def build_plot(self, usePCA):
import pylab
self.normaliser = MorphologyForRenderingOperator(self.morph, usePCA=usePCA)
# Find the Point that is the furthest distance way from
# the centre when the cell is centred and rotated:
rotator = lambda s: self.normaliser(s.get_distal_npa3())
rotated_section_dict = DictBuilderSectionVisitorHomo(morph=self.morph, functor=rotator)()
# Add in the parents manually:
dummy_scetion = self.morph._dummysection
rotated_section_dict[dummy_scetion] = self.normaliser(dummy_scetion.get_distal_npa3())
max_axis = max([numpy.linalg.norm(rotated_section_pt) for rotated_section_pt in rotated_section_dict.values()])
plot_lims = (max_axis * -1.1, max_axis * 1.1)
max_x = max([numpy.fabs(rotated_section_pt[0]) for rotated_section_pt in rotated_section_dict.values()])
max_y = max([numpy.fabs(rotated_section_pt[1]) for rotated_section_pt in rotated_section_dict.values()])
max_z = max([numpy.fabs(rotated_section_pt[2]) for rotated_section_pt in rotated_section_dict.values()])
maxes = [max_x, max_y, max_z]
# allMax = max(maxes)
for i in self.plot_views:
maxes[i] = maxes[i] + 0.2 * max([max_x, max_y, max_z])
self.fig = pylab.figure(**self.fig_kwargs) # figsize=(7, 7))
self.fig.subplots_adjust(left=0.05, top=0.95, right=0.95, bottom=0.05, wspace=0.15, hspace=0.15)
self.subplots = {}
for i in self.plot_views:
self.subplots[i] = self.build_draw_sub_plot(rotated_section_dict, self.fig, i, plot_lims)
def create_mock_sample(data,dfc,trueVsolar,spiral=False):
if spiral:
#Read spiral vlos field
spvlos= galpy_simulations.vlos('../sim/bar_rect_alpha0.015_hivres.sav')
potscale= 0.85
xgrid= numpy.linspace(_RCXMIN,_RCXMAX-_RCDX,19)
ygrid= numpy.linspace(_RCYMIN,_RCYMAX-_RCDX,19)
ndata= len(data)
mockvel= numpy.empty(ndata)
dphil= data['RC_GALPHI']+data['GLON']/180.*numpy.pi
cosdphil= numpy.cos(dphil)
sindphil= numpy.sin(dphil)
cosl= numpy.cos(data['GLON']/180.*numpy.pi)
sinl= numpy.sin(data['GLON']/180.*numpy.pi)
for ii in range(ndata):
vrvt= dfc.sampleVRVT(data['RC_GALR'][ii]/8.,n=1.)
mockvel[ii]= -vrvt[0,0]*cosdphil[ii]\
+vrvt[0,1]*sindphil[ii]\
-10.5*cosl[ii]/220.\
-(1.+trueVsolar)*sinl[ii]
if spiral:
#Find which pixel this sample is in
pixIndxX= numpy.argmin(numpy.fabs(data['RC_GALR'][ii]\
*numpy.cos(data['RC_GALPHI'][ii])\
-xgrid))
pixIndxY= numpy.argmin(numpy.fabs(data['RC_GALR'][ii]\
*numpy.sin(data['RC_GALPHI'][ii])\
-ygrid))
spiraldev= spvlos[pixIndxX,pixIndxY]
mockvel[ii]+= spiraldev*potscale
data['VHELIO_AVG']= mockvel*220.
return data
def getStepsize(self, mix_den, ht):
mix_den_fil = np.fabs(mix_den) > 1.E-7
a = ht[mix_den_fil] / mix_den[mix_den_fil]
b = 1.0 + a
b_fil = np.fabs(b) > 1.E-7
w = self.w
sl = w * ht[b_fil] / b[b_fil]
s11 = sl.sum()
s0 = (w * ht).sum()
step, oldstep = 0., 0.
for i in range(50):
grad1, grad2 = 0., 0.
for j in range(self.n):
a = mix_den[j] + step * ht[j]
if math.fabs(a) > 1.E-7:
b = ht[j] / a
grad1 = grad1 + w * b
grad2 = grad2 - w * b * b
if math.fabs(grad2) > 1.E-10:
step = step - grad1 / grad2
if oldstep > 1.0 and step > oldstep:
step = 1.
break
if grad1 < 1.E-7:
break
oldstep = step
if step > 1.0:
return 1.0
return step
def ActionNodeStd(self, o):
print
print repr(o)
print '-' * len(repr(o))
ann = self.annotations.annotations[o]
print ann
# Lets go symmetrical, about 0:
vmin = ann.val_min.float_in_si()
vmax = ann.val_max.float_in_si()
ext = max( [np.abs(vmin),np.abs(vmax) ] )
if ext != 0.0:
#Include some padding:
upscaling_pow = int( np.ceil( np.log2(ext ) ) )
else:
upscaling_pow = 0
# Lets remap the limits:
upscaling_val = 2 ** (-upscaling_pow)
vmin_scaled = vmin * upscaling_val
vmax_scaled = vmax * upscaling_val
print 'vMin, vMax', vmin, vmax
print 'Scaling:', '2**', upscaling_pow, ' ->', upscaling_val
print 'vMin_scaled, vMax_scaled', vmin_scaled, vmax_scaled
ann.fixed_scaling_power = upscaling_pow
assert 0.1 < max( [np.fabs(vmin_scaled), np.fabs(vmax_scaled) ] ) <= 1.0 or vmin_scaled == vmax_scaled == 0.0
def setup_sampling(self,
gradient,
soln,
linear_randomization,
quadratic_coef):
self.accept_beta, self.total_beta = 0, 0
random_direction = 2 * quadratic_coef * soln + linear_randomization
negative_subgrad = gradient + random_direction
self.active_set = (soln != 0)
self.initial_parameters = np.empty(1, self.dtype)
self.initial_parameters['signs'] = np.sign(soln[self.active_set])
abs_l1part = np.fabs(soln[self.active_set])
l1norm_ = abs_l1part.sum()
self.initial_parameters['simplex'] = (abs_l1part / l1norm_)[:-1]
subgrad = -negative_subgrad[self.inactive_set]
supnorm_ = np.fabs(negative_subgrad).max()
if self.lagrange is not None:
self.initial_parameters['cube'] = subgrad / self.lagrange
self.initial_parameters['scale'] = l1norm_
else:
if self._active_set.sum() != self.shape:
self.initial_parameters['cube'] = subgrad / supnorm_
self.initial_parameters['scale'] = supnorm_
if self.lagrange is None:
raise NotImplementedError("only lagrange form is implemented")
return soln[self.active_set], subgrad
def _calc_shift_ranges(self, x_shift, y_shift):
'''Calculate shift indices for input and output arrays.
'''
LOGGER.debug("Calculating shift ranges.")
# width of the portion to be moved
width = self._img_shape[1] - int(np.fabs(x_shift))
# height of the portion to be moved
height = self._img_shape[0] - int(np.fabs(y_shift))
# Calculate the corner indices of the area to be moved
if x_shift < 0:
n_x1, n_x2 = 0, width
o_x1, o_x2 = -1*x_shift, -1*x_shift+width
else:
n_x1, n_x2 = x_shift, x_shift+width
o_x1, o_x2 = 0, width
if y_shift < 0:
n_y1, n_y2 = 0, height
o_y1, o_y2 = -1*y_shift, -1*y_shift+height
else:
n_y1, n_y2 = y_shift, y_shift+height
o_y1, o_y2 = 0, height
output_ranges = ((n_x1, n_x2), (n_y1, n_y2))
input_ranges = ((o_x1, o_x2), (o_y1, o_y2))
return (output_ranges[0], output_ranges[1],
input_ranges[0], input_ranges[1])
def _findUSpace(self):
"""Find independent U components with respect to invariant
rotations.
"""
n = len(self.invariants)
R6zall = numpy.tile(-numpy.identity(6, dtype=float), (n, 1))
R6zall_iter = numpy.split(R6zall, n, axis=0)
i6kl = ((0, (0, 0)), (1, (1, 1)), (2, (2, 2)),
(3, (0, 1)), (4, (0, 2)), (5, (1, 2)))
for op, R6z in zip(self.invariants, R6zall_iter):
R = op.R
for j, Ucj in enumerate(self.Ucomponents):
Ucj2 = numpy.dot(R, numpy.dot(Ucj, R.T))
for i, kl in i6kl:
R6z[i,j] += Ucj2[kl]
Usp6 = nullSpace(R6zall)
# normalize Usp6 by its maximum component
mxcols = numpy.argmax(numpy.fabs(Usp6), axis=1)
mxrows = numpy.arange(len(mxcols))
Usp6 /= Usp6[mxrows,mxcols].reshape(-1, 1)
Usp6 = numpy.around(Usp6, 2)
# normalize again after rounding to get correct signs
mxcols = numpy.argmax(numpy.fabs(Usp6), axis=1)
Usp6 /= Usp6[mxrows,mxcols].reshape(-1, 1)
self.Uspace = numpy.tensordot(Usp6, self.Ucomponents, axes=(1, 0))
self.Uisotropy = (len(self.Uspace) == 1)
return
def ransac(kernel, threshold):
'''Robustly fit a model to data.
>>> x = np.array([1., 2., 3.])
>>> y = np.array([2., 4., 7.])
>>> kernel = TestLinearKernel(x, y)
>>> ransac(kernel, 0.1)
(2.0, array([0, 1]), 0.10000000000000001)
'''
max_iterations = 1000
best_error = float('inf')
best_model = None
best_inliers = []
i = 0
while i < max_iterations:
try:
samples = kernel.sampling()
except AttributeError:
samples = random.sample(range(kernel.num_samples()),
kernel.required_samples)
models = kernel.fit(samples)
for model in models:
errors = kernel.evaluate(model)
inliers = np.flatnonzero(np.fabs(errors) < threshold)
error = np.fabs(errors).clip(0, threshold).sum()
if len(inliers) and error < best_error:
best_error = error
best_model = model
best_inliers = inliers
max_iterations = min(max_iterations,
ransac_max_iterations(kernel, best_inliers, 0.01))
i += 1
return best_model, best_inliers, best_error
def test_actionConservation():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20.,Delta=Delta,normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1.,0.1,1.1,0.01,0.1]
o= Orbit(vxvv=vxvv)
#_____integrate the orbit with C_____
ts= numpy.linspace(0,101,100)
o.integrate(ts,pot,method='leapfrog_c')
#_____Setup ActionAngle object and calculate actions (Staeckel approximation)_____
aAS = actionAngleStaeckel(pot=pot,delta=Delta,c=True)
jrs,lzs,jzs = aAS(o.R(ts),o.vR(ts),o.vT(ts),o.z(ts),o.vz(ts))
assert numpy.all(numpy.fabs(jrs - jrs[0]) < 10.**-8.), \
'Radial action is not conserved along orbit.'
assert numpy.all(numpy.fabs(lzs - lzs[0]) < 10.**-8.), \
'Angular momentum is not conserved along orbit.'
assert numpy.all(numpy.fabs(jzs - jzs[0]) < 10.**-8.), \
'Vertical action is not conserved along orbit.'
return None
def trazo(ini, fin, ancho):
'''Recibe la coordenada de inicio del trazo, el final y el ancho del
trazo, devuelve un arreglo con las coordenadas de los puntos que lo
conformman. Sólo funciona para trazos rectos.
(recibe los puntos más izquierdos, o más abajo del trazo)'''
ancho = int(ancho)+1
actual = ini
if es_horizontal(ini, fin):
paso = np.array([1, 0])
ancho_1 = np.array([0, 1])
rango = int(np.fabs(fin[0]-ini[0]))+1
else:
paso = np.array([0, 1])
ancho_1 = np.array([1, 0])
rango = int(np.fabs(fin[1]-ini[1]))
trazo = np.zeros([(rango)*(ancho), 2])
for a in range(ancho):
for i in range(rango):
trazo[i+(rango)*a] = np.array([actual])
actual += paso
actual = ini
actual += (a+1)*ancho_1
return trazo
def test_orbitIntegrationC():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20.,Delta=Delta,normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1.,0.1,1.1,0.,0.1]
o_P= Orbit(vxvv=vxvv)
o_C= Orbit(vxvv=vxvv)
#_____integrate the orbit with python and C_____
ts= numpy.linspace(0,100,101)
o_P.integrate(ts,pot,method='leapfrog') #python
o_C.integrate(ts,pot,method='leapfrog_c')#C
for ii in range(5):
exp3= -1.7
if ii == 0: Python, CC, string, exp1, exp2 = o_P.R(ts) , o_C.R(ts) , 'R' , -5., -10.
elif ii == 1: Python, CC, string, exp1, exp2 = o_P.z(ts) , o_C.z(ts) , 'z' , -3.25, -4.
elif ii == 2: Python, CC, string, exp1, exp2 = o_P.vR(ts), o_C.vR(ts), 'vR', -3., -10.
elif ii == 3: Python, CC, string, exp1, exp2, exp3 = o_P.vz(ts), o_C.vz(ts), 'vz', -3., -4., -1.3
elif ii == 4: Python, CC, string, exp1, exp2 = o_P.vT(ts), o_C.vT(ts), 'vT', -5., -10.
rel_diff = numpy.fabs((Python-CC)/CC) < 10.**exp1
abs_diff = (numpy.fabs(Python-CC) < 10.**exp2) * (numpy.fabs(Python) < 10.**exp3)
assert numpy.all(rel_diff+abs_diff), \
'Orbit integration for '+string+' coordinate different in ' + \
'C and Python implementation.'
return None
def weights(self, z):
"""
Hampel weighting function for the IRLS algorithm
The psi function scaled by z
Parameters
----------
z : array-like
1d array
Returns
-------
weights : array
weights(z) = 1 for \|z\| <= a
weights(z) = a/\|z\| for a < \|z\| <= b
weights(z) = a*(c - \|z\|)/(\|z\|*(c-b)) for b < \|z\| <= c
weights(z) = 0 for \|z\| > c
"""
z = np.asarray(z)
a = self.a; b = self.b; c = self.c
t1, t2, t3 = self._subset(z)
v = (t1 +
t2 * a/np.fabs(z) +
t3 * a*(c-np.fabs(z))/(np.fabs(z)*(c-b)))
v[np.where(np.isnan(v))]=1. # for some reason 0 returns a nan?
return v
def test_estimateDelta():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20.,Delta=Delta,normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1.,0.1,1.1,0.01,0.1]
o= Orbit(vxvv=vxvv)
#_____integrate the orbit with C_____
ts= numpy.linspace(0,101,100)
o.integrate(ts,pot,method='leapfrog_c')
#____estimate Focal length Delta_____
#for each time step individually:
deltas_estimate = numpy.zeros(len(ts))
for ii in range(len(ts)):
deltas_estimate[ii] = estimateDeltaStaeckel(pot,o.R(ts[ii]),o.z(ts[ii]))
assert numpy.all(numpy.fabs(deltas_estimate - Delta) < 10.**-8), \
'Focal length Delta estimated along the orbit is not constant.'
