def testSnrFuncs(self):
"""test for signal to noise ratio functions"""
# trivial
data_triv = sp.ones((3, 10))
snr_triv_test = sp.ones(3)
assert_equal(
snr_peak(data_triv, 1.0),
snr_triv_test)
assert_equal(
snr_power(data_triv, 1.0),
snr_triv_test)
assert_equal(
snr_maha(data_triv, sp.eye(data_triv.shape[1])),
snr_triv_test)
# application
data = sp.array([
sp.sin(sp.linspace(0.0, 2 * sp.pi, 100)),
sp.sin(sp.linspace(0.0, 2 * sp.pi, 100)) * 2,
sp.sin(sp.linspace(0.0, 2 * sp.pi, 100)) * 5,
])
assert_equal(
snr_peak(data, 1.0),
sp.absolute(data).max(axis=1))
assert_equal(
snr_power(data, 1.0),
sp.sqrt((data * data).sum(axis=1) / data.shape[1]))
assert_almost_equal(
snr_maha(data, sp.eye(data.shape[1])),
sp.sqrt((data * data).sum(axis=1) / data.shape[1]))
def __init__(self,alphai,eparall,eperp,nrj):
"""
Incident wave above a surface.
Coordinates:
- z is perpendicular to the surface, >0 going UP (different from H Dosch's convention)
- x is the projection of the wavevector on the surface
- y is parallel to the surface
alphai: incident angle, with respect to the surface
eparallel: component of the electric field parallel to the incident plane (vertical plane)
eperp: component of the electric field perpendicular to the incident plane (along y)
nrj: values of the energy of the incident wave, in eV
alphai *or* nrj can be arrays, but not together
"""
self.alphai=alphai
self.eparall=eparall
self.eperp=eperp
self.ex=scipy.sin(alphai)*eparall
self.ey=eperp
self.ez=scipy.cos(alphai)*eparall
self.kx= 2*pi/W2E(nrj)*scipy.cos(alphai)
self.ky= 2*pi/W2E(nrj)*0
self.kz=-2*pi/W2E(nrj)*scipy.sin(alphai)
self.nrj=nrj
def rotate(self, angle, mask=None):
"""Rotate the grids (arena centered)
Grids to be rotated can be optionally specified by bool/index array
*mask*, otherwise population is rotated. Specified *angle* can be a
scalar value to be applied to the population or a population- or
mask-sized array depending on whether *mask* is specified.
"""
rot2D = lambda psi: [[cos(psi), sin(psi)], [-sin(psi), cos(psi)]]
if mask is not None and type(mask) is np.ndarray:
if mask.dtype.kind == 'b':
mask = mask.nonzero()[0]
if type(angle) is np.ndarray and angle.size == mask.size:
for i,ix in enumerate(mask):
self._phi[ix] = np.dot(self._phi[ix], rot2D(angle[i]))
elif type(angle) in (int, float, np.float64):
angle = float(angle)
self._phi[mask] = np.dot(self._phi[mask], rot2D(angle))
else:
raise TypeError, 'angle must be mask-sized array or float'
self._psi[mask] = np.fmod(self._psi[mask]+angle, 2*pi)
elif mask is None:
if type(angle) is np.ndarray and angle.size == self.num_maps:
for i in xrange(self.num_maps):
self._phi[i] = np.dot(self._phi[i], rot2D(angle[i]))
elif type(angle) in (int, float, np.float64):
angle = float(angle)
self._phi = np.dot(self._phi, rot2D(angle))
else:
raise TypeError, 'angle must be num_maps array or float'
self._psi = np.fmod(self._psi+angle, 2*pi)
else:
raise TypeError, 'mask must be bool/index array'
def ned2ecef(lat, lon, alt, n, e, d):
X0, Y0, Z0 = coord.geodetic2ecef(lat, lon, alt)
lat, lon = radians(lat), radians(lon)
pitch = math.pi/2 + lat
yaw = -lon
my = mat('[%f %f %f; %f %f %f; %f %f %f]' %
(cos(pitch), 0, -sin(pitch),
0,1,0,
sin(pitch), 0, cos(pitch)))
mz = mat('[%f %f %f; %f %f %f; %f %f %f]' %
(cos(yaw), sin(yaw),0,
-sin(yaw),cos(yaw),0,
0,0,1))
mr = mat('[%f %f %f; %f %f %f; %f %f %f]' %
(-cos(lon)*sin(lat), -sin(lon), -cos(lat) * cos(lon),
-sin(lat)*sin(lon), cos(lon), -sin(lon)*cos(lat),
cos(lat), 0, -sin(lat)))
geo = mat('[%f; %f; %f]' % (X0, Y0, Z0))
ned = mat('[%f; %f; %f]' % (n, e, d))
res = mr*ned + geo
return res[0], res[1], res[2]
def Spm2(k,dx):
from scipy import sqrt,sin,exp
im = sqrt(-1)
Sp = exp(im*k*dx)*(1 - 0.5*(im*sin(im*k*dx)))
Sm = (1 + 0.5*(im*sin(im*k*dx)))
return Sp, Sm
def lla2ecef(lla: Sequence[float], cst: ConstantsFile, lla_as_degrees: bool=False) -> Tuple[float, float, float]:
"""
converts LLA (Latitude, Longitude, Altitude) coordinates
to ECEF (Earth-Centre, Earth-First) XYZ coordinates.
"""
lat, lon, alt = lla
if lla_as_degrees:
lat = radians(lat)
lon = radians(lon)
a = cst.semi_major_axis
b = cst.semi_minor_axis
# calc. ellipsoid flatness
f = (a - b) / a
# calc. eccentricity
e = sqrt(f * (2 - f))
# Calculate length of the normal to the ellipsoid
N = a / sqrt(1 - (e * sin(lat)) ** 2)
# Calculate ecef coordinates
x = (N + alt) * cos(lat) * cos(lon)
y = (N + alt) * cos(lat) * sin(lon)
z = (N * (1 - e ** 2) + alt) * sin(lat)
# Return the ecef coordinates
return x, y, z
def form_point_set(self, histo, point_set):
(slices, numbins) = histo.shape
phases = numpy.arange(numbins)
phases = phases * (360. / numbins)
phases += phases[1] / 2.
phi_step = phases[0]
for time in xrange(slices):
z = float(time)
for bin in xrange(numbins):
r = histo[time,bin]
theta = phi_step * (bin+1)
theta *= (scipy.pi / 180.)
x = r*scipy.cos(theta)
y = r*scipy.sin(theta)
point_set.InsertNextPoint(x, y, z)
for bin in xrange(numbins):
curbin = bin
lastbin = bin-1
if lastbin < 0:
lastbin = numbins-1
r = (histo[time,bin] - histo[time,lastbin]) / 2.
theta = curbin * 360. / numbins
x = r*scipy.cos(theta)
y = r*scipy.sin(theta)
point_set.InsertNextPoint(x, y, z)
def cyl_to_rect_vec(vr,vt,vz,phi):
"""
NAME:
cyl_to_rect_vec
PURPOSE:
transform vectors from cylindrical to rectangular coordinate vectors
INPUT:
vr - radial velocity
vt - tangential velocity
vz - vertical velocity
phi - azimuth
OUTPUT:
vx,vy,vz
HISTORY:
2011-02-24 - Written - Bovy (NYU)
"""
vx= vr*sc.cos(phi)-vt*sc.sin(phi)
vy= vr*sc.sin(phi)+vt*sc.cos(phi)
return (vx,vy,vz)
def radec_to_lb(ra,dec,degree=False,epoch=2000.0):
"""
NAME:
radec_to_lb
PURPOSE:
transform from equatorial coordinates to Galactic coordinates
INPUT:
ra - right ascension
dec - declination
degree - (Bool) if True, ra and dec are given in degree and l and b will be as well
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported)
OUTPUT:
l,b
For vector inputs [:,2]
HISTORY:
2009-11-12 - Written - Bovy (NYU)
"""
#First calculate the transformation matrix T
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
T= sc.dot(sc.array([[sc.cos(theta),sc.sin(theta),0.],[sc.sin(theta),-sc.cos(theta),0.],[0.,0.,1.]]),sc.dot(sc.array([[-sc.sin(dec_ngp),0.,sc.cos(dec_ngp)],[0.,1.,0.],[sc.cos(dec_ngp),0.,sc.sin(dec_ngp)]]),sc.array([[sc.cos(ra_ngp),sc.sin(ra_ngp),0.],[-sc.sin(ra_ngp),sc.cos(ra_ngp),0.],[0.,0.,1.]])))
transform={}
transform['T']= T
if sc.array(ra).shape == ():
return radec_to_lb_single(ra,dec,transform,degree)
else:
function= sc.frompyfunc(radec_to_lb_single,4,2)
return sc.array(function(ra,dec,transform,degree),dtype=sc.float64).T
def f(self, x):
res = 0
for i in range(self.xdim):
Ai = sum(self.A[i] * sin(self.alphas) + self.B[i] * cos(self.alphas))
Bix = sum(self.A[i] * sin(x) + self.B[i] * cos(x))
res += (Ai - Bix) ** 2
return res
def _genBFEdgeZero(plasma, zeros, rcent, zcent):
""" this will absolutely need to be rewritten"""
theta = scipy.linspace(-scipy.pi,scipy.pi,zeros)
cent = geometry.Point(geometry.Vecr([rcent,0,zcent]),plasma)
zerobeam = []
outline = []
for i in xrange(len(plasma.norm.s)-1):
outline += [geometry.Vecx([plasma.sagi.s[i],
0,
plasma.norm.s[i]])-cent]
for i in xrange(zeros):
temp2 = geometry.Vecr([scipy.cos(theta[i]),
0,
scipy.sin(theta[i])])
s = 0
for j in outline:
temp4 = j*temp2
if temp4 > s:
s = temp4
temp2.s = s
zerobeam += [Ray(geometry.Point(cent+temp2,
plasma),
geometry.Vecr([scipy.sin(theta[i]),
0,
-scipy.cos(theta[i])]))]
return zerobeam
def radec_to_lb(ra,dec,degree=False,epoch=2000.0):
"""
NAME:
radec_to_lb
PURPOSE:
transform from equatorial coordinates to Galactic coordinates
INPUT:
ra - right ascension
dec - declination
degree - (Bool) if True, ra and dec are given in degree and l and b will be as well
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported)
OUTPUT:
l,b
For vector inputs [:,2]
HISTORY:
2009-11-12 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
import math as m
import numpy as nu
import scipy as sc
#First calculate the transformation matrix T
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
T= sc.dot(sc.array([[sc.cos(theta),sc.sin(theta),0.],[sc.sin(theta),-sc.cos(theta),0.],[0.,0.,1.]]),sc.dot(sc.array([[-sc.sin(dec_ngp),0.,sc.cos(dec_ngp)],[0.,1.,0.],[sc.cos(dec_ngp),0.,sc.sin(dec_ngp)]]),sc.array([[sc.cos(ra_ngp),sc.sin(ra_ngp),0.],[-sc.sin(ra_ngp),sc.cos(ra_ngp),0.],[0.,0.,1.]])))
#Whether to use degrees and scalar input is handled by decorators
XYZ= nu.array([nu.cos(dec)*nu.cos(ra),
nu.cos(dec)*nu.sin(ra),
nu.sin(dec)])
galXYZ= nu.dot(T,XYZ)
b= nu.arcsin(galXYZ[2])
l= nu.arctan2(galXYZ[1]/sc.cos(b),galXYZ[0]/sc.cos(b))
l[l<0.]+= 2.*nu.pi
out= nu.array([l,b])
return out.T
def InitJackArrays(self,freq,samples): """Initialize Jack Arrays""" self.iIa = sp.zeros(samples).astype(sp.float32) self.iQa = sp.zeros(samples).astype(sp.float32) self.oIa = sp.zeros(samples, dtype=sp.float32 ) self.oQa = sp.zeros(samples, dtype=sp.float32 ) ## 100 frames warmup sf = 0 ef = self.rtframes2sync samples = sp.pi + (2*sp.pi*freq*(self.dt * sp.r_[sf:ef])) self.oIa[sf:ef] = self.amp * sp.cos(samples) self.oQa[sf:ef] = self.amp * sp.sin(samples) # For IQ balancing #self.oIa[sf:ef] = sp.cos(samples) - (sp.sin(samples)*(1+self.oalpha)*sp.sin(self.ophi)) #self.oQa[sf:ef] = sp.sin(samples)*(1+self.oalpha)*sp.cos(self.ophi) ## 180 phase change sf = ef ef = ef + self.sync2fft + self.fftn + self.fft2end samples = (2*sp.pi*freq*(self.dt * sp.r_[sf:ef])) self.oIa[sf:ef] = self.amp * sp.cos(samples) self.oQa[sf:ef] = self.amp * sp.sin(samples)
def residuals(self, p,errors, f,freq_val):
theta = self.theta
# Isrc = 19.6*pow((750.0/freq_val[f]),0.495)*2
# Isrc = 19.6*pow((750.0/freq_val[f]),0.495)*(2.28315426-0.000484307905*freq_val[f]) # Added linear fit for Jansky to Kelvin conversion.
# Isrc = 19.74748409*pow((750.0/freq_val[f]),0.49899785)*(2.28315426-0.000484307905*freq_val[f]) # My fit solution for 3C286
Isrc = 25.15445092*pow((750.0/freq_val[f]),0.75578842)*(2.28315426-0.000484307905*freq_val[f]) # My fit solution for 3C48
# Isrc = 4.56303633*pow((750.0/freq_val[f]),0.59237327)*(2.28315426-0.000484307905*freq_val[f]) # My fit solution for 3C67
PAsrc = 33.0*sp.pi/180.0 # for 3C286, doesn't matter for unpolarized.
