def FilterCoeffs(x):
""" return filter coefficients """
p1i = x[0] < 0 and -x[0] * 1j or x[0]
p1 = np.exp(p1i + x[1])
p1c = np.exp(-p1i + x[1])
p2i = x[2] < 0 and -x[2] * 1j or x[2]
p2 = np.exp(p2i + x[3])
p2c = np.exp(-p2i + x[3])
if np.imag(p1) == 0 and np.real(p1) > 1.0:
p1 = 1.0 - p1
if np.imag(p1c) == 0 and np.real(p1c) > 1.0:
p1c = 1.0 - p1c
if np.imag(p2) == 0 and np.real(p2) > 1.0:
p2 = 1.0 - p2
if np.imag(p2c) == 0 and np.real(p2c) > 1.0:
p2c = 1.0 - p2c
z1 = np.exp(x[4])
# first biquad:
# (z - z1) / [(z - p1) (z - p1*)]
a1 = np.real(p1 + p1c)
b1 = -np.real(p1 * p1c)
# second:
# 1.0 / [(z - p2) (z - p3)]
# (1 - p2 z^-1) (1 - p3 z^-1)
a2 = np.real(p2 + p2c)
b2 = -np.real(p2 * p2c)
z = np.exp(2j * np.pi / T)
gain = 1.0 / np.abs(FilterResponse(z, x))
return np.array([gain, -z1, a1, b1, a2, b2])
def FilterResponse(z, x):
''' -b +- sqrt(b^2 - 4c) / 2
so we want to independently control b and the discriminant
which really just turns out to be + -> real, - -> imag
so we allow the "frequency" component to go positive or negative
if it's negative we use complex conjugates
if it's positive we use "real conjugates"
s^2 + bs + c = (s-p1)(s-p2)
p1,p2 = b/2 +- sqrt(b^2 - 4ac)/2 = x1 +- sqrt(x2))
b = x1*2
sqrt(b^2 - 4c)/2 = sqrt(x2)
b^2/4 - c = x2
c = b^2/4 - x2
wait, the quadratic form isn't all that useful though; we need to map the
poles and zeros so we might as well just make it a distance either in real
or in imag
'''
p1i = x[0] < 0 and -x[0] * 1j or x[0]
p1 = np.exp(p1i + x[1])
p1c = np.exp(-p1i + x[1])
p2i = x[2] < 0 and -x[2] * 1j or x[2]
p2 = np.exp(p2i + x[3])
p2c = np.exp(-p2i + x[3])
z1 = np.exp(x[4])
if np.imag(p1) == 0 and np.real(p1) > 1.0:
p1 = 1.0 - p1
if np.imag(p1c) == 0 and np.real(p1c) > 1.0:
p1c = 1.0 - p1c
if np.imag(p2) == 0 and np.real(p2) > 1.0:
p2 = 1.0 - p2
if np.imag(p2c) == 0 and np.real(p2c) > 1.0:
p2c = 1.0 - p2c
h = (z - z1) / ((z - p1) * (z - p1c) * (z - p2) * (z - p2c))
return h
def TrackCurvature(x):
# use quadratic b-splines at each point to estimate curvature
# i get almost the same formula i had before but it's off by a factor of 4!
xx = np.concatenate([x[-1:], x, x[:1]])
p0 = xx[:-2]
p1 = xx[1:-1]
p2 = xx[2:]
T = p2 - p0 # track derivative
uT = np.abs(T)
TT = 4*(p0 - 2*p1 + p2)
k = (np.real(T)*np.imag(TT) - np.imag(T)*np.real(TT)) / (uT**3)
return k
def TrackCurvature(x):