#for all time steps together:
delta_estimate = estimateDeltaStaeckel(pot,o.R(ts),o.z(ts))
assert numpy.fabs(delta_estimate - Delta) < 10.**-8, \
'Focal length Delta estimated from the orbit is not the same as the input focal length.'
return None
def truncate_hist1( self, xmin, xmax ):
buf = get_buffer_hist1( self )
sbuf = get_err_buffer_hist1( self )
edges, fixed = get_bin_edges_axis( self.GetXaxis(), type=True )
e1 = numpy.fabs(edges[:-1]-xmin)<1.e-9
e2 = numpy.fabs(edges[1:]-xmax)<1.e-9
assert numpy.any( e1 ) and numpy.any( e2 ), 'Invalid new histogram limits'
i1 = numpy.nonzero( e1 )[0][0]
i2 = numpy.nonzero( e2 )[0][-1]+1
if fixed:
newhist = self.__class__( self.GetName(), self.GetTitle(), i2-i1, xmin, xmax )
else:
newhist = self.__class__( self.GetName(), self.GetTitle(), i2-i1, edges[i1:i2] )
newbuf = get_buffer_hist1( newhist )
if sbuf is None:
newsbuf = None
else:
newhist.Sumw2()
newsbuf = get_err_buffer_hist1( newhist )
newbuf[:] = buf[i1:i2]
if not sbuf is None:
newsbuf[:] = sbuf[i1:i2]
newhist.SetEntries( newhist.Integral() )
return newhist
def test_monopole_fluxpoints(self):
"""Tests monopole flux points."""
field = ElectricField([PointCharge(2, [0, 0])])
circle = GaussianCircle([0, 0], 10)
fluxpoints = circle.fluxpoints(field, 4)
self.assertEqual(len(fluxpoints), 4)
self.assertTrue(isclose(fluxpoints,
[[10, 0], [0, 10], [-10, 0], [0, -10]]).all())
fluxpoints = circle.fluxpoints(field, 14)
self.assertEqual(len(fluxpoints), 14)
self.assertTrue(isclose(fluxpoints[0], [10, 0]).all())
self.assertTrue(isclose(fluxpoints[7], [-10, 0]).all())
x1 = fluxpoints[1:7]
x2 = fluxpoints[-1:7:-1]
x2[:, 1] = fabs(x2[:, 1])
self.assertTrue(isclose(x1, x2).all())
x1 = append(fluxpoints[-3:], fluxpoints[:4], axis=0)
x2 = fluxpoints[-4:3:-1]
x2[:, 0] = fabs(x2[:, 0])
self.assertEqual(len(x1), len(x2))
self.assertTrue(isclose(x1, x2).all())
def _get_edr(self, obs, expected, stddev, bandwidth=0.01, multiplier=3.0):
"""
Calculated the Euclidean Distanced-Based Rank for a set of
observed and expected values from a particular GMPE
"""
nvals = len(obs)
min_d = bandwidth / 2.
kappa = self._get_kappa(obs, expected)
mu_d = obs - expected
d1c = np.fabs(obs - (expected - (multiplier * stddev)))
d2c = np.fabs(obs - (expected + (multiplier * stddev)))
dc_max = ceil(np.max(np.array([np.max(d1c), np.max(d2c)])))
num_d = len(np.arange(min_d, dc_max, bandwidth))
mde = np.zeros(nvals)
for iloc in range(0, num_d):
d_val = (min_d + (float(iloc) * bandwidth)) * np.ones(nvals)
d_1 = d_val - min_d
d_2 = d_val + min_d
p_1 = norm.cdf((d_1 - mu_d) / stddev) -\
norm.cdf((-d_1 - mu_d) / stddev)
p_2 = norm.cdf((d_2 - mu_d) / stddev) -\
norm.cdf((-d_2 - mu_d) / stddev)
mde += (p_2 - p_1) * d_val
inv_n = 1.0 / float(nvals)
mde_norm = np.sqrt(inv_n * np.sum(mde ** 2.))
edr = np.sqrt(kappa * inv_n * np.sum(mde ** 2.))
return mde_norm, np.sqrt(kappa), edr
def find_nearest(array, value):
"""
Return the array value that is closest to the input value (Abigail Stevens:
Thanks StackOverflow!)
Parameters
----------
array : np.array of ints or floats
1-D array of numbers to search through. Should already be sorted
from low values to high values.
value : int or float
The value you want to find the closest to in the array.
Returns
-------
array[idx] : int or float
The array value that is closest to the input value.
idx : int
The index of the array of the closest value.
"""
idx = np.searchsorted(array, value, side="left")
if idx == len(array) or np.fabs(value - array[idx - 1]) < \
np.fabs(value - array[idx]):
return array[idx - 1], idx - 1
else:
return array[idx], idx
def deliverStim(currTime):
global injectionCurrent
global spineVm
global somaVm
if numpy.fabs( currTime - baselineTime ) < frameRunTime/2.0 :
#start
eList = moose.wildcardFind( '/model/elec/#soma#' )
assert( len(eList) > 0 )
eList[0].inject = injectionCurrent
#print "1. injected current = ", injectionCurrent
injectionCurrent += deltaCurrent
#print "del stim first ", moose.element('/clock').currentTime
if numpy.fabs( currTime - baselineTime - currPulseTime) < frameRunTime/2.0 :
#end
eList = moose.wildcardFind( '/model/elec/#soma#' )
assert( len(eList) > 0 )
eList[0].inject = 0.0
#print "2. injected current = ", injectionCurrent
#print "del stim second ", moose.element('/clock').currentTime
if runtime - currTime < frameRunTime * 2.0 :
#print "3. reinit-ing"
somaVm.append( moose.element( '/graphs/VmTab' ).vector )
spineVm.append( moose.element( '/graphs/eSpineVmTab' ).vector )
iList.append(injectionCurrent)
if injectionCurrent < maxCurrent :
moose.reinit()
def get_weights_cs2ll(self, dst, alpha, beta, panel, gids):
cs_obj = self.cs_obj
(a1,b1), (a2,b2), (a3,b3), (a4,b4) = \
[cs_obj.alpha_betas[gid] for gid in gids]
assert np.fabs(a1-a3)<1e-15
assert np.fabs(a2-a4)<1e-15
assert np.fabs(b1-b2)<1e-15
assert np.fabs(b3-b4)<1e-15
assert flge(a1,alpha,a2), "dst={}, a1={}, a2={}, alpha={}".format(dst,a1,a2,alpha)
assert flge(b1,beta,b3), "dst={}, b1={}, b3={}, beta={}".format(dst,b1,b3,beta)
panels = [cs_obj.gq_indices[gid,0] for gid in gids]
for p in panels:
if p != panel:
print("(alpha,beta) ({},{})".foramt(alpha, beta))
print("panel: {}, {}".format(panel, panels))
print("dst: {}".format(dst))
print("gids: {}".format(gids))
sys.exit()
# weights
x, y = alpha, beta
x1, x2 = a1, a2
y1, y2 = b1, b3
return self.get_bilinear_weights(dst, (x,y), (x1,y1), (x2,y2))
def get_weights_ll2cs(self, dst, lat, lon, idxs):
cs_obj = self.cs_obj
ll_obj = self.ll_obj
idx1, idx2, idx3, idx4 = idxs
lat1, lon1 = ll_obj.latlons[idx1]
lat2, lon2 = ll_obj.latlons[idx2]
lat3, lon3 = ll_obj.latlons[idx3]
lat4, lon4 = ll_obj.latlons[idx4]
assert np.fabs(lon1-lon3)<1e-15
assert np.fabs(lon2-lon4)<1e-15
assert np.fabs(lat1-lat2)<1e-15
assert np.fabs(lat3-lat4)<1e-15
if lon2 < lon1: lon2 = lon1 + ll_obj.dlon
if lon4 < lon3: lon4 = lon3 + ll_obj.dlon
if np.fabs(lon-lon1) > np.pi: lon += 2*np.pi
assert flge(lon1,lon,lon2), "dst={}, lon1={}, lon2={}, lon={}".format(dst,lon1,lon2,lon)
assert flge(lat1,lat,lat3), "dst={}, lat1={}, lat3={}, lat={}".format(dst,lat1,lat2,lat)
# weights
x, y = lon, lat
x1, x2 = lon1, lon2
y1, y2 = lat1, lat3
return self.get_bilinear_weights(dst, (x,y), (x1,y1), (x2,y2))
def bartlettTest(self):
M = -(self.n-1/2*(self.p+self.q+3))
for i in range(len(self.s)):
#有意水準を求める
alf = self.sigAlf
sig = sp.special.chdtri((self.p-i)*(self.q-i), alf)
test = 1
#ウィルクスのラムダ
for j in range(len(self.s)-i):
test = test*(1-self.s[len(self.s)-j-1])
chi = M*math.log(test)
#帰無仮説棄却/採用
if chi > sig:
print "test["+str(i)+"]:"+str(chi) +" > sig("+str(alf)+"):"+str(sig)
run = np.fabs(self.A[:,i:i+1])
rvn = np.fabs(self.B[:,i:i+1])
arg_u = np.argmax(run)
arg_v = np.argmax(rvn)
self.eigArray.append(str(i))
val = [arg_u, arg_v]
self.eigValArray.append(val)
print "eigen:"+str(np.sqrt(self.s[i]))
print "ru-max arg:"+str(arg_u)
print "rv-max arg:"+str(arg_v)
else:
break
def plot(filename, x=0, y=1, x_abs=False, y_abs=False,
xscale='linear', yscale='linear', xlabel='x', ylabel='y',
scatter=False, size=12, title='', xmin=-np.inf, xmax=np.inf,
ymin=-np.inf, ymax=np.inf):
filtercols = (x, y)
mins = (xmin, ymin)
maxs = (xmax, ymax)
data_filtered = __filter_outranged_x(filename, filtercols, mins, maxs)
xs, ys = np.loadtxt(data_filtered, usecols=(x, y), unpack=True)
if x_abs:
xs = np.fabs(xs)
if y_abs:
ys = np.fabs(ys)
f, ax = plt.subplots(1, 1)
ax.set_xscale(xscale)
ax.set_yscale(yscale)
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
if title:
plt.title(title)
if scatter:
ax.scatter(xs, ys, s=size)
else:
ax.plot(xs, ys, linewidth=size)
plt.axis('tight')
plt.show()
plt.close()
def replicate_line_with_threshold(g_expr, g_expr_c, M, K, threshold):
'''Compare whether two lines are the same lines.'''
coeffi_1 = np.zeros((M, K))
coeffi_2 = np.zeros((M, K))
coeff1_constant = g_expr[-1]
coeff2_constant = g_expr_c[-1]
#calculate the sum of all coefficients
sum_coeff1 = coeff1_constant
sum_coeff2 = coeff2_constant
for i in xrange(M):
for j in xrange(K):
coeffi_1[i][j] = g_expr[i*K + j]
coeffi_2[i][j] = g_expr_c[i*K + j]
sum_coeff1 += coeffi_1[i][j]
sum_coeff2 += coeffi_2[i][j]
#check constant
if np.fabs(sum_coeff1 * coeff2_constant - sum_coeff2 * coeff1_constant) > threshold:
return 0
#check all other coefficients
for i in xrange(M):
for j in xrange(K):
if np.fabs(sum_coeff1 * coeffi_2[i][j] - sum_coeff2 * coeffi_1[i][j]) > threshold:
#sum_coeff1 * coeffi_2[i][j] != sum_coeff2 * coeffi_1[i][j]
return 0
#1 represents the two lines are the same equation
return 1
def weighted_mean(_line):
max_weight = 50
# print _line.shape
median_2d = bottleneck.nanmedian(_line, axis=1).reshape(_line.shape[0],1).repeat(_line.shape[1], axis=1)
std = bottleneck.nanstd(_line, axis=1)
std_2d = std.reshape(_line.shape[0],1).repeat(_line.shape[1], axis=1)
weight_2d = numpy.fabs(std_2d / (_line - median_2d))
# weight_2d[weight_2d > max_weight] = max_weight
weight_2d[numpy.isinf(weight_2d)] = max_weight
for i in range(3):
avg = bottleneck.nansum(_line*weight_2d, axis=1)/bottleneck.nansum(weight_2d, axis=1)
avg_2d = avg.reshape(_line.shape[0],1).repeat(_line.shape[1], axis=1)
std = numpy.sqrt(bottleneck.nansum(((_line - avg_2d)**2 * weight_2d), axis=1)/bottleneck.nansum(weight_2d, axis=1))
std_2d = std.reshape(_line.shape[0],1).repeat(_line.shape[1], axis=1)
weight_2d = numpy.fabs(std_2d / (_line - avg_2d))
#weight_2d[weight_2d > max_weight] = max_weight
weight_2d[numpy.isinf(weight_2d)] = max_weight
return bottleneck.nansum(_line*weight_2d, axis=1)/bottleneck.nansum(weight_2d, axis=1)
def __init__(self, num):
global h, edge_times, edge_probs, state_density, states, Phdelta
states, state_density, edge_probs, edge_times, Phdelta = [],[],[],[],[]
h = (zmax-zmin)/float(num)
self.tot_vert = num+1
states = np.linspace(zmin, zmax, self.tot_vert)
for s in states:
c = process_var + h*np.fabs(self.drift(s))
htime = h*h/c
edge_times.append(htime)
for i in range(self.tot_vert):
s = states[i]
c = process_var + h*np.fabs(self.drift(s))
if (i != 0) and (i != self.tot_vert-1):
edge_probs.append([(process_var/2 + h*np.fabs(self.drift(s)))/c, process_var/2/c])
elif (i == self.tot_vert -1):
edge_probs.append([1.0, 0.])
elif (i == 0):
edge_probs.append([0., 1.0])
"""
# get filtering one_step transition probabilities using matrices
self.delta = min(edge_times)*0.999
P1 = np.zeros((self.tot_vert, self.tot_vert))
P0 = np.zeros((self.tot_vert, self.tot_vert))
for i in range(self.tot_vert):
pt = edge_times[i]/(self.delta + edge_times[i])
if( (i!=0) and (i!=self.tot_vert-1)):
P1[i,i-1] = edge_probs[i][0]*pt
P1[i,i+1] = edge_probs[i][1]*pt
P0[i,i-1] = edge_probs[i][0]*(1-pt)
P0[i,i+1] = edge_probs[i][1]*(1-pt)
elif(i ==0):
P1[i,i+1] = edge_probs[i][1]*pt
P0[i,i+1] = edge_probs[i][1]*(1-pt)
else:
P1[i,i-1] = edge_probs[i][0]*pt
P0[i,i-1] = edge_probs[i][0]*(1-pt)
Phdelta = np.linalg.inv(eye(self.tot_vert) - P0)*P1
"""
self.delta = min(edge_times)*0.999
#self.delta = 0.0001
#print 'min_htime: ', min(edge_times),' delta: ', self.delta
if(min(edge_times) < self.delta):
print "Add less nodes"
sys.exit(0)
# explicit method
Phdelta = np.zeros((self.tot_vert, self.tot_vert))
for i in range(self.tot_vert):
ps = 1 - self.delta/edge_times[i]
Phdelta[i,i] = ps
if( (i!=0) and (i!=self.tot_vert-1)):
Phdelta[i,i+1] = edge_probs[i][1]*(1- ps)
Phdelta[i,i-1] = edge_probs[i][0]*(1- ps)
elif(i ==0):
Phdelta[i,i+1] = edge_probs[i][1]*(1- ps)
else:
Phdelta[i,i-1] = edge_probs[i][0]*(1- ps)
def test_get_distance(self):
"""
Test GridMol.get_distance.