# Psrc = 0.07 #for 3C286
Psrc = 0 #for #3C48,3C67
Qsrc = Isrc*Psrc*sp.cos(2*PAsrc)
Usrc = Isrc*Psrc*sp.sin(2*PAsrc)
Vsrc = 0
XXsrc0 = Isrc-Qsrc
YYsrc0 = Isrc+Qsrc
# XXsrc = (0.5*(1+sp.cos(2*theta[i]))*XXsrc0-sp.sin(2*theta[i])*Usrc+0.5*(1-sp.cos(2*theta[i]))*YYsrc0)
# YYsrc = (0.5*(1-sp.cos(2*theta[i]))*XXsrc0+sp.sin(2*theta[i])*Usrc+0.5*(1+sp.cos(2*theta[i]))*YYsrc0)
source = sp.zeros(4*self.file_num)
for i in range(0,len(source),4):
source[i] = (0.5*(1+sp.cos(2*theta[i]))*XXsrc0-sp.sin(2*theta[i])*Usrc+0.5*(1-sp.cos(2*theta[i]))*YYsrc0)
source[i+1] = 0
source[i+2] = 0
source[i+3] = (0.5*(1-sp.cos(2*theta[i]))*XXsrc0+sp.sin(2*theta[i])*Usrc+0.5*(1+sp.cos(2*theta[i]))*YYsrc0)
err = (source-self.peval(p,f))/errors
return err
def elaz2radec_lst(el, az, lst, lat = 38.43312) :
"""DO NOT USE THIS ROUTINE FOR ANTHING THAT NEEDS TO BE RIGHT. IT DOES NOT
CORRECT FOR PRECESSION.
Calculates the Ra and Dec from elavation, aximuth, LST and Latitude.
This function is vectorized with numpy so should be fast. Standart numpy
broadcasting should also work.
All angles in degrees, lst in seconds. Latitude defaults to GBT.
"""
# Convert everything to radians.
el = sp.radians(el)
az = sp.radians(az)
lst = sp.array(lst, dtype = float)*2*sp.pi/86400
lat = sp.radians(lat)
# Calculate dec.
dec = sp.arcsin(sp.sin(el)*sp.sin(lat) +
sp.cos(el)*sp.cos(lat)*sp.cos(az))
# Calculate the hour angle
ha = sp.arccos((sp.sin(el) - sp.sin(lat)*sp.sin(dec)) /
(sp.cos(lat)*sp.cos(dec)))
ra = sp.degrees(lst - ha) % 360
return ra, sp.degrees(dec)
def sparse_orth(d):
""" Constructs a sparse orthogonal matrix.
The method is described in:
Gi-Sang Cheon et al., Constructions for the sparsest orthogonal matrices,
Bull. Korean Math. Soc 36 (1999) No.1 pp.199-129
"""
from scipy.sparse import eye
from scipy import r_, pi, sin, cos
if d % 2 == 0:
seq = r_[0:d:2, 1:d - 1:2]
else:
seq = r_[0:d - 1:2, 1:d:2]
Q = eye(d, d).tocsc()
for i in seq:
theta = random() * 2 * pi
flip = (random() - 0.5) > 0;
Qi = eye(d, d).tocsc()
Qi[i, i] = cos(theta)
Qi[(i + 1), i] = sin(theta)
if flip > 0:
Qi[i, (i + 1)] = -sin(theta)
Qi[(i + 1), (i + 1)] = cos(theta)
else:
Qi[i, (i + 1)] = sin(theta)
Qi[(i + 1), (i + 1)] = -cos(theta)
Q = Q * Qi;
return Q
def f_Refl_Thin_Film_fit(Data):
strain = Data[0]
DW = Data[1]
dat = Data[2]
wl = dat[0]
N = dat[2]
phi = dat[3]
t_l = dat[4]
thB_S = dat[6]
G = dat[7]
F0 = dat[8]
FH = dat[9]
FmH = dat[10]
th = dat[19]
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
eta = 0
res = 0
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[n]*FmH[n])**0.5) * t_l * DW[n] / (wl * (abs(g0*gH)**0.5))
eta = (-b*(th-thB[n])*sin(2*thB_S) - 0.5*G*F0[n]*(1-b)) / ((abs(b)**0.5) * G * DW[n] * (FH[n]*FmH[n])**0.5)
S1 = (res - eta + (eta*eta-1)**0.5)*exp(-1j*T*(eta*eta-1)**0.5)
S2 = (res - eta - (eta*eta-1)**0.5)*exp(1j*T*(eta*eta-1)**0.5)
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n += 1
return res
def CalcXY2GPSParam_2p(x1,x2,g1,g2,K=[0,0]): # Kx = dLng/dx; Ky = dlat/dy; # In China: # Kx = (133.4-1.2*lat)*1e3 # Ky = (110.2+0.002*lat)*1e3 X1 = array(x1) Y1 = array(g1) X2 = array(x2) Y2 = array(g2) detX = X2-X1 detY = Y2-Y1 lat = Y1[1] if K[0] == 0: Kx = (133.4-1.2*lat)*1e3 Ky = (110.2+0.002*lat)*1e3 K = array([Kx,Ky]) else: Kx = K[0] Ky = K[1] detKY = detY*K alpha = myArctan(detX[0],detX[1]) - myArctan(detKY[0],detKY[1]) A = array([[sp.cos(alpha),sp.sin(alpha)],[-sp.sin(alpha),sp.cos(alpha)]]) X01 = X1 - dot(linalg.inv(A),Y1*K) X02 = X2 - dot(linalg.inv(A),Y2*K) X0 = (X01+X02) /2 return A,X0,K
def get_bl(self,ra=None,dec=None):
"""
http://scienceworld.wolfram.com/astronomy/GalacticCoordinates.html
"""
if ra==None: ra=self.get_column("RA")
if dec==None: dec=self.get_column("DEC")
if type(ra)==float:
ral=scipy.zeros(1)
ral[0]=ra
ra=ral
if type(dec)==float:
decl=scipy.zeros(1)
decl[0]=dec
dec=decl
c62=math.cos(62.6*D2R)
s62=math.sin(62.6*D2R)
b=scipy.sin(dec*D2R)*c62
b-=scipy.cos(dec*D2R)*scipy.sin((ra-282.25)*D2R)*s62
b=scipy.arcsin(b)*R2D
cosb=scipy.cos(b*D2R)
#l minus 33 degrees
lm33=(scipy.cos(dec*D2R)/cosb)*scipy.cos((ra-282.25))
l=scipy.arccos(lm33)*R2D+33.0
return b,l
def distance_fn(p1, l1, p2, l2, units='m'):
"""
Simplified Vincenty formula.
Returns distance between coordinates.
"""
assert (units in ['km', 'm', 'nm']), 'Units must be km, m, or nm'
if units == 'km':
r = 6372.7974775959065
elif units == 'm':
r = 6372.7974775959065 * 0.621371
elif units == 'nm':
r = 6372.7974775959065 * 0.539957
# compute Vincenty formula
l = abs(l1 - l2)
num = scipy.sqrt(((scipy.cos(p2) * scipy.sin(l)) ** 2) +\
(((scipy.cos(p1) * scipy.sin(p2)) - (scipy.sin(p1) * scipy.cos(p2) * scipy.cos(l))) ** 2))
den = scipy.sin(p1) * scipy.sin(p2) + scipy.cos(p1) * scipy.cos(p2) * scipy.cos(l)
theta = scipy.arctan(num / den)
distance = abs(int(round(r * theta)))
return distance
def pix2sky(header,x,y): hdr_info = parse_header(header) x0 = x-hdr_info[1][0]+1. # Plus 1 python->image y0 = y-hdr_info[1][1]+1. x0 = x0.astype(scipy.float64) y0 = y0.astype(scipy.float64) x = hdr_info[2][0,0]*x0 + hdr_info[2][0,1]*y0 y = hdr_info[2][1,0]*x0 + hdr_info[2][1,1]*y0 if hdr_info[3]=="DEC": a = x.copy() x = y.copy() y = a.copy() ra0 = hdr_info[0][1] dec0 = hdr_info[0][0]/raddeg else: ra0 = hdr_info[0][0] dec0 = hdr_info[0][1]/raddeg if hdr_info[5]=="TAN": r_theta = scipy.sqrt(x*x+y*y)/raddeg theta = arctan(1./r_theta) phi = arctan2(x,-1.*y) elif hdr_info[5]=="SIN": r_theta = scipy.sqrt(x*x+y*y)/raddeg theta = arccos(r_theta) phi = artan2(x,-1.*y) ra = ra0 + raddeg*arctan2(-1.*cos(theta)*sin(phi-pi), sin(theta)*cos(dec0)-cos(theta)*sin(dec0)*cos(phi-pi)) dec = raddeg*arcsin(sin(theta)*sin(dec0)+cos(theta)*cos(dec0)*cos(phi-pi)) return ra,dec
def f(self, x):
B1 = 0.5 * sin(x[0]) - 2*cos(x[0]) + sin(x[1]) -1.5*cos(x[1])
B2 = 1.5 * sin(x[0]) - cos(x[0]) + 2*sin(x[1]) -0.5*cos(x[1])
f1 = 1 + (self._A1-B1)**2 + (self._A2-B2)**2
f2 = (x[0]+3)**2 + (x[1]+1)**2
return -array([f1, f2])
def radec_to_lb_single(ra,dec,T,degree=False):
"""
NAME:
radec_to_lb_single
PURPOSE:
transform from equatorial coordinates to Galactic coordinates for a single pair of ra,dec
INPUT:
ra - right ascension
dec - declination
T - epoch dependent transformation matrix (dictionary)
degree - (Bool) if True, ra and dec are given in degree and l and b will be as well
OUTPUT:
l,b
HISTORY:
2009-11-12 - Written - Bovy (NYU)
"""
T=T['T']
if degree:
thisra= ra/180.*sc.pi
thisdec= dec/180.*sc.pi
else:
thisra= ra
thisdec= dec
XYZ=sc.array([sc.cos(thisdec)*sc.cos(thisra),sc.cos(thisdec)*sc.sin(thisra),sc.sin(thisdec)])
galXYZ= sc.dot(T,XYZ)
b= m.asin(galXYZ[2])
l= m.atan(galXYZ[1]/galXYZ[0])
if galXYZ[0]/sc.cos(b) < 0.:
l+= sc.pi
if l < 0.:
l+= 2.*sc.pi
if degree:
return (l/sc.pi*180.,b/sc.pi*180.)
else:
return (l,b)
def xyzfield(gcoefs, hcoefs, phi, theta, rparam=1.0, order=13):
# no usar esta función, es peor en rendimiento
x, y, z = 0, 0, 0
legendre, dlegendre = scipy.special.lpmn(order + 1, order + 1, scipy.cos(theta))
for l in range(1, order + 1):
for m in range(0, l + 1):
deltax = (
rparam ** (l + 2)
* (gcoefs[m, l] * scipy.cos(m * phi) + hcoefs[m, l] * scipy.sin(m * phi))
* dlegendre[m, l]
* (-scipy.sin(theta))
)
deltay = (
rparam ** (l + 2)
* (gcoefs[m, l] * scipy.sin(m * phi) - hcoefs[m, l] * scipy.cos(m * phi))
* m
* legendre[m, l]
/ (scipy.sin(theta))
)
deltaz = (
rparam ** (l + 2)
* (l + 1)
* (gcoefs[m, l] * scipy.cos(m * phi) + hcoefs[m, l] * scipy.sin(m * phi))
* legendre[m, l]
)
x += deltax
y += deltay
z += deltaz
return (x, y, z)
def __init__(self,id,matName,orientation,source=0.0):
self.id = id
self.matName = matName
self.orientation = orientation
self.source = source
self.T = array([[cos(orientation),-sin(orientation)],
[sin(orientation), cos(orientation)]])
def calc_max_width_in_slab(out_of_dip, slab_width, max_width):
"""Calculate the max width of a rupture within a slab in kms; given
the slab width, and the out of dip angle. the returned max width values
are compared to the calculated width and the fault width, and then
the mimium value of the 3 is used as the rupture width.
out_of_dip out of dip angle in Degrees
slab_width width of slab in kms
max_width width of the fault
Returns the max width of ruptures within a slab in kms.
"""
max_width_in_slab = zeros(len(out_of_dip))
i = where(out_of_dip >= 180)
out_of_dip[i] = out_of_dip[i] - 180
i = where(out_of_dip <= 1)
max_width_in_slab[i] = max_width
j = where(((out_of_dip < 90) & (out_of_dip > 1)))
max_width_in_slab[j] = slab_width / (sin(radians(out_of_dip[j])))
k = where(out_of_dip == 90)
max_width_in_slab[k] = slab_width
k = where((out_of_dip > 90) & (out_of_dip < 179))
max_width_in_slab[k] = slab_width / (sin(radians(180 - out_of_dip[k])))
i = where(out_of_dip >= 179)
max_width_in_slab[i] = max_width
return max_width_in_slab
def binary_ephem(P, T, e, a, i, O_node, o_peri, t):
# Grados a radianes
d2rad = pi/180.
