a fixed number of
predetermined bins. The gradient magnitudes of the pixels in the
cell are used to vote into the orientation histogram.
"""
s_row, s_col = image.shape[:2]
c_row, c_col = pixels_per_cell
b_row, b_col = cells_per_block
n_cells_row = int(s_row // c_row) # number of cells along row-axis
n_cells_col = int(s_col // c_col) # number of cells along col-axis
# compute orientations integral images
orientation_histogram = np.zeros((n_cells_row, n_cells_col, orientations))
_hoghistogram.hog_histograms(g_col, g_row, c_col, c_row, s_col, s_row,
n_cells_col, n_cells_row,
orientations, orientation_histogram)
# now compute the histogram for each cell
hog_image = None
if visualise is not None:
visualize = visualise
warn('Argument `visualise` is deprecated and will '
'be changed to `visualize` in v0.16', skimage_deprecation)
if visualize:
from .. import draw
radius = min(c_row, c_col) // 2 - 1
orientations_arr = np.arange(orientations)
# set dr_arr, dc_arr to correspond to midpoints of orientation bins
orientation_bin_midpoints = (
np.pi * (orientations_arr + .5) / orientations)
dr_arr = radius * np.sin(orientation_bin_midpoints)
dc_arr = radius * np.cos(orientation_bin_midpoints)
hog_image = np.zeros((s_row, s_col), dtype=float)
for r in range(n_cells_row):
for c in range(n_cells_col):
for o, dr, dc in zip(orientations_arr, dr_arr, dc_arr):
centre = tuple([r * c_row + c_row // 2,
c * c_col + c_col // 2])
rr, cc = draw.line(int(centre[0] - dc),
int(centre[1] + dr),
int(centre[0] + dc),
int(centre[1] - dr))
hog_image[rr, cc] += orientation_histogram[r, c, o]
"""
The fourth stage computes normalization, which takes local groups of
cells and contrast normalizes their overall responses before passing
to next stage. Normalization introduces better invariance to illumination,
shadowing, and edge contrast. It is performed by accumulating a measure
of local histogram "energy" over local groups of cells that we call
"blocks". The result is used to normalize each cell in the block.
Typically each individual cell is shared between several blocks, but
its normalizations are block dependent and thus different. The cell
thus appears several times in the final output vector with different
normalizations. This may seem redundant but it improves the performance.
We refer to the normalized block descriptors as Histogram of Oriented
Gradient (HOG) descriptors.
"""
n_blocks_row = (n_cells_row - b_row) + 1
n_blocks_col = (n_cells_col - b_col) + 1
normalized_blocks = np.zeros((n_blocks_row, n_blocks_col,
b_row, b_col, orientations))
for r in range(n_blocks_row):
for c in range(n_blocks_col):
block = orientation_histogram[r:r + b_row, c:c + b_col, :]
normalized_blocks[r, c, :] = \
_hog_normalize_block(block, method=block_norm)
"""
The final step collects the HOG descriptors from all blocks of a dense
overlapping grid of blocks covering the detection window into a combined
feature vector for use in the window classifier.
"""
if feature_vector:
normalized_blocks = normalized_blocks.ravel()
if visualize:
return normalized_blocks, hog_image
else:
return normalized_blocks
def cart2pol(x, y):
theta = np.arctan2(y, x)
rho = np.hypot(x, y)
return theta, rho
def calibrate_objects(obj,
cat,
sr=15.0 / 3600,
smooth=False,
correct_brightness=False,
smoothr=100,
smoothmin=20,
retval='std'):
h = htm.HTM(10)
m = h.match(obj['ra'], obj['dec'], cat['ra'], cat['dec'], sr, maxmatch=0)
oidx = m[0]
cidx = m[1]
dist = m[2] * 3600
if len(oidx) < 300:
return None
x, y = obj['x'][oidx], obj['y'][oidx]
x = (x - 2560 / 2) * 2 / 2560
y = (y - 2160 / 2) * 2 / 2160
omag = obj['mag'][oidx]
omagerr = obj['magerr'][oidx]
oflux = obj['flux'][oidx]
ofluxerr = obj['fluxerr'][oidx]
oflags = obj['flags'][oidx]
ochisq = obj['chisq'][oidx]
omag0 = (omag - np.min(omag)) / (np.max(omag) - np.min(omag))
try:
cb = cat['g'][cidx]
cv = cat['r'][cidx]
cr = cat['i'][cidx]
cmagerr = np.hypot(cat['gerr'][cidx], cat['rerr'][cidx],
cat['ierr'][cidx])
except:
cb = cat['b'][cidx]
cv = cat['v'][cidx]
cr = cat['r'][cidx]
try:
cmagerr = np.hypot(cat['berr'][cidx], cat['verr'][cidx],
cat['rerr'][cidx])
except:
cmagerr = np.hypot(cat['ebt'][cidx], cat['evt'][cidx])
cmag = cv
tmagerr = np.hypot(cmagerr, omagerr)
delta_mag = cmag - omag
weights = 1.0 / tmagerr
X = [
np.ones(len(delta_mag)), x, y, x * x, x * y, y * y, x * x * x,
x * x * y, x * y * y, y * y * y, x * x * x * x, x * x * x * y,
x * x * y * y, x * y * y * y, y * y * y * y, x * x * x * x * x,
x * x * x * x * y, x * x * x * y * y, x * x * y * y * y,
x * y * y * y * y, y * y * y * y * y, x * x * x * x * x * x,
x * x * x * x * x * y, x * x * x * x * y * y, x * x * x * y * y * y,
x * x * y * y * y * y, x * y * y * y * y * y, y * y * y * y * y * y