"""
self.mol.add_atom((1, 2, 1), 1.6)
self.mol.add_atom((1, 1, 1), 1.6)
distances = self.mol.get_distance()
# confirm that negative values are inside atoms
# this tests distance correspondence with occupancy
mask = self.mol.get_occupancy()
assert np.all(distances[mask] <= 0)
assert np.all(distances[~mask] > 0)
# check for sane positive distances
assert np.amax(distances) < max(self.mol.get_real_shape())
# check that negative distances are not too large
# min should be no larger than the largest atom radius plus the probe
# radius (by definition)
assert np.fabs(np.amin(distances)) <= (
self.mol.atoms[0].radius + self.mol.probe_radius)
# check that most distances are significantly less than max
threshold = max(self.mol.get_real_shape()) / 2.
assert np.count_nonzero(np.fabs(distances) < threshold) > (
0.9 * distances.size)
def visiting(self, x, step, temperature):
dim = x.size
if step < dim:
# Changing all coordinates with a new visting value
visits = np.array([self.visit_fn(
temperature) for _ in range(dim)])
upper_sample = self.rs.random_sample()
lower_sample = self.rs.random_sample()
visits[visits > self.tail_limit] = self.tail_limit * upper_sample
visits[visits < -self.tail_limit] = -self.tail_limit * lower_sample
x_visit = visits + x
a = x_visit - self.lower
b = np.fmod(a, self.b_range) + self.b_range
x_visit = np.fmod(b, self.b_range) + self.lower
x_visit[np.fabs(
x_visit - self.lower) < self.min_visit_bound] += 1.e-10
else:
# Changing only one coordinate at a time based on Markov chain step
x_visit = np.copy(x)
visit = self.visit_fn(temperature)
if visit > self.tail_limit:
visit = self.tail_limit * self.rs.random_sample()
elif visit < -self.tail_limit:
visit = -self.tail_limit * self.rs.random_sample()
index = step - dim
x_visit[index] = visit + x[index]
a = x_visit[index] - self.lower[index]
b = np.fmod(a, self.b_range[index]) + self.b_range[index]
x_visit[index] = np.fmod(b, self.b_range[
index]) + self.lower[index]
if np.fabs(x_visit[index] - self.lower[
index]) < self.min_visit_bound:
x_visit[index] += self.min_visit_bound
return x_visit
def remove_duplicate_candidates(self, verbosity=1):
"""Remove lower-significance 'duplicate' (i.e. same period)
candidates from a list of candidates. For the highest
significance candidate, include a list of the DMs (and SNRs)
of all the other detections.
Inputs:
verbosity: Verbosity level. (Default: 1)
Ouputs:
None
"""
if verbosity >= 1:
print " Sorting the %d candidates by frequency..." % \
self.get_numcands()
self.cands.sort(cmp_freq)
if verbosity >= 1:
print " Searching for dupes..."
ii = 0
# Find any match
while ii < self.get_numcands():
jj = ii + 1
if jj < self.get_numcands() and \
Num.fabs(self.cands[ii].r-self.cands[jj].r) < r_err:
# Find others that match
jj += 1
while jj < self.get_numcands() and \
Num.fabs(self.cands[ii].r-self.cands[jj].r) < r_err:
jj += 1
matches = self.cands[ii:jj]
matches.sort(cmp_sigma)
bestindex = self.cands.index(matches[0])
#sigmas = [c.sigma for c in matches]
#bestindex = Num.argmax(sigmas)+ii
# flag the duplicates
bestcand = self.cands[bestindex]
# Add other matching cands as hit of highest-sigma cand
for matchind in reversed(range(ii, jj)):
if matchind == bestindex:
# The current candidate is the highest-sigma cand
# Don't remove it
continue
match = self.cands[matchind]
bestcand.add_as_hit(match)
match.note = "This candidate is a duplicate of %s:%d" % \
(bestcand.filename, bestcand.candnum)
self.duplicate_cands.append(self.cands.pop(matchind))
if verbosity >= 2:
print "Removing %s:%d (index: %d)" % \
(match.filename, match.candnum, matchind)
print " %s" % match.note
# If the best candidate isn't at the same freq
# as ii, then it's possible even more hits should
# be added. So we don't increment the index
# (note that the best cand has moved into position ii).
else:
ii += 1 # No candidates to be added as hits, move on
if verbosity >= 1:
print "Found %d candidates.\n" % self.get_numcands()
self.cands.sort(cmp_sigma)
def fresnelR(n1, n2, theta):
temp1 = np.sqrt(1.0-((n1/n2)*np.sin(theta))**2)
temp2 = np.cos(theta)
R_s = np.fabs( (n1*temp2-n2*temp1)/(n1*temp2+n2*temp1) )**2
R_p = np.fabs( (n1*temp1-n2*temp2)/(n1*temp1+n2*temp2) )**2
R = (R_s + R_p)/2
return R
def geigen(Amat, Bmat, Cmat):
"""
generalized eigenvalue problem of the form
max tr L'AM / sqrt(tr L'BL tr M'CM) w.r.t. L and M
:param Amat numpy ndarray of shape (M,N)
:param Bmat numpy ndarray of shape (M,N)
:param Bmat numpy ndarray of shape (M,N)
:rtype: numpy ndarray
:return values: eigenvalues
:return Lmat: left eigenvectors
:return Mmat: right eigenvectors
"""
if Bmat.shape[0] != Bmat.shape[1]:
print("BMAT is not square.\n")
sys.exit(1)
if Cmat.shape[0] != Cmat.shape[1]:
print("CMAT is not square.\n")
sys.exit(1)
p = Bmat.shape[0]
q = Cmat.shape[0]
s = min(p, q)
tmp = fabs(Bmat - Bmat.transpose())
tmp1 = fabs(Bmat)
if tmp.max() / tmp1.max() > 1e-10:
print("BMAT not symmetric..\n")
sys.exit(1)
tmp = fabs(Cmat - Cmat.transpose())
tmp1 = fabs(Cmat)
if tmp.max() / tmp1.max() > 1e-10:
print("CMAT not symmetric..\n")
sys.exit(1)
Bmat = (Bmat + Bmat.transpose()) / 2.
Cmat = (Cmat + Cmat.transpose()) / 2.
Bfac = cholesky(Bmat)
Cfac = cholesky(Cmat)
Bfacinv = inv(Bfac)
Bfacinvt = Bfacinv.transpose()
Cfacinv = inv(Cfac)
Dmat = Bfacinvt.dot(Amat).dot(Cfacinv)
if p >= q:
u, d, v = svd(Dmat)
values = d
Lmat = Bfacinv.dot(u)
Mmat = Cfacinv.dot(v.transpose())
else:
u, d, v = svd(Dmat.transpose())
values = d
Lmat = Bfacinv.dot(u)
Mmat = Cfacinv.dot(v.transpose())
return values, Lmat, Mmat
def to_offset(freq):
"""
Return DateOffset object from string or tuple representation
or datetime.timedelta object
Parameters
----------
freq : str, tuple, datetime.timedelta, DateOffset or None
Returns
-------
delta : DateOffset
None if freq is None
Raises
------
ValueError
If freq is an invalid frequency
See Also
--------
pandas.DateOffset
Examples
--------
>>> to_offset('5min')
<5 * Minutes>
>>> to_offset('1D1H')
<25 * Hours>
>>> to_offset(('W', 2))
<2 * Weeks: weekday=6>
>>> to_offset((2, 'B'))
<2 * BusinessDays>
>>> to_offset(datetime.timedelta(days=1))
<Day>
>>> to_offset(Hour())
<Hour>
"""
if freq is None:
return None
if isinstance(freq, DateOffset):
return freq
if isinstance(freq, tuple):
name = freq[0]
stride = freq[1]
if isinstance(stride, compat.string_types):
name, stride = stride, name
name, _ = _base_and_stride(name)
delta = get_offset(name) * stride
elif isinstance(freq, timedelta):
delta = None
freq = Timedelta(freq)
try:
for name in freq.components._fields:
offset = _name_to_offset_map[name]
stride = getattr(freq.components, name)
if stride != 0:
offset = stride * offset
if delta is None:
delta = offset
else:
delta = delta + offset
except Exception:
raise ValueError(_INVALID_FREQ_ERROR.format(freq))
else:
delta = None
stride_sign = None
try:
splitted = re.split(opattern, freq)
if splitted[-1] != '' and not splitted[-1].isspace():
# the last element must be blank
raise ValueError('last element must be blank')
for sep, stride, name in zip(splitted[0::4], splitted[1::4],
splitted[2::4]):
if sep != '' and not sep.isspace():
raise ValueError('separator must be spaces')
prefix = _lite_rule_alias.get(name) or name
if stride_sign is None:
stride_sign = -1 if stride.startswith('-') else 1
if not stride:
stride = 1
if prefix in Resolution._reso_str_bump_map.keys():
stride, name = Resolution.get_stride_from_decimal(
float(stride), prefix)
stride = int(stride)
offset = get_offset(name)
offset = offset * int(np.fabs(stride) * stride_sign)
if delta is None:
delta = offset
else:
delta = delta + offset
except Exception:
raise ValueError(_INVALID_FREQ_ERROR.format(freq))
if delta is None:
raise ValueError(_INVALID_FREQ_ERROR.format(freq))
return delta
def test_compute_gradient(self):
for y, y_pred in zip(self.y_list, self.predict_list):
fair_grad = self.fair_loss.compute_grad(y, y_pred)
diff = y_pred - y
grad = self.c * diff / (np.abs(diff) + self.c)
self.assertTrue(np.fabs(fair_grad - grad) < consts.FLOAT_ZERO)
def test_compute_gradient(self):
for y, y_pred in zip(self.y_list, self.predict_list):
lse_grad = self.lse_loss.compute_grad(y, y_pred)
grad = 2 * (y_pred - y)
self.assertTrue(np.fabs(lse_grad - grad) < consts.FLOAT_ZERO)
def test_predict(self):
for y in self.y_list:
y_pred = self.lse_loss.predict(y)
self.assertTrue(np.fabs(y_pred - y) < consts.FLOAT_ZERO)
def test_compute_gradient(self):
for y, y_pred in zip(self.y_list, self.predict_list):
tweedie_grad = self.tweedie_loss.compute_grad(y, y_pred)
grad = -y * np.exp(1 - self.rho) * y_pred + np.exp(
2 - self.rho) * y_pred
self.assertTrue(np.fabs(tweedie_grad - grad) < consts.FLOAT_ZERO)
def test_compute_hess(self):
for y, y_pred in zip(self.y_list, self.predict_list):
log_cosh_hess = self.log_cosh_loss.compute_hess(y, y_pred)
diff = y_pred - y
hess = 1 - np.tanh(diff)**2
self.assertTrue(np.fabs(log_cosh_hess - hess) < consts.FLOAT_ZERO)
def test_compute_gradient(self):
for y, y_pred in zip(self.y_list, self.predict_list):
log_cosh_grad = self.log_cosh_loss.compute_grad(y, y_pred)
diff = y_pred - y
grad = np.tanh(diff)
self.assertTrue(np.fabs(log_cosh_grad - grad) < consts.FLOAT_ZERO)
def test_compute_hess(self):
for y, y_pred in zip(self.y_list, self.predict_list):
fair_hess = self.fair_loss.compute_hess(y, y_pred)
diff = y_pred - y
hess = self.c**2 / (np.abs(diff) + self.c)**2
self.assertTrue(np.fabs(fair_hess - hess) < consts.FLOAT_ZERO)
def test_compute_gradient(self):
for y, y_pred in zip(self.y_list, self.predict_list):
huber_grad = self.huber_loss.compute_grad(y, y_pred)
diff = y_pred - y
grad = diff / np.sqrt(diff * diff / self.delta**2 + 1)
self.assertTrue(np.fabs(huber_grad - grad) < consts.FLOAT_ZERO)
def test_compute_hess(self):
for y, y_pred in zip(self.y_list, self.predict_list):
huber_hess = self.huber_loss.compute_hess(y, y_pred)
diff = y_pred - y
hess = 1.0 / (1 + diff * diff / self.delta**2)**1.5
self.assertTrue(np.fabs(huber_hess - hess) < consts.FLOAT_ZERO)
gene_fixation_positions = {}
for snp_change in (mutations + reversions):
gene_name = snp_change[0]
position = snp_change[2]
if gene_name not in gene_fixation_positions:
gene_fixation_positions[gene_name] = []
gene_fixation_positions[gene_name].append(position)
for gene_name in gene_fixation_positions:
if len(gene_fixation_positions[gene_name]) >= 2:
# Calculate max position difference between SNPs.
positions = numpy.array(gene_fixation_positions[gene_name])
max_distance = numpy.fabs(positions[:, None] -
positions[None, :]).max()
if max_distance > 100:
print gene_name
highlighted_gene_set.add(gene_name)
for snp_change in (mutations + reversions):
if snp_change[0] in highlighted_gene_set:
print snp_change
highlighted_gene_names[pair_idx] = highlighted_gene_set
final_line_number = 0
while final_line_number >= 0:
def test_compute_loss(self):
sklearn_loss = metrics.mean_absolute_error(self.y_list,
self.predict_list)
lae_loss = self.lae_loss.compute_loss(self.y, self.predict)
self.assertTrue(np.fabs(lae_loss - sklearn_loss) < consts.FLOAT_ZERO)
def get_body_heliographic_stonyhurst(body,
time='now',
observer=None,
*,
include_velocity=False):
"""
Return a `~sunpy.coordinates.frames.HeliographicStonyhurst` frame for the location of a
solar-system body at a specified time. The location can be corrected for light travel time
to an observer.