# use quadratic b-splines at each point to estimate curvature
# i get almost the same formula i had before but it's off by a factor of 4!
xx = np.concatenate([x[-1:], x, x[:1]])
p0 = xx[:-2]
p1 = xx[1:-1]
p2 = xx[2:]
T = p2 - p0 # track derivative
uT = np.abs(T)
TT = 4 * (p0 - 2 * p1 + p2)
k = (np.real(T) * np.imag(TT) - np.imag(T) * np.real(TT)) / (uT**3)
return k
def constraint(x):
arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg = expand(x)
arr_C_pos = list()
arr_C_neg = list()
def conj(z):
return np.real(z) - 1j * np.imag(z)
for i in range(n_decomp):
arr_C_pos.append(conj(arr_Y_pos[i].T) @ arr_Y_pos[i])
arr_C_neg.append(conj(arr_Y_neg[i].T) @ arr_Y_neg[i])
retvec = np.array([])
# TP constraint
for i in range(n_decomp):
pt = anp_partial_trace(arr_C_pos[i], [2**n_qubits, 2**n_qubits], 1)
vec = (pt - arr_a_pos[i] * np.identity(2**n_qubits)).flatten()
retvec = np.hstack([retvec, vec])
pt = anp_partial_trace(arr_C_neg[i], [2**n_qubits, 2**n_qubits], 1)
vec = (pt - arr_a_neg[i] * np.identity(2**n_qubits)).flatten()
retvec = np.hstack([retvec, vec])
# equality constraint
C_sum = np.zeros_like(target_choi)
for i in range(n_decomp):
C_sum += arr_C_pos[i] - arr_C_neg[i]
vec = (C_sum - target_choi).flatten()
retvec = np.hstack([retvec, vec])
# separate complex and real part
retvec = np.hstack([np.real(retvec), np.imag(retvec)])
return retvec
def imvoigt_vjp(g, ans, x, y):
from scipy.special import wofz
z = x + 1j*y
zw = z*wofz(z)
dx = -2*np.imag(zw) + 2/np.sqrt(np.pi)
dy = -2*np.real(zw)
return g*dx, g*dy
def dynamic_residual(self,
x: np.ndarray,
f_exc: np.ndarray, # TODO: make this a property of WEC
f_pto_fun: types.FunctionType,
f_ext_fun: types.FunctionType) -> np.ndarray:
"""
Solves WEC dynamics in residual form so that they may be enforced through
a nonlinear constraint within an optimization problem
Parameters
----------
x : np.ndarray
Decision variable for optimization problem
f_exc : np.ndarray
Time history of excitation forcing at collocation points in body
coordinate system
f_pto_fun : types.FunctionType
Function that acceps decision variable and WEC, returns PTO forcing at
collocation points in body coordinate system
f_ext_fun : types.FunctionType
Function that acceps decision variable and WEC, returns other forcing at
collocation points in body coordinate system
Returns
-------
np.ndarray
Residuals at collocation points
"""
assert isinstance(x, np.ndarray)
assert isinstance(f_exc, np.ndarray)
assert isinstance(f_pto_fun, types.FunctionType)
assert isinstance(f_ext_fun, types.FunctionType)
# WEC position
x_wec, _, nf, nm = self.decompose_decision_var(x)
# WEC velocity (each row is a mode, each column is a Fourier component)
X = np.reshape(x_wec, (nm, -1))
# complex velocity with position at beginning
X_hat = np.concatenate((np.reshape(X[:,0],(-1,1)), X[:,1::2] - X[:,2::2]*1j ), axis=1)
Gi_block_scaled = self.num_scale * self.Gi_block.toarray() # TODO: do this only once
Fi = np.squeeze(np.reshape(Gi_block_scaled @ X_hat.flatten(), (nm, -1)))
Fi_fs_tmp_0 = np.real(Fi[0])
Fi_fs_tmp_1 = np.vstack([np.real(Fi[1::]), -np.imag(Fi[1::])]).ravel('F')
Fi_fs = np.hstack((np.array(Fi_fs_tmp_0), Fi_fs_tmp_1))
fi = Fi_fs @ self.Phi
residual = f_exc + f_pto_fun(x) + f_ext_fun(x) - fi
return residual.flatten()
def PlotPoles(x, n):
Q, p3, p4, z1, w0, w1, wdecay = x
w = w1 * np.exp(-np.arange(n) * wdecay) + w0
p1 = (w * (-1.0 / Q + 1j))
p2 = np.conj(p1)
p3 = (w * p3 / Q)
p4 = (w * p4)
z1 = (w * z1)
a = np.vstack((p1, p2, p3, p4, z1))
plt.axvline(0)
plt.plot(np.real(a), np.imag(a), 'x')
def ifft2(var_real, var_imag, axes=(-2, -1), backend='autograd', normalize=False):
if backend == 'autograd':
var = var_real + 1j * var_imag
norm = None if not normalize else 'ortho'
var = anp.fft.ifft2(var, axes=axes, norm=norm)
return anp.real(var), anp.imag(var)
elif backend == 'pytorch':
var = tc.stack([var_real, var_imag], dim=-1)
var = tc.ifft(var, signal_ndim=2, normalized=normalize)
var_real, var_imag = tc.split(var, 1, dim=-1)
slicer = [slice(None)] * (len(var_real.shape) - 1) + [0]
return var_real[tuple(slicer)], var_imag[tuple(slicer)]
def g_out_antihess(y):
lp = snp_log_probs(y)
ret = 0.0
for l in seg_sites._get_likelihood_sequences(lp):
L = len(l)
lc = make_constant(l)
fft = np.fft.fft(l)
# (assumes l is REAL)
assert np.all(np.imag(l) == 0.0)
fft_rev = np.conj(fft) * np.exp(
2 * np.pi * 1j * np.arange(L) / float(L))
curr = 0.5 * (fft * fft_rev - fft * make_constant(fft_rev) -