]
#X += [omag0, omag0**2, omag0**3, omag0**4, omag0**5, omag0**6]
X += [
cb - cv, (cb - cv) * x,
(cb - cv) * y, (cb - cv) * x * x, (cb - cv) * x * y, (cb - cv) * y * y,
(cb - cv) * x * x * x, (cb - cv) * x * x * y, (cb - cv) * x * y * y,
(cb - cv) * y * y * y
]
X += [
cv - cr, (cv - cr) * x,
(cv - cr) * y, (cv - cr) * x * x, (cv - cr) * x * y, (cv - cr) * y * y,
(cv - cr) * x * x * x, (cv - cr) * x * x * y, (cv - cr) * x * y * y,
(cv - cr) * y * y * y
]
X = np.vstack(X).T
Y = delta_mag
idx = (oflags == 0) & (ochisq < 2.0)
for iter in range(5):
if len(X[idx]) < 100:
print "Fit failed - %d objects" % len(X[idx])
return None
C = sm.WLS(Y[idx], X[idx], weights=weights[idx]).fit()
YY = np.sum(X * C.params, axis=1)
idx = (np.abs(Y - YY) < 2.0 * np.std(Y - YY)) & (oflags
== 0) & (ochisq < 2.0)
print np.std((Y - YY)[idx]), np.std(Y - YY), '-', np.std(
((Y - YY) / tmagerr)), np.std(
(((Y - YY) / tmagerr))[idx]), '-', len(idx[idx])
mag0 = YY
mag = omag + mag0
x = (obj['x'] - 2560 / 2) * 2 / 2560
y = (obj['y'] - 2160 / 2) * 2 / 2160
omag0 = (obj['mag'] - np.min(omag)) / (np.max(omag) - np.min(omag))
obj['mag0'] = C.params[0] * np.ones_like(
obj['mag']
) + C.params[1] * x + C.params[2] * y + C.params[3] * x * x + C.params[
4] * x * y + C.params[5] * y * y + C.params[6] * x * x * x + C.params[
7] * x * x * y + C.params[8] * x * y * y + C.params[9] * y * y * y + C.params[
10] * x * x * x * x + C.params[11] * x * x * x * y + C.params[
12] * x * x * y * y + C.params[13] * x * y * y * y + C.params[
14] * y * y * y * y + C.params[15] * x * x * x * x * x + C.params[
16] * x * x * x * x * y + C.params[17] * x * x * x * y * y + C.params[
18] * x * x * y * y * y + C.params[19] * x * y * y * y * y + C.params[
20] * y * y * y * y * y + C.params[
21] * x * x * x * x * x * x + C.params[
22] * x * x * x * x * x * y + C.params[
23] * x * x * x * x * y * y + C.params[
24] * x * x * x * y * y * y + C.params[
25] * x * x * y * y * y * y + C.params[
26] * x * y * y * y * y * y + C.params[
27] * y * y * y * y * y * y
#obj['mag0'] += C.params[28]*omag0 + C.params[29]*omag0**2 + C.params[30]*omag0**3 + C.params[31]*omag0**4 + C.params[32]*omag0**5 + C.params[33]*omag0**6
obj['cmag'] = obj['mag'] + obj['mag0']
obj['Cbv'] = np.ones_like(obj['mag']) * C.params[-20] + x * C.params[
-19] + y * C.params[-18] + x * x * C.params[-17] + x * y * C.params[
-16] + y * y * C.params[-15] + x * x * x * C.params[
-14] + x * x * y * C.params[-13] + x * y * y * C.params[
-12] + y * y * y * C.params[-11]
obj['Cvr'] = np.ones_like(obj['mag']) * C.params[-10] + x * C.params[
-9] + y * C.params[-8] + x * x * C.params[-7] + x * y * C.params[
-6] + y * y * C.params[-5] + x * x * x * C.params[
-4] + x * x * y * C.params[-3] + x * y * y * C.params[
-2] + y * y * y * C.params[-1]
# Correct uncorrected brightness-dependent variations
obj['bcorr'] = np.zeros_like(obj['cmag'])
if correct_brightness:
step = 0.5
omag0 = omag + np.median(cmag - omag)
for vmin in np.arange(5, 16, step):
idx0 = (omag0[idx] >= vmin) & (omag0[idx] < vmin + step)
if len(omag0[idx][idx0] > 20):
omag1 = obj['mag'] + np.median(cmag - omag)
idx1 = (omag1 >= vmin) & (omag1 < vmin + step)
obj['bcorr'][idx1] = np.average(
(Y - YY)[idx][idx0], weights=1.0 / tmagerr[idx][idx0])
# Local smoothing of residuals
if smooth:
kd0 = cKDTree(np.array([obj['x'][oidx][idx], obj['y'][oidx][idx]]).T)
kd = cKDTree(np.array([obj['x'], obj['y']]).T)
m = kd.query_ball_tree(kd0, smoothr)
nm = np.array(([len(_) for _ in m]))
corr = np.array([
np.average((Y - YY)[idx][_], weights=weights[idx][_])
if len(_) > smoothmin else 0 for _ in m
])
icorr = nm > smoothmin
obj['corr'] = corr
obj['corrected'] = icorr
obj['ncorr'] = nm
else:
obj['corr'] = np.zeros_like(obj['mag'])
obj['corrected'] = np.ones_like(obj['mag'], dtype=np.bool)
obj['ncorr'] = np.zeros_like(obj['mag'])
if retval == 'std':
return np.std(Y - YY)
elif retval == 'map':
return Y
elif retval == 'fit':
return YY
elif retval == 'diff':
return Y - YY
elif retval == 'all':
return Y, YY, obj['corr'], oidx
def _integrate_rk12(x0, y0, dmap, f, maxlength):
"""
2nd-order Runge-Kutta algorithm with adaptive step size.
This method is also referred to as the improved Euler's method, or Heun's
method. This method is favored over higher-order methods because:
1. To get decent looking trajectories and to sample every mask cell
on the trajectory we need a small timestep, so a lower order
solver doesn't hurt us unless the data is *very* high resolution.
In fact, for cases where the user inputs
data smaller or of similar grid size to the mask grid, the higher
order corrections are negligible because of the very fast linear
interpolation used in `interpgrid`.