Parameters
----------
body : `str`
The solar-system body for which to calculate positions
time : {parse_time_types}
Time to use in a parse_time-compatible format
observer : `~astropy.coordinates.SkyCoord`
If None, the returned coordinate is the instantaneous or "true" location.
If not None, the returned coordinate is the astrometric location (i.e., accounts for light
travel time to the specified observer)
Keyword Arguments
-----------------
include_velocity : `bool`
If True, include the body's velocity in the output coordinate. Defaults to False.
Returns
-------
out : `~sunpy.coordinates.frames.HeliographicStonyhurst`
Location of the solar-system body in the `~sunpy.coordinates.HeliographicStonyhurst` frame
Notes
-----
There is no correction for aberration due to observer motion. For a body close to the Sun in
angular direction relative to the observer, the correction can be negligible because the
apparent location of the body will shift in tandem with the Sun.
Examples
--------
>>> from sunpy.coordinates.ephemeris import get_body_heliographic_stonyhurst
Obtain the location of Venus
>>> get_body_heliographic_stonyhurst('venus', '2012-06-06 04:07:29')
<HeliographicStonyhurst Coordinate (obstime=2012-06-06T04:07:29.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, AU)
(0.07349535, 0.05223575, 0.72605496)>
Obtain the location of Venus as seen from Earth when adjusted for light travel time
>>> earth = get_body_heliographic_stonyhurst('earth', '2012-06-06 04:07:29')
>>> get_body_heliographic_stonyhurst('venus', '2012-06-06 04:07:29', observer=earth)
INFO: Apparent body location accounts for 144.07 seconds of light travel time [sunpy.coordinates.ephemeris]
<HeliographicStonyhurst Coordinate (obstime=2012-06-06T04:07:29.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, AU)
(0.07084926, 0.0520573, 0.72605477)>
Obtain the location and velocity of Mars
>>> mars = get_body_heliographic_stonyhurst('mars', '2001-02-03', include_velocity=True)
>>> mars
<HeliographicStonyhurst Coordinate (obstime=2001-02-03T00:00:00.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, AU)
(63.03105777, -5.20656151, 1.6251161)
(d_lon, d_lat, d_radius) in (arcsec / s, arcsec / s, km / s)
(-0.02323686, 0.00073376, -1.4798387)>
Transform that same location and velocity of Mars to a different frame using
`~astropy.coordinates.SkyCoord`.
>>> from astropy.coordinates import SkyCoord
>>> from sunpy.coordinates import Helioprojective
>>> SkyCoord(mars).transform_to(Helioprojective(observer=earth))
<SkyCoord (Helioprojective: obstime=2001-02-03T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate (obstime=2012-06-06T04:07:29.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, AU)
(7.835757e-15, -0.00766698, 1.01475668)>): (Tx, Ty, distance) in (arcsec, arcsec, AU)
(-298029.94625805, -21753.50941181, 1.40010091)
(d_Tx, d_Ty, d_distance) in (arcsec / s, arcsec / s, km / s)
(-0.01652981, -0.00059216, -15.14320414)>
"""
obstime = parse_time(time)
if observer is None:
# If there is no observer, there is not adjustment for light travel time
emitted_time = obstime
else:
observer_icrs = SkyCoord(observer).icrs.cartesian
# This implementation is modeled after Astropy's `_get_apparent_body_position`
light_travel_time = 0. * u.s
emitted_time = obstime
delta_light_travel_time = 1. * u.s # placeholder value
while np.any(np.fabs(delta_light_travel_time) > 1.0e-8 * u.s):
body_icrs = get_body_barycentric(body, emitted_time)
distance = (body_icrs - observer_icrs).norm()
delta_light_travel_time = light_travel_time - distance / speed_of_light
light_travel_time = distance / speed_of_light
emitted_time = obstime - light_travel_time
if light_travel_time.isscalar:
ltt_string = f"{light_travel_time.to_value('s'):.2f}"
else:
ltt_string = f"{light_travel_time.to_value('s')}"
log.info(
f"Apparent body location accounts for {ltt_string} seconds of light travel time"
)
if include_velocity:
pos, vel = get_body_barycentric_posvel(body, emitted_time)
body_icrs = pos.with_differentials(
vel.represent_as(CartesianDifferential))
else:
body_icrs = get_body_barycentric(body, emitted_time)
body_hgs = ICRS(body_icrs).transform_to(
HeliographicStonyhurst(obstime=obstime))
return body_hgs
def apply_forces(self, system, time=0.0):
# calculate axial and rolling directions
plane_response_force_mag, no_contact_point_idx = self.apply_normal_force(system)
normal_plane_collection = np.repeat(
self.plane_normal.reshape(3, 1), plane_response_force_mag.shape[0], axis=1
)
# First compute component of rod tangent in plane. Because friction forces acts in plane not out of plane. Thus
# axial direction has to be in plane, it cannot be out of plane. We are projecting rod element tangent vector in
# to the plane. So friction forces can only be in plane forces and not out of plane.
tangent_along_normal_direction = np.einsum(
"ij, ij->j", system.tangents, normal_plane_collection
)
tangent_perpendicular_to_normal_direction = system.tangents - np.einsum(
"j, ij->ij", tangent_along_normal_direction, normal_plane_collection
)
tangent_perpendicular_to_normal_direction_mag = np.einsum(
"ij, ij->j",
tangent_perpendicular_to_normal_direction,
tangent_perpendicular_to_normal_direction,
)
# Normalize tangent_perpendicular_to_normal_direction. This is axial direction for plane. Here we are adding
# small tolerance (1e-10) for normalization, in order to prevent division by 0.
axial_direction = np.einsum(
"ij, j-> ij",
tangent_perpendicular_to_normal_direction,
1 / (tangent_perpendicular_to_normal_direction_mag + 1e-14),
)
element_velocity = 0.5 * (
system.velocity_collection[..., :-1] + system.velocity_collection[..., 1:]
)
# first apply axial kinetic friction
velocity_mag_along_axial_direction = np.einsum(
"ij,ij->j", element_velocity, axial_direction
)
velocity_along_axial_direction = np.einsum(
"j, ij->ij", velocity_mag_along_axial_direction, axial_direction
)
# Friction forces depends on the direction of velocity, in other words sign
# of the velocity vector.
velocity_sign_along_axial_direction = np.sign(
velocity_mag_along_axial_direction
)
# Check top for sign convention
kinetic_mu = 0.5 * (
self.kinetic_mu_forward * (1 + velocity_sign_along_axial_direction)
+ self.kinetic_mu_backward * (1 - velocity_sign_along_axial_direction)
)
# Call slip function to check if elements slipping or not
slip_function_along_axial_direction = find_slipping_elements(
velocity_along_axial_direction, self.slip_velocity_tol
)
kinetic_friction_force_along_axial_direction = -(
(1.0 - slip_function_along_axial_direction)
* kinetic_mu
* plane_response_force_mag
* velocity_sign_along_axial_direction
* axial_direction
)
# If rod element does not have any contact with plane, plane cannot apply friction
# force on the element. Thus lets set kinetic friction force to 0.0 for the no contact points.
kinetic_friction_force_along_axial_direction[..., no_contact_point_idx] = 0.0
system.external_forces[..., :-1] += (
0.5 * kinetic_friction_force_along_axial_direction
)
system.external_forces[..., 1:] += (
0.5 * kinetic_friction_force_along_axial_direction
)
# Now rolling kinetic friction
rolling_direction = _batch_cross(axial_direction, normal_plane_collection)
torque_arm = -system.radius * normal_plane_collection
velocity_along_rolling_direction = np.einsum(
"ij ,ij ->j ", element_velocity, rolling_direction
)
directors_transpose = np.einsum("ijk -> jik", system.director_collection)
# w_rot = Q.T @ omega @ Q @ r
rotation_velocity = _batch_matvec(
directors_transpose,
_batch_cross(
system.omega_collection,
_batch_matvec(system.director_collection, torque_arm),
),
)
rotation_velocity_along_rolling_direction = np.einsum(
"ij,ij->j", rotation_velocity, rolling_direction
)
slip_velocity_mag_along_rolling_direction = (
velocity_along_rolling_direction + rotation_velocity_along_rolling_direction
)
slip_velocity_along_rolling_direction = np.einsum(
"j, ij->ij", slip_velocity_mag_along_rolling_direction, rolling_direction
)
slip_velocity_sign_along_rolling_direction = np.sign(
slip_velocity_mag_along_rolling_direction
)
slip_function_along_rolling_direction = find_slipping_elements(
slip_velocity_along_rolling_direction, self.slip_velocity_tol
)
kinetic_friction_force_along_rolling_direction = -(
(1.0 - slip_function_along_rolling_direction)
* self.kinetic_mu_sideways
* plane_response_force_mag
* slip_velocity_sign_along_rolling_direction
* rolling_direction
)
# If rod element does not have any contact with plane, plane cannot apply friction
# force on the element. Thus lets set kinetic friction force to 0.0 for the no contact points.
kinetic_friction_force_along_rolling_direction[..., no_contact_point_idx] = 0.0
system.external_forces[..., :-1] += (
0.5 * kinetic_friction_force_along_rolling_direction
)
system.external_forces[..., 1:] += (
0.5 * kinetic_friction_force_along_rolling_direction
)
# torque = Q @ r @ Fr
system.external_torques += _batch_matvec(
system.director_collection,
_batch_cross(torque_arm, kinetic_friction_force_along_rolling_direction),
)
# now axial static friction
nodal_total_forces = system.internal_forces + system.external_forces
element_total_forces = nodes_to_elements(nodal_total_forces)
force_component_along_axial_direction = np.einsum(
"ij,ij->j", element_total_forces, axial_direction
)
force_component_sign_along_axial_direction = np.sign(
force_component_along_axial_direction
)
# check top for sign convention
static_mu = 0.5 * (
self.static_mu_forward * (1 + force_component_sign_along_axial_direction)
+ self.static_mu_backward * (1 - force_component_sign_along_axial_direction)
)
max_friction_force = (
slip_function_along_axial_direction * static_mu * plane_response_force_mag
)
# friction = min(mu N, pushing force)
static_friction_force_along_axial_direction = -(
np.minimum(
np.fabs(force_component_along_axial_direction), max_friction_force
)
* force_component_sign_along_axial_direction
* axial_direction
)
# If rod element does not have any contact with plane, plane cannot apply friction
# force on the element. Thus lets set static friction force to 0.0 for the no contact points.
static_friction_force_along_axial_direction[..., no_contact_point_idx] = 0.0
system.external_forces[..., :-1] += (
0.5 * static_friction_force_along_axial_direction
)
system.external_forces[..., 1:] += (
0.5 * static_friction_force_along_axial_direction
)
# now rolling static friction
# there is some normal, tangent and rolling directions inconsitency from Elastica
total_torques = _batch_matvec(
directors_transpose, (system.internal_torques + system.external_torques)
)
# Elastica has opposite defs of tangents in interaction.h and rod.cpp
total_torques_along_axial_direction = np.einsum(
"ij,ij->j", total_torques, axial_direction
)
force_component_along_rolling_direction = np.einsum(
"ij,ij->j", element_total_forces, rolling_direction
)
noslip_force = -(
(
system.radius * force_component_along_rolling_direction
- 2.0 * total_torques_along_axial_direction
)
/ 3.0
/ system.radius
)
max_friction_force = (
slip_function_along_rolling_direction
* self.static_mu_sideways
* plane_response_force_mag
)
noslip_force_sign = np.sign(noslip_force)
static_friction_force_along_rolling_direction = (
np.minimum(np.fabs(noslip_force), max_friction_force)
* noslip_force_sign
* rolling_direction
)
# If rod element does not have any contact with plane, plane cannot apply friction
# force on the element. Thus lets set plane static friction force to 0.0 for the no contact points.
static_friction_force_along_rolling_direction[..., no_contact_point_idx] = 0.0
system.external_forces[..., :-1] += (
0.5 * static_friction_force_along_rolling_direction
)
system.external_forces[..., 1:] += (
0.5 * static_friction_force_along_rolling_direction
)
system.external_torques += _batch_matvec(
system.director_collection,
_batch_cross(torque_arm, static_friction_force_along_rolling_direction),
)
def mad(x):
return np.fabs(x - x.mean()).mean()
def update(self, space: Space, iteration: int, n_iterations: int) -> None:
"""Wraps Whale Optimization Algorithm over all agents and variables.