rad2d = 180./pi
i = i*d2rad
O_node = (O_node*d2rad)%(2*pi)
o_peri = (o_peri*d2rad)%(2*pi)
# Anomalia media
M = ((2.0*pi)/P)*(t - T) # radianes
if M >2*pi: M = M - 2*pi
M=M%(2*pi)
# Anomalia excentrica (1ra aproximacion)
E0 = M + e*sin(M) + (e**2/M) * sin(2.0*M)
for itera in range(15):
M0 = E0 - e*sin(E0)
E0 = E0 + (M-M0)/(1-e*cos(E0))
true_anom = 2.0*arctan(sqrt((1+e)/(1-e))*tan(E0/2.0))
#radius = (a*(1-e**2))/(1+e*cos(true_anom))
radius = a*(1-e*cos(E0))
theta = arctan( tan(true_anom + o_peri)*cos(i) ) + O_node
rho = radius * (cos(true_anom + o_peri)/cos(theta - O_node))
# revuelve rho ("), theta (grad), Anomalia excentrica (grad), Anomalia verdadera (grad)
return rho, (theta*rad2d)%360. #, E0*rad2d, M*rad2d, true_anom*rad2d
def rect_to_cyl_vec(vx,vy,vz,X,Y,Z,cyl=False):
"""
NAME:
rect_to_cyl_vec
PURPOSE:
transform vectors from rectangular to cylindrical coordinates vectors
INPUT:
vx -
vy -
vz -
X - X
Y - Y
Z - Z
cyl - if True, X,Y,Z are already cylindrical
OUTPUT:
vR,vT,vz
HISTORY:
2010-09-24 - Written - Bovy (NYU)
"""
if not cyl:
R,phi,Z= rect_to_cyl(X,Y,Z)
else:
phi= Y
vr=+vx*sc.cos(phi)+vy*sc.sin(phi)
vt= -vx*sc.sin(phi)+vy*sc.cos(phi)
return (vr,vt,vz)
def evaluateSphericalVariation (phi,theta,cntPhi,cntTheta):
global conf,cons
success = False
alpha0 =sp.zeros([dim['alpha']],complex)
alpha0[conf['id0']]=sp.cos(phi)*sp.sin(theta)+0j
alpha0[conf['id1']]=sp.sin(phi)*sp.sin(theta)+0j
alpha0[conf['id2']]=sp.cos(theta)+0j
# if (sp.absolute(alpha0[conf['id0']]) <= 1e-10):
# alpha0[conf['id0']]=0.0+0j
# if (sp.absolute(alpha0[conf['id1']]) <= 1e-10):
# alpha0[conf['id1']]=0.0+0j
# if (sp.absolute(alpha0[conf['id2']]) <= 1e-10):
# alpha0[conf['id2']]=0.0+0j
#
# normalize coefficients for alpha -> defines net-power
alpha0[:]=alpha0[:]/sp.linalg.norm(alpha0[:])*cons['alpha_norm']
__,res = MemoryPulseFunctional.evaluateFunctional(alpha0,1.0+0j)
myRes = sp.zeros([conf['entries']+3])
myRes[0] = alpha0[conf['id0']].real
myRes[1] = alpha0[conf['id1']].real
myRes[2] = alpha0[conf['id2']].real
myRes[3:]= res
print "### spherical map: phi/pi={0:5.3f}, theta/pi={1:5.3f}, fun={2:f}".format(phi/sp.pi,theta/sp.pi,myRes[conf['funval']])
myRes[conf['funval']] = min(conf['cutoff'],res[conf['funval']])
return myRes,cntPhi,cntTheta
def getObservation(self):
obs = array(impl.getObs())
if self.verbose:
print(('obs', obs))
obs.resize(self.outdim)
if self.extraObservations:
cartpos = obs[-1]
if self.markov:
angle1 = obs[1]
else:
angle1 = obs[0]
obs[-1 + self.extraRandoms] = 0.1 * cos(angle1) + cartpos
obs[-2 + self.extraRandoms] = 0.1 * sin(angle1) + cartpos
if self.numPoles == 2:
if self.markov:
angle2 = obs[3]
else:
angle2 = obs[1]
obs[-3 + self.extraRandoms] = 0.05 * cos(angle2) + cartpos
obs[-4 + self.extraRandoms] = 0.05 * sin(angle2) + cartpos
if self.extraRandoms > 0:
obs[-self.extraRandoms:] = randn(self.extraRandoms)
if self.verbose:
print(('obs', obs))
return obs
def solve(self, wls):
"""Anisotropic solver.
INPUT
wls = wavelengths to scan (any asarray-able object).
OUTPUT
self.DEO1, self.DEE1, self.DEO3, self.DEE3 = power reflected
and transmitted.
"""
self.wls = S.atleast_1d(wls)
LAMBDA = self.LAMBDA
n = self.n
multilayer = self.multilayer
alpha = self.alpha
delta = self.delta
psi = self.psi
phi = self.phi
nlayers = len(multilayer)
i = S.arange(-n, n + 1)
nood = 2 * n + 1
hmax = nood - 1
DEO1 = S.zeros((nood, self.wls.size))
DEO3 = S.zeros_like(DEO1)
DEE1 = S.zeros_like(DEO1)
DEE3 = S.zeros_like(DEO1)
c1 = S.array([1.0, 0.0, 0.0])
c3 = S.array([1.0, 0.0, 0.0])
# grating on the xy plane
K = 2 * pi / LAMBDA * S.array([S.sin(phi), 0.0, S.cos(phi)], dtype=complex)
dirk1 = S.array(
[S.sin(alpha) * S.cos(delta), S.sin(alpha) * S.sin(delta), S.cos(alpha)]
)
# D polarization vector
u = S.array(
[
S.cos(psi) * S.cos(alpha) * S.cos(delta) - S.sin(psi) * S.sin(delta),
S.cos(psi) * S.cos(alpha) * S.sin(delta) + S.sin(psi) * S.cos(delta),
-S.cos(psi) * S.sin(alpha),
]
)
kO1i = S.zeros((3, i.size), dtype=complex)
kE1i = S.zeros_like(kO1i)
kO3i = S.zeros_like(kO1i)
kE3i = S.zeros_like(kO1i)
Mp = S.zeros((4 * nood, 4 * nood, nlayers), dtype=complex)
M = S.zeros((4 * nood, 4 * nood, nlayers), dtype=complex)
dlt = (i == 0).astype(int)
for iwl, wl in enumerate(self.wls):
nO1 = nE1 = multilayer[0].mat.n(wl).item()
nO3 = nE3 = multilayer[-1].mat.n(wl).item()
# wavevectors
k = 2 * pi / wl
eps1 = S.diag(S.asarray([nE1, nO1, nO1]) ** 2)
eps3 = S.diag(S.asarray([nE3, nO3, nO3]) ** 2)
# ordinary wave
abskO1 = k * nO1
# abskO3 = k * nO3
# extraordinary wave
# abskE1 = k * nO1 *nE1 / S.sqrt(nO1**2 + (nE1**2 - nO1**2) * S.dot(-c1, dirk1)**2)
# abskE3 = k * nO3 *nE3 / S.sqrt(nO3**2 + (nE3**2 - nO3**2) * S.dot(-c3, dirk1)**2)
k1 = abskO1 * dirk1
kO1i[0, :] = k1[0] - i * K[0]
kO1i[1, :] = k1[1] * S.ones_like(i)
kO1i[2, :] = -dispersion_relation_ordinary(kO1i[0, :], kO1i[1, :], k, nO1)
kE1i[0, :] = kO1i[0, :]
kE1i[1, :] = kO1i[1, :]
kE1i[2, :] = -dispersion_relation_extraordinary(
kE1i[0, :], kE1i[1, :], k, nO1, nE1, c1
)
kO3i[0, :] = kO1i[0, :]
kO3i[1, :] = kO1i[1, :]
kO3i[2, :] = dispersion_relation_ordinary(kO3i[0, :], kO3i[1, :], k, nO3)
kE3i[0, :] = kO1i[0, :]
kE3i[1, :] = kO1i[1, :]
kE3i[2, :] = dispersion_relation_extraordinary(
kE3i[0, :], kE3i[1, :], k, nO3, nE3, c3
)
# k2i = S.r_[[k1[0] - i * K[0]], [k1[1] - i * K[1]], [k1[2] - i * K[2]]]
k2i = S.r_[[k1[0] - i * K[0]], [k1[1] - i * K[1]], [-i * K[2]]]
# aliases for constant wavevectors
kx = kO1i[0, :] # o kE1i(1,;), tanto e' lo stesso
ky = k1[1]
# matrices
I = S.eye(nood, dtype=complex)
ZERO = S.zeros((nood, nood), dtype=complex)
Kx = S.diag(kx / k)
Ky = ky / k * I
Kz = S.diag(k2i[2, :] / k)
KO1z = S.diag(kO1i[2, :] / k)
KE1z = S.diag(kE1i[2, :] / k)
KO3z = S.diag(kO3i[2, :] / k)
KE3z = S.diag(kE3i[2, :] / k)
ARO = Kx * eps1[0, 0] + Ky * eps1[1, 0] + KO1z * eps1[2, 0]
BRO = Kx * eps1[0, 1] + Ky * eps1[1, 1] + KO1z * eps1[2, 1]
CRO_1 = inv(Kx * eps1[0, 2] + Ky * eps1[1, 2] + KO1z * eps1[2, 2])
ARE = Kx * eps1[0, 0] + Ky * eps1[1, 0] + KE1z * eps1[2, 0]
BRE = Kx * eps1[0, 1] + Ky * eps1[1, 1] + KE1z * eps1[2, 1]
CRE_1 = inv(Kx * eps1[0, 2] + Ky * eps1[1, 2] + KE1z * eps1[2, 2])
ATO = Kx * eps3[0, 0] + Ky * eps3[1, 0] + KO3z * eps3[2, 0]
BTO = Kx * eps3[0, 1] + Ky * eps3[1, 1] + KO3z * eps3[2, 1]
CTO_1 = inv(Kx * eps3[0, 2] + Ky * eps3[1, 2] + KO3z * eps3[2, 2])
ATE = Kx * eps3[0, 0] + Ky * eps3[1, 0] + KE3z * eps3[2, 0]
BTE = Kx * eps3[0, 1] + Ky * eps3[1, 1] + KE3z * eps3[2, 1]
CTE_1 = inv(Kx * eps3[0, 2] + Ky * eps3[1, 2] + KE3z * eps3[2, 2])
DRE = c1[1] * KE1z - c1[2] * Ky
ERE = c1[2] * Kx - c1[0] * KE1z
FRE = c1[0] * Ky - c1[1] * Kx
DTE = c3[1] * KE3z - c3[2] * Ky
ETE = c3[2] * Kx - c3[0] * KE3z
FTE = c3[0] * Ky - c3[1] * Kx
b = S.r_[
u[0] * dlt,
u[1] * dlt,
(k1[1] / k * u[2] - k1[2] / k * u[1]) * dlt,
(k1[2] / k * u[0] - k1[0] / k * u[2]) * dlt,
]
Ky_CRO_1 = ky / k * CRO_1
Ky_CRE_1 = ky / k * CRE_1
Kx_CRO_1 = kx[:, S.newaxis] / k * CRO_1
Kx_CRE_1 = kx[:, S.newaxis] / k * CRE_1
MR31 = -S.dot(Ky_CRO_1, ARO)
MR32 = -S.dot(Ky_CRO_1, BRO) - KO1z
MR33 = -S.dot(Ky_CRE_1, ARE)
MR34 = -S.dot(Ky_CRE_1, BRE) - KE1z
MR41 = S.dot(Kx_CRO_1, ARO) + KO1z
MR42 = S.dot(Kx_CRO_1, BRO)
MR43 = S.dot(Kx_CRE_1, ARE) + KE1z
MR44 = S.dot(Kx_CRE_1, BRE)
MR = S.asarray(
S.bmat(
[
[I, ZERO, I, ZERO],
[ZERO, I, ZERO, I],
[MR31, MR32, MR33, MR34],
[MR41, MR42, MR43, MR44],
]
)
)
Ky_CTO_1 = ky / k * CTO_1
Ky_CTE_1 = ky / k * CTE_1
Kx_CTO_1 = kx[:, S.newaxis] / k * CTO_1
Kx_CTE_1 = kx[:, S.newaxis] / k * CTE_1
MT31 = -S.dot(Ky_CTO_1, ATO)
MT32 = -S.dot(Ky_CTO_1, BTO) - KO3z
MT33 = -S.dot(Ky_CTE_1, ATE)
MT34 = -S.dot(Ky_CTE_1, BTE) - KE3z
MT41 = S.dot(Kx_CTO_1, ATO) + KO3z
MT42 = S.dot(Kx_CTO_1, BTO)
MT43 = S.dot(Kx_CTE_1, ATE) + KE3z
MT44 = S.dot(Kx_CTE_1, BTE)
MT = S.asarray(
S.bmat(
[
[I, ZERO, I, ZERO],
[ZERO, I, ZERO, I],
[MT31, MT32, MT33, MT34],
[MT41, MT42, MT43, MT44],
]
)
)
Mp.fill(0.0)
M.fill(0.0)
for nlayer in range(nlayers - 2, 0, -1): # internal layers
layer = multilayer[nlayer]
thickness = layer.thickness
EPS2, EPS21 = layer.getEPSFourierCoeffs(wl, n, anisotropic=True)
# Exx = S.squeeze(EPS2[0, 0, :])
# Exx = toeplitz(S.flipud(Exx[0:hmax + 1]), Exx[hmax:])
Exy = S.squeeze(EPS2[0, 1, :])
Exy = toeplitz(S.flipud(Exy[0 : hmax + 1]), Exy[hmax:])
Exz = S.squeeze(EPS2[0, 2, :])
Exz = toeplitz(S.flipud(Exz[0 : hmax + 1]), Exz[hmax:])
Eyx = S.squeeze(EPS2[1, 0, :])
Eyx = toeplitz(S.flipud(Eyx[0 : hmax + 1]), Eyx[hmax:])
Eyy = S.squeeze(EPS2[1, 1, :])
Eyy = toeplitz(S.flipud(Eyy[0 : hmax + 1]), Eyy[hmax:])
Eyz = S.squeeze(EPS2[1, 2, :])
Eyz = toeplitz(S.flipud(Eyz[0 : hmax + 1]), Eyz[hmax:])
Ezx = S.squeeze(EPS2[2, 0, :])
Ezx = toeplitz(S.flipud(Ezx[0 : hmax + 1]), Ezx[hmax:])
Ezy = S.squeeze(EPS2[2, 1, :])
Ezy = toeplitz(S.flipud(Ezy[0 : hmax + 1]), Ezy[hmax:])
Ezz = S.squeeze(EPS2[2, 2, :])
Ezz = toeplitz(S.flipud(Ezz[0 : hmax + 1]), Ezz[hmax:])
Exx_1 = S.squeeze(EPS21[0, 0, :])
Exx_1 = toeplitz(S.flipud(Exx_1[0 : hmax + 1]), Exx_1[hmax:])
Exx_1_1 = inv(Exx_1)
# lalanne
Ezz_1 = inv(Ezz)
Ky_Ezz_1 = ky / k * Ezz_1
Kx_Ezz_1 = kx[:, S.newaxis] / k * Ezz_1
Exz_Ezz_1 = S.dot(Exz, Ezz_1)
Eyz_Ezz_1 = S.dot(Eyz, Ezz_1)
H11 = 1j * S.dot(Ky_Ezz_1, Ezy)
H12 = 1j * S.dot(Ky_Ezz_1, Ezx)
H13 = S.dot(Ky_Ezz_1, Kx)
H14 = I - S.dot(Ky_Ezz_1, Ky)
H21 = 1j * S.dot(Kx_Ezz_1, Ezy)
H22 = 1j * S.dot(Kx_Ezz_1, Ezx)
H23 = S.dot(Kx_Ezz_1, Kx) - I
H24 = -S.dot(Kx_Ezz_1, Ky)
H31 = S.dot(Kx, Ky) + Exy - S.dot(Exz_Ezz_1, Ezy)
H32 = Exx_1_1 - S.dot(Ky, Ky) - S.dot(Exz_Ezz_1, Ezx)
H33 = 1j * S.dot(Exz_Ezz_1, Kx)
H34 = -1j * S.dot(Exz_Ezz_1, Ky)
H41 = S.dot(Kx, Kx) - Eyy + S.dot(Eyz_Ezz_1, Ezy)
H42 = -S.dot(Kx, Ky) - Eyx + S.dot(Eyz_Ezz_1, Ezx)
H43 = -1j * S.dot(Eyz_Ezz_1, Kx)
H44 = 1j * S.dot(Eyz_Ezz_1, Ky)
H = 1j * S.diag(S.repeat(S.diag(Kz), 4)) + S.asarray(
S.bmat(
[
[H11, H12, H13, H14],
[H21, H22, H23, H24],
[H31, H32, H33, H34],
[H41, H42, H43, H44],
]
)
)
q, W = eig(H)
W1, W2, W3, W4 = S.split(W, 4)