2. For high resolution input data (i.e. beyond the mask
resolution), we must reduce the timestep. Therefore, an adaptive
timestep is more suited to the problem as this would be very hard
to judge automatically otherwise.
This integrator is about 1.5 - 2x as fast as RK4 and RK45 solvers (using
similar Python implementations) in most setups.
"""
# This error is below that needed to match the RK4 integrator. It
# is set for visual reasons -- too low and corners start
# appearing ugly and jagged. Can be tuned.
maxerror = 0.003
# This limit is important (for all integrators) to avoid the
# trajectory skipping some mask cells. We could relax this
# condition if we use the code which is commented out below to
# increment the location gradually. However, due to the efficient
# nature of the interpolation, this doesn't boost speed by much
# for quite a bit of complexity.
maxds = min(1. / dmap.mask.nx, 1. / dmap.mask.ny, 0.1)
ds = maxds
stotal = 0
xi = x0
yi = y0
xf_traj = []
yf_traj = []
while True:
try:
if dmap.grid.within_grid(xi, yi):
xf_traj.append(xi)
yf_traj.append(yi)
else:
raise OutOfBounds
# Compute the two intermediate gradients.
# f should raise OutOfBounds if the locations given are
# outside the grid.
k1x, k1y = f(xi, yi)
k2x, k2y = f(xi + ds * k1x, yi + ds * k1y)
except OutOfBounds:
# Out of the domain during this step.
# Take an Euler step to the boundary to improve neatness
# unless the trajectory is currently empty.
if xf_traj:
ds, xf_traj, yf_traj = _euler_step(xf_traj, yf_traj, dmap, f)
stotal += ds
break
except TerminateTrajectory:
break
dx1 = ds * k1x
dy1 = ds * k1y
dx2 = ds * 0.5 * (k1x + k2x)
dy2 = ds * 0.5 * (k1y + k2y)
nx, ny = dmap.grid.shape
# Error is normalized to the axes coordinates
error = np.hypot((dx2 - dx1) / (nx - 1), (dy2 - dy1) / (ny - 1))
# Only save step if within error tolerance
if error < maxerror:
xi += dx2
yi += dy2
try:
dmap.update_trajectory(xi, yi)
except InvalidIndexError:
break
if stotal + ds > maxlength:
break
stotal += ds
# recalculate stepsize based on step error
if error == 0:
ds = maxds
else:
ds = min(maxds, 0.85 * ds * (maxerror / error)**0.5)
return stotal, xf_traj, yf_traj
def transect_yx(z, atr, start_yx, end_yx, interpolation='nearest'):
"""Extract 2D matrix (z) value along the line [x0,y0;x1,y1]
Ref link: http://stackoverflow.com/questions/7878398/how-to-e
xtract-an-arbitrary-line-of-values-from-a-numpy-array
Parameters: z : (np.array) 2D data matrix
atr : (dict) attribute
start_yx : (list) y,x coordinate of start point
end_yx : (list) y,x coordinate of end point
interpolation : str, sampling/interpolation method, including:
'nearest' - nearest neighbour, by default
'cubic' - cubic interpolation
'bilinear' - bilinear interpolation
Returns: transect: (dict) containing 1D matrix:
'X' - 1D np.array for X/column coordinates in float32
'Y' - 1D np.array for Y/row. coordinates in float32
'value' - 1D np.array for z value in float32
'distance' - 1D np.array for distance in float32
Example: transect = transect_yx(dem, demRsc, [10,15], [100,115])
"""
[y0, x0] = start_yx
[y1, x1] = end_yx
# check
length, width = int(atr['LENGTH']), int(atr['WIDTH'])
if not all(0 <= i < width and 0 <= j < length
for i, j in zip([x0, x1], [y0, y1])):
msg = 'input start/end point is out of data coverage'
msg += '\nstart_yx: {}'.format(start_yx)
msg += '\nend_yx:{}'.format(end_yx)
msg += '\ndata size: ({}, {})'.format(length, width)
raise ValueError(msg)
# Determine points coordinates along the line
num_pts = int(np.hypot(x1 - x0, y1 - y0))
ys = np.linspace(y0, y1, num_pts, dtype=np.float32)
xs = np.linspace(x0, x1, num_pts, dtype=np.float32)
# Extract z value along the line
if interpolation.lower() == 'nearest':
z_line = z[np.rint(ys).astype(np.int), np.rint(xs).astype(np.int)]
elif interpolation.lower() == 'cubic':
z_line = map_coordinates(z, np.vstack((ys, xs)), order=3)
elif interpolation.lower() == 'bilinear':
z_line = map_coordinates(z, np.vstack((ys, xs)), order=2)
else:
print('Un-recognized interpolation method: ' + interpolation)
print('Continue with nearest ...')
z_line = z[np.rint(ys).astype(np.int),
np.rint(xs).astype(np.int)] # nearest neighbour
# Calculate Distance along the line
earth_radius = 6.3781e6 # in meter
if 'Y_FIRST' in atr.keys():
[lat0, lat1] = coordinate(atr).yx2lalo([y0, y1], coord_type='y')
lat_c = (lat0 + lat1) / 2.