make_constant(fft) * fft_rev)
curr = np.fft.ifft(curr)[(L - 1)::-1]
# make real
assert np.allclose(np.imag(curr / L), 0.0)
curr = np.real(curr)
curr = curr[0] + 2.0 * np.sum(curr[1:int(np.sqrt(L))])
ret = ret + curr
return ret
def QuadFitCurvatureMap(x):
curv = []
for i in range(len(x)):
# do a look-ahead quadratic fit, just like the car would do
pts = x[(np.arange(6) + i) % len(x)] / 100 # convert to meters
basis = (pts[1] - pts[0]) / np.abs(pts[1] - pts[0])
# project onto forward direction
pts = (np.conj(basis) * (pts - pts[0]))
p = np.polyfit(np.real(pts), np.imag(pts), 2)
curv.append(p[0] / 2)
return np.float32(curv)
def QuadFitCurvatureMap(x):
curv = []
for i in range(len(x)):
# do a look-ahead quadratic fit, just like the car would do
pts = x[(np.arange(6) + i) % len(x)] / 100 # convert to meters
basis = (pts[1] - pts[0]) / np.abs(pts[1] - pts[0])
# project onto forward direction
pts = (np.conj(basis) * (pts - pts[0]))
p = np.polyfit(np.real(pts), np.imag(pts), 2)
curv.append(p[0] / 2)
return np.float32(curv)
def ifft2(var_real,
var_imag,
axes=(-2, -1),
override_backend=None,
normalize=False):
bn = override_backend if override_backend is not None else global_settings.backend
if bn == 'autograd':
var = var_real + 1j * var_imag
norm = None if not normalize else 'ortho'
var = anp.fft.ifft2(var, axes=axes, norm=norm)
return anp.real(var), anp.imag(var)
elif bn == 'pytorch':
var = tc.stack([var_real, var_imag], axis=-1)
var = tc.ifft(var, signal_ndim=2, normalized=normalize)
var_real, var_imag = tc.split(var, 1, dim=-1)
slicer = [slice(None)] * (var_real.ndim - 1) + [0]
return var_real[tuple(slicer)], var_imag[tuple(slicer)]
def pu2i(*tlist):
"""
Returns imaginary part of u2, and registers it as being primitive.
Primitive means that its derivative will be provided in a defvjp (
def of vector-jacobian-product) so no need for autograd to calculate it
from the u2 definition.
Parameters
----------
tlist : list[float]
len = 4
Returns
-------
np.ndarray
shape=(2,2)
"""
return np.imag(u2_alt(*tlist))
def complex_as_matrix(z, n):
"""Represent a complex number as a matrix.
Parameters
----------
z : complex float
n : int (even)
Returns
-------
Z : ndarray (n,n)
Real-valued n*n tri-diagonal matrix representing z in the ring of n*n matrices.
"""
Z = np.zeros((n, n))
ld = np.zeros(n - 1)
ld[0::2] = np.imag(z)
np.fill_diagonal(Z[1:], ld)
Z = Z - Z.T
np.fill_diagonal(Z, np.real(z))
return Z
def realify(Y):
"""Convert data in k-dimensional complex space to 2k-dimensional
real space.
Parameters
----------
Y : ndarray (k,n)
Real-valued array of data, `k` must be even.
Returns
-------
Yreal : ndarray (2k,n)
Complex-valued array of data.
"""
if Y.ndim == 1:
Yreal = np.zeros(2 * Y.shape[0])
else:
Yreal = np.zeros((2 * Y.shape[0], Y.shape[1]))
Yreal[0::2] = np.real(Y)
Yreal[1::2] = np.imag(Y)
return Yreal
def serialize_recurrent_layer(self, weights):
evals, evecs = np.linalg.eig(weights[1])
diagonal_evals = np.real(np.diag(evals))
real_parts = evals.real
img_parts = evals.imag
evecs_c = np.real(evecs)
#reconstructed_matrices = []
for i in range(len(weights[1])):
#diagonal_evals = np.zeros((24, 24))
#diagonal_evals[i, i] = evals[i]**(1/24)
#reconstructed_weights = evecs @ diagonal_evals @ np.linalg.pinv(evecs)
if img_parts[i] > 0:
diagonal_evals[i, i + 1] = img_parts[i]
diagonal_evals[i + 1, i] = img_parts[i + 1]
evecs_c[:, i] = np.real(evecs[:, i])
evecs_c[:, i + 1] = np.imag(evecs[:, i])
i += 2
#reconstructed_matrices.append(reconstructed_weights)
return diagonal_evals
defvjp(
pu2r,
# defines vector-jacobian-product of pu2r
# g.shape == pu2r.shape
lambda ans, *tlist: lambda g: np.sum(g * np.real(d_u2(0, *tlist))),
lambda ans, *tlist: lambda g: np.sum(g * np.real(d_u2(1, *tlist))),
lambda ans, *tlist: lambda g: np.sum(g * np.real(d_u2(2, *tlist))),
lambda ans, *tlist: lambda g: np.sum(g * np.real(d_u2(3, *tlist))),
argnums=range(4))
defvjp(
pu2i,
# defines vector-jacobian-product of pu2i
# g.shape == pu2i.shape
lambda ans, *tlist: lambda g: np.sum(g * np.imag(d_u2(0, *tlist))),
lambda ans, *tlist: lambda g: np.sum(g * np.imag(d_u2(1, *tlist))),
lambda ans, *tlist: lambda g: np.sum(g * np.imag(d_u2(2, *tlist))),
lambda ans, *tlist: lambda g: np.sum(g * np.imag(d_u2(3, *tlist))),
argnums=range(4))
def d_auto_pu2(dwrt, *tlist):
"""
Returns the automatic derivative of pu2. We have defined things so that
this derivative is stipulated analytically a priori rather than being
calculated by autograd from def of u2.