#
# boundary conditions
#
# x = [R T]
# R = [ROx ROy REx REy]
# T = [TOx TOy TEx TEy]
# b + MR.R = M1p.c
# M1.c = M2p.c
# ...
# ML.c = MT.T
# therefore: b + MR.R = (M1p.M1^-1.M2p.M2^-1. ...).MT.T
# missing equations from (46)..(49) in glytsis_rigorous
# [b] = [-MR Mtot.MT] [R]
# [0] [...........] [T]
z = S.zeros_like(q)
z[S.where(q.real > 0)] = -thickness
D = S.exp(k * q * z)
Sy0 = W1 * D[S.newaxis, :]
Sx0 = W2 * D[S.newaxis, :]
Uy0 = W3 * D[S.newaxis, :]
Ux0 = W4 * D[S.newaxis, :]
z = thickness * S.ones_like(q)
z[S.where(q.real > 0)] = 0
D = S.exp(k * q * z)
D1 = S.exp(-1j * k2i[2, :] * thickness)
Syd = D1[:, S.newaxis] * W1 * D[S.newaxis, :]
Sxd = D1[:, S.newaxis] * W2 * D[S.newaxis, :]
Uyd = D1[:, S.newaxis] * W3 * D[S.newaxis, :]
Uxd = D1[:, S.newaxis] * W4 * D[S.newaxis, :]
Mp[:, :, nlayer] = S.r_[Sx0, Sy0, -1j * Ux0, -1j * Uy0]
M[:, :, nlayer] = S.r_[Sxd, Syd, -1j * Uxd, -1j * Uyd]
Mtot = S.eye(4 * nood, dtype=complex)
for nlayer in range(1, nlayers - 1):
Mtot = S.dot(S.dot(Mtot, Mp[:, :, nlayer]), inv(M[:, :, nlayer]))
BC_b = S.r_[b, S.zeros_like(b)]
BC_A1 = S.c_[-MR, S.dot(Mtot, MT)]
BC_A2 = S.asarray(
S.bmat(
[
[
(c1[0] * I - c1[2] * S.dot(CRO_1, ARO)),
(c1[1] * I - c1[2] * S.dot(CRO_1, BRO)),
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
],
[
ZERO,
ZERO,
(DRE - S.dot(S.dot(FRE, CRE_1), ARE)),
(ERE - S.dot(S.dot(FRE, CRE_1), BRE)),
ZERO,
ZERO,
ZERO,
ZERO,
],
[
ZERO,
ZERO,
ZERO,
ZERO,
(c3[0] * I - c3[2] * S.dot(CTO_1, ATO)),
(c3[1] * I - c3[2] * S.dot(CTO_1, BTO)),
ZERO,
ZERO,
],
[
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
(DTE - S.dot(S.dot(FTE, CTE_1), ATE)),
(ETE - S.dot(S.dot(FTE, CTE_1), BTE)),
],
]
)
)
BC_A = S.r_[BC_A1, BC_A2]
x = linsolve(BC_A, BC_b)
ROx, ROy, REx, REy, TOx, TOy, TEx, TEy = S.split(x, 8)
ROz = -S.dot(CRO_1, (S.dot(ARO, ROx) + S.dot(BRO, ROy)))
REz = -S.dot(CRE_1, (S.dot(ARE, REx) + S.dot(BRE, REy)))
TOz = -S.dot(CTO_1, (S.dot(ATO, TOx) + S.dot(BTO, TOy)))
TEz = -S.dot(CTE_1, (S.dot(ATE, TEx) + S.dot(BTE, TEy)))
denom = (k1[2] - S.dot(u, k1) * u[2]).real
DEO1[:, iwl] = (
-(
(S.absolute(ROx) ** 2 + S.absolute(ROy) ** 2 + S.absolute(ROz) ** 2)
* S.conj(kO1i[2, :])
- (ROx * kO1i[0, :] + ROy * kO1i[1, :] + ROz * kO1i[2, :])
* S.conj(ROz)
).real
/ denom
)
DEE1[:, iwl] = (
-(
(S.absolute(REx) ** 2 + S.absolute(REy) ** 2 + S.absolute(REz) ** 2)
* S.conj(kE1i[2, :])
- (REx * kE1i[0, :] + REy * kE1i[1, :] + REz * kE1i[2, :])
* S.conj(REz)
).real
/ denom
)
DEO3[:, iwl] = (
(S.absolute(TOx) ** 2 + S.absolute(TOy) ** 2 + S.absolute(TOz) ** 2)
* S.conj(kO3i[2, :])
- (TOx * kO3i[0, :] + TOy * kO3i[1, :] + TOz * kO3i[2, :]) * S.conj(TOz)
).real / denom
DEE3[:, iwl] = (
(S.absolute(TEx) ** 2 + S.absolute(TEy) ** 2 + S.absolute(TEz) ** 2)
* S.conj(kE3i[2, :])
- (TEx * kE3i[0, :] + TEy * kE3i[1, :] + TEz * kE3i[2, :]) * S.conj(TEz)
).real / denom
# save the results
self.DEO1 = DEO1
self.DEE1 = DEE1
self.DEO3 = DEO3
self.DEE3 = DEE3
return self
def solve(self, wls):
"""Isotropic solver.
INPUT
wls = wavelengths to scan (any asarray-able object).
OUTPUT
self.DE1, self.DE3 = power reflected and transmitted.
NOTE
see:
Moharam, "Formulation for stable and efficient implementation
of the rigorous coupled-wave analysis of binary gratings",
JOSA A, 12(5), 1995
Lalanne, "Highly improved convergence of the coupled-wave
method for TM polarization", JOSA A, 13(4), 1996
Moharam, "Stable implementation of the rigorous coupled-wave
analysis for surface-relief gratings: enhanced trasmittance
matrix approach", JOSA A, 12(5), 1995
"""
self.wls = S.atleast_1d(wls)
LAMBDA = self.LAMBDA
n = self.n
multilayer = self.multilayer
alpha = self.alpha
delta = self.delta
psi = self.psi
phi = self.phi
nlayers = len(multilayer)
i = S.arange(-n, n + 1)
nood = 2 * n + 1
hmax = nood - 1
# grating vector (on the xz plane)
# grating on the xy plane
K = 2 * pi / LAMBDA * S.array([S.sin(phi), 0.0, S.cos(phi)], dtype=complex)
DE1 = S.zeros((nood, self.wls.size))
DE3 = S.zeros_like(DE1)
dirk1 = S.array(
[S.sin(alpha) * S.cos(delta), S.sin(alpha) * S.sin(delta), S.cos(alpha)]
)
# usefull matrices
I = S.eye(i.size)
I2 = S.eye(i.size * 2)
ZERO = S.zeros_like(I)
X = S.zeros((2 * nood, 2 * nood, nlayers), dtype=complex)
MTp1 = S.zeros((2 * nood, 2 * nood, nlayers), dtype=complex)
MTp2 = S.zeros_like(MTp1)
EPS2 = S.zeros(2 * hmax + 1, dtype=complex)
EPS21 = S.zeros_like(EPS2)
dlt = (i == 0).astype(int)
for iwl, wl in enumerate(self.wls):
# free space wavevector
k = 2 * pi / wl
n1 = multilayer[0].mat.n(wl).item()
n3 = multilayer[-1].mat.n(wl).item()
# incident plane wave wavevector
k1 = k * n1 * dirk1
# all the other wavevectors
tmp_x = k1[0] - i * K[0]
tmp_y = k1[1] * S.ones_like(i)
tmp_z = dispersion_relation_ordinary(tmp_x, tmp_y, k, n1)
k1i = S.r_[[tmp_x], [tmp_y], [tmp_z]]
# k2i = S.r_[[k1[0] - i*K[0]], [k1[1] - i * K[1]], [-i * K[2]]]
tmp_z = dispersion_relation_ordinary(tmp_x, tmp_y, k, n3)
k3i = S.r_[[k1i[0, :]], [k1i[1, :]], [tmp_z]]
# aliases for constant wavevectors
kx = k1i[0, :]
ky = k1[1]
# angles of reflection
# phi_i = S.arctan2(ky,kx)
phi_i = S.arctan2(ky, kx.real) # OKKIO
Kx = S.diag(kx / k)
Ky = ky / k * I
Z1 = S.diag(k1i[2, :] / (k * n1 ** 2))
Y1 = S.diag(k1i[2, :] / k)
Z3 = S.diag(k3i[2, :] / (k * n3 ** 2))
Y3 = S.diag(k3i[2, :] / k)
# Fc = S.diag(S.cos(phi_i))
fc = S.cos(phi_i)
# Fs = S.diag(S.sin(phi_i))
fs = S.sin(phi_i)
MR = S.asarray(
S.bmat([[I, ZERO], [-1j * Y1, ZERO], [ZERO, I], [ZERO, -1j * Z1]])
)
MT = S.asarray(
S.bmat([[I, ZERO], [1j * Y3, ZERO], [ZERO, I], [ZERO, 1j * Z3]])
)
# internal layers (grating or layer)
X.fill(0.0)
MTp1.fill(0.0)
MTp2.fill(0.0)
for nlayer in range(nlayers - 2, 0, -1): # internal layers
layer = multilayer[nlayer]
d = layer.thickness
EPS2, EPS21 = layer.getEPSFourierCoeffs(wl, n, anisotropic=False)
E = toeplitz(EPS2[hmax::-1], EPS2[hmax:])
E1 = toeplitz(EPS21[hmax::-1], EPS21[hmax:])
E11 = inv(E1)
# B = S.dot(Kx, linsolve(E,Kx)) - I
B = kx[:, S.newaxis] / k * linsolve(E, Kx) - I
# A = S.dot(Kx, Kx) - E
A = S.diag((kx / k) ** 2) - E
# Note: solution bug alfredo
# randomizzo Kx un po' a caso finche' cond(A) e' piccolo (<1e10)
# soluzione sporca... :-(
# per certi kx, l'operatore di helmholtz ha 2 autovalori nulli e A, B
# non sono invertibili --> cambio leggermente i kx... ma dovrei invece
# trattare separatamente (analiticamente) questi casi
if cond(A) > 1e10:
warning("BAD CONDITIONING: randomization of kx")
while cond(A) > 1e10:
Kx = Kx * (1 + 1e-9 * S.rand())
B = kx[:, S.newaxis] / k * linsolve(E, Kx) - I
A = S.diag((kx / k) ** 2) - E
if S.absolute(K[2] / k) > 1e-10:
raise ValueError(
"First Order Helmholtz Operator not implemented, yet!"
)
elif ky == 0 or S.allclose(S.diag(Ky / ky * k), 1):
# lalanne
# H_U_reduced = S.dot(Ky, Ky) + A
H_U_reduced = (ky / k) ** 2 * I + A
# H_S_reduced = S.dot(Ky, Ky) + S.dot(Kx, linsolve(E, S.dot(Kx, E11))) - E11
H_S_reduced = (
(ky / k) ** 2 * I
+ kx[:, S.newaxis] / k * linsolve(E, kx[:, S.newaxis] / k * E11)
- E11
)
q1, W1 = eig(H_U_reduced)
q1 = S.sqrt(q1)
q2, W2 = eig(H_S_reduced)
q2 = S.sqrt(q2)
# boundary conditions
# V11 = S.dot(linsolve(A, W1), S.diag(q1))
V11 = linsolve(A, W1) * q1[S.newaxis, :]
V12 = (ky / k) * S.dot(linsolve(A, Kx), W2)
V21 = (ky / k) * S.dot(linsolve(B, Kx), linsolve(E, W1))
# V22 = S.dot(linsolve(B, W2), S.diag(q2))
V22 = linsolve(B, W2) * q2[S.newaxis, :]
# Vss = S.dot(Fc, V11)
Vss = fc[:, S.newaxis] * V11
# Wss = S.dot(Fc, W1) + S.dot(Fs, V21)
Wss = fc[:, S.newaxis] * W1 + fs[:, S.newaxis] * V21
# Vsp = S.dot(Fc, V12) - S.dot(Fs, W2)
Vsp = fc[:, S.newaxis] * V12 - fs[:, S.newaxis] * W2
# Wsp = S.dot(Fs, V22)
Wsp = fs[:, S.newaxis] * V22
# Wpp = S.dot(Fc, V22)
Wpp = fc[:, S.newaxis] * V22
# Vpp = S.dot(Fc, W2) + S.dot(Fs, V12)
Vpp = fc[:, S.newaxis] * W2 + fs[:, S.newaxis] * V12
# Wps = S.dot(Fc, V21) - S.dot(Fs, W1)
Wps = fc[:, S.newaxis] * V21 - fs[:, S.newaxis] * W1
# Vps = S.dot(Fs, V11)
Vps = fs[:, S.newaxis] * V11
Mc2bar = S.asarray(
S.bmat(
[
[Vss, Vsp, Vss, Vsp],
[Wss, Wsp, -Wss, -Wsp],
[Wps, Wpp, -Wps, -Wpp],
[Vps, Vpp, Vps, Vpp],
]
)
)
x = S.r_[S.exp(-k * q1 * d), S.exp(-k * q2 * d)]
# Mc1 = S.dot(Mc2bar, S.diag(S.r_[S.ones_like(x), x]))
xx = S.r_[S.ones_like(x), x]
Mc1 = Mc2bar * xx[S.newaxis, :]
X[:, :, nlayer] = S.diag(x)
MTp = linsolve(Mc2bar, MT)
MTp1[:, :, nlayer] = MTp[0 : 2 * nood, :]
MTp2 = MTp[2 * nood :, :]
MT = S.dot(
Mc1,
S.r_[
I2,
S.dot(MTp2, linsolve(MTp1[:, :, nlayer], X[:, :, nlayer])),
],
)
else:
ValueError("Second Order Helmholtz Operator not implemented, yet!")