Args:
space: Space containing agents and update-related information.
iteration: Current iteration.
n_iterations (int): Maximum number of iterations
"""
# Linearly decreases the coefficient
coefficient = 2 - 2 * iteration / (n_iterations - 1)
# Iterates through all agents
for agent in space.agents:
# Generates an uniform random number
r1 = r.generate_uniform_random_number()
# Calculates the `A` coefficient
A = 2 * coefficient * r1 - coefficient
# Calculates the `C` coefficient
C = 2 * r1
# Generates a random number between 0 and 1
p = r.generate_uniform_random_number()
# If `p` is smaller than 0.5
if p < 0.5:
# If `A` is smaller than 1
if np.fabs(A) < 1:
# Calculates the distance coefficient
D = np.fabs(C * space.best_agent.position - agent.position)
# Updates the agent's position
agent.position = space.best_agent.position - A * D
# If `A` is bigger or equal to 1
else:
# Generates a random-based agent
a = self._generate_random_agent(agent)
# Calculates the distance coefficient
D = np.fabs(C * a.position - agent.position)
# Updates the agent's position
agent.position = a.position - A * D
# If `p` is bigger or equal to 1
else:
# Generates a random number between -1 and 1
l = r.generate_gaussian_random_number()
# Calculates the distance coefficient
D = np.fabs(space.best_agent.position - agent.position)
# Updates the agent's position
agent.position = (
D * np.exp(self.b * l) * np.cos(2 * np.pi * l)
+ space.best_agent.position
)
def test_compute_hess(self):
for y, y_pred in zip(self.y_list, self.predict_list):
hess = 2
lse_hess = self.lse_loss.compute_hess(y, y_pred)
self.assertTrue(np.fabs(lse_hess - hess) < consts.FLOAT_ZERO)
x = y = 0
wsp_x = [0]
wsp_y = [0]
for i in range(0, n):
#Wylosuj kąt i zamień go na radiany
rad = math.radians(float(random.randint(0, 360)))
x = x + np.cos(rad) # wyliczamy współrzędne x i y
y = y + np.sin(rad)
print(x, y)
wsp_x.append(x)
wsp_y.append(y)
c = np.sqrt((wsp_x[i] - wsp_x[i - 1])**2 + (wsp_y[i] - wsp_y[i - 1])**2)
print(wsp_x, wsp_y)
# Obliczamy wektor końcowego przesunięcia
s = np.fabs(np.sqrt(x**2 + y**2))
w_x = [0, wsp_x[len(wsp_x) - 1]]
w_y = [0, wsp_y[len(wsp_y) - 1]]
print("Wektor przesunięcia: ", s)
plt.plot(wsp_x, wsp_y, "o:", color="green", linewidth=3, alpha=0.5)
plt.plot(wsp_x, wsp_y, c, "r:", color="blue", linewidth=1, alpha=0.2)
plt.plot(w_x, w_y, s, "o:", color="blue", linewidth=2, alpha=1)
plt.legend(["Dane x, y\nPrzemieszczenie: " + str(s)], loc="upper left")
plt.xlabel("Wsp_x")
plt.ylabel("Wsp_y")
plt.title("Ruchy Browna")
plt.grid(True)
plt.show()
def draw_boxes(im,
bboxes,
is_display=True,
color=None,
caption="Image",
wait=True):
"""
boxes: bounding boxes
"""
text_recs = np.zeros((len(bboxes), 8), np.int)
im = im.copy()
index = 0
for box in bboxes:
if color == None:
if len(box) == 8 or len(box) == 9:
c = tuple(cm.jet([box[-1]])[0, 2::-1] * 255)
else:
c = tuple(np.random.randint(0, 256, 3))
else:
c = color
b1 = box[6] - box[7] / 2
b2 = box[6] + box[7] / 2
x1 = box[0]
y1 = box[5] * box[0] + b1
x2 = box[2]
y2 = box[5] * box[2] + b1
x3 = box[0]
y3 = box[5] * box[0] + b2
x4 = box[2]
y4 = box[5] * box[2] + b2
disX = x2 - x1
disY = y2 - y1
width = np.sqrt(disX * disX + disY * disY)
fTmp0 = y3 - y1
fTmp1 = fTmp0 * disY / width
x = np.fabs(fTmp1 * disX / width)
y = np.fabs(fTmp1 * disY / width)
if box[5] < 0:
x1 -= x
y1 += y
x4 += x
y4 -= y
else:
x2 += x
y2 += y
x3 -= x
y3 -= y
cv2.line(im, (int(x1), int(y1)), (int(x2), int(y2)), c, 2)
cv2.line(im, (int(x1), int(y1)), (int(x3), int(y3)), c, 2)
cv2.line(im, (int(x4), int(y4)), (int(x2), int(y2)), c, 2)
cv2.line(im, (int(x3), int(y3)), (int(x4), int(y4)), c, 2)
text_recs[index, 0] = x1
text_recs[index, 1] = y1
text_recs[index, 2] = x2
text_recs[index, 3] = y2
text_recs[index, 4] = x3
text_recs[index, 5] = y3
text_recs[index, 6] = x4
text_recs[index, 7] = y4
index = index + 1
#cv2.rectangle(im, tuple(box[:2]), tuple(box[2:4]), c,2)
if is_display:
cv2.imshow('result', im)
#if wait:
#cv2.waitKey(0)
return text_recs
#print a
uvar = file.variables["UGRD_P0_L100_GLC0"][:, :, :]
uvar = numpy.squeeze(uvar[-1, :, :])
dim = numpy.shape(uvar)
print dim
vvar = file.variables["VGRD_P0_L100_GLC0"][:, :, :]
vvar = numpy.squeeze(vvar[-1, :, :])
lat = file.variables["gridlat_0"][:, :]
lon = file.variables["gridlon_0"][:, :]
#Find the index of the origin
print "want lat lon", Latorg, Lonorg
for i in range(dim[0]):
for j in range(dim[1]):
if numpy.fabs(lat[i, j] - Latorg) < tol and numpy.fabs(lon[i, j] -
Lonorg) < tol:
print 'closest we can get is', lat[i, j], lon[i, j]
print i, j
iorg = i
jorg = j
u = 3.6 * uvar
v = 3.6 * vvar
umax = numpy.max(u)
vmax = numpy.max(v)
print "Max u", umax
print "Max v", vmax
space0 = gridspacing * (dim[0] - iorg - 1)
def mape_vectorized_v2(a, b):
mask = a != 0
return (np.fabs(a[mask] - b[mask])/a[mask]).mean()
import numpy as np x = 1.0 #define a float y = 2.0 #define another float #exponents and logarithms print(np.exp(x)) #e^x print(np.log(x)) #ln x print(np.log10(x)) #log_10 x print(np.log2(x)) #log_2 x #min/max/misc print(np.fabs(x)) #absolute value as a float print(np.fmin(x, y)) #min of x and y print(np.fmax(x, y)) #max of x and y #populate arrays n = 100 z = np.arange(n, dtype=float) #get an array [0,0,n-1.] z *= 2.0 * np.pi / float(n - 1) #z = [0,2*pi] sin_z = np.sin(z) #get an array sin(z) #interpolation print(np.interp(0.75, z, sin_z)) #interpolate sin(0.75) print(np.sin(0.75))
def dic_constr(data3d, groundtruth, win_size, cluster_num, K,
selected_dic_percent, target_dic_num):
"""
:param data3d: the original 3D hyperpsectral image
:param groundtruth: a 2D matrix reflect the label of corresponding pixels
:param win_size: the size of window, such as 3X3, 5X5, 7X7
:param cluster_num: the number of classters such as 5, 10, 15, 20
:param K: the level of sparsity
:param selected_dic_percent: the selected percent of the atoms to build the background dictionary
:param target_dic_num: the selected number to build the anomaly dictionary
:return: data2d: the normalized data
bg_dic: the background dictionary
tg_dic: the anomaly dictionary
bg_dic_ac_label: the index of background dictionary atoms
tg_dic_label: the index of anomaly dictionary atoms
"""
data2d = hyper.hyperconvert2d(data3d)
rows, cols, bands = data3d.shape
data2d = hyper.hypernorm(data2d, "L2_norm")
sio.savemat("data2d.mat", {'data2d': data2d})
data3d = hyper.hyperconvert3d(data2d, rows, cols, bands)
pca = decomposition.PCA(n_components=20, copy=True, whiten=False)
dim_data = pca.fit_transform(data2d.transpose())
data3d_dim = hyper.hyperconvert3d(dim_data.transpose(), rows, cols, 10)
win_dim = hyper.hyperwincreat(data3d_dim, win_size)
cluster_assment = hyper.Kmeans_win(win_dim, cluster_num)
sio.savemat("cluster_assment.mat", {'cluster_assment': cluster_assment})
win_matrix = hyper.hyperwincreat(data3d, win_size)
sio.savemat("win_matrix.mat", {'win_matrix': win_matrix})
wm_rows, wm_cols, wm_n = win_matrix.shape
resdiual_stack = np.zeros((bands, win_size * win_size, wm_n))
save_num = 0
bg_dic_tuple = []
bg_dic_ac_tuple = []
bg_dic_fc_tuple = []
class_order_data_index_tuple = []
anomaly_weight_tuple = []
for i in range(cluster_num):
print("current calculate cluster {0} ...".format(i))
tmp = np.where(cluster_assment == i)
if tmp[0].size == 0:
continue
else:
class_data = win_matrix[:, :, tmp[0]]
cd_rows, cd_cols, cd_n = class_data.shape
dictionary = class_data[:, int((win_size * win_size + 1) / 2), :]
dic_rows, dic_cols = dictionary.shape
class_alpha = np.zeros((K, cd_cols, cd_n))
class_index = np.zeros((K, cd_n))
for j in range(cd_n):
X = class_data[:, :, j]
dictionary[:, (j * cd_cols):(j * cd_cols + cd_cols - 1)] = 0
alpha, index, chosen_atom, resdiual = hyper.somp(
dictionary, X, K)
class_alpha[:, :, j] = alpha
class_index[:, j] = index.transpose()
resdiual_stack[:, :, save_num + j] = resdiual
save_num = save_num + cd_n
class_index = class_index.astype('int')
class_global_alpha = np.zeros((dic_cols, cd_cols, cd_n))
class_global_frequency = np.zeros((dic_cols, cd_cols, cd_n))
for n_index in range(cd_n):
class_global_alpha[class_index[:, n_index], :,
n_index] = class_alpha[:, :, n_index]
class_global_frequency[class_index[:, n_index], :, n_index] = 1
posti_class_global_alpha = np.fabs(class_global_alpha)
data_frequency = class_global_frequency[:, 0, :]
frequency = np.sum(data_frequency, axis=1)
sum_frequency = np.sum(frequency)
norm_frequency = frequency / sum_frequency
data_mean_alpha = np.mean(posti_class_global_alpha, axis=1)
sum_alpha_2 = np.sum(data_mean_alpha, axis=1)
norm_tmp = np.linalg.norm(sum_alpha_2)
sparsity_score = sum_alpha_2 / norm_tmp
anomaly_weight = norm_frequency
anomaly_weight[frequency > 0] = sparsity_score[
frequency > 0] / frequency[frequency > 0]
# sparsity_score = sparsity_score * norm_frequency
sparsity_sort_index = np.argsort(-sparsity_score)
sparsity_sort_index = sparsity_sort_index.astype('int')
frequency_sort_index = np.argsort(-norm_frequency)
frequency_sort_index = frequency_sort_index.astype('int')
tmp_class_dic_label = np.array(tmp[0])
class_order_data_index_tuple.append(tmp_class_dic_label)
selected_dic_num = np.round(selected_dic_percent * cd_n)
selected_dic_num = selected_dic_num.astype('int')
bg_dic_ac_tuple.append(
tmp_class_dic_label[sparsity_sort_index[0:selected_dic_num]])
bg_dic_fc_tuple.append(
tmp_class_dic_label[frequency_sort_index[0:selected_dic_num]])
anomaly_weight_tuple.append(anomaly_weight)
bg_dic_tuple.append(
dictionary[:, sparsity_sort_index[0:selected_dic_num]])
# sio.savemat(result_path + "dic_{0}_frequency.mat".format(i), {'dic_frequency': frequency})
# sio.savemat(result_path + "dic_{0}_reflect.mat".format(i), {'dic_reflect': sum_alpha_2})
bg_dic = np.column_stack(bg_dic_tuple)
bg_dic_ac_label = np.hstack(bg_dic_ac_tuple)
bg_dic_fc_label = np.hstack(bg_dic_fc_tuple)
anomaly_weight = np.hstack(anomaly_weight_tuple)
class_order_data_index = np.hstack(class_order_data_index_tuple)
norm_res = np.zeros((wm_n, win_size * win_size))
for i in range(wm_n):
norm_res[i, :] = np.linalg.norm(resdiual_stack[:, :, i], axis=0)
mean_norm_res = np.mean(norm_res, axis=1) * anomaly_weight.transpose()
anomaly_level = mean_norm_res / np.linalg.norm(mean_norm_res)
tg_sort_index = np.argsort(-anomaly_level)
tg_dic = data2d[:, class_order_data_index[tg_sort_index[0:target_dic_num]]]
print("successs!!")
sio.savemat("bg_dic.mat", {'bg_dic': bg_dic})
sio.savemat("bg_dic_ac_label.mat", {'bg_dic_ac_label': bg_dic_ac_label})
sio.savemat("bg_dic_fc_label.mat", {'bg_dic_fc_label': bg_dic_fc_label})
sio.savemat("tg_dic.mat", {'tg_dic': tg_dic})
tg_dic_label = class_order_data_index[tg_sort_index[0:target_dic_num]]
sio.savemat("tg_dic_label.mat", {'tg_dic_label': tg_dic_label})
return data2d, bg_dic, tg_dic, bg_dic_ac_label, tg_dic_label
def find_steady_states(dataframe,
min_n_samples=2,
stateThreshold=15,
noise_level=70):
"""
Finds steady states given a DataFrame of power
Parameters
----------
dataframe: pd.DataFrame with DateTimeIndex
min_n_samples(int): number of samples to consider constituting a
steady state.
stateThreshold: maximum difference between highest and lowest
value in steady state.
noise_level: the level used to define significant
appliances, transitions below this level will be ignored.
See Hart 1985. p27.