Parameters
----------
dwrt : int
def polyinterp(points, doPlot=None, xminBound=None, xmaxBound=None):
""" polynomial interpolation
Parameters
----------
points: shape(pointNum, 3), three columns represents x, f, g
doPolot: set to 1 to plot, default 0
xmin: min value that brackets minimum (default: min of points)
xmax: max value that brackets maximum (default: max of points)
set f or g to sqrt(-1)=1j if they are not known
the order of the polynomial is the number of known f and g values minus 1
Returns
-------
minPos:
fmin:
"""
if doPlot == None:
doPlot = 0
nPoints = points.shape[0]
order = np.sum(np.imag(points[:, 1:3]) == 0) -1
# code for most common case: cubic interpolation of 2 points
if nPoints == 2 and order == 3 and doPlot == 0:
[minVal, minPos] = [np.min(points[:,0]), np.argmin(points[:,0])]
notMinPos = 1 - minPos
d1 = points[minPos,2] + points[notMinPos,2] - 3*(points[minPos,1]-\
points[notMinPos,1])/(points[minPos,0]-points[notMinPos,0])
t_d2 = d1**2 - points[minPos,2]*points[notMinPos,2]
if t_d2 > 0:
d2 = np.sqrt(t_d2)
else:
d2 = np.sqrt(-t_d2) * np.complex(0,1)
if np.isreal(d2):
t = points[notMinPos,0] - (points[notMinPos,0]-points[minPos,0])*\
((points[notMinPos,2]+d2-d1)/(points[notMinPos,2]-\
points[minPos,2]+2*d2))
minPos = np.min([np.max([t,points[minPos,0]]), points[notMinPos,0]])
else:
minPos = np.mean(points[:,0])
fmin = minVal
return (minPos, fmin)
xmin = np.min(points[:,0])
xmax = np.max(points[:,0])
# compute bounds of interpolation area
if xminBound == None:
xminBound = xmin
if xmaxBound == None:
xmaxBound = xmax
# constraints based on available function values
A = np.zeros((0, order+1))
b = np.zeros((0, 1))
for i in range(nPoints):
if np.imag(points[i,1]) == 0:
constraint = np.zeros(order+1)
for j in np.arange(order,-1,-1):
constraint[order-j] = points[i,0]**j
A = np.vstack((A, constraint))
b = np.append(b, points[i,1])
# constraints based on availabe derivatives
for i in range(nPoints):
if np.isreal(points[i,2]):
constraint = np.zeros(order+1)
for j in range(1,order+1):
constraint[j-1] = (order-j+1)* points[i,0]**(order-j)
A = np.vstack((A, constraint))
b = np.append(b,points[i,2])
# find interpolating polynomial
params = np.linalg.solve(A, b)
# compute critical points
dParams = np.zeros(order)
for i in range(params.size-1):
dParams[i] = params[i] * (order-i)
if np.any(np.isinf(dParams)):
cp = np.concatenate((np.array([xminBound, xmaxBound]), points[:,0]))
else:
cp = np.concatenate((np.array([xminBound, xmaxBound]), points[:,0], \
np.roots(dParams)))
# test critical points
fmin = np.infty;
minPos = (xminBound + xmaxBound)/2.