x_step = float(atr['X_STEP']) * np.pi / 180.0 * earth_radius * np.cos(
lat_c * np.pi / 180)
y_step = float(atr['Y_STEP']) * np.pi / 180.0 * earth_radius
else:
x_step = range_ground_resolution(atr)
y_step = azimuth_ground_resolution(atr)
dist_line = np.hypot((xs - x0) * x_step, (ys - y0) * y_step)
# remove points in masked out areas
mask = ~np.isnan(z_line)
mask *= z_line != 0.0
# prepare output
transect = {}
transect['Y'] = ys[mask]
transect['X'] = xs[mask]
transect['value'] = z_line[mask]
transect['distance'] = dist_line[mask]
return transect
def get_euclidean_dist(a, b):
dx = a[0] - b[0]
dy = a[1] - b[1]
dist = np.hypot(dx, dy)
return dist
def sobel_filter(im):
sx = sp.ndimage.sobel(im, axis=0, mode='constant')
sy = sp.ndimage.sobel(im, axis=1, mode='constant')
sob = np.hypot(sx, sy)
return sob
# from mpl_toolkits.mplot3d import Axes3D
# from matplotlib import cm
# from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
n = 20
x, y = 8 * np.pi * (np.indices((n, n)) - n // 2) / n
d = 0.5
z = np.sin(np.hypot(x, y - d)) + np.sin(np.hypot(x, y + d))
surf = ax.plot_surface(x, y, z, antialiased=True, color='#3BBDF7',
linewidth=0) #, cmap=cm.coolwarm, antialiased=False)
# Customize the z axis.
# ax.set_zlim(0., 2.)
# ax.zaxis.set_major_locator(LinearLocator(10))
# ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
# Add a color bar which maps values to colors.
# fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
def streamplot(axes,
x,
y,
u,
v,
density=1,
linewidth=None,
color=None,
cmap=None,
norm=None,
arrowsize=1,
arrowstyle='-|>',
minlength=0.1,
transform=None,
zorder=None,
start_points=None,
maxlength=4.0,
integration_direction='both'):
"""
Draw streamlines of a vector flow.
Parameters
----------
x, y : 1D/2D arrays
Evenly spaced strictly increasing arrays to make a grid.
u, v : 2D arrays
*x* and *y*-velocities. The number of rows and columns must match
the length of *y* and *x*, respectively.
density : float or (float, float)
Controls the closeness of streamlines. When ``density = 1``, the domain
is divided into a 30x30 grid. *density* linearly scales this grid.
Each cell in the grid can have, at most, one traversing streamline.
For different densities in each direction, use a tuple
(density_x, density_y).
linewidth : float or 2D array
The width of the stream lines. With a 2D array the line width can be
varied across the grid. The array must have the same shape as *u*
and *v*.
color : color or 2D array
The streamline color. If given an array, its values are converted to
colors using *cmap* and *norm*. The array must have the same shape
as *u* and *v*.
cmap : `~matplotlib.colors.Colormap`
Colormap used to plot streamlines and arrows. This is only used if
*color* is an array.
norm : `~matplotlib.colors.Normalize`
Normalize object used to scale luminance data to 0, 1. If ``None``,
stretch (min, max) to (0, 1). This is only used if *color* is an array.
arrowsize : float
Scaling factor for the arrow size.
arrowstyle : str
Arrow style specification.
See `~matplotlib.patches.FancyArrowPatch`.
minlength : float
Minimum length of streamline in axes coordinates.
start_points : Nx2 array
Coordinates of starting points for the streamlines in data coordinates
(the same coordinates as the *x* and *y* arrays).
zorder : int
The zorder of the stream lines and arrows.
Artists with lower zorder values are drawn first.
maxlength : float
Maximum length of streamline in axes coordinates.
integration_direction : {'forward', 'backward', 'both'}, default: 'both'
Integrate the streamline in forward, backward or both directions.
Returns
-------
StreamplotSet
Container object with attributes
- ``lines``: `.LineCollection` of streamlines
- ``arrows``: `.PatchCollection` containing `.FancyArrowPatch`
objects representing the arrows half-way along stream lines.
This container will probably change in the future to allow changes
to the colormap, alpha, etc. for both lines and arrows, but these
changes should be backward compatible.
"""
grid = Grid(x, y)
mask = StreamMask(density)
dmap = DomainMap(grid, mask)
if zorder is None:
zorder = mlines.Line2D.zorder
# default to data coordinates
if transform is None:
transform = axes.transData
if color is None:
color = axes._get_lines.get_next_color()
if linewidth is None:
linewidth = matplotlib.rcParams['lines.linewidth']
line_kw = {}
arrow_kw = dict(arrowstyle=arrowstyle, mutation_scale=10 * arrowsize)
_api.check_in_list(['both', 'forward', 'backward'],
integration_direction=integration_direction)
if integration_direction == 'both':
maxlength /= 2.
use_multicolor_lines = isinstance(color, np.ndarray)
if use_multicolor_lines:
if color.shape != grid.shape:
raise ValueError("If 'color' is given, it must match the shape of "
"'Grid(x, y)'")
line_colors = []
color = np.ma.masked_invalid(color)
else:
line_kw['color'] = color
arrow_kw['color'] = color
if isinstance(linewidth, np.ndarray):
if linewidth.shape != grid.shape:
raise ValueError("If 'linewidth' is given, it must match the "
"shape of 'Grid(x, y)'")
line_kw['linewidth'] = []
else:
line_kw['linewidth'] = linewidth
arrow_kw['linewidth'] = linewidth
line_kw['zorder'] = zorder
arrow_kw['zorder'] = zorder
# Sanity checks.
if u.shape != grid.shape or v.shape != grid.shape:
raise ValueError("'u' and 'v' must match the shape of 'Grid(x, y)'")
u = np.ma.masked_invalid(u)
v = np.ma.masked_invalid(v)
integrate = get_integrator(u, v, dmap, minlength, maxlength,
integration_direction)
trajectories = []
if start_points is None:
for xm, ym in _gen_starting_points(mask.shape):
if mask[ym, xm] == 0:
xg, yg = dmap.mask2grid(xm, ym)
t = integrate(xg, yg)
if t is not None:
trajectories.append(t)
else:
sp2 = np.asanyarray(start_points, dtype=float).copy()
# Check if start_points are outside the data boundaries
for xs, ys in sp2:
if not (grid.x_origin <= xs <= grid.x_origin + grid.width
and grid.y_origin <= ys <= grid.y_origin + grid.height):
raise ValueError("Starting point ({}, {}) outside of data "
"boundaries".format(xs, ys))