# M = S.asarray(S.bmat([-MR, MT]))
M = S.c_[-MR, MT]
b = S.r_[
S.sin(psi) * dlt,
1j * S.sin(psi) * n1 * S.cos(alpha) * dlt,
-1j * S.cos(psi) * n1 * dlt,
S.cos(psi) * S.cos(alpha) * dlt,
]
x = linsolve(M, b)
R, T = S.split(x, 2)
Rs, Rp = S.split(R, 2)
for ii in range(1, nlayers - 1):
T = S.dot(linsolve(MTp1[:, :, ii], X[:, :, ii]), T)
Ts, Tp = S.split(T, 2)
DE1[:, iwl] = (k1i[2, :] / (k1[2])).real * S.absolute(Rs) ** 2 + (
k1i[2, :] / (k1[2] * n1 ** 2)
).real * S.absolute(Rp) ** 2
DE3[:, iwl] = (k3i[2, :] / (k1[2])).real * S.absolute(Ts) ** 2 + (
k3i[2, :] / (k1[2] * n3 ** 2)
).real * S.absolute(Tp) ** 2
# save the results
self.DE1 = DE1
self.DE3 = DE3
return self
def FF(x): # подсчёт значения функции f(x) через сумму ряда в точке x
S = a0 / 2
for i in range(1, k):
S += AK[i] * sp.cos(i * x) + BK[i] * sp.sin(i * x)
return S
import os
import sys
example = 'example_1d_cubic'
title = 'Sine Wave using two 1D Cubic Lagrange Element'
testdatadir = 'data'
docimagedir = os.path.join('..', 'doc', 'images')
# sphinx tag start
import scipy
import morphic
x = scipy.linspace(0, 2 * scipy.pi, 7)
y = scipy.sin(x)
X = scipy.array([x, y]).T
mesh = morphic.Mesh()
for i, xn in enumerate(X):
mesh.add_stdnode(i + 1, xn)
mesh.add_element(1, ['L3'], [1, 2, 3, 4])
mesh.add_element(2, ['L3'], [4, 5, 6, 7])
# sphinx tag end
if len(sys.argv) > 1:
action = sys.argv[1]
from matplotlib import pyplot
import pickle
Xn = mesh.get_nodes()
def generate_base_points(num_points, domain_size, prob=None):
r"""
Generates a set of base points for passing into the DelaunayVoronoiDual
class. The points can be distributed in spherical, cylindrical, or
rectilinear patterns.
Parameters
----------
num_points : scalar
The number of base points that lie within the domain. Note that the
actual number of points returned will be larger, with the extra points
lying outside the domain.
domain_size : list or array
Controls the size and shape of the domain, as follows:
**sphere** : If a single value is received, its treated as the radius
[r] of a sphere centered on [0, 0, 0].
**cylinder** : If a two-element list is received it's treated as the
radius and height of a cylinder [r, z] positioned at [0, 0, 0] and
extending in the positive z-direction.
**rectangle** : If a three element list is received, it's treated
as the outer corner of rectangle [x, y, z] whose opposite corner lies
at [0, 0, 0].
prob : 3D array, optional
A 3D array that contains fractional (0-1) values indicating the
liklihood that a point in that region should be kept. If not specified
an array containing 1's in the shape of a sphere, cylinder, or cube is
generated, depnending on the give ``domain_size`` with zeros outside.
When specifying a custom probabiliy map is it recommended to also set
values outside the given domain to zero. If not, then the correct
shape will still be returned, but with too few points in it.
Notes
-----
This method places the given number of points within the specified domain,
then reflects these points across each domain boundary. This results in
smooth flat faces at the boundaries once these excess pores are trimmed.
The reflection approach tends to create larger pores near the surfaces, so
it might be necessary to use the ``prob`` argument to specify a slightly
higher density of points near the surfaces.
For rough faces, it is necessary to define a larger than desired domain
then trim to the desired size. This will discard the reflected points
plus some of the original points.
Examples
--------
The following generates a spherical array with higher values near the core.
It uses a distance transform to create a sphere of radius 10, then a
second distance transform to create larger values in the center away from
the sphere surface. These distance values could be further skewed by
applying a power, with values higher than 1 resulting in higher values in
the core, and fractional values smoothinging them out a bit.
>>> import OpenPNM as op
>>> import scipy as sp
>>> import scipy.ndimage as spim
>>> im = sp.ones([21, 21, 21], dtype=int)
>>> im[10, 10, 10] = 0
>>> im = spim.distance_transform_edt(im) <= 20 # Create sphere of 1's
>>> prob = spim.distance_transform_edt(im)
>>> prob = prob / sp.amax(prob) # Normalize between 0 and 1
>>> pts = op.Network.tools.generate_base_points(num_points=50,
... domain_size=[2],
... prob=prob)
>>> net = op.Network.DelaunayVoronoiDual(points=pts, domain_size=[2])
"""
def _try_points(num_points, prob):
prob = _sp.array(prob)/_sp.amax(prob) # Ensure prob is normalized
base_pts = []
N = 0
while N < num_points:
pt = _sp.random.rand(3) # Generate a point
# Test whether to keep it or not
[indx, indy, indz] = _sp.floor(pt*_sp.shape(prob)).astype(int)
if _sp.random.rand(1) <= prob[indx][indy][indz]:
base_pts.append(pt)
N += 1
base_pts = _sp.array(base_pts)
return base_pts
if len(domain_size) == 1: # Spherical
domain_size = _sp.array(domain_size)
if prob is None:
prob = _sp.ones([41, 41, 41])
prob[20, 20, 20] = 0
prob = _spim.distance_transform_bf(prob) <= 20
base_pts = _try_points(num_points, prob)
# Convert to spherical coordinates
[X, Y, Z] = _sp.array(base_pts - [0.5, 0.5, 0.5]).T # Center at origin
r = 2*_sp.sqrt(X**2 + Y**2 + Z**2)*domain_size[0]
theta = 2*_sp.arctan(Y/X)
phi = 2*_sp.arctan(_sp.sqrt(X**2 + Y**2)/Z)
# Trim points outside the domain (from improper prob images)
inds = r <= domain_size[0]
[r, theta, phi] = [r[inds], theta[inds], phi[inds]]
# Reflect base points across perimeter
new_r = 2*domain_size - r
r = _sp.hstack([r, new_r])
theta = _sp.hstack([theta, theta])
phi = _sp.hstack([phi, phi])
# Convert to Cartesean coordinates
X = r*_sp.cos(theta)*_sp.sin(phi)
Y = r*_sp.sin(theta)*_sp.sin(phi)
Z = r*_sp.cos(phi)
base_pts = _sp.vstack([X, Y, Z]).T
elif len(domain_size) == 2: # Cylindrical
domain_size = _sp.array(domain_size)
if prob is None:
prob = _sp.ones([41, 41, 41])
prob[20, 20, :] = 0
prob = _spim.distance_transform_bf(prob) <= 20
base_pts = _try_points(num_points, prob)
# Convert to cylindrical coordinates
[X, Y, Z] = _sp.array(base_pts - [0.5, 0.5, 0]).T # Center on z-axis
r = 2*_sp.sqrt(X**2 + Y**2)*domain_size[0]
theta = 2*_sp.arctan(Y/X)
z = Z*domain_size[1]
# Trim points outside the domain (from improper prob images)
inds = r <= domain_size[0]
[r, theta, z] = [r[inds], theta[inds], z[inds]]
inds = ~((z > domain_size[1]) + (z < 0))
[r, theta, z] = [r[inds], theta[inds], z[inds]]
# Reflect base points about faces and perimeter
new_r = 2*domain_size[0] - r
r = _sp.hstack([r, new_r])
theta = _sp.hstack([theta, theta])
z = _sp.hstack([z, z])
r = _sp.hstack([r, r, r])
theta = _sp.hstack([theta, theta, theta])
z = _sp.hstack([z, -z, 2-z])
# Convert to Cartesean coordinates
X = r*_sp.cos(theta)
Y = r*_sp.sin(theta)
Z = z
base_pts = _sp.vstack([X, Y, Z]).T
elif len(domain_size) == 3: # Rectilinear
domain_size = _sp.array(domain_size)
Nx, Ny, Nz = domain_size
if prob is None:
prob = _sp.ones([10, 10, 10], dtype=float)
base_pts = _try_points(num_points, prob)
base_pts = base_pts*domain_size
# Reflect base points about all 6 faces
orig_pts = base_pts
base_pts = _sp.vstack((base_pts, [-1, 1, 1]*orig_pts +
[2.0*Nx, 0, 0]))
base_pts = _sp.vstack((base_pts, [1, -1, 1]*orig_pts +
[0, 2.0*Ny, 0]))
base_pts = _sp.vstack((base_pts, [1, 1, -1]*orig_pts +
[0, 0, 2.0*Nz]))
base_pts = _sp.vstack((base_pts, [-1, 1, 1]*orig_pts))
base_pts = _sp.vstack((base_pts, [1, -1, 1]*orig_pts))
base_pts = _sp.vstack((base_pts, [1, 1, -1]*orig_pts))
return base_pts
N = 8
array = buildAntennaArray(num_elements=N,
ref_element=1,
seperation=wavelength / 2)
plt.axis([-2, 2, -2, 2])
plt.ion()
plt.show()
for angle in range(-89, 89, 1):
plt.clf()
plt.axis([-2, 2, -2, 2])
plt.plot(array, sp.zeros(N, dtype=sp.double), 'or')
pd = calculatePhaseDelay(array, (angle * sp.pi / 180), wavelength)
aoa = calculateAOA(array, pd, wavelength)
#print aoa
for i in range(N):
mag = 1
ang = aoa[i]
x = array[i]
y = 0
# remember, 0 degrees should be boresight
plt.plot([x, mag * sp.cos((90 - ang) * sp.pi / 180) + x],
[y, mag * sp.sin((90 - ang) * sp.pi / 180) + y], 'r')
plt.draw()
plt.pause(0.001)
#raw_input("paused...")
def g(wind_angle, num_iterations=num_iterations):
# wind_angle = 7*np.pi/4
wind_mag = 1.2
#Loop through pickle files for that parameter value and merge counts
for i in range(num_iterations):
# file_name = 'trap_arrival_by_wind_live_coarse_dt'
# file_name = 'trap_time_course_by_wind'
# file_name = 'trap_arrival_by_wind_fit_gauss'
file_name = 'trap_arrival_by_wind_adjusted_fit_gauss'
file_name = file_name + '_wind_mag_' + str(
wind_mag) #+'_wind_angle_'+str(wind_angle)[0:4]+'_iter_'+str(i)
# file_name = file_name +'_wind_mag_'+str(wind_mag)+'_wind_angle_'+str(wind_angle)[0:4]+'_iter_'+str(i)
# file_name = file_name +'_wind_mag_'+str(wind_mag)
output_file = file_name + '.pkl'
with open(output_file, 'r') as f:
(_, swarm) = pickle.load(f)
# swarm = pickle.load(f)
if i == 0:
sim_trap_counts_cumul = np.zeros(swarm.num_traps)
sim_trap_counts_cumul += swarm.get_trap_counts()
# print(sim_trap_counts_cumul)
#Trap arrival plot
#Set 0s to 1 for plotting purposes
sim_trap_counts_cumul /= num_iterations
sim_trap_counts_cumul[sim_trap_counts_cumul == 0] = .5
trap_locs = (2 * scipy.pi / swarm.num_traps) * scipy.array(
swarm.list_all_traps())
radius_scale = 0.3
plot_size = 1.5
fig = plt.figure(200 + int(10 * wind_mag))
ax = plt.subplot(aspect=1)
trap_locs_2d = [(scipy.cos(trap_loc), scipy.sin(trap_loc))
for trap_loc in trap_locs]
patches = [
plt.Circle(center, size) for center, size in zip(
trap_locs_2d, radius_scale * sim_trap_counts_cumul /
max(sim_trap_counts_cumul))
]
biggest_trap_loc = trap_locs_2d[np.where(
sim_trap_counts_cumul == max(sim_trap_counts_cumul))[0][0]]
coll = matplotlib.collections.PatchCollection(patches,
facecolors='blue',
edgecolors='blue')
ax.add_collection(coll)
ax.set_ylim([-plot_size, plot_size])
ax.set_xlim([-plot_size, plot_size])
ax.set_xticks([])
ax.set_xticklabels('')
ax.set_yticks([])
ax.set_yticklabels('')
#Label max trap count
ax.text(biggest_trap_loc[0],
biggest_trap_loc[1],
str(max(sim_trap_counts_cumul)),
horizontalalignment='center',
verticalalignment='center',
fontsize=18,
color='white')
#Wind arrow
plt.arrow(
0.5,
0.5,
0.1 * scipy.cos(wind_angle),
0.1 * scipy.sin(wind_angle),
transform=ax.transAxes,
color='b',
width=0.001,
head_width=0.03,
head_length=0.05,
)
# ax.text(0.55, 0.5,'Wind',transform=ax.transAxes,color='b')
ax.text(0,
1.5,
'N',
horizontalalignment='center',
verticalalignment='center',
fontsize=25)
ax.text(0,
-1.5,
'S',
horizontalalignment='center',
verticalalignment='center',
fontsize=25)
ax.text(1.5,
0,
'E',
horizontalalignment='center',
verticalalignment='center',
fontsize=25)
ax.text(-1.5,
0,
'W',
horizontalalignment='center',
verticalalignment='center',
fontsize=25)
# plt.title('Simulated')
fig.patch.set_facecolor('white')
plt.axis('off')
ax.text(0,
1.7,
'Trap Counts' + ' (Wind Mag: ' + str(wind_mag)[0:3] + ')',
horizontalalignment='center',
verticalalignment='center',
fontsize=20)
# file_name = 'trap_arrival_by_wind_live_coarse_dt'
file_name = 'trap_arrival_by_wind_adjusted_fit_gauss'
png_file_name = file_name + '_wind_mag_' + str(
wind_mag) + '_wind_angle_' + str(wind_angle)[0:4]
plt.savefig(png_file_name + '.png', format='png')
import scipy as sp
import scipy.misc
import scipy.constants
from scipy import pi
if __name__ == "__main__" and __package__ is None:
sys.path.append('..')