Returns
-------
"""
# Tells whether we have both real and reactive power or only real power
num_measurements = len(dataframe.columns)
estimatedSteadyPower = np.array([0] * num_measurements)
lastSteadyPower = np.array([0] * num_measurements)
previousMeasurement = np.array([0] * num_measurements)
# These flags store state of power
instantaneousChange = False # power changing this second
ongoingChange = False # power change in progress over multiple seconds
index_transitions = [] # Indices to use in returned Dataframe
index_steadystates = []
transitions = [] # holds information on transitions
steadyStates = [] # steadyStates to store in returned Dataframe
N = 0 # N stores the number of samples in state
time = dataframe.iloc[0].name # first state starts at beginning
# Iterate over the rows performing algorithm
print("Finding Edges, please wait ...", end="\n")
sys.stdout.flush()
for row in dataframe.itertuples():
# test if either active or reactive moved more than threshold
# http://stackoverflow.com/questions/17418108/elegant-way-to-perform-tuple-arithmetic
# http://stackoverflow.com/questions/13168943/expression-for-elements-greater-than-x-and-less-than-y-in-python-all-in-one-ret
# Step 2: this does the threshold test and then we sum the boolean
# array.
thisMeasurement = row[1:3]
# logging.debug('The current measurement is: %s' % (thisMeasurement,))
# logging.debug('The previous measurement is: %s' %
# (previousMeasurement,))
stateChange = np.fabs(np.subtract(thisMeasurement,
previousMeasurement))
# logging.debug('The State Change is: %s' % (stateChange,))
if np.sum(stateChange > stateThreshold):
instantaneousChange = True
else:
instantaneousChange = False
# Step 3: Identify if transition is just starting, if so, process it
if (instantaneousChange and (not ongoingChange)):
# Calculate transition size
lastTransition = np.subtract(estimatedSteadyPower, lastSteadyPower)
# logging.debug('The steady state transition is: %s' %
# (lastTransition,))
# Sum Boolean array to verify if transition is above noise level
if np.sum(np.fabs(lastTransition) > noise_level):
# 3A, C: if so add the index of the transition start and the
# power information
# Avoid outputting first transition from zero
index_transitions.append(time)
# logging.debug('The current row time is: %s' % (time))
transitions.append(lastTransition)
# I think we want this, though not specifically in Hart's algo notes
# We don't want to append a steady state if it's less than min samples in length.
# if N > min_n_samples:
index_steadystates.append(time)
# logging.debug('The ''time'' stored is: %s' % (time))
# last states steady power
steadyStates.append(estimatedSteadyPower)
# 3B
lastSteadyPower = estimatedSteadyPower
# 3C
time = row[0]
# Step 4: if a new steady state is starting, zero counter
if instantaneousChange:
N = 0
# Hart step 5: update our estimate for steady state's energy
estimatedSteadyPower = np.divide(
np.add(np.multiply(N, estimatedSteadyPower), thisMeasurement),
(N + 1))
# logging.debug('The steady power estimate is: %s' %
# (estimatedSteadyPower,))
# Step 6: increment counter
N = N + 1
# Step 7
ongoingChange = instantaneousChange
# Step 8
previousMeasurement = thisMeasurement
print("Edge detection complete.")
print("Creating transition frame ...")
sys.stdout.flush()
cols_transition = {
1: ['active transition'],
2: ['active transition', 'reactive transition']
}
cols_steady = {
1: ['active average'],
2: ['active average', 'reactive average']
}
if len(index_transitions) == 0:
# No events
return pd.DataFrame(), pd.DataFrame()
else:
transitions = pd.DataFrame(data=transitions,
index=index_transitions,
columns=cols_transition[num_measurements])
print("Transition frame created.")
print("Creating states frame ...")
sys.stdout.flush()
steadyStates = pd.DataFrame(data=steadyStates,
index=index_steadystates,
columns=cols_steady[num_measurements])
print("States frame created.")
print("Finished.")
return steadyStates, transitions
def linear_regression(X, y, add_intercept=True, weights=None, coef_only=False,
alpha=0.05, as_dataframe=True, remove_na=False,
relimp=False):
"""(Multiple) Linear regression.
Parameters
----------
X : array_like
Predictor(s), of shape *(n_samples, n_features)* or *(n_samples)*.
y : array_like
Dependent variable, of shape *(n_samples)*.
add_intercept : bool
If False, assume that the data are already centered. If True, add a
constant term to the model. In this case, the first value in the
output dict is the intercept of the model.
.. note:: It is generally recommanded to include a constant term
(intercept) to the model to limit the bias and force the residual
mean to equal zero. Note that intercept coefficient and p-values
are however rarely meaningful.
weights : array_like
An optional vector of sample weights to be used in the fitting
process, of shape *(n_samples)*. Missing or negative weights are not
allowed. If not null, a weighted least squares is calculated.
.. versionadded:: 0.3.5
coef_only : bool
If True, return only the regression coefficients.
alpha : float
Alpha value used for the confidence intervals.
:math:`\\text{CI} = [\\alpha / 2 ; 1 - \\alpha / 2]`
as_dataframe : bool
If True, returns a pandas DataFrame. If False, returns a dictionnary.
remove_na : bool
If True, apply a listwise deletion of missing values (i.e. the entire
row is removed). Default is False, which will raise an error if missing
values are present in either the predictor(s) or dependent
variable.
relimp : bool
If True, returns the relative importance (= contribution) of
predictors. This is irrelevant when the predictors are uncorrelated:
the total :math:`R^2` of the model is simply the sum of each univariate
regression :math:`R^2`-values. However, this does not apply when
predictors are correlated. Instead, the total :math:`R^2` of the model
is partitioned by averaging over all combinations of predictors,
as done in the `relaimpo
<https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf>`_
R package (``calc.relimp(type="lmg")``).
.. warning:: The computation time roughly doubles for each
additional predictor and therefore this can be extremely slow for
models with more than 12-15 predictors.
.. versionadded:: 0.3.0
Returns
-------
stats : :py:class:`pandas.DataFrame` or dict
Linear regression summary:
* ``'names'``: name of variable(s) in the model (e.g. x1, x2...)
* ``'coef'``: regression coefficients
* ``'se'``: standard errors
* ``'T'``: T-values
* ``'pval'``: p-values
* ``'r2'``: coefficient of determination (:math:`R^2`)
* ``'adj_r2'``: adjusted :math:`R^2`
* ``'CI[2.5%]'``: lower confidence intervals
* ``'CI[97.5%]'``: upper confidence intervals
* ``'relimp'``: relative contribution of each predictor to the final\
:math:`R^2` (only if ``relimp=True``).
* ``'relimp_perc'``: percent relative contribution
In addition, the output dataframe comes with hidden attributes such as
the residuals, and degrees of freedom of the model and residuals, which
can be accessed as follow, respectively:
>>> lm = pg.linear_regression() # doctest: +SKIP
>>> lm.residuals_, lm.df_model_, lm.df_resid_ # doctest: +SKIP
Note that to follow scikit-learn convention, these hidden atributes end
with an "_". When ``as_dataframe=False`` however, these attributes
are no longer hidden and can be accessed as any other keys in the
output dictionnary:
>>> lm = pg.linear_regression() # doctest: +SKIP
>>> lm['residuals'], lm['df_model'], lm['df_resid'] # doctest: +SKIP
See also
--------
logistic_regression, mediation_analysis, corr
Notes
-----
The :math:`\\beta` coefficients are estimated using an ordinary least
squares (OLS) regression, as implemented in the
:py:func:`scipy.linalg.lstsq` function. The OLS method minimizes
the sum of squared residuals, and leads to a closed-form expression for
the estimated :math:`\\beta`:
.. math:: \\hat{\\beta} = (X^TX)^{-1} X^Ty
It is generally recommanded to include a constant term (intercept) to the
model to limit the bias and force the residual mean to equal zero.
Note that intercept coefficient and p-values are however rarely meaningful.
The standard error of the estimates is a measure of the accuracy of the
prediction defined as:
.. math:: \\sigma = \\sqrt{\\text{MSE} \\cdot (X^TX)^{-1}}
where :math:`\\text{MSE}` is the mean squared error,
.. math::
\\text{MSE} = \\frac{SS_{\\text{resid}}}{n - p - 1}
= \\frac{\\sum{(\\text{true} - \\text{pred})^2}}{n - p - 1}
:math:`p` is the total number of predictor variables in the model
(excluding the intercept) and :math:`n` is the sample size.
Using the :math:`\\beta` coefficients and the standard errors,
the T-values can be obtained:
.. math:: T = \\frac{\\beta}{\\sigma}
and the p-values approximated using a T-distribution with
:math:`n - p - 1` degrees of freedom.
The coefficient of determination (:math:`R^2`) is defined as:
.. math:: R^2 = 1 - (\\frac{SS_{\\text{resid}}}{SS_{\\text{total}}})
The adjusted :math:`R^2` is defined as:
.. math:: \\overline{R}^2 = 1 - (1 - R^2) \\frac{n - 1}{n - p - 1}
The relative importance (``relimp``) column is a partitioning of the
total :math:`R^2` of the model into individual :math:`R^2` contribution.
This is calculated by taking the average over average contributions in
models of different sizes. For more details, please refer to
`Groemping et al. 2006 <http://dx.doi.org/10.18637/jss.v017.i01>`_
and the R package `relaimpo
<https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf>`_.
Note that Pingouin will automatically remove any duplicate columns
from :math:`X`, as well as any column with only one unique value
(constant), excluding the intercept.
Results have been compared against sklearn, R, statsmodels and JASP.
Examples
--------
1. Simple linear regression
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> mean, cov, n = [4, 6], [[1, 0.5], [0.5, 1]], 30
>>> x, y = np.random.multivariate_normal(mean, cov, n).T
>>> lm = pg.linear_regression(x, y)
>>> lm.round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 4.40 0.54 8.16 0.00 0.24 0.21 3.29 5.50
1 x1 0.39 0.13 2.99 0.01 0.24 0.21 0.12 0.67
2. Multiple linear regression
>>> np.random.seed(42)
>>> z = np.random.normal(size=n)
>>> X = np.column_stack((x, z))
>>> lm = pg.linear_regression(X, y)
>>> print(lm['coef'].to_numpy())
[4.54123324 0.36628301 0.17709451]
3. Get the residuals
>>> np.round(lm.residuals_, 2)
array([ 1.18, -1.17, 1.32, 0.76, -1.25, 0.34, -1.54, -0.2 , 0.36,
-0.39, 0.69, 1.39, 0.2 , -1.14, -0.21, -1.68, 0.67, -0.69,
0.62, 0.92, -1. , 0.64, -0.21, -0.78, 1.08, -0.03, -1.3 ,
0.64, 0.81, -0.04])
4. Using a Pandas DataFrame
>>> import pandas as pd
>>> df = pd.DataFrame({'x': x, 'y': y, 'z': z})
>>> lm = pg.linear_regression(df[['x', 'z']], df['y'])
>>> print(lm['coef'].to_numpy())
[4.54123324 0.36628301 0.17709451]
5. No intercept and return coef only
>>> pg.linear_regression(X, y, add_intercept=False, coef_only=True)
array([ 1.40935593, -0.2916508 ])
6. Return a dictionnary instead of a DataFrame
>>> lm_dict = linear_regression(X, y, as_dataframe=False)
7. Remove missing values
>>> X[4, 1] = np.nan
>>> y[7] = np.nan
>>> pg.linear_regression(X, y, remove_na=True, coef_only=True)
array([4.64069731, 0.35455398, 0.1888135 ])
8. Get the relative importance of predictors
>>> lm = pg.linear_regression(X, y, remove_na=True, relimp=True)
>>> lm[['names', 'relimp', 'relimp_perc']]
names relimp relimp_perc
0 Intercept NaN NaN
1 x1 0.217265 82.202201
2 x2 0.047041 17.797799
The ``relimp`` column is a partitioning of the total :math:`R^2` of the
model into individual contribution. Therefore, it sums to the :math:`R^2`
of the full model. The ``relimp_perc`` is normalized to sum to 100%. See
`Groemping 2006 <https://www.jstatsoft.org/article/view/v017i01>`_
for more details.
>>> lm[['relimp', 'relimp_perc']].sum()
relimp 0.264305
relimp_perc 100.000000
dtype: float64
9. Weighted linear regression
>>> X = [1, 2, 3, 4, 5, 6]
>>> y = [10, 22, 11, 13, 13, 16]
>>> w = [1, 0.1, 1, 1, 0.5, 1] # Array of weights. Must be >= 0.
>>> lm = pg.linear_regression(X, y, weights=w)
>>> lm.round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 9.00 2.03 4.42 0.01 0.51 0.39 3.35 14.64
1 x1 1.04 0.50 2.06 0.11 0.51 0.39 -0.36 2.44
"""
# Extract names if X is a Dataframe or Series
if isinstance(X, pd.DataFrame):
names = X.keys().tolist()
elif isinstance(X, pd.Series):
names = [X.name]
else:
names = []
# Convert input to numpy array
X = np.asarray(X)
y = np.asarray(y)
assert y.ndim == 1, 'y must be one-dimensional.'
assert 0 < alpha < 1
if X.ndim == 1:
# Convert to (n_samples, n_features) shape
X = X[..., np.newaxis]
# Check for NaN / Inf
if remove_na:
X, y = rm_na(X, y[..., np.newaxis], paired=True, axis='rows')
y = np.squeeze(y)
y_gd = np.isfinite(y).all()
X_gd = np.isfinite(X).all()
assert y_gd, ("Target (y) contains NaN or Inf. Please remove them "
"manually or use remove_na=True.")
assert X_gd, ("Predictors (X) contain NaN or Inf. Please remove them "
"manually or use remove_na=True.")
# Check that X and y have same length
assert y.shape[0] == X.shape[0], 'X and y must have same number of samples'
if not names:
names = ['x' + str(i + 1) for i in range(X.shape[1])]
if add_intercept:
# Add intercept
X = np.column_stack((np.ones(X.shape[0]), X))
names.insert(0, "Intercept")
# FINAL CHECKS BEFORE RUNNING LEAST SQUARES REGRESSION
# 1. Let's remove column(s) with only zero, otherwise the regression fails
n_nonzero = np.count_nonzero(X, axis=0)
idx_zero = np.flatnonzero(n_nonzero == 0) # Find columns that are only 0
if len(idx_zero):
X = np.delete(X, idx_zero, 1)
names = np.delete(names, idx_zero)
# 2. We also want to make sure that there is no more than one constant
# column (= intercept), otherwise the regression fails
# This is equivalent, but much faster, to pd.DataFrame(X).nunique()
idx_unique = np.where(np.all(X == X[0, :], axis=0))[0]
if len(idx_unique) > 1:
# We remove all but the first "Intercept" column.
X = np.delete(X, idx_unique[1:], 1)
names = np.delete(names, idx_unique[1:])
# Is there a constant in our predictor matrix? Useful for dof and R^2.
constant = 1 if len(idx_unique) > 0 else 0
# 3. Finally, we want to remove duplicate columns
if X.shape[1] > 1:
idx_duplicate = []
for pair in itertools.combinations(range(X.shape[1]), 2):
if np.array_equal(X[:, pair[0]], X[:, pair[1]]):
idx_duplicate.append(pair[1])
if len(idx_duplicate):
X = np.delete(X, idx_duplicate, 1)
names = np.delete(names, idx_duplicate)
# 4. Check that we have enough samples / features
n, p = X.shape[0], X.shape[1]
assert n >= 3, 'At least three valid samples are required in X.'
assert p >= 1, 'X must have at least one valid column.'
# 5. Handle weights
if weights is not None:
if relimp:
raise ValueError("relimp = True is not supported when using "
"weights.")
w = np.asarray(weights)
assert w.ndim == 1, 'weights must be a 1D array.'
assert w.size == n, 'weights must be of shape n_samples.'
assert not np.isnan(w).any(), 'Missing weights are not accepted.'
assert not (w < 0).any(), 'Negative weights are not accepted.'