# Convert start_points from data to array coords
# Shift the seed points from the bottom left of the data so that
# data2grid works properly.
sp2[:, 0] -= grid.x_origin
sp2[:, 1] -= grid.y_origin
for xs, ys in sp2:
xg, yg = dmap.data2grid(xs, ys)
t = integrate(xg, yg)
if t is not None:
trajectories.append(t)
if use_multicolor_lines:
if norm is None:
norm = mcolors.Normalize(color.min(), color.max())
if cmap is None:
cmap = cm.get_cmap(matplotlib.rcParams['image.cmap'])
else:
cmap = cm.get_cmap(cmap)
streamlines = []
arrows = []
for t in trajectories:
tgx = np.array(t[0])
tgy = np.array(t[1])
# Rescale from grid-coordinates to data-coordinates.
tx, ty = dmap.grid2data(*np.array(t))
tx += grid.x_origin
ty += grid.y_origin
points = np.transpose([tx, ty]).reshape(-1, 1, 2)
streamlines.extend(np.hstack([points[:-1], points[1:]]))
# Add arrows half way along each trajectory.
s = np.cumsum(np.hypot(np.diff(tx), np.diff(ty)))
n = np.searchsorted(s, s[-1] / 2.)
arrow_tail = (tx[n], ty[n])
arrow_head = (np.mean(tx[n:n + 2]), np.mean(ty[n:n + 2]))
if isinstance(linewidth, np.ndarray):
line_widths = interpgrid(linewidth, tgx, tgy)[:-1]
line_kw['linewidth'].extend(line_widths)
arrow_kw['linewidth'] = line_widths[n]
if use_multicolor_lines:
color_values = interpgrid(color, tgx, tgy)[:-1]
line_colors.append(color_values)
arrow_kw['color'] = cmap(norm(color_values[n]))
p = patches.FancyArrowPatch(arrow_tail,
arrow_head,
transform=transform,
**arrow_kw)
axes.add_patch(p)
arrows.append(p)
lc = mcollections.LineCollection(streamlines,
transform=transform,
**line_kw)
lc.sticky_edges.x[:] = [grid.x_origin, grid.x_origin + grid.width]
lc.sticky_edges.y[:] = [grid.y_origin, grid.y_origin + grid.height]
if use_multicolor_lines:
lc.set_array(np.ma.hstack(line_colors))
lc.set_cmap(cmap)
lc.set_norm(norm)
axes.add_collection(lc)
axes.autoscale_view()
ac = matplotlib.collections.PatchCollection(arrows)
stream_container = StreamplotSet(lc, ac)
return stream_container
def process_func(idx):
# Load original image.
orig_idx = fields['orig_idx'][idx]
orig_file = fields['orig_file'][idx]
orig_path = os.path.join(celeba_dir, 'img_celeba', orig_file)
img = PIL.Image.open(orig_path)
# Choose oriented crop rectangle.
lm = landmarks[orig_idx]
eye_avg = (lm[0] + lm[1]) * 0.5 + 0.5
mouth_avg = (lm[3] + lm[4]) * 0.5 + 0.5
eye_to_eye = lm[1] - lm[0]
eye_to_mouth = mouth_avg - eye_avg
x = eye_to_eye - rot90(eye_to_mouth)
x /= np.hypot(*x)
x *= max(np.hypot(*eye_to_eye) * 2.0, np.hypot(*eye_to_mouth) * 1.8)
y = rot90(x)
c = eye_avg + eye_to_mouth * 0.1
quad = np.stack([c - x - y, c - x + y, c + x + y, c + x - y])
zoom = 1024 / (np.hypot(*x) * 2)
# Shrink.
shrink = int(np.floor(0.5 / zoom))
if shrink > 1:
size = (int(np.round(float(img.size[0]) / shrink)),
int(np.round(float(img.size[1]) / shrink)))
img = img.resize(size, PIL.Image.ANTIALIAS)
quad /= shrink
zoom *= shrink
# Crop.
border = max(int(np.round(1024 * 0.1 / zoom)), 3)
crop = (int(np.floor(min(quad[:, 0]))), int(np.floor(min(quad[:, 1]))),
int(np.ceil(max(quad[:, 0]))), int(np.ceil(max(quad[:, 1]))))
crop = (max(crop[0] - border, 0), max(crop[1] - border, 0),
min(crop[2] + border,
img.size[0]), min(crop[3] + border, img.size[1]))
if crop[2] - crop[0] < img.size[0] or crop[3] - crop[1] < img.size[1]:
img = img.crop(crop)
quad -= crop[0:2]
# Simulate super-resolution.
superres = int(np.exp2(np.ceil(np.log2(zoom))))
if superres > 1:
img = img.resize((img.size[0] * superres, img.size[1] * superres),
PIL.Image.ANTIALIAS)
quad *= superres
zoom /= superres
# Pad.
pad = (int(np.floor(min(quad[:, 0]))), int(np.floor(min(quad[:, 1]))),
int(np.ceil(max(quad[:, 0]))), int(np.ceil(max(quad[:, 1]))))
pad = (max(-pad[0] + border,
0), max(-pad[1] + border,
0), max(pad[2] - img.size[0] + border,
0), max(pad[3] - img.size[1] + border, 0))
if max(pad) > border - 4:
pad = np.maximum(pad, int(np.round(1024 * 0.3 / zoom)))
img = np.pad(np.float32(img),
((pad[1], pad[3]), (pad[0], pad[2]), (0, 0)),
'reflect')
h, w, _ = img.shape
y, x, _ = np.mgrid[:h, :w, :1]
mask = 1.0 - np.minimum(
np.minimum(np.float32(x) / pad[0],
np.float32(y) / pad[1]),
np.minimum(
np.float32(w - 1 - x) / pad[2],
np.float32(h - 1 - y) / pad[3]))
blur = 1024 * 0.02 / zoom
img += (scipy.ndimage.gaussian_filter(img, [blur, blur, 0]) -
img) * np.clip(mask * 3.0 + 1.0, 0.0, 1.0)
img += (np.median(img, axis=(0, 1)) - img) * np.clip(
mask, 0.0, 1.0)
img = PIL.Image.fromarray(np.uint8(np.clip(np.round(img), 0, 255)),
'RGB')
quad += pad[0:2]