__package__ = "doamusic"
import doamusic
from doamusic import music
from doamusic import _music
from doamusic import util
# 16 element unit circle in the y-z plane
antx = sp.arange(16)
circarray = sp.array([0*antx, sp.cos(antx), sp.sin(antx)]).T
# 3 offset circles in planes paralell to y-z
front = circarray + [1,0,0]
back = circarray - [1,0,0]
triplecircarray = sp.concatenate((front,circarray,back))
# unit spacing grid (5x5)
gridarray = sp.array(
[ (0,y,z) for y,z in itertools.product(range(-3,4),repeat=2) ]
)
# unit spacing linear
linarray = sp.array( [ (0,y,0) for y in range(10) ] )
# Arrays as constructed.
def f(x, y):
return 3.0 * scipy.sin(x * y + 1e-4) / (x * y + 1e-4)
def calculatePhaseDelay(array, angle, wavelength):
phasedelay = 2 * sp.pi * array * sp.sin(angle) / wavelength
phasedelay = abs(phasedelay) % (2 * sp.pi) * phasedelay / abs(
phasedelay
) # this adds realism, you'd never be able to detect the overall phasedelays beyond the -pi to pi range
return phasedelay
else:
print "plotting only supported for indim=1 or indim=2."
if __name__ == '__main__':
from pylab import figure, show
# --- example on how to use the GP in 1 dimension
ds = SupervisedDataSet(1, 1)
gp = GaussianProcess(indim=1, start=-3, stop=3, step=0.05)
figure()
x = mgrid[-3:3:0.2]
y = 0.1 * x**2 + x + 1
z = sin(x) + 0.5 * cos(y)
ds.addSample(-2.5, -1)
ds.addSample(-1.0, 3)
gp.mean = 0
# new feature "autonoise" adds uncertainty to data depending on
# it's distance to other points in the dataset. not tested much yet.
# gp.autonoise = True
gp.trainOnDataset(ds)
gp.plotCurves(showSamples=True)
# you can also test the gp on single points, but this deletes the
# original testing grid. it can be restored with a call to _buildGrid()
print gp.testOnArray(array([[0.4]]))
import matplotlib.pyplot as plt
from matplotlib import rc
rc('text', usetex=True)
################################# USER SETTINGS ###################################
"""
Diffeq params
"""
lmd1 = 1.0
lmd2 = 2.0
xa = 0.0
xg = 1.0
xb = 2.0
ua = 1.0
ub = 3.0
f1 = lambda x: sc.sin(x)
f2 = lambda x: sc.cos(3*x)
globres = 1000 #Resoltion of global discretisations
dnres1 = 5 # Resolution of the dir/neu alg discretisations
dnres2 = 7
"""
Discretisation params
"""
dirDisc = "FEM" # FDM,FEM,FVM
neuDisc = "FVM" # FDM,FEM,FVM
############################# PROGRAM ##############################
def Ldense(x):
return sc.expm1(3*x)/(sc.exp(3)-1)
def __init__(self):
""" Constructor or the initializer """
QMainWindow.__init__(self)
# Set some default attributes of the window
self.setAttribute(Qt.WA_DeleteOnClose)
self.setWindowTitle("Reflection and Refraction")
# define the main widget as self
self.main_widget = QWidget(self)
# Add the label widgets and sliders
# Refractive Index - Object Side
self.loRIOne = QVBoxLayout()
self.lblRIOne = QLabel("Refractive Index: n1", self)
self.sldRIOne = QSlider(Qt.Horizontal)
self.sldRIOne.setMinimum(100)
self.sldRIOne.setMaximum(200)
self.sldRIOne.setValue(100)
self.sldRIOne.setTickPosition(QSlider.TicksBelow)
self.sldRIOne.setTickInterval(10)
self.edtRIOne = QLineEdit(self)
self.edtRIOne.setMaxLength(5)
self.loRIOne.addWidget(self.lblRIOne)
self.loRIOne.addSpacing(3)
self.loRIOne.addWidget(self.sldRIOne)
self.loRIOne.addSpacing(3)
self.loRIOne.addWidget(self.edtRIOne)
# Refractive Index - Object Side
self.loRITwo = QVBoxLayout()
self.lblRITwo = QLabel("Refractive Index: n2", self)
self.sldRITwo = QSlider(Qt.Horizontal)
self.sldRITwo.setMinimum(100)
self.sldRITwo.setMaximum(200)
self.sldRITwo.setValue(152)
self.sldRITwo.setTickPosition(QSlider.TicksBelow)
self.sldRITwo.setTickInterval(10)
self.edtRITwo = QLineEdit(self)
self.edtRITwo.setMaxLength(5)
self.loRITwo.addWidget(self.lblRITwo)
self.loRITwo.addSpacing(3)
self.loRITwo.addWidget(self.sldRITwo)
self.loRITwo.addSpacing(3)
self.loRITwo.addWidget(self.edtRITwo)
# Angle of incidence
self.loIncAng = QVBoxLayout()
self.lblIncAng = QLabel("Angle of Incidence", self)
self.sldIncAng = QSlider(Qt.Horizontal)
self.sldIncAng.setMinimum(0)
self.sldIncAng.setMaximum(90)
self.sldIncAng.setValue(30)
self.sldIncAng.setTickPosition(QSlider.TicksBelow)
self.sldIncAng.setTickInterval(10)
self.edtIncAng = QLineEdit(self)
self.edtIncAng.setMaxLength(2)
self.loIncAng.addWidget(self.lblIncAng)
self.loIncAng.addSpacing(3)
self.loIncAng.addWidget(self.sldIncAng)
self.loIncAng.addSpacing(3)
self.loIncAng.addWidget(self.edtIncAng)
# Angle of refraction
self.loRefrAng = QHBoxLayout()
self.lblRefrAng = QLabel("Angle of Refraction", self)
self.edtRefrAng = QLineEdit(self)
self.loRefrAng.addWidget(self.lblRefrAng)
self.loRefrAng.addSpacing(3)
self.loRefrAng.addWidget(self.edtRefrAng)
refrAng = 180.0 / pi * arcsin(1.0 * sin(pi / 180.0 * 30) / 1.52)
self.edtRefrAng.setText(str('%5.3f' % (refrAng)))
# Waves Param Layout
self.loRayParams = QHBoxLayout()
self.loRayParams.addLayout(self.loRIOne)
self.loRayParams.addStretch()
self.loRayParams.addLayout(self.loRITwo)
self.loRayParams.addStretch()
self.loRayParams.addLayout(self.loIncAng)
# Get the values from the sliders
nOne = self.sldRIOne.value() / 100
nTwo = self.sldRITwo.value() / 100
incAng = self.sldIncAng.value()
self.edtRIOne.setText(str(nOne))
self.edtRITwo.setText(str(nTwo))
self.edtIncAng.setText(str(incAng))
# Create an instance of the FigureCanvas
self.loCanvas = MplCanvas(self.main_widget,
width=5,
height=4,
nOne=nOne,
nTwo=nTwo,
incAng=incAng)
# Set the focus to the main_widget and set it to be central widget
self.main_widget.setFocus()
self.setCentralWidget(self.main_widget)
# Populate the master layout
self.loMaster = QVBoxLayout(self.main_widget)
self.loMaster.addLayout(self.loRayParams)
self.loMaster.addWidget(self.loCanvas)
self.loMaster.addLayout(self.loRefrAng)
# Connect slots
self.sldRIOne.valueChanged.connect(self.OnRIOneChanged)
self.sldRITwo.valueChanged.connect(self.OnRITwoChanged)
self.sldIncAng.valueChanged.connect(self.OnIncAngChanged)
self.edtRIOne.editingFinished.connect(self.OnEdtRIOneChanged)
self.edtRITwo.editingFinished.connect(self.OnEdtRITwoChanged)
self.edtIncAng.editingFinished.connect(self.OnEdtIncAngChanged)
def drawPlot(self, nOne, nTwo, incAng):
self.ax.clear()
# Angle of reflection
reflAng = incAng
# Angle of refraction
refrAng = 180.0 / pi * arcsin(nOne * sin(pi / 180.0 * incAng) / nTwo)
# The canvas
x = linspace(-3.0, 3.0, 1024)
y = linspace(-3.0, 3.0, 1024)
X, Y = meshgrid(x, y)
y = sin(2 * pi * x / (nOne / 1000) + nTwo)
# Draw the boundary between the two media
bdy = mlines.Line2D([0, 0], [-3, 3], color='k')
self.ax.add_line(bdy)
# Draw the normal
nml = mlines.Line2D([-2, 2], [0, 0], ls='dashed', color='k')
self.ax.add_line(nml)
# Draw the incident and reflected ray
lIncRay = lRefrRay = lReflRay = 2.8
xIncRay = -lIncRay * cos(pi / 180.0 * incAng)
yIncRay = -lIncRay * sin(pi / 180.0 * incAng)
xReflRay = xIncRay
yReflRay = -yIncRay
incRay = mlines.Line2D([xIncRay, 0], [yIncRay, 0], color='k')
self.ax.add_line(incRay)
# Draw the arrow at the middle of the ray
self.ax.arrow(xIncRay / 2,
yIncRay / 2,
0.05,
0.05 * tan(pi / 180.0 * incAng),
length_includes_head=True,
head_width=0.1,
color='k',
shape='full')
reflRay = mlines.Line2D([xReflRay, 0], [yReflRay, 0], color='k')
self.ax.add_line(reflRay)
# Draw the arrow at the middle of the ray
self.ax.arrow(xReflRay / 2,
yReflRay / 2,
-0.05,
0.05 * tan(pi / 180.0 * reflAng),
length_includes_head=True,
head_width=0.1,
color='k',
shape='full')
# Draw the refracted ray
if not isinstance(refrAng, complex):
xRefrRay = lRefrRay * cos(pi / 180.0 * refrAng)
yRefrRay = lRefrRay * sin(pi / 180.0 * refrAng)
refrRay = mlines.Line2D([0, xRefrRay], [0, yRefrRay], color='k')
self.ax.add_line(refrRay)
# Draw the arrow at the middle of the ray
self.ax.arrow(xRefrRay / 2,
yRefrRay / 2,
0.05,
0.05 * tan(pi / 180.0 * refrAng),
length_includes_head=True,
head_width=0.1,
color='k',
shape='full')
# Set the axes properties
self.ax.set_ylim(-3, 3)
self.ax.set_xlim(-3, 3)
self.ax.set_xticklabels([])
self.ax.set_yticklabels([])
self.ax.text(-2.5, 2.5, 'Medium 1')
self.ax.text(1.0, 2.5, 'Medium 2')
# Draw the axes
self.draw()
import scipy as sp import matplotlib.pylab as plt t = sp.arange(0, 10, 1 / 100) plt.plot(t, sp.sin(1.7 * 2 * sp.pi * t) + sp.sin(1.9 * 2 * sp.pi * t)) plt.show()
def get_E_crit(N):
return - 2 * abs(sp.sin(sp.pi * (2 * sp.arange(N) + 1) / (2 * (2 * N + 1)))).sum()
def Heat_1D(c, L, t, T1, T2, fun=lambda x: 100):
"""
This function gives the solution to the 1D heat equation:
du(x,t)/dt = c^2 d^2(u(x,t))/dx^2
Evaluated at multiple times and positions.
The function only considers members with no internal heat sources. The bar is
assumed to be homogeneous, made of a single material.
This function's resolution is not very fine, it you want better resolution use
single_heat as it will be evaluated at a single position and time.
Inputs:
c: the diffusivity, k/(s*rho)
L: the length of the member
t: the time of interest
T1: boundary condition: u(0,t) = T1
T2: boundary condition: u(L,t) = T2
fun: boundary condition: u(x,0) = f(x)
fun defaults to 100, this means that the bar is at a uniform temperature of 100 when
you start observing the system.