for xCP in cp:
if np.imag(xCP) == 0 and xCP >= xminBound and xCP <= xmaxBound:
fCP = np.polyval(params, xCP)
if np.imag(fCP) == 0 and fCP < fmin:
minPos = np.double(np.real(xCP))
fmin = np.double(np.real(fCP))
# plot situation (omit this part for now since we are not going to use it
# anyway)
return (minPos, fmin)
def isLegal(v):
return np.sum(np.any(np.imag(v)))==0 and np.sum(np.isnan(v))==0 and \
np.sum(np.isinf(v))==0
def emissivity_f(dofold,ctrl):
''' ctrl: ctrl's frequency calculation
average over p/s polarizations, sum over forward and backward directions
'''
freq = freqL.flatten()[ctrl]
theta = thetaL.flatten()[ctrl]
phi = phiL.flatten()[ctrl]
# RCWA
freqcmp = freq*(1+1j/2/Qabs)
planewave={'p_amp':0,'s_amp':1,'p_phase':0,'s_phase':0}
obj,dof,epsdiff = rcwa_assembly(dofold,freqcmp,theta,phi,planewave)
if absmethod == 'V':
Mv = []
FMFL=[]
MtL=[]
solveinsideL=[]
for i in range(Nlayer):
Mv.append(get_conv(1./Nx/Ny,dof[i*Nx*Ny:(i+1)*Nx*Ny].reshape((Nx,Ny)),obj.G))
FMF,Mt, solveinside = obj.Volume_integralpart1(1+i,Mv[i],Mv[i],Mv[i])
FMFL.append(FMF)
MtL.append(Mt)
solveinsideL.append(solveinside)
elif absmethod == 'RT':
fun = obj.RT_Solvepart1()
# planewave excitation
p_phase = 0.
s_phase = 0.
vals=0.
if absmethod == 'V':
for i in range(Nlayer):
p_amp = 0.
s_amp = 1.
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='forward')
vals = vals + np.real(obj.Volume_integralpart2(obj.a0,obj.bN,FMFL[i],MtL[i], solveinsideL[i], normalize=1))*np.imag(epsdiff[i])*np.real(obj.omega)
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='backward')
vals = vals + np.real(obj.Volume_integralpart2(obj.a0,obj.bN,FMFL[i],MtL[i], solveinsideL[i], normalize=1))*np.imag(epsdiff[i])*np.real(obj.omega)
p_amp = 1.
s_amp = 0.
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='forward')
vals = vals + np.real(obj.Volume_integralpart2(obj.a0,obj.bN,FMFL[i],MtL[i], solveinsideL[i], normalize=1))*np.imag(epsdiff[i])*np.real(obj.omega)
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='backward')
vals = vals + np.real(obj.Volume_integralpart2(obj.a0,obj.bN,FMFL[i],MtL[i], solveinsideL[i], normalize=1))*np.imag(epsdiff[i])*np.real(obj.omega)
elif absmethod == 'RT':
p_amp = 0.
s_amp = 1.
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='forward')
R,T = obj.RT_Solvepart2(fun,normalize=1)
vals = vals + 1-R-T
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='backward')
R,T = obj.RT_Solvepart2(fun,normalize=1)
vals = vals + 1-R-T
p_amp = 1.
s_amp = 0.
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='forward')
R,T = obj.RT_Solvepart2(fun,normalize=1)
vals = vals + 1-R-T
obj.MakeExcitationPlanewave(p_amp,p_phase,s_amp,s_phase,order = 0,direction='backward')
R,T = obj.RT_Solvepart2(fun,normalize=1)
vals = vals + 1-R-T
val = vals*np.sin(theta)*np.cos(theta)/np.pi
val = val * dtheta*dphi*prefactorT
return val
def fun_owen(ep):
sigma = np.imag(ep)/np.abs(ep-1)**2
fun = lambda h:h-2/np.pi*sigma/(1-np.sinc(2*h)**2)
init = 1/np.imag(np.sqrt(ep))/2/np.pi
return solve(fun,init)[0]
def fun(a):
r, i = np.real(a), np.imag(a)
a = np.abs(r)**1.4 + np.abs(i)**1.3
return np.sum(np.sin(a))
def norm(x):
return np.mean(np.square(np.real(x)) + np.square(np.imag(x)))
def imag(a: Numeric):
return anp.imag(a)
Nr = TrackNormal(rx)
# psie is sort of backwards: higher angles go to the left
return np.angle(Nx) - np.angle(Nr)
if __name__ == '__main__':
TRACK_SPACING = 19.8 # cm
x = SVGPathToTrackPoints("oakwarehouse.path", TRACK_SPACING)[:-1]
xm = np.array(x)[:, 0] / 50 # 50 pixels / meter
track_k = TrackCurvature(xm)
Nx = TrackNormal(xm)
u = 1j * Nx
np.savetxt("track_x.txt",
np.vstack([np.real(xm), np.imag(xm)]).T.reshape(-1),
newline=",\n")
np.savetxt("track_u.txt",
np.vstack([np.real(u), np.imag(u)]).T.reshape(-1),
newline=",\n")
np.savetxt("track_k.txt", track_k, newline=",\n")
ye, val, stuff = OptimizeTrack(xm, 1.4, 0.1)
psie = RelativePsie(ye, xm)
rx = u*ye + xm
raceline_k = TrackCurvature(rx)
np.savetxt("raceline_k.txt", raceline_k, newline=",\n")
np.savetxt("raceline_ye.txt", ye, newline=",\n")
np.savetxt("raceline_psie.txt", psie, newline=",\n")
def nonlinearity(value):
return np.tanh(np.real(value)) + np.tanh(np.imag(value))
def test_imag_type():
fun = lambda x: np.sum(np.imag(x))
df = grad(fun)
assert base_class(type(df(1.0 ))) == float
assert base_class(type(df(1.0j))) == complex
def fun(a):
r, i = np.real(a), np.imag(a)
a = np.abs(r)**1.4 + np.abs(i)**1.3
return to_scalar(a)
def p_abs(dofold,nG,bproj,method='RT'):
dof = b_filter(dofold,bproj)
planewave={'p_amp':0,'s_amp':1,'p_phase':0,'s_phase':0}
theta = 0.