# Transform.
img = img.transform((4096, 4096), PIL.Image.QUAD,
(quad + 0.5).flatten(), PIL.Image.BILINEAR)
img = img.resize((1024, 1024), PIL.Image.ANTIALIAS)
img = np.asarray(img).transpose(2, 0, 1)
# Verify MD5.
md5 = hashlib.md5()
md5.update(img.tobytes())
assert md5.hexdigest() == fields['proc_md5'][idx]
# Load delta image and original JPG.
with zipfile.ZipFile(
os.path.join(delta_dir, 'deltas%05d.zip' % (idx - idx % 1000)),
'r') as zip:
delta_bytes = zip.read('delta%05d.dat' % idx)
with open(orig_path, 'rb') as file:
orig_bytes = file.read()
# Decrypt delta image, using original JPG data as decryption key.
algorithm = cryptography.hazmat.primitives.hashes.SHA256()
backend = cryptography.hazmat.backends.default_backend()
salt = bytes(orig_file, 'ascii')
kdf = cryptography.hazmat.primitives.kdf.pbkdf2.PBKDF2HMAC(
algorithm=algorithm,
length=32,
salt=salt,
iterations=100000,
backend=backend)
key = base64.urlsafe_b64encode(kdf.derive(orig_bytes))
delta = np.frombuffer(bz2.decompress(
cryptography.fernet.Fernet(key).decrypt(delta_bytes)),
dtype=np.uint8).reshape(3, 1024, 1024)
# Apply delta image.
img = img + delta
# Verify MD5.
md5 = hashlib.md5()
md5.update(img.tobytes())
assert md5.hexdigest() == fields['final_md5'][idx]
return img
def streamplot(axes,
x,
y,
u,
v,
density=1,
linewidth=None,
color=None,
cmap=None,
norm=None,
arrowsize=1,
arrowstyle='-|>',
minlength=0.1,
transform=None,
zorder=None,
start_points=None,
maxlength=4.0,
integration_direction='both'):
"""Draw streamlines of a vector flow.
*x*, *y* : 1d arrays
an *evenly spaced* grid.
*u*, *v* : 2d arrays
x and y-velocities. Number of rows should match length of y, and
the number of columns should match x.
*density* : float or 2-tuple
Controls the closeness of streamlines. When `density = 1`, the domain
is divided into a 30x30 grid---*density* linearly scales this grid.
Each cell in the grid can have, at most, one traversing streamline.
For different densities in each direction, use [density_x, density_y].
*linewidth* : numeric or 2d array
vary linewidth when given a 2d array with the same shape as velocities.
*color* : matplotlib color code, or 2d array
Streamline color. When given an array with the same shape as
velocities, *color* values are converted to colors using *cmap*.
*cmap* : :class:`~matplotlib.colors.Colormap`
Colormap used to plot streamlines and arrows. Only necessary when using
an array input for *color*.
*norm* : :class:`~matplotlib.colors.Normalize`
Normalize object used to scale luminance data to 0, 1. If None, stretch
(min, max) to (0, 1). Only necessary when *color* is an array.
*arrowsize* : float
Factor scale arrow size.
*arrowstyle* : str
Arrow style specification.
See :class:`~matplotlib.patches.FancyArrowPatch`.
*minlength* : float
Minimum length of streamline in axes coordinates.
*start_points*: Nx2 array
Coordinates of starting points for the streamlines.
In data coordinates, the same as the ``x`` and ``y`` arrays.
*zorder* : int
any number
*maxlength* : float
Maximum length of streamline in axes coordinates.
*integration_direction* : ['forward', 'backward', 'both']
Integrate the streamline in forward, backward or both directions.
Returns:
*stream_container* : StreamplotSet
Container object with attributes
- lines: `matplotlib.collections.LineCollection` of streamlines
- arrows: collection of `matplotlib.patches.FancyArrowPatch`
objects representing arrows half-way along stream
lines.
This container will probably change in the future to allow changes
to the colormap, alpha, etc. for both lines and arrows, but these
changes should be backward compatible.
"""
grid = Grid(x, y)
mask = StreamMask(density)
dmap = DomainMap(grid, mask)
if zorder is None:
zorder = mlines.Line2D.zorder
# default to data coordinates
if transform is None:
transform = axes.transData
if color is None:
color = axes._get_lines.get_next_color()
if linewidth is None:
linewidth = matplotlib.rcParams['lines.linewidth']
line_kw = {}
arrow_kw = dict(arrowstyle=arrowstyle, mutation_scale=10 * arrowsize)
if integration_direction not in ['both', 'forward', 'backward']:
errstr = ("Integration direction '%s' not recognised. "
"Expected 'both', 'forward' or 'backward'." %
integration_direction)
raise ValueError(errstr)
if integration_direction == 'both':
maxlength /= 2.