"""
if L <= 10:
point = int(10 * L)
else:
point = 100
if t <= 60:
times = int(5 * t)
else:
times = 350
T = sp.linspace(0, t, times) # the time increments needed
X = sp.linspace(0, L, point) # the points on the bar
N1 = 10 #these are different upperbounds to the series solution to be used as comparison
N2 = 30
N3 = 80
Sol1 = [
] # in the end these will each contain a list for every time value of the solution at the different points on the bar
Sol2 = []
Sol3 = []
for ts in T: #this loops through the different time increments
s1 = [
T1
] #the ends are defined by the boundary conditions so this saves needless calculations
s2 = [T1]
s3 = [T1]
for x in X[
1:-1]: # this loops through the defined positions on the bar
sn1 = [
] #this is list that contains the values of the solution at each n up to N1
sn2 = [
] #this is list that contains the values of the solution at each n up to N2
sn3 = [
] #this is list that contains the values of the solution at each n up to N3
for n in range(1, N1 +
1): # these itterate the n values within the series
lam1 = c * n * pi / L
u1_1 = (
T2 - T1
) * x / L + T1 #this is steady state, time independent solution.
b1_n = integrate.quad(b_n, 0, L, args=(
L,
T1,
T2,
n,
fun,
))[0] #this finds the fourier coefficient
u1_2 = b1_n * sp.exp(-lam1**2 * ts) * sp.sin(
n * pi * x / L) #this is the time dependent solution
u1 = u1_1 + u1_2
sn1.append(
u1) # i think if i had been a little more clever and
#had a bit more time i could have made a subfunction so i would
#not be doing the same calculation 3 times. Use an appropriate bound conditions on for loop as well
for n in range(1, N2 +
1): # these itterate the n values within the series
lam2 = c * n * pi / L
u2_1 = (
T2 - T1
) * x / L + T1 #this is steady state, time independent solution.
b2_n = integrate.quad(b_n, 0, L, args=(
L,
T1,
T2,
n,
fun,
))[0] #this finds the fourier coefficient
u2_2 = b2_n * sp.exp(-lam2**2 * ts) * sp.sin(
n * pi * x / L) #this is the time dependent solution
u2 = u2_1 + u2_2
sn2.append(u2)
for n in range(1, N3 +
1): # these itterate the n values within the series
lam3 = c * n * pi / L
u3_1 = (
T2 - T1
) * x / L + T1 #this is steady state, time independent solution.
b3_n = integrate.quad(b_n, 0, L, args=(
L,
T1,
T2,
n,
fun,
))[0] #this finds the fourier coefficient
u3_2 = b3_n * sp.exp(-lam3**2 * ts) * sp.sin(
n * pi * x / L) #this is the time dependent solution
u3 = u3_1 + u3_2
sn3.append(u3)
sol1 = sumr(
sn1
) #this sums up all the values within the list of the solution evaluated at different n's getting the numerical answer at the position
sol2 = sumr(sn2)
sol3 = sumr(sn3)
s1.append(sol1)
s2.append(sol2)
s3.append(sol3)
if x == X[-2]:
s1.append(
T2
) #the ends are defined by the boundary conditions so this saves needless calculations
s2.append(T2)
s3.append(T2)
Sol1.append(s1)
Sol2.append(s2)
Sol3.append(s3)
return Sol1, Sol2, Sol3, X, T
def somefunc1(x): # function of a scalar argument
if x < 0:
r = 0
else:
r = scipy.sin(x)
return r
# print freq_limit
m_total = sp.zeros((4, 4, freq_limit), float)
m_tot = sp.zeros((freq_limit, 17), float)
for i in range(0, freq_limit):
#Note that this version is based on the combined matrix I derived corrected for linear feed:
dG = mp[i, 1]
al = mp[i, 2] * sp.pi / 180
ps = mp[i, 3] * sp.pi / 180
ph = mp[i, 4] * sp.pi / 180
ep = mp[i, 5]
ch = mp[i, 6] * sp.pi / 180
flux = mp[i, 7]
be = mp[i, 8] * sp.pi / 180
m_total[0, 0, i] = flux
m_total[0, 1, i] = flux * (0.5 * dG * sp.cos(2 * al) - 2 * ep * sp.sin(
2 * al) * sp.cos(ph - ch)) * sp.cos(be) - flux * (
0.5 * dG * sp.sin(2 * al) * sp.cos(ch) + 2 * ep *
(sp.cos(al) * sp.cos(al) * sp.sin(ph) -
sp.sin(al) * sp.sin(al) * sp.cos(ph - 2 * ch))) * sp.sin(be)
m_total[0, 2, i] = flux * (0.5 * dG * sp.cos(2 * al) - 2 * ep * sp.sin(
2 * al) * sp.cos(ph - ch)) * sp.sin(be) + flux * (
0.5 * dG * sp.sin(2 * al) * sp.cos(ch) + 2 * ep *
(sp.cos(al) * sp.cos(al) * sp.sin(ph) -
sp.sin(al) * sp.sin(al) * sp.cos(ph - 2 * ch))) * sp.cos(be)
m_total[0, 3,
i] = flux * (0.5 * dG * sp.sin(2 * al) * sp.sin(ch) + 2 * ep *
(sp.cos(al) * sp.cos(al) * sp.sin(ph) +
sp.sin(al) * sp.sin(al) * sp.sin(ph - 2 * ch)))
m_total[1, 0, i] = flux * 0.5 * dG
m_total[1, 1, i] = flux * sp.cos(2 * al) * sp.cos(be) - flux * sp.sin(
2 * al) * sp.cos(ch) * sp.sin(be)
def single_heat(c, L, x, t, T1, T2, fun=lambda x: 100):
"""
This function gives the solution to the 1D heat equation:
du(x,t)/dt = c^2 d^2(u(x,t))/dx^2
Evaluated at a single time, t, and position, x.
The function only considers members with no internal heat sources. The bar is
assumed to be homogeneous, made of a single material.
Inputs:
c: the diffusivity, k/(s*rho)
L: the length of the member
x: the position of interest
t: the time of interest
T1: boundary condition: u(0,t) = T1
T2: boundary condition: u(L,t) = T2
fun: boundary condition: u(x,0) = f(x)
fun defaults to 100, this means that the bar is at a uniform temperature of 100 when
you start observing the system.
"""
N = 115
sn = [] #this list will contain the solution at each itteration, n
if x == 0:
sol = T1
elif x == L:
sol = T2
else:
for n in range(1,
N + 1): # these itterate the n values within the series
lam1 = c * n * pi / L
u1_1 = (
T2 - T1
) * x / L + T1 #this is steady state, time independent solution.
b1_n = integrate.quad(b_n, 0, L, args=(
L,
T1,
T2,
n,
fun,
))[0] #this finds the fourier coefficient
u1_2 = b1_n * sp.exp(-lam1**2 * t) * sp.sin(
n * pi * x / L) #this is the time dependent solution
u1 = u1_1 + u1_2
sn.append(u1)
sol = sumr(
sn
) #this sums up all the solutions at the values n getting the solution at x,t
return sol, x, t
"""
import matplotlib.pyplot as plt
import scipy as sp
#CADA FIGURE ES UNA VENTANA
#FIGURA 1---------
plt.figure(1)
ejeX = sp.linspace(1,10,100)
y = sp.cos(ejeX)
plt.title('Figura 1')
plt.xlabel('eje x')
plt.ylabel('Mi función coseno')
plt.plot(ejeX, y, 'bo')
#FIGURA 2---------
plt.figure(2)
ejeX2 = sp.linspace(10, 50, 20)
g = sp.sin(ejeX2)
plt.xlabel('eje x')
plt.ylabel('Mi función seno')
plt.title('Figura 2')
plt.plot(ejeX2, g, 'r--')
#FIGURA 3
plt.figure(3)
with plt.style.context(('dark_background')):
plt.plot(ejeX2, g, 'r-o')
plt.show()
def run(hps=None):
defaults = PaperDefaults()
#David's globals
_DECODER_TYPE = None #'circular_vote'
_DEFAULT_KW97_TILTEFFECT_DEGPERPIX = .45 # <OToole77>
_DEFAULT_TILTEFFECT_SIZE = 101 #101
_DEFAULT_KW97_TILTEFFECT_CSIZE = iround(3.6 /
_DEFAULT_KW97_TILTEFFECT_DEGPERPIX)
_DEFAULT_KW97_TILTEFFECT_NSIZE = iround(5.4 /
_DEFAULT_KW97_TILTEFFECT_DEGPERPIX)
_DEFAULT_KW97_TILTEFFECT_FSIZE = iround(10.7 /
_DEFAULT_KW97_TILTEFFECT_DEGPERPIX)
_DEFAULT_TILTEFFECT_CVAL = .5
_DEFAULT_TILTEFFECT_SVALS = np.linspace(0.0, 0.5, 10)
_DEFAULT_KW97_TILTEFFECT_SCALE = 1.25
_DEFAULT_TILTEFFECT_NPOINTS = 25 #100
_DEFAULT_TILTEFFECT_CIRCULAR = True
_DEFAULT_TILTEFFECT_DECODER_TYPE = 'circular_vote'
csvfiles = [
os.path.join(defaults._DATADIR, 'KW97_GH.csv'),
os.path.join(defaults._DATADIR, 'KW97_JHK.csv'),
os.path.join(defaults._DATADIR, 'KW97_LL.csv'),
os.path.join(defaults._DATADIR, 'KW97_SJL.csv'),
]
# experiment parameters
m = (lambda x: sp.sin(sp.pi * x)) if _DEFAULT_TILTEFFECT_CIRCULAR else (
lambda x: x)
cpt = (_DEFAULT_TILTEFFECT_SIZE // 2, _DEFAULT_TILTEFFECT_SIZE // 2)
spt = (_DEFAULT_TILTEFFECT_SIZE // 2,
_DEFAULT_TILTEFFECT_SIZE // 2 + _DEFAULT_KW97_TILTEFFECT_CSIZE)
dt_in = _DEFAULT_TILTEFFECT_CVAL - _DEFAULT_TILTEFFECT_SVALS
dtmin = dt_in.min()
dtmax = dt_in.max()
# simulate populations
im = sp.array([[
stim.get_center_nfsurrounds(size=_DEFAULT_TILTEFFECT_SIZE,
csize=_DEFAULT_KW97_TILTEFFECT_CSIZE,
nsize=_DEFAULT_KW97_TILTEFFECT_NSIZE,
fsize=_DEFAULT_KW97_TILTEFFECT_FSIZE,
cval=_DEFAULT_TILTEFFECT_CVAL,
nval=sp.nan,
fval=sval,
bgval=sp.nan)
] for sval in _DEFAULT_TILTEFFECT_SVALS])
# get shifts for model for both papers, and from digitized data
sortidx = sp.argsort(dt_in) # re-order in increasing angular differences
# O'Toole and Wenderoth (1977)
n_subjects = len(csvfiles)
ds_kw97_paper_x = sp.zeros((n_subjects, 9))
ds_kw97_paper_y = sp.zeros((n_subjects, 9))
for sidx, csv in enumerate(csvfiles):
ds_kw97_paper_x[sidx], ds_kw97_paper_y[sidx] = \
sp.genfromtxt(csv, delimiter=',').T
dt_model = (_DEFAULT_TILTEFFECT_CVAL -
_DEFAULT_TILTEFFECT_SVALS)[sortidx] * 360
ds_kw97_paper_x = (ds_kw97_paper_x + 360.) % 360. - 45.
ds_kw97_paper_y = 45. - ds_kw97_paper_y
for sidx in range(n_subjects):
ds_kw97_paper_x[sidx] = ds_kw97_paper_x[sidx][sp.argsort(
ds_kw97_paper_x[sidx])]
extra_vars = {}
extra_vars['scale'] = _DEFAULT_KW97_TILTEFFECT_SCALE
extra_vars['decoder'] = _DEFAULT_TILTEFFECT_DECODER_TYPE
extra_vars['npoints'] = _DEFAULT_TILTEFFECT_NPOINTS
extra_vars['npoints'] = _DEFAULT_TILTEFFECT_NPOINTS
extra_vars['cval'] = _DEFAULT_TILTEFFECT_CVAL
extra_vars['sortidx'] = sortidx
extra_vars['cpt'] = cpt
extra_vars['spt'] = spt
extra_vars['sval'] = sval
extra_vars['kind'] = 'circular'
extra_vars['figure_name'] = 'f3b'
extra_vars['return_var'] = 'O'
adjusted_gt = signal.resample(np.mean(ds_kw97_paper_y, axis=0), 10)
defaults = adjust_parameters(defaults, hps)
optimize_model(im, adjusted_gt, extra_vars, defaults)
def f(r, t):
theta = r[0]
omega = r[1]
ftheta = omega
fomega = -(g / l) * sin(theta)
return array([ftheta, fomega], float)
def fit(
self,
raw_data=None,
n_slices=None,
n_scans=None,
timing=None,
):
"""Fits an STC transform that can be later used (using the
transform(..) method) to re-slice compatible data.
Each row of the fitter transform is precisely the filter by
which the signal will be convolved to introduce the phase
shift in the corresponding slice. It is constructed explicitly
in the Fourier domain. In the time domain, it can be described
via the Whittaker-Shannon formula (sinc interpolation).
Parameters
----------
raw_data: 4D array of shape (n_rows, n_colomns, n_slices,
n_scans) (optional, default None)
raw data to fit the transform on. If this is specified, then
n_slices and n_scans parameters should not be specified.
n_slices: int (optional, default None)
number of slices in each 3D volume. If the raw_data parameter
is specified then this parameter should not be specified
n_scans: int (optional, default None)
number of 3D volumes. If the raw_data parameter
is specified then this parameter should not be specified
timing: list or tuple of length 2 (optional, default None)
additional information for sequence timing
timing[0] = time between slices
timing[1] = time between last slices and next volume
Returns
-------
self: fitted STC object
Raises
------
ValueError, in case parameters are insane
"""
# set basic meta params
if not raw_data is None:
raw_data = self._sanitize_raw_data(
raw_data,
fitting=True,
)
self.n_slices = raw_data.shape[2]
self.n_scans = raw_data.shape[-1]
self.raw_data = raw_data
else:
if n_slices is None:
raise ValueError(
"raw_data parameter not specified. You need to"
" specify a value for n_slices!")
else:
self.n_slices = n_slices
if n_scans is None:
raise ValueError(
"raw_data parameter not specified. You need to"
" specify a value for n_scans!")
else:
self.n_scans = n_scans
# fix slice indices consistently with slice order
self.slice_indices = get_slice_indices(self.n_slices,
slice_order=self.slice_order,
return_final=True,
interleaved=self.interleaved)
# fix ref slice index, to be consistent with the slice order
self.ref_slice = self.slice_indices[self.ref_slice]
# timing info (slice_TR is the time of acquisition of a single slice,
# as a fractional multiple of the TR)
if not timing is None:
TR = (self.n_slices - 1) * timing[0] + timing[1]
slice_TR = timing[0] / TR
assert 0 <= slice_TR < 1
self._log("Your TR is %s" % TR)
else:
# TR normalized to 1 (
slice_TR = 1. / self.n_slices
# least power of 2 not less than n_scans
N = 2**int(np.floor(np.log2(self.n_scans)) + 1)
# this will hold phase shifter of each slice k
self.kernel_ = np.ndarray(
(self.n_slices, N),
dtype=np.complex, # beware, default dtype is float!