phi = 0.
t1 = time.time()
obj= rcwa_assembly(dof,nG,bproj,theta,phi,planewave)
vals = 0.
R = 0.
T = 0.
if method == 'V':
for i in range(Nlayer):
Mv=get_conv(1./Mx/My,dof[i*Mx*My:(i+1)*Mx*My].reshape((Mx,My)),obj.G)
vals = vals + np.real(obj.Volume_integral(1+i,Mv,Mv,Mv,normalize=1))*np.real(obj.omega)*np.imag(epsdiff)
elif method == 'RT':
R,T = obj.RT_Solve(normalize=1)
vals = 1-R-T
t2 = time.time()
if 'autograd' not in str(type(vals)):
global ctrl
np.savetxt('dof.txt',dof)
if ctrl<=1:
print(t2-t1)
if method == 'V':
print(ctrl,vals)
elif method == 'RT':
print(ctrl, 'R =',R,'T =',T,'Abs=',vals,'time=',t2-t1)
ctrl +=1
return vals
def u2i(*tlist1):
return np.imag(u2_alt(*tlist1))
def run_lf(load_p, net, tol=1e-9, comp_tol=1e-3, max_iter=10000):
""" Perform Gauss-Seidel power flow on the given pandapower network.
The ``load_p`` array is an iterable of additional real power load to add
to each bus. By providing this as an input, this python function becomes
the function ``slack_power = f(load_power)`` and thus the derivative of
slack power with respect to load power can be calculated.
By restricting the values of `load_p` to be very small we can ensure that
this function is solving the load flow correctly by comparing it to the
results in the pandapower network. Restricting to very small does not interfere
with calculation of the derivative - that is, the derivative of
x (the small value given as input) plus a constant (the load power specified
in the pandapower network object) is equal to the derivative of x alone.
Args:
load_p (iterable): Iterable of additional loads to add to network.
Index i will add load to bus i.
These should be very small values so that the consistency
assertion with pandapower succeeeds.
net (pp.Network): Solved Pandapower network object that defines the
elements of the network and contains the ybus matrix.
tol (float): Convergence tolerance (voltage).
comp_tol (float): Tolerance for comparison check against pandapower.
max_iter(int): Max iterations to solve load flow.
Returns:
float: Sum of real power injected by slack buses in the network.
"""
ybus = np.array(net._ppc["internal"]["Ybus"].todense())
pd2ppc = net._pd2ppc_lookups["bus"] # Pandas bus num --> internal bus num.
n = ybus.shape[0] # Number of buses.
slack_buses = set(pd2ppc[net.ext_grid['bus']])
gen_buses = set([pd2ppc[b] for b in net.gen['bus']])
ybus_hollow = ybus * (1 - np.eye(n)) # ybus with diagonal elements zeroed.
v = init_v(net, n, pd2ppc)
psch, qsch = scheduled_p_q(net, n, pd2ppc)
# Incorporate the variables we are differentiating with respect to:
psch = {b: p - load_p[b] for b, p in psch.items()}
it = 0
while it < max_iter:
old_v, v = v, [x for x in v]
for b in [b for b in range(n) if b not in slack_buses]:
qsch_b = (-1 *
np.imag(np.conj(old_v[b]) * np.sum(ybus[b, :] * old_v))
if b in gen_buses else qsch[b])
v[b] = (1 / ybus[b, b]) * (
(psch[b] - 1j * qsch_b) / np.conj(old_v[b]) -
np.sum(ybus_hollow[b, :] * old_v))
if b in gen_buses:
v[b] = np.abs(old_v[b]) * v[b] / np.abs(
v[b]) # Only use angle.
it += 1
v = np.array(v)
if np.allclose(v, old_v, rtol=tol, atol=0):
break
p_slack = sum((np.real(np.conj(v[b]) * np.sum(ybus[b, :] * v)) - psch[b])
for b in slack_buses)
# Assert convergence and consistency with pandapower.
assert it < max_iter, f'Load flow not converged in {it} iterations.'