use_multicolor_lines = isinstance(color, np.ndarray)
if use_multicolor_lines:
if color.shape != grid.shape:
raise ValueError(
"If 'color' is given, must have the shape of 'Grid(x,y)'")
line_colors = []
color = np.ma.masked_invalid(color)
else:
line_kw['color'] = color
arrow_kw['color'] = color
if isinstance(linewidth, np.ndarray):
if linewidth.shape != grid.shape:
raise ValueError(
"If 'linewidth' is given, must have the shape of 'Grid(x,y)'")
line_kw['linewidth'] = []
else:
line_kw['linewidth'] = linewidth
arrow_kw['linewidth'] = linewidth
line_kw['zorder'] = zorder
arrow_kw['zorder'] = zorder
## Sanity checks.
if u.shape != grid.shape or v.shape != grid.shape:
raise ValueError("'u' and 'v' must be of shape 'Grid(x,y)'")
u = np.ma.masked_invalid(u)
v = np.ma.masked_invalid(v)
integrate = get_integrator(u, v, dmap, minlength, maxlength,
integration_direction)
trajectories = []
if start_points is None:
for xm, ym in _gen_starting_points(mask.shape):
if mask[ym, xm] == 0:
xg, yg = dmap.mask2grid(xm, ym)
t = integrate(xg, yg)
if t is not None:
trajectories.append(t)
else:
sp2 = np.asanyarray(start_points, dtype=float).copy()
# Check if start_points are outside the data boundaries
for xs, ys in sp2:
if not (grid.x_origin <= xs <= grid.x_origin + grid.width
and grid.y_origin <= ys <= grid.y_origin + grid.height):
raise ValueError("Starting point ({}, {}) outside of data "
"boundaries".format(xs, ys))
# Convert start_points from data to array coords
# Shift the seed points from the bottom left of the data so that
# data2grid works properly.
sp2[:, 0] -= grid.x_origin
sp2[:, 1] -= grid.y_origin
for xs, ys in sp2:
xg, yg = dmap.data2grid(xs, ys)
t = integrate(xg, yg)
if t is not None:
trajectories.append(t)
if use_multicolor_lines:
if norm is None:
norm = mcolors.Normalize(color.min(), color.max())
if cmap is None:
cmap = cm.get_cmap(matplotlib.rcParams['image.cmap'])
else:
cmap = cm.get_cmap(cmap)
streamlines = []
arrows = []
for t in trajectories:
tgx = np.array(t[0])
tgy = np.array(t[1])
# Rescale from grid-coordinates to data-coordinates.
tx, ty = dmap.grid2data(*np.array(t))
tx += grid.x_origin
ty += grid.y_origin
points = np.transpose([tx, ty]).reshape(-1, 1, 2)
streamlines.extend(np.hstack([points[:-1], points[1:]]))
# Add arrows half way along each trajectory.
s = np.cumsum(np.hypot(np.diff(tx), np.diff(ty)))
n = np.searchsorted(s, s[-1] / 2.)
arrow_tail = (tx[n], ty[n])
arrow_head = (np.mean(tx[n:n + 2]), np.mean(ty[n:n + 2]))
if isinstance(linewidth, np.ndarray):
line_widths = interpgrid(linewidth, tgx, tgy)[:-1]
line_kw['linewidth'].extend(line_widths)
arrow_kw['linewidth'] = line_widths[n]
if use_multicolor_lines:
color_values = interpgrid(color, tgx, tgy)[:-1]
line_colors.append(color_values)
arrow_kw['color'] = cmap(norm(color_values[n]))
p = patches.FancyArrowPatch(arrow_tail,
arrow_head,
transform=transform,
**arrow_kw)
axes.add_patch(p)
arrows.append(p)
lc = mcollections.LineCollection(streamlines,
transform=transform,
**line_kw)
lc.sticky_edges.x[:] = [grid.x_origin, grid.x_origin + grid.width]
lc.sticky_edges.y[:] = [grid.y_origin, grid.y_origin + grid.height]
if use_multicolor_lines:
lc.set_array(np.ma.hstack(line_colors))
lc.set_cmap(cmap)
lc.set_norm(norm)
axes.add_collection(lc)
axes.autoscale_view()
ac = matplotlib.collections.PatchCollection(arrows)
stream_container = StreamplotSet(lc, ac)
return stream_container
from platescale_ss import Tpsfunc, Rps, Mps, Sps, Tps
from petal_metrology import get_petal
for petal_id in [4, #5,
6, 3, #8,
10, #11,
2, 7, #9
]:
print('Petal', petal_id)
petal = get_petal(petal_id)
g1x,g1y = petal.gfa_mm_to_focal_mm(petal.gfa.gif_1_mm_x, petal.gfa.gif_1_mm_y)
g2x,g2y = petal.gfa_mm_to_focal_mm(petal.gfa.gif_2_mm_x, petal.gfa.gif_2_mm_y)
print('Scatter in GIF1 fit positions: %.3f mm' % (np.mean(np.hypot(petal.gif1.x - g1x, petal.gif1.y - g1y))))
print('Scatter in GIF2 fit positions: %.3f mm' % (np.mean(np.hypot(petal.gif2.x - g2x, petal.gif2.y - g2y))))
