def ks(x, alpha=1, D=1):
# If x is list, convert to 1d array.
if (isinstance(x, list)):
x = pylab.array(x)
# Length of the output signal must be larger than the length of the
# input signal that is, D must be larger than 1.
D = max(D, 1)
# Number of input samples.
M = len(x)
# Create a vector of the powers of alpha, [alpha^0 alpha^1 ....].
size_alphaVector = D;
alphaVector = (alpha * pylab.ones(
size_alphaVector)) ** range(size_alphaVector)
# Create a matrix with M columns, each being the vector of the powers
# of alpha.
alphaMatrix = pylab.tile(alphaVector, (M, 1)).T;
# Create a matrix with D rows filled by the input signal x.
xMatrix = pylab.tile(x, (D, 1));
# Multipliy the two
yMatrix = alphaMatrix * xMatrix
# Read out the output row by row
y = yMatrix.flatten(0)
return y
def magicsq(N):
"""
copied from internet (lost the source...)
Creates an N x N magic square.
**Input:**
*N* -- an integer in some form, may be float or quotted.
**Output:**
an ``'int32'`` *N* by *N* array -- the same magic square as in
Matlab and Octave ``magic(N)`` commands. In particular, the
Siamese method is used for odd *N* (but with a different
implementation.)
"""
from pylab import tile, arange
global _constant
n = int(N)
if n < 0 or n == 2: # consistent with Octave
raise TypeError("No such magic squares exist.")
elif n % 2 == 1:
m = n >> 1
b = n * n + 1
_constant = n * b >> 1
return (
tile(arange(1, b, n), n + 2)[m:-m - 1].reshape(n, n + 1)[..., 1:] +
tile(arange(n), n + 2).reshape(n, n + 2)[..., 1:-1]).transpose()
elif n % 4 == 0:
b = n * n + 1
_constant = n * b >> 1
d = arange(1, b).reshape(n, n)
d[0:n:4, 0:n:4] = b - d[0:n:4, 0:n:4]
d[0:n:4, 3:n:4] = b - d[0:n:4, 3:n:4]
d[3:n:4, 0:n:4] = b - d[3:n:4, 0:n:4]
d[3:n:4, 3:n:4] = b - d[3:n:4, 3:n:4]
d[1:n:4, 1:n:4] = b - d[1:n:4, 1:n:4]
d[1:n:4, 2:n:4] = b - d[1:n:4, 2:n:4]
d[2:n:4, 1:n:4] = b - d[2:n:4, 1:n:4]
d[2:n:4, 2:n:4] = b - d[2:n:4, 2:n:4]
return d
else:
m = n >> 1
k = m >> 1
b = m * m
d = tile(magicsq(m), (2, 2)) # that changes the _constant
_constant = _constant * 8 - n - m
d[:m, :k] += 3 * b
d[m:, k:m] += 3 * b
d[k, k] += 3 * b
d[k, 0] -= 3 * b
d[m + k, 0] += 3 * b
d[m + k, k] -= 3 * b
d[:m, m:n - k + 1] += b + b
d[m:, m:n - k + 1] += b
d[:m, n - k + 1:] += b
d[m:, n - k + 1:] += b + b
return d
def magicsq(N):
"""
copied from internet (lost the source...)
Creates an N x N magic square.
**Input:**
*N* -- an integer in some form, may be float or quotted.
**Output:**
an ``'int32'`` *N* by *N* array -- the same magic square as in
Matlab and Octave ``magic(N)`` commands. In particular, the
Siamese method is used for odd *N* (but with a different
implementation.)
"""
from pylab import tile,arange
global _constant
n = int(N)
if n < 0 or n == 2: # consistent with Octave
raise TypeError("No such magic squares exist.")