assert np.allclose(v, net._ppc["internal"]["V"], atol=comp_tol, rtol=0),\
f'Voltage\npp:\t\t{net._ppc["internal"]["V"]}\nsolved:\t{v}'
assert np.allclose(p_slack, net.res_ext_grid['p_mw'].sum(), atol=comp_tol, rtol=0),\
f'Slack Power\npp:\t\t{net.res_ext_grid["p_mw"].sum()}\nsolved:\t{p_slack}'
return p_slack
def complex_to_real(self,
z): # complex vector of length n -> real of length 2n
return np.real(np.concatenate((np.real(z), np.imag(z))))
Nr = TrackNormal(rx)
# psie is sort of backwards: higher angles go to the left
return np.angle(Nx) - np.angle(Nr)
if __name__ == '__main__':
TRACK_SPACING = 19.8 # cm
x = SVGPathToTrackPoints("oakwarehouse.path", TRACK_SPACING)[:-1]
xm = np.array(x)[:, 0] / 50 # 50 pixels / meter
track_k = TrackCurvature(xm)
Nx = TrackNormal(xm)
u = 1j * Nx
np.savetxt("track_x.txt",
np.vstack([np.real(xm), np.imag(xm)]).T.reshape(-1),
newline=",\n")
np.savetxt("track_u.txt",
np.vstack([np.real(u), np.imag(u)]).T.reshape(-1),
newline=",\n")
np.savetxt("track_k.txt", track_k, newline=",\n")
ye, val, stuff = OptimizeTrack(xm, 1.4, 0.1)
psie = RelativePsie(ye, xm)
rx = u * ye + xm
raceline_k = TrackCurvature(rx)
np.savetxt("raceline_k.txt", raceline_k, newline=",\n")
np.savetxt("raceline_ye.txt", ye, newline=",\n")
np.savetxt("raceline_psie.txt", psie, newline=",\n")
def p_abs(dofold,ctrl):
''' ctrl: ctrl's frequency calculation
'''
# RCWA
freqcmp = freq_list[ctrl]*(1+1j/2/Qabs)
planewave={'p_amp':0,'s_amp':1,'p_phase':0,'s_phase':0}
theta = 0.
phi = 0.
obj,dof,epsdiff = rcwa_assembly(dofold,freqcmp,theta,phi,planewave)
vals = 0.0
# volume integration
if absmethod == 'V':
for i in range(Nlayer):
Mv=get_conv(1./Nx/Ny,dof[i*Nx*Ny:(i+1)*Nx*Ny].reshape((Nx,Ny)),obj.G)
vals = vals + np.real(obj.Volume_integral(1+i,Mv,Mv,Mv,normalize=1))*np.real(obj.omega)*np.imag(epsdiff[i])
vals = vals*laserP
elif absmethod == 'RT':
R,T = obj.RT_Solve(normalize=1)
vals = (1-R-T)*laserP
else:
raise Exception('absmethod undefined')
vals = vals * (1-beta[ctrl])/(1+beta[ctrl]) # relativistic correction
return vals
def calculate_loss(obj_delta, obj_beta, probe_real, probe_imag, probe_defocus_mm, probe_pos_offset, this_i_theta, this_pos_batch, this_prj_batch):
if optimize_probe_defocusing:
h_probe = get_kernel(probe_defocus_mm * 1e6, lmbda_nm, voxel_nm, probe_size, fresnel_approx=fresnel_approx)
probe_complex = probe_real + 1j * probe_imag
probe_complex = np.fft.ifft2(np.fft.ifftshift(np.fft.fftshift(np.fft.fft2(probe_complex)) * h_probe))
probe_real = np.real(probe_complex)
probe_imag = np.imag(probe_complex)
if optimize_probe_pos_offset:
this_pos_batch = this_pos_batch + probe_pos_offset[this_i_theta]
if not shared_file_object:
obj_stack = np.stack([obj_delta, obj_beta], axis=3)
if not two_d_mode:
obj_rot = apply_rotation(obj_stack, coord_ls[this_i_theta])
# obj_rot = sp_rotate(obj_stack, theta, axes=(1, 2), reshape=False)
else:
obj_rot = obj_stack
probe_pos_batch_ls = []
exiting_ls = []
i_dp = 0
while i_dp < minibatch_size:
probe_pos_batch_ls.append(this_pos_batch[i_dp:min([i_dp + n_dp_batch, minibatch_size])])
i_dp += n_dp_batch
# Pad if needed
obj_rot, pad_arr = pad_object(obj_rot, this_obj_size, probe_pos, probe_size)
for k, pos_batch in enumerate(probe_pos_batch_ls):
subobj_ls = []
for j in range(len(pos_batch)):
pos = pos_batch[j]
pos = [int(x) for x in pos]