)
# loop over slices (z axis)
for z in range(self.n_slices):
self._log(("STC: Estimating phase-shift transform for slice "
"%i/%i...") % (z + 1, self.n_slices))
# compute time delta for shifting this slice w.r.t. the reference
shift_amount = (self.slice_indices[z] - self.ref_slice) * slice_TR
# phi represents a range of phases up to the Nyquist
# frequency
phi = np.ndarray(N)
phi[0] = 0.
for f in range(int(N / 2)):
phi[f + 1] = -1. * shift_amount * 2 * np.pi * (f + 1) / N
# check if signal length is odd or even -- impacts how phases
# (phi) are reflected across Nyquist frequency
offset = N % 2
# mirror phi about the center
phi[int(1 + N / 2 - offset):] = -phi[int(N / 2 + offset - 1):0:-1]
# map phi to frequency domain: phi -> complex
# point z = exp(i * phi) on unit circle
self.kernel_[z] = scipy.cos(phi) + scipy.sqrt(-1) * scipy.sin(phi)
self._log("Done.")
# return fitted object
return self
def f(wind_angle, i):
random_state = np.random.RandomState(i)
wind_mag = 1.2
file_name = 'trap_arrival_by_wind_live_coarse_dt'
file_name = file_name + '_wind_mag_' + str(
wind_mag) + '_wind_angle_' + str(wind_angle)[0:4] + '_iter_' + str(i)
output_file = file_name + '.pkl'
dt = 0.25
plume_dt = 0.25
frame_rate = 20
times_real_time = 20 # seconds of simulation / sec in video
capture_interval = int(scipy.ceil(times_real_time * (1. / frame_rate) /
dt))
simulation_time = 50. * 60. #seconds
release_delay = 30. * 60 #/(wind_mag)
t_start = 0.0
t = 0. - release_delay
wind_param = {
'speed': wind_mag,
'angle': wind_angle,
'evolving': False,
'wind_dt': None,
'dt': dt
}
wind_field_noiseless = wind_models.WindField(param=wind_param)
#traps
number_sources = 8
radius_sources = 1000.0
trap_radius = 0.5
location_list, strength_list = utility.create_circle_of_sources(
number_sources, radius_sources, None)
trap_param = {
'source_locations': location_list,
'source_strengths': strength_list,
'epsilon': 0.01,
'trap_radius': trap_radius,
'source_radius': radius_sources
}
traps = trap_models.TrapModel(trap_param)
#Wind and plume objects
#Odor arena
xlim = (-1500., 1500.)
ylim = (-1500., 1500.)
sim_region = models.Rectangle(xlim[0], ylim[0], xlim[1], ylim[1])
wind_region = models.Rectangle(xlim[0] * 1.2, ylim[0] * 1.2, xlim[1] * 1.2,
ylim[1] * 1.2)
source_pos = scipy.array(
[scipy.array(tup) for tup in traps.param['source_locations']]).T
#wind model setup
diff_eq = False
constant_wind_angle = wind_angle
aspect_ratio = (xlim[1] - xlim[0]) / (ylim[1] - ylim[0])
noise_gain = 3.
noise_damp = 0.071
noise_bandwidth = 0.71
wind_grid_density = 200
Kx = Ky = 10000 #highest value observed to not cause explosion: 10000
wind_field = models.WindModel(wind_region,
int(wind_grid_density * aspect_ratio),
wind_grid_density,
noise_gain=noise_gain,
noise_damp=noise_damp,
noise_bandwidth=noise_bandwidth,
Kx=Kx,
Ky=Ky,
noise_rand=random_state,
diff_eq=diff_eq,
angle=constant_wind_angle,
mag=wind_mag)
# Set up plume model
centre_rel_diff_scale = 2.
# puff_release_rate = 0.001
puff_release_rate = 10
puff_spread_rate = 0.005
puff_init_rad = 0.01
max_num_puffs = int(2e5)
# max_num_puffs=100
plume_model = models.PlumeModel(
sim_region,
source_pos,
wind_field,
simulation_time + release_delay,
plume_dt,
plume_cutoff_radius=1500,
centre_rel_diff_scale=centre_rel_diff_scale,
puff_release_rate=puff_release_rate,
puff_init_rad=puff_init_rad,
puff_spread_rate=puff_spread_rate,
max_num_puffs=max_num_puffs,
prng=random_state)
puff_mol_amount = 1.
#Setup fly swarm
wind_slippage = (0., 1.)
swarm_size = 2000
use_empirical_release_data = False
#Grab wind info to determine heading mean
wind_x, wind_y = wind_mag * scipy.cos(wind_angle), wind_mag * scipy.sin(
wind_angle)
beta = 1.
release_times = scipy.random.exponential(beta, (swarm_size, ))
kappa = 2.
heading_data = None
swarm_param = {
'swarm_size':
swarm_size,
'heading_data':
heading_data,
'initial_heading':
scipy.radians(scipy.random.uniform(0.0, 360.0, (swarm_size, ))),
'x_start_position':
scipy.zeros(swarm_size),
'y_start_position':
scipy.zeros(swarm_size),
'flight_speed':
scipy.full((swarm_size, ), 1.5),
'release_time':
release_times,
'release_delay':
release_delay,
'cast_interval': [1, 3],
'wind_slippage':
wind_slippage,
'odor_thresholds': {
'lower': 0.0005,
'upper': 0.05
},
'schmitt_trigger':
False,
'low_pass_filter_length':
3, #seconds
'dt_plot':
capture_interval * dt,
't_stop':
3000.,
'cast_timeout':
20,
'airspeed_saturation':
True
}
swarm = swarm_models.BasicSwarmOfFlies(wind_field_noiseless,
traps,
param=swarm_param,
start_type='fh',
track_plume_bouts=False,
track_arena_exits=False)
# xmin,xmax,ymin,ymax = -1000,1000,-1000,1000
#Conc array gen to be used for the flies
sim_region_tuple = plume_model.sim_region.as_tuple()
#for the plume distance cutoff version, make sure this is at least 2x radius
box_min, box_max = -3000., 3000.
r_sq_max = 20
epsilon = 0.00001
N = 1e6
array_gen_flies = processors.ConcentrationValueFastCalculator(
box_min, box_max, r_sq_max, epsilon, puff_mol_amount, N)
while t < simulation_time:
for k in range(capture_interval):
#update flies
print('t: {0:1.2f}'.format(t))
#update the swarm
for j in range(int(dt / plume_dt)):
wind_field.update(plume_dt)
plume_model.update(plume_dt, verbose=True)
if t > 0.:
swarm.update(t,
dt,
wind_field_noiseless,
array_gen_flies,
traps,
plumes=plume_model,
pre_stored=False)
t += dt
with open(output_file, 'w') as f:
pickle.dump((wind_field_noiseless, swarm), f)
def orbitPos(self, t): #exact orbit position as f(t)
x = self.orbitR * sp.cos(self.omega * t + self.theta)
y = self.orbitR * sp.sin(self.omega * t + self.theta)
return sp.array([x,y])
def rotation_matrix(angle):
A = scipy.array([[scipy.cos(angle), -scipy.sin(angle)],
[scipy.sin(angle), scipy.cos(angle)]])
return A
def rotate_vecs(x, y, angle):
xrot = x * scipy.cos(angle) - y * scipy.sin(angle)
yrot = x * scipy.sin(angle) + y * scipy.cos(angle)
return xrot, yrot
def base(model, state_vec, noise_diff_coeffs, turn_rate):
""" Base test for n-dimensional ConstantAcceleration Transition Models """
# Create an ConstantTurn model object
model = model
model_obj = model(noise_diff_coeffs=noise_diff_coeffs, turn_rate=turn_rate)
# State related variables
state_vec = state_vec
old_timestamp = datetime.datetime.now()
timediff = 1 # 1sec
new_timestamp = old_timestamp + datetime.timedelta(seconds=timediff)
time_interval = new_timestamp - old_timestamp
# Model-related components
noise_diff_coeffs = noise_diff_coeffs # m/s^3
turn_rate = turn_rate
turn_ratedt = turn_rate * timediff
F = sp.array([[
1,
sp.sin(turn_ratedt) / turn_rate, 0,
-(1 - sp.cos(turn_ratedt)) / turn_rate
], [0, sp.cos(turn_ratedt), 0, -sp.sin(turn_ratedt)],
[
0, (1 - sp.cos(turn_ratedt)) / turn_rate, 1,
sp.sin(turn_ratedt) / turn_rate
], [0, sp.sin(turn_ratedt), 0,
sp.cos(turn_ratedt)]])
qx = noise_diff_coeffs[0]
qy = noise_diff_coeffs[1]
Q = sp.array([[
sp.power(qx, 2) * sp.power(timediff, 3) / 3,
sp.power(qx, 2) * sp.power(timediff, 2) / 2, 0, 0
],
[
sp.power(qx, 2) * sp.power(timediff, 2) / 2,
sp.power(qx, 2) * timediff, 0, 0
],
[
0, 0,
sp.power(qy, 2) * sp.power(timediff, 3) / 3,
sp.power(qy, 2) * sp.power(timediff, 2) / 2
],
[
0, 0,
sp.power(qy, 2) * sp.power(timediff, 2) / 2,
sp.power(qy, 2) * timediff
]])
# Ensure ```model_obj.transfer_function(time_interval)``` returns F
assert sp.array_equal(
F,
model_obj.matrix(timestamp=new_timestamp, time_interval=time_interval))
# Ensure ```model_obj.covar(time_interval)``` returns Q
assert sp.array_equal(
Q, model_obj.covar(timestamp=new_timestamp,
time_interval=time_interval))
# Propagate a state vector through the model
# (without noise)
new_state_vec_wo_noise = model_obj.function(state_vec,
noise=0,
timestamp=new_timestamp,
time_interval=time_interval)
assert sp.array_equal(new_state_vec_wo_noise, F @ state_vec)
# Evaluate the likelihood of the predicted state, given the prior
# (without noise)
prob = model_obj.pdf(new_state_vec_wo_noise,
state_vec,
timestamp=new_timestamp,
time_interval=time_interval)
assert approx(prob) == multivariate_normal.pdf(new_state_vec_wo_noise.T,
mean=sp.array(
F @ state_vec).ravel(),
cov=Q)
# Propagate a state vector throughout the model
# (with internal noise)
new_state_vec_w_inoise = model_obj.function(state_vec,
timestamp=new_timestamp,
time_interval=time_interval)
assert not sp.array_equal(new_state_vec_w_inoise, F @ state_vec)
# Evaluate the likelihood of the predicted state, given the prior
# (with noise)
prob = model_obj.pdf(new_state_vec_w_inoise,
state_vec,
timestamp=new_timestamp,
time_interval=time_interval)
assert approx(prob) == multivariate_normal.pdf(new_state_vec_w_inoise.T,
mean=sp.array(
F @ state_vec).ravel(),
cov=Q)
# Propagate a state vector through the model
# (with external noise)
noise = model_obj.rvs(timestamp=new_timestamp, time_interval=time_interval)
new_state_vec_w_enoise = model_obj.function(state_vec,
timestamp=new_timestamp,
time_interval=time_interval,
noise=noise)
assert sp.array_equal(new_state_vec_w_enoise, F @ state_vec + noise)
# Evaluate the likelihood of the predicted state, given the prior
# (with noise)
prob = model_obj.pdf(new_state_vec_w_enoise,
state_vec,
timestamp=new_timestamp,
time_interval=time_interval)
assert approx(prob) == multivariate_normal.pdf(new_state_vec_w_enoise.T,
mean=sp.array(
F @ state_vec).ravel(),
cov=Q)
def elevDeriv(val_mat, direction_mat, inc):
import scipy
import scipy.linalg
import math
cell_angles = scipy.flipud(
scipy.array([[3 * math.pi / 4, math.pi / 2, math.pi / 4],
[math.pi, scipy.nan, 0],
[-3 * math.pi / 4, -1 * math.pi / 2, -1 * math.pi / 4]]))
cell_incs = scipy.array([[(inc**2 + inc**2)**0.5, inc,
(inc**2 + inc**2)**0.5], [inc, scipy.nan, inc],
[(inc**2 + inc**2)**0.5, inc,
(inc**2 + inc**2)**0.5]])
angle = direction_mat[1, 1]
cell_cosines_f = scipy.cos(angle - cell_angles)
cell_cosines_b = scipy.cos(angle - cell_angles)
cell_sines_f = scipy.sin(angle - cell_angles)
cell_sines_b = scipy.sin(angle - cell_angles)
cell_cosines_f[cell_cosines_f < 0.00001] = scipy.nan
cell_cosines_f = cell_cosines_f**2
cell_cosines_f = cell_cosines_f / sum(
cell_cosines_f[~scipy.isnan(cell_cosines_f)])
cell_cosines_b[cell_cosines_b > -0.00001] = scipy.nan
cell_cosines_b = cell_cosines_b**2
cell_cosines_b = cell_cosines_b / sum(
cell_cosines_b[~scipy.isnan(cell_cosines_b)])
cell_sines_f[cell_sines_f < 0.00001] = scipy.nan
cell_sines_f = cell_sines_f**2
cell_sines_f = cell_sines_f / sum(cell_sines_f[~scipy.isnan(cell_sines_f)])
cell_sines_b[cell_sines_b > -0.00001] = scipy.nan
cell_sines_b = cell_sines_b**2
cell_sines_b = cell_sines_b / sum(cell_sines_b[~scipy.isnan(cell_sines_b)])
temp = val_mat * cell_cosines_f
h_x_f = sum(temp[~scipy.isnan(temp)])
temp = val_mat * cell_cosines_b
h_x_b = sum(temp[~scipy.isnan(temp)])
temp = val_mat * cell_sines_f
h_y_f = sum(temp[~scipy.isnan(temp)])
temp = val_mat * cell_sines_b
h_y_b = sum(temp[~scipy.isnan(temp)])
h_x = scipy.array([h_x_b, val_mat[1, 1], h_x_f])
h_y = scipy.array([h_y_b, val_mat[1, 1], h_y_f])
xs = scipy.array([-1 * int(inc), 0, int(inc)])
A = scipy.vstack([xs, scipy.ones(len(xs))]).T
# print("A: " + str(A));
# print("h_x_b: " + str(h_x_b));
# print("val_mat[1,1]: " + str(val_mat[1,1]));
# print("h_x_f: " + str(h_x_f));
dh_dx, intercept = scipy.linalg.lstsq(A, h_x)[0]
dh_dy, intercept = scipy.linalg.lstsq(A, h_y)[0]
return dh_dx, dh_dy