# Now fit a SIP polynomial distortion model for how the echo22 optics projects onto GFA CCD pixels.
#
# Evaluate a grid of points in CCD space and in RA,Dec, using the metrology transformations to go from GFA CCD pixels
# to focal plane coordinates, and from there to Theta and RA,Dec.
x0 = min([min(petal.gfa.gif_1_pix_x), min(petal.gfa.gif_2_pix_x), 0]) - 100
y0 = min([min(petal.gfa.gif_1_pix_y), min(petal.gfa.gif_2_pix_y), 0]) - 100
x1 = max([max(petal.gfa.gif_1_pix_x), max(petal.gfa.gif_2_pix_x), petal.ccdw]) + 100
y1 = max([max(petal.gfa.gif_1_pix_y), max(petal.gfa.gif_2_pix_y), petal.ccdh]) + 100
ccdgridpx, ccdgridpy = np.meshgrid(np.linspace(x0, x1, 20), np.linspace(y0, y1, 20))
ccdgridpx = ccdgridpx.ravel()
ccdgridpy = ccdgridpy.ravel()
def cost(self, from_node, to_node):
a = from_node
b = to_node
v = (b[0] - a[0], b[1] - a[1])
return np.hypot(v[0], v[1])
# load image
yuv_frame = Image.open("../images/output-161.png").convert("YCbCr")
# creates array from the image
frame_asArray = np.array(yuv_frame)
# extract y chanel:
y_frame_asArray = frame_asArray[:, :, Y]
# creates image from the y chanel for display
y_frame = Image.fromarray(y_frame_asArray, "L")
# convert the array to displayable type
y_frame_asArray = y_frame_asArray.astype('int32')
# apply Sobel filter to the Y channel
# apply sobel for x, y directions
sobel_frame_x = ndimage.sobel(y_frame_asArray, axis=0, mode='constant')
sobel_frame_y = ndimage.sobel(y_frame_asArray, axis=1, mode='constant')
# combine the x, y deriatives
sobel_frame = np.hypot(sobel_frame_x, sobel_frame_y)
# plot the original image, the Y component, and the Sobel filtered Y component
plt.subplot(1, 3, 1), plt.imshow(yuv_frame)
plt.title('Original Frame'), plt.xticks([]), plt.yticks([])
plt.subplot(1, 3, 2), plt.imshow(y_frame)
plt.title('Y channel of Frame'), plt.xticks([]), plt.yticks([])
plt.subplot(1, 3, 3), plt.imshow(sobel_frame, cmap='gray')
plt.title('Sobel filtered Y channel of Frame'), plt.xticks([]), plt.yticks([])
plt.savefig("../figures/q1_b-c-scipy.png")
plt.show()
def __init__(self, nbi=None, nshot=None, runid=''):
# distances: cm; angles: rad
# op: distance box-torus axis
# phi_box: absolute angle of NBI box (does not matter in poloidal cross section)
# inj_tor_box: toroidal angle between mid source and torus axis
# inj: toroidal angle between source and box aligned
# src_slit: distance ion source - aperture, for the center of the beamlines
# src_hw: horizontal semi-displacement of sources
# xybsca: source vertical elevation w.r.t. midplane
# rabsca: source horizontal half width w.r.t. mid-point
# RTCENA: R_tang
# vert_incl: vertical inclination
# XLBAPA: length = midpl1 / COS(vert_incl)
# midpl2: Grid - P(RTCENA) projected on horizont. midplane
# XLBTNA: length = midpl2 / COS(vert_incl)
# XYBAPA: elevation at slit
# Rectangular half aperture in point P
self.rapedga = 16
self.xzpedga = 19
self.phi_box = np.array(4 * [np.radians(33.75)] +
4 * [np.radians(209)])
# Read from namelist
import tr_path
from parsenml import parsenml
tr = tr_path.TR_PATH(runid)
print('Namelist: %s' % tr.fnml)
self.rtcena = parsenml(tr.fnml, 'RTCENA', fmt=5)
self.xlbapa = parsenml(tr.fnml, 'XLBAPA', fmt=5)
self.xybapa = parsenml(tr.fnml, 'XYBAPA', fmt=5)
self.xybsca = parsenml(tr.fnml, 'XYBSCA', fmt=5)
self.xlbtna = parsenml(tr.fnml, 'XLBTNA', fmt=5)
self.xbzeta = parsenml(tr.fnml, 'XBZETA', fmt=5)
self.src_slit = parsenml(tr.fnml, 'FOCLRA', fmt=5)
self.ffulla = parsenml(tr.fnml, 'FFULLA', fmt=5)
self.fhalfa = parsenml(tr.fnml, 'FHALFA', fmt=5)
self.einja = parsenml(tr.fnml, 'EINJA', fmt=5)
# Derived TRANSP variables
self.theta_los = np.arcsin((self.xybapa - self.xybsca) / self.xlbapa)
self.vert_incl = np.abs(self.theta_los)
self.midpl2 = self.xlbtna * np.cos(self.vert_incl)
self.midpl1 = self.xlbapa * np.cos(self.vert_incl)
self.op = np.hypot((self.midpl2 - self.midpl1), self.rtcena)
self.alpha = np.arcsin(self.rtcena / self.op)
self.xsrc, self.ysrc, self.phi_los = tr2xy(self.rtcena, self.midpl2, \
self.alpha, self.phi_box)
self.magic_angle = np.arccos(self.src_slit /
self.midpl1) # missing sign
self.rabsca = self.midpl1 * np.sin(self.magic_angle) # missing sign
self.inj_tor_box = self.alpha - self.magic_angle
def f(x, y):
s = np.hypot(x, y)
phi = np.arctan2(y, x)
tau = s + s * (1 - s) / 5 * np.sin(6 * phi)
return 5 * (1 - tau) + tau
gc.collect()
## Make Gaia subset of useful objects:
need_srcs = 3
useful_ids = [kk for kk,vv in gcounter.items() if vv>need_srcs]
use_gaia = gm._srcdata[gm._srcdata.source_id.isin(useful_ids)]
n_useful = len(use_gaia)
sys.stderr.write("Found possible matches to %d of %d Gaia sources.\n"
% (n_useful, len(gm._srcdata)))
gc.collect()
if n_useful < 5:
sys.stderr.write("Gaia match error: found %d useful objects\n" % n_useful)
sys.exit(1)
## Total Gaia-detected PM in surviving object set:
use_gaia = use_gaia.assign(pmtot=np.hypot(use_gaia.pmra, use_gaia.pmdec))
gaia_pmsrt = use_gaia.sort_values(by='pmtot', ascending=False)
#for nmin in range(100):
# passing = [kk for kk,vv in gcounter.items() if vv>nmin]
# nkept = len(passing)
# sys.stderr.write("Kept %d sources for nmin=%d.\n" % (nkept, nmin))
## Robust (non-double-counted) matching of Gaia sources using slimmed list:
sys.stderr.write("Associating catalog objects with Gaia sources:\n")
tik = time.time()
gmatches = {x:[] for x in use_gaia.source_id}
for ci,extcat in enumerate(cdata, 1):
#for ci,extcat in enumerate(cdata[:10], 1):
#sys.stderr.write("\n------------------------------\n")
sys.stderr.write("\rChecking image %d of %d ... " % (ci, len(cdata)))