# Do not count weights == 0 in dof
# This gives similar results as R lm() but different from statsmodels
n = np.count_nonzero(w)
# Rescale (whitening)
wts = np.diag(np.sqrt(w))
Xw = wts @ X
yw = wts @ y
else:
# Set all weights to one, [1, 1, 1, ...]
w = np.ones(n)
Xw = X
yw = y
# FIT (WEIGHTED) LEAST SQUARES REGRESSION USING SCIPY.LINALG.LSTST
coef, ss_res, rank, _ = lstsq(Xw, yw)
if coef_only:
return coef
# Degrees of freedom
df_model = rank - constant
df_resid = n - p
# Calculate predicted values and (weighted) residuals
pred = Xw @ coef
resid = yw - pred
# ss_res = (resid ** 2).sum()
# Calculate total (weighted) sums of squares and R^2
ss_tot = yw @ yw
ss_wtot = np.sum(w * (y - np.average(y, weights=w))**2)
if constant:
r2 = 1 - ss_res / ss_wtot
else:
r2 = 1 - ss_res / ss_tot
adj_r2 = 1 - (1 - r2) * (n - constant) / df_resid
# Compute mean squared error, variance and SE
mse = ss_res / df_resid
beta_var = mse * (np.linalg.pinv(Xw.T @ Xw).diagonal())
beta_se = np.sqrt(beta_var)
# Compute T and p-values
T = coef / beta_se
pval = 2 * t.sf(np.fabs(T), df_resid)
# Compute confidence intervals
crit = t.ppf(1 - alpha / 2, df_resid)
marg_error = crit * beta_se
ll = coef - marg_error
ul = coef + marg_error
# Rename CI
ll_name = 'CI[%.1f%%]' % (100 * alpha / 2)
ul_name = 'CI[%.1f%%]' % (100 * (1 - alpha / 2))
# Create dict
stats = {'names': names, 'coef': coef, 'se': beta_se, 'T': T,
'pval': pval, 'r2': r2, 'adj_r2': adj_r2, ll_name: ll,
ul_name: ul}
# Relative importance
if relimp:
data = pd.concat([pd.DataFrame(y, columns=['y']),
pd.DataFrame(X, columns=names)], sort=False, axis=1)
if 'Intercept' in names:
# Intercept is the first column
reli = _relimp(data.drop(columns=['Intercept']).cov())
reli['names'] = ['Intercept'] + reli['names']
reli['relimp'] = np.insert(reli['relimp'], 0, np.nan)
reli['relimp_perc'] = np.insert(reli['relimp_perc'], 0, np.nan)
else:
reli = _relimp(data.cov())
stats.update(reli)
if as_dataframe:
stats = pd.DataFrame(stats)
stats.df_model_ = df_model
stats.df_resid_ = df_resid
stats.residuals_ = 0 # Trick to avoid Pandas warning
stats.residuals_ = resid # Residuals is a hidden attribute
else:
stats['df_model'] = df_model
stats['df_resid'] = df_resid
stats['residuals'] = resid
return stats
def fidnet_doRecon2D(model_weights,
file,
ss_file,
max_points,
outfile,
f1180='y',
shift='n'):
if f1180.lower() in ['y', 'n']:
if f1180.lower() == 'y':
f1180 = True
else:
f1180 = False
if shift.lower() in ['y', 'n']:
if shift.lower() == 'y':
shift = True
else:
shift = False
dic, data = ng.pipe.read(file)
model = build_model()
model.load_weights(model_weights)
ss = load_ss(ss_file, max_points)
ind_points = data.shape[0] # sampled points in indirect dim
dir_points = data.shape[1] # sampled points in direct dim
if ind_points > 512:
print('the input spectrum contains too many sampled points')
print('the network can have a maximum of 256 complex points in the')
print('reconstructed spectra. Please reduce the size of the input')
print('aborting now...')
sys.exit()
if ss.shape[0] == ind_points // 2:
print(
'number of recorded points in indirect dimension matches sampling schedule'
)
print('proceeding with reconstruction...')
else:
print(
'there is a mis-match between the sampling schedule and number of recorded points'
)
print(
'in the indirect dimension. Please check the sampling schedule or your input spectrum'
)
print('may need to be transposed')
print('aborting now...')
sys.exit()
if max_points > 256:
print(
'the maximum size of the final spectrum is 256 complex points in')
print(
'the indirect dimension. The output will be truncated at this point'
)
max_points = 256
data = expand_data(data, ss, max_points, dir_points)
data = tf.convert_to_tensor(data)
dl_dic = make_dl_dic(dic, max_points)
shape = tf.shape(data).numpy()
max_val = tf.reduce_max(data)
data = data / max_val
Hpoints = shape[1]
Npoints = shape[0]
padding_2 = [[0, 512 - tf.shape(data)[0]], [0, 0]]
data_samp = tf.pad(data, padding_2, 'Constant', constant_values=0.0)
data_samp = tf.transpose(data_samp)
padding_recon = [[3, 3], [0, 0]]
data_samp = tf.pad(data_samp,
padding_recon,
'Constant',
constant_values=0.0)
scale = np.array(
[np.max(np.fabs(data_samp[i:i + 4, :])) for i in range((Hpoints + 3))])
sampy = np.zeros((scale.shape[0], 4, tf.shape(data_samp)[1]))
for i in range(scale.shape[0]):
sampy[i, :, :] = data_samp[i:i + 4, :]
samp_av = tf.convert_to_tensor(sampy)
samp_av = tf.transpose(samp_av, perm=[1, 2, 0])
samp_av = samp_av / scale
samp_av = tf.transpose(samp_av, perm=[2, 1, 0])
samp_av = tf.expand_dims(samp_av, axis=3)
data = tf.expand_dims(data, axis=0)
res = model.predict(samp_av)
res = tf.convert_to_tensor(res[0])
res = rescale_dat(res, scale)
res_keep = copy.deepcopy(res)
res = get_average_results(res, Hpoints)
res = res[:, :Npoints, :, 0]
res_ft = ft_second(res,
npoints1=Hpoints,
npoints2=Npoints,
f1180=f1180,
shift=shift)
data_ft = ft_second(data,
npoints1=Hpoints,
npoints2=Npoints,
f1180=f1180,
shift=shift)
data_ft = data_ft / tf.reduce_max(data_ft)
res_ft = res_ft / tf.reduce_max(res_ft)
ng.pipe.write(outfile, dl_dic, res.numpy()[0], overwrite=True)
ax1 = plt.subplot(2, 2, 1)
ax2 = plt.subplot(2, 2, 3)
ax3 = plt.subplot(2, 2, 2)
ax4 = plt.subplot(2, 2, 4)
plot_contour(ax1, data)
plot_contour(ax2, data_ft, invert=True)
plot_contour(ax3, res)
plot_contour(ax4, res_ft, invert=True)
plt.show()
get_ind_spectra(res_keep,
res_ft,
Hpoints,
Npoints,
dl_dic,
f1180=f1180,
shift=shift)
plt.ylabel('HSE ' r'$T_{m}$')
axHistx = plt.axes(rect_histx)
axHisty = plt.axes(rect_histy)
# no labels
axHistx.xaxis.set_major_formatter(nullfmt)
axHisty.yaxis.set_major_formatter(nullfmt)
# the scatter plot:
axScatter.scatter(x, y, s=6, facecolors='none', edgecolors='black', alpha=0.1)
# now determine nice limits by hand:
binwidth = 5
#binwidth = 0.25
xymax = np.max([np.max(np.fabs(x)), np.max(np.fabs(y))])
lim = (int(xymax / binwidth) + 1) * binwidth
axScatter.set_xlim((-lim, lim))
axScatter.set_ylim((-lim, lim))
#axScatter.set_xlim((min_Tm-10, max_Tm+10))
#axScatter.set_ylim((min_Tm-10, max_Tm+10))
bins = np.arange(-lim, lim + binwidth, binwidth)
#print bins
# histogram
axHistx.hist(x, bins=bins, color='grey')
axHisty.hist(y, bins=bins, orientation='horizontal', color='grey')
def logistic_regression(X, y, coef_only=False, alpha=0.05,
as_dataframe=True, remove_na=False, **kwargs):
"""(Multiple) Binary logistic regression.
Parameters
----------
X : np.array or list
Predictor(s). Shape = (n_samples, n_features) or (n_samples,).
y : np.array or list
Dependent variable. Shape = (n_samples).
``y`` must be binary, i.e. only contains 0 or 1. Multinomial logistic
regression is not supported.
coef_only : bool
If True, return only the regression coefficients.
alpha : float
Alpha value used for the confidence intervals.
:math:`\\text{CI} = [\\alpha / 2 ; 1 - \\alpha / 2]`
as_dataframe : bool
If True, returns a pandas DataFrame. If False, returns a dictionnary.
remove_na : bool
If True, apply a listwise deletion of missing values (i.e. the entire
row is removed). Default is False, which will raise an error if missing
values are present in either the predictor(s) or dependent
variable.
**kwargs : optional
Optional arguments passed to
:py:class:`sklearn.linear_model.LogisticRegression` (see Notes).
Returns
-------
stats : :py:class:`pandas.DataFrame` or dict
Logistic regression summary:
* ``'names'``: name of variable(s) in the model (e.g. x1, x2...)
* ``'coef'``: regression coefficients (log-odds)
* ``'se'``: standard error
* ``'z'``: z-scores
* ``'pval'``: two-tailed p-values
* ``'CI[2.5%]'``: lower confidence interval
* ``'CI[97.5%]'``: upper confidence interval
See also
--------
linear_regression
Notes
-----
This is a wrapper around the
:py:class:`sklearn.linear_model.LogisticRegression` class. Importantly,
Pingouin automatically disables the L2 regularization applied by
scikit-learn. This can be modified by changing the ``penalty`` argument.
The logistic regression assumes that the log-odds (the logarithm of the
odds) for the value labeled "1" in the response variable is a linear
combination of the predictor variables. The log-odds are given by the
`logit <https://en.wikipedia.org/wiki/Logit>`_ function,
which map a probability :math:`p` of the response variable being "1"
from :math:`[0, 1)` to :math:`(-\\infty, +\\infty)`.
.. math:: \\text{logit}(p) = \\ln \\frac{p}{1 - p} = \\beta_0 + \\beta X
The odds of the response variable being "1" can be obtained by
exponentiating the log-odds:
.. math:: \\frac{p}{1 - p} = e^{\\beta_0 + \\beta X}
and the probability of the response variable being "1" is given by:
.. math:: p = \\frac{1}{1 + e^{-(\\beta_0 + \\beta X})}
Note that the above function that converts log-odds to probability is
called the `logistic function
<https://en.wikipedia.org/wiki/Logistic_function>`_.
The first coefficient is always the constant term (intercept) of
the model. Scikit-learn will automatically add the intercept
to your predictor(s) matrix, therefore, :math:`X` should not include a
constant term. Pingouin will remove any constant term (e.g column with only
one unique value), or duplicate columns from :math:`X`.
The calculation of the p-values and confidence interval is adapted from a
code found at
https://gist.github.com/rspeare/77061e6e317896be29c6de9a85db301d
Results have been compared against statsmodels, R, and JASP.
Examples
--------
1. Simple binary logistic regression
>>> import numpy as np
>>> from pingouin import logistic_regression
>>> np.random.seed(123)
>>> x = np.random.normal(size=30)
>>> y = np.random.randint(0, 2, size=30)
>>> lom = logistic_regression(x, y)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -0.27 0.37 -0.74 0.46 -1.00 0.45
1 x1 0.07 0.32 0.21 0.84 -0.55 0.68
2. Multiple binary logistic regression
>>> np.random.seed(42)
>>> z = np.random.normal(size=30)
>>> X = np.column_stack((x, z))
>>> lom = logistic_regression(X, y)
>>> print(lom['coef'].to_numpy())
[-0.36736745 -0.04374684 -0.47829392]
3. Using a Pandas DataFrame
>>> import pandas as pd
>>> df = pd.DataFrame({'x': x, 'y': y, 'z': z})
>>> lom = logistic_regression(df[['x', 'z']], df['y'])
>>> print(lom['coef'].to_numpy())
[-0.36736745 -0.04374684 -0.47829392]
4. Return only the coefficients
>>> logistic_regression(X, y, coef_only=True)
array([-0.36736745, -0.04374684, -0.47829392])
5. Passing custom parameters to sklearn
>>> lom = logistic_regression(X, y, solver='sag', max_iter=10000,
... random_state=42)
>>> print(lom['coef'].to_numpy())
[-0.36751796 -0.04367056 -0.47841908]
**How to interpret the log-odds coefficients?**
We'll use the `Wikipedia example
<https://en.wikipedia.org/wiki/Logistic_regression#Probability_of_passing_an_exam_versus_hours_of_study>`_
of the probability of passing an exam
versus the hours of study:
*A group of 20 students spends between 0 and 6 hours studying for an
exam. How does the number of hours spent studying affect the
probability of the student passing the exam?*
>>> # First, let's create the dataframe
>>> Hours = [0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 1.75, 2.00, 2.25, 2.50,
... 2.75, 3.00, 3.25, 3.50, 4.00, 4.25, 4.50, 4.75, 5.00, 5.50]
>>> Pass = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]
>>> df = pd.DataFrame({'HoursStudy': Hours, 'PassExam': Pass})
>>> # And then run the logistic regression
>>> lr = logistic_regression(df['HoursStudy'], df['PassExam']).round(3)
>>> lr
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -4.078 1.761 -2.316 0.021 -7.529 -0.626
1 HoursStudy 1.505 0.629 2.393 0.017 0.272 2.737
The ``Intercept`` coefficient (-4.078) is the log-odds of ``PassExam=1``
when ``HoursStudy=0``. The odds ratio can be obtained by exponentiating
the log-odds:
>>> np.exp(-4.078)
0.016941314421496552
i.e. :math:`0.017:1`. Conversely the odds of failing the exam are
:math:`(1/0.017) \\approx 59:1`.
The probability can then be obtained with the following equation
.. math:: p = \\frac{1}{1 + e^{-(-4.078 + 0 * 1.505)}}
>>> 1 / (1 + np.exp(-(-4.078)))
0.016659087580814722
The ``HoursStudy`` coefficient (1.505) means that for each additional hour
of study, the log-odds of passing the exam increase by 1.505, and the odds
are multipled by :math:`e^{1.505} \\approx 4.50`.