pos[0] = pos[0] + pad_arr[0, 0]
pos[1] = pos[1] + pad_arr[1, 0]
subobj = obj_rot[pos[0]:pos[0] + probe_size[0], pos[1]:pos[1] + probe_size[1], :, :]
subobj_ls.append(subobj)
subobj_ls = np.stack(subobj_ls)
exiting = multislice_propagate_batch_numpy(subobj_ls[:, :, :, :, 0], subobj_ls[:, :, :, :, 1], probe_real,
probe_imag, energy_ev, psize_cm * ds_level, kernel=h, free_prop_cm=free_prop_cm,
obj_batch_shape=[len(pos_batch), *probe_size, this_obj_size[-1]],
fresnel_approx=fresnel_approx, pure_projection=pure_projection)
exiting_ls.append(exiting)
exiting_ls = np.concatenate(exiting_ls, 0)
loss = np.mean((np.abs(exiting_ls) - np.abs(this_prj_batch)) ** 2)
else:
probe_pos_batch_ls = []
exiting_ls = []
i_dp = 0
while i_dp < minibatch_size:
probe_pos_batch_ls.append(this_pos_batch[i_dp:min([i_dp + n_dp_batch, minibatch_size])])
i_dp += n_dp_batch
pos_ind = 0
for k, pos_batch in enumerate(probe_pos_batch_ls):
subobj_ls_delta = obj_delta[pos_ind:pos_ind + len(pos_batch), :, :, :]
subobj_ls_beta = obj_beta[pos_ind:pos_ind + len(pos_batch), :, :, :]
exiting = multislice_propagate_batch_numpy(subobj_ls_delta, subobj_ls_beta, probe_real,
probe_imag, energy_ev, psize_cm * ds_level, kernel=h,
free_prop_cm=free_prop_cm,
obj_batch_shape=[len(pos_batch), *probe_size,
this_obj_size[-1]],
fresnel_approx=fresnel_approx,
pure_projection=pure_projection)
exiting_ls.append(exiting)
pos_ind += len(pos_batch)
exiting_ls = np.concatenate(exiting_ls, 0)
loss = np.mean((np.abs(exiting_ls) - np.abs(this_prj_batch)) ** 2)
# dxchange.write_tiff(abs(exiting_ls._value[0]), output_folder + '/det/det', dtype='float32', overwrite=True)
# raise
# Regularization
if reweighted_l1:
if alpha_d not in [None, 0]:
loss = loss + alpha_d * np.mean(weight_l1 * np.abs(obj_delta))
if alpha_b not in [None, 0]:
loss = loss + alpha_b * np.mean(weight_l1 * np.abs(obj_beta))
else:
if alpha_d not in [None, 0]:
loss = loss + alpha_d * np.mean(np.abs(obj_delta))
if alpha_b not in [None, 0]:
loss = loss + alpha_b * np.mean(np.abs(obj_beta))
if gamma not in [None, 0]:
if shared_file_object:
loss = loss + gamma * total_variation_3d(obj_delta, axis_offset=1)
else:
loss = loss + gamma * total_variation_3d(obj_delta, axis_offset=0)
# Write convergence data
global current_loss
current_loss = loss._value
f_conv.write('{},{},{},'.format(i_epoch, i_batch, current_loss))
f_conv.flush()
return loss
L1 = [Lx,0.]
L2 = [0.,Ly]
epsuniform = 1.
epsbkg = 1.
epsdiff = silicon.epsilon(lam0/freq,'lambda')-epsbkg
thick0 = 1.
thickN = 1.
def fun_owen(ep):
sigma = np.imag(ep)/np.abs(ep-1)**2
fun = lambda h:h-2/np.pi*sigma/(1-np.sinc(2*h)**2)
init = 1/np.imag(np.sqrt(ep))/2/np.pi
return solve(fun,init)[0]
print('epsilon=',epsdiff+epsbkg,'skin deptph=',1/np.imag(np.sqrt(epsdiff+epsbkg))/2/np.pi,'owen=',fun_owen(epsdiff+epsbkg))
def b_filter(dof,bproj):
eta = 0.5
dofnew = np.where(dof<=eta,eta*(np.exp(-bproj*(1-dof/eta))-(1-dof/eta)*np.exp(-bproj)),(1-eta)*(1-np.exp(-bproj*(dof-eta)/(1-eta)) + (dof - eta)/(1-eta) * np.exp(-bproj)) + eta)
return dofnew
def rcwa_assembly(dof,nG,bproj,theta,phi,planewave):
'''
planewave:{'p_amp',...}
'''
freqcmp = freq*(1+1j/2/Qabs)
obj = rcwa.RCWA_obj(nG,L1,L2,freqcmp,theta,phi,verbose=0)
obj.Add_LayerUniform(thick0,epsuniform)
for i in range(Nlayer):
obj.Add_LayerGrid(thickness[i],epsdiff,epsbkg,Mx,My)