For example, a student who studies 2 hours has a probability of passing
the exam of 25%:
>>> 1 / (1 + np.exp(-(-4.078 + 2 * 1.505)))
0.2557836148964987
The table below shows the probability of passing the exam for several
values of ``HoursStudy``:
+----------------+----------+----------------+------------------+
| Hours of Study | Log-odds | Odds | Probability |
+================+==========+================+==================+
| 0 | −4.08 | 0.017 ≈ 1:59 | 0.017 |
+----------------+----------+----------------+------------------+
| 1 | −2.57 | 0.076 ≈ 1:13 | 0.07 |
+----------------+----------+----------------+------------------+
| 2 | −1.07 | 0.34 ≈ 1:3 | 0.26 |
+----------------+----------+----------------+------------------+
| 3 | 0.44 | 1.55 | 0.61 |
+----------------+----------+----------------+------------------+
| 4 | 1.94 | 6.96 | 0.87 |
+----------------+----------+----------------+------------------+
| 5 | 3.45 | 31.4 | 0.97 |
+----------------+----------+----------------+------------------+
| 6 | 4.96 | 141.4 | 0.99 |
+----------------+----------+----------------+------------------+
"""
# Check that sklearn is installed
from pingouin.utils import _is_sklearn_installed
_is_sklearn_installed(raise_error=True)
from sklearn.linear_model import LogisticRegression
# Extract names if X is a Dataframe or Series
if isinstance(X, pd.DataFrame):
names = X.keys().tolist()
elif isinstance(X, pd.Series):
names = [X.name]
else:
names = []
# Convert to numpy array
X = np.asarray(X)
y = np.asarray(y)
assert y.ndim == 1, 'y must be one-dimensional.'
assert 0 < alpha < 1, 'alpha must be between 0 and 1.'
# Add axis if only one-dimensional array
if X.ndim == 1:
X = X[..., np.newaxis]
# Check for NaN / Inf
if remove_na:
X, y = rm_na(X, y[..., np.newaxis], paired=True, axis='rows')
y = np.squeeze(y)
y_gd = np.isfinite(y).all()
X_gd = np.isfinite(X).all()
assert y_gd, ("Target (y) contains NaN or Inf. Please remove them "
"manually or use remove_na=True.")
assert X_gd, ("Predictors (X) contain NaN or Inf. Please remove them "
"manually or use remove_na=True.")
# Check that X and y have same length
assert y.shape[0] == X.shape[0], 'X and y must have same number of samples'
# Check that y is binary
if np.unique(y).size != 2:
raise ValueError('Dependent variable must be binary.')
if not names:
names = ['x' + str(i + 1) for i in range(X.shape[1])]
# We also want to make sure that there is no column
# with only one unique value, otherwise the regression fails
# This is equivalent, but much faster, to pd.DataFrame(X).nunique()
idx_unique = np.where(np.all(X == X[0, :], axis=0))[0]
if len(idx_unique):
X = np.delete(X, idx_unique, 1)
names = np.delete(names, idx_unique).tolist()
# Finally, we want to remove duplicate columns
if X.shape[1] > 1:
idx_duplicate = []
for pair in itertools.combinations(range(X.shape[1]), 2):
if np.array_equal(X[:, pair[0]], X[:, pair[1]]):
idx_duplicate.append(pair[1])
if len(idx_duplicate):
X = np.delete(X, idx_duplicate, 1)
names = np.delete(names, idx_duplicate).tolist()
# Initialize and fit
if 'solver' not in kwargs:
kwargs['solver'] = 'lbfgs'
if 'multi_class' not in kwargs:
kwargs['multi_class'] = 'auto'
if 'penalty' not in kwargs:
kwargs['penalty'] = 'none'
lom = LogisticRegression(**kwargs)
lom.fit(X, y)
coef = np.append(lom.intercept_, lom.coef_)
if coef_only:
return coef
# Design matrix -- add intercept
names.insert(0, "Intercept")
X_design = np.column_stack((np.ones(X.shape[0]), X))
n, p = X_design.shape
# Fisher Information Matrix
denom = (2 * (1 + np.cosh(lom.decision_function(X))))
denom = np.tile(denom, (p, 1)).T
fim = (X_design / denom).T @ X_design
crao = np.linalg.pinv(fim)
# Standard error and Z-scores
se = np.sqrt(np.diag(crao))
z_scores = coef / se
# Two-tailed p-values
pval = 2 * norm.sf(np.fabs(z_scores))
# Confidence intervals
crit = norm.ppf(1 - alpha / 2)
ll = coef - crit * se
ul = coef + crit * se
# Rename CI
ll_name = 'CI[%.1f%%]' % (100 * alpha / 2)
ul_name = 'CI[%.1f%%]' % (100 * (1 - alpha / 2))
# Create dict
stats = {'names': names, 'coef': coef, 'se': se, 'z': z_scores,
'pval': pval, ll_name: ll, ul_name: ul}
if as_dataframe:
return pd.DataFrame(stats)
else:
return stats
class RandomLayer(BaseRandomLayer):
"""RandomLayer is a transformer that creates a feature mapping of the
inputs that corresponds to a layer of hidden units with randomly
generated components.
The transformed values are a specified function of input activations
that are a weighted combination of dot product (multilayer perceptron)
and distance (rbf) activations:
input_activation = alpha * mlp_activation + (1-alpha) * rbf_activation
mlp_activation(x) = dot(x, weights) + bias
rbf_activation(x) = rbf_width * ||x - center||/radius
alpha and rbf_width are specified by the user
weights and biases are taken from normal distribution of
mean 0 and sd of 1
centers are taken uniformly from the bounding hyperrectangle
of the inputs, and radii are max(||x-c||)/sqrt(n_centers*2)
The input activation is transformed by a transfer function that defaults
to numpy.tanh if not specified, but can be any callable that returns an
array of the same shape as its argument (the input activation array, of
shape [n_samples, n_hidden]). Functions provided are 'sine', 'tanh',
'tribas', 'inv_tribas', 'sigmoid', 'hardlim', 'softlim', 'gaussian',
'multiquadric', or 'inv_multiquadric'.
Parameters
----------
`n_hidden` : int, optional (default=20)
Number of units to generate
`alpha` : float, optional (default=0.5)
Mixing coefficient for distance and dot product input activations:
activation = alpha*mlp_activation + (1-alpha)*rbf_width*rbf_activation
`rbf_width` : float, optional (default=1.0)
multiplier on rbf_activation
`user_components`: dictionary, optional (default=None)
dictionary containing values for components that woud otherwise be
randomly generated. Valid key/value pairs are as follows:
'radii' : array-like of shape [n_hidden]
'centers': array-like of shape [n_hidden, n_features]
'biases' : array-like of shape [n_hidden]
'weights': array-like of shape [n_features, n_hidden]
`activation_func` : {callable, string} optional (default='tanh')
Function used to transform input activation
It must be one of 'tanh', 'sine', 'tribas', 'inv_tribas',
'sigmoid', 'hardlim', 'softlim', 'gaussian', 'multiquadric',
'inv_multiquadric' or a callable. If None is given, 'tanh'
will be used.
If a callable is given, it will be used to compute the activations.
`activation_args` : dictionary, optional (default=None)
Supplies keyword arguments for a callable activation_func
`random_state` : int, RandomState instance or None (default=None)
Control the pseudo random number generator used to generate the
hidden unit weights at fit time.
Attributes
----------
`input_activations_` : numpy array of shape [n_samples, n_hidden]
Array containing dot(x, hidden_weights) + bias for all samples
`components_` : dictionary containing two keys:
`bias_weights_` : numpy array of shape [n_hidden]
`hidden_weights_` : numpy array of shape [n_features, n_hidden]
See Also
--------
"""
# triangular activation function
_tribas = (lambda x: np.clip(1.0 - np.fabs(x), 0.0, 1.0))
# inverse triangular activation function
_inv_tribas = (lambda x: np.clip(np.fabs(x), 0.0, 1.0))
# sigmoid activation function
_sigmoid = (lambda x: 1.0 / (1.0 + np.exp(-x)))
# hard limit activation function
_hardlim = (lambda x: np.array(x > 0.0, dtype=float))
_softlim = (lambda x: np.clip(x, 0.0, 1.0))
# gaussian RBF
_gaussian = (lambda x: np.exp(-pow(x, 2.0)))
# multiquadric RBF
_multiquadric = (lambda x: np.sqrt(1.0 + pow(x, 2.0)))
# inverse multiquadric RBF
_inv_multiquadric = (lambda x: 1.0 / (np.sqrt(1.0 + pow(x, 2.0))))
# internal activation function table
_internal_activation_funcs = {
'sine': np.sin,
'tanh': np.tanh,
'tribas': _tribas,
'inv_tribas': _inv_tribas,
'sigmoid': _sigmoid,
'softlim': _softlim,
'hardlim': _hardlim,
'gaussian': _gaussian,
'multiquadric': _multiquadric,
'inv_multiquadric': _inv_multiquadric,
}
def __init__(self,
n_hidden=20,
alpha=0.5,
random_state=None,
activation_func='tanh',
activation_args=None,
user_components=None,
rbf_width=1.0):
super(RandomLayer, self).__init__(n_hidden=n_hidden,
random_state=random_state,
activation_func=activation_func,
activation_args=activation_args)
if (isinstance(self.activation_func, str)):
func_names = self._internal_activation_funcs.keys()
if (self.activation_func not in func_names):
msg = "unknown activation function '%s'" % self.activation_func
raise ValueError(msg)
self.alpha = alpha
self.rbf_width = rbf_width
self.user_components = user_components
self._use_mlp_input = (self.alpha != 0.0)
self._use_rbf_input = (self.alpha != 1.0)
def _get_user_components(self, key):
"""Look for given user component"""
try:
return self.user_components[key]
except (TypeError, KeyError):
return None
def _compute_radii(self):
"""Generate RBF radii"""
# use supplied radii if present
radii = self._get_user_components('radii')
# compute radii
if (radii is None):
centers = self.components_['centers']
n_centers = centers.shape[0]
max_dist = np.max(pairwise_distances(centers))
radii = np.ones(n_centers) * max_dist / sqrt(2.0 * n_centers)
self.components_['radii'] = radii
def _compute_centers(self, X, sparse, rs):
"""Generate RBF centers"""
# use supplied centers if present
centers = self._get_user_components('centers')
# use points taken uniformly from the bounding
# hyperrectangle
if (centers is None):
n_features = X.shape[1]
if (sparse):
fxr = range(n_features)
cols = [X.getcol(i) for i in fxr]
min_dtype = X.dtype.type(1.0e10)
sp_min = lambda col: np.minimum(min_dtype, np.min(col.data))
min_Xs = np.array(map(sp_min, cols))
max_dtype = X.dtype.type(-1.0e10)
sp_max = lambda col: np.maximum(max_dtype, np.max(col.data))
max_Xs = np.array(map(sp_max, cols))
else:
min_Xs = X.min(axis=0)
max_Xs = X.max(axis=0)
spans = max_Xs - min_Xs
ctrs_size = (self.n_hidden, n_features)
centers = min_Xs + spans * rs.uniform(0.0, 1.0, ctrs_size)
self.components_['centers'] = centers
def _compute_biases(self, rs):
"""Generate MLP biases"""
# use supplied biases if present
biases = self._get_user_components('biases')
if (biases is None):
b_size = self.n_hidden
biases = rs.normal(size=b_size)
self.components_['biases'] = biases
def _compute_weights(self, X, rs):
"""Generate MLP weights"""
# use supplied weights if present
weights = self._get_user_components('weights')
if (weights is None):
n_features = X.shape[1]
hw_size = (n_features, self.n_hidden)
weights = rs.normal(size=hw_size)
self.components_['weights'] = weights
def _generate_components(self, X):
"""Generate components of hidden layer given X"""
rs = check_random_state(self.random_state)
if (self._use_mlp_input):
self._compute_biases(rs)
self._compute_weights(X, rs)
if (self._use_rbf_input):
self._compute_centers(X, sp.issparse(X), rs)
self._compute_radii()
def _compute_input_activations(self, X):
"""Compute input activations given X"""
n_samples = X.shape[0]
mlp_acts = np.zeros((n_samples, self.n_hidden))
if (self._use_mlp_input):
b = self.components_['biases']
w = self.components_['weights']
mlp_acts = self.alpha * (safe_sparse_dot(X, w) + b)
rbf_acts = np.zeros((n_samples, self.n_hidden))
if (self._use_rbf_input):
radii = self.components_['radii']
centers = self.components_['centers']
scale = self.rbf_width * (1.0 - self.alpha)
rbf_acts = scale * cdist(X, centers) / radii
self.input_activations_ = mlp_acts + rbf_acts
def get_field(self, x, y, z):
"""Calculates the magnetic field at point(s) x,y,z due to a 3D magnet
The calculations are always performed in local coordinates with the centre of the magnet at origin and z magnetisation pointing along the local z' axis.
The rotations and translations are performed first, and the internal field calculation functions are called.
Args:
x (ndarray): x co-ordinates
y (ndarray): y co-ordinates
z (ndarray): z co-ordinates
Returns:
tuple: Bx(ndarray), By(ndarray), Bz(ndarray) field vector
"""
from ..utils._routines3D import _tile_arrays, _apply_mask
# If any rotation angle is set, transform the data
if _np.any(
_np.fabs(
_np.array([
self.alpha_rad,
self.beta_rad,
self.gamma_rad,
])) > Magnet.tol):
forward_rotation, reverse_rotation = self._generate_rotation_quaternions(
)
# Generate 3xN array for quaternion rotation
pos_vec = Quaternion._prepare_vector(x - self.center[0],
y - self.center[1],
z - self.center[2])
# Rotate points
x_rot, y_rot, z_rot = forward_rotation * pos_vec
# Calls internal child method to calculate the field
B_local = self._get_field_internal(x_rot, y_rot, z_rot)
mask = self._generate_mask(x_rot, y_rot, z_rot)
B_local = _apply_mask(self, B_local, mask)
# Rearrange the field vectors in a 3xN array for quaternion rotation
Bvec = Quaternion._prepare_vector(B_local.x, B_local.y, B_local.z)
# Rotate the local fields back into the global frame using quaternions
Bx, By, Bz = reverse_rotation * Bvec
# finally return the fields
return Bx, By, Bz
else:
# Otherwise directly calculate the magnetic fields
B = self._get_field_internal(x - self.center[0],
y - self.center[1],
z - self.center[2])
xloc, yloc, zloc = _tile_arrays(x - self.center[0],
y - self.center[1],
z - self.center[2])
mask = self._generate_mask(xloc, yloc, zloc)
B = _apply_mask(self, B, mask)
return B.x, B.y, B.z