elif n%2 == 1:
m = n>>1
b = n*n + 1
_constant = n*b>>1
return (tile(arange(1,b,n),n+2)[m:-m-1].reshape(n,n+1)[...,1:]+
tile(arange(n),n+2).reshape(n,n+2)[...,1:-1]).transpose()
elif n%4 == 0:
b = n*n + 1
_constant = n*b>>1
d=arange(1, b).reshape(n, n)
d[0:n:4, 0:n:4] = b - d[0:n:4, 0:n:4]
d[0:n:4, 3:n:4] = b - d[0:n:4, 3:n:4]
d[3:n:4, 0:n:4] = b - d[3:n:4, 0:n:4]
d[3:n:4, 3:n:4] = b - d[3:n:4, 3:n:4]
d[1:n:4, 1:n:4] = b - d[1:n:4, 1:n:4]
d[1:n:4, 2:n:4] = b - d[1:n:4, 2:n:4]
d[2:n:4, 1:n:4] = b - d[2:n:4, 1:n:4]
d[2:n:4, 2:n:4] = b - d[2:n:4, 2:n:4]
return d
else:
m = n>>1
k = m>>1
b = m*m
d = tile(magicsq(m), (2,2)) # that changes the _constant
_constant = _constant*8 - n - m
d[:m, :k] += 3*b
d[m:,k:m] += 3*b
d[ k, k] += 3*b
d[ k, 0] -= 3*b
d[m+k, 0] += 3*b
d[m+k, k] -= 3*b
d[:m,m:n-k+1] += b+b
d[m:,m:n-k+1] += b
d[:m, n-k+1:] += b
d[m:, n-k+1:] += b+b
return d
def classify(self, x, k):
d = self.X - tile(x.reshape(self.n, 1), self.N)
dsq = sum(d * d, 0)
minindex = argmin(dsq)
temp = argsort(dsq)
### Custom code starting here ###
# Save the data for each class around the point in a array
score = [0, 0, 0]
# With the help of k surrounding points score each class
for x in range(0, k):
if ((self.c[temp[x]]) == 1.0):
score[0] += 1
elif ((self.c[temp[x]]) == 2.0):
score[1] += 1
elif ((self.c[temp[x]]) == 3.0):
score[2] += 1
# Check to which class the point is classified
if (score[0] > score[1] and score[0] > score[2]):
return 1.0
elif (score[1] > score[2]):
return 2.0
# If there are points with the same value, assign the class of the nearest neighbour.
elif (score[0] == score[1] and score[0] == score[2]):
return self.c[minindex]
else:
return 3.0
def ssc(signal,samplerate=16000,winlen=0.025,winstep=0.01,
nfilt=26,nfft=512,lowfreq=0,highfreq=None,preemph=0.97):
"""Compute Spectral Subband Centroid features from an audio signal.
:param signal: the audio signal from which to compute features. Should be an N*1 array
:param samplerate: the samplerate of the signal we are working with.
:param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
:param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
:param nfilt: the number of filters in the filterbank, default 26.
:param nfft: the FFT size. Default is 512.
:param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
:param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
:param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
:returns: A numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector.
"""
highfreq= highfreq or samplerate/2
signal = sigproc.preemphasis(signal,preemph)
frames = sigproc.framesig(signal, winlen*samplerate, winstep*samplerate)
pspec = sigproc.powspec(frames,nfft)
pspec = pylab.where(pspec == 0,pylab.finfo(float).eps,pspec) # if things are all zeros we get problems
fb = get_filterbanks(nfilt,nfft,samplerate,lowfreq,highfreq)
feat = pylab.dot(pspec,fb.T) # compute the filterbank energies
R = pylab.tile(pylab.linspace(1,samplerate/2,pylab.size(pspec,1)),(pylab.size(pspec,0),1))
return pylab.dot(pspec*R,fb.T) / feat
def _grad_theta(psi, xxx_todo_changeme1):
"""
Compute the 1D gradient of a scalar field in the theta direction on a unit-
radius spherical shell. Assumes psi is a 2D array with theta changing along
axis 1. We use central differences for interior points, one-sided differences
for exterior points, and address simple periodic boundaries.
"""
(phi,theta) = xxx_todo_changeme1
dphi = p.diff(phi,axis=0)
dtheta = p.diff(theta,axis=1)
# pre-allocate output grid
dpsidtheta = p.zeros(theta.shape)
# use weighted central differences to compute theta gradient on the interior
dpsidtheta[:,1:-1] = (((p.diff(psi[:,:-1],axis=1) / dtheta[:,:-1]**2 +
p.diff(psi[:,1:],axis=1) / dtheta[:,1:]**2) /
(1/dtheta[:,:-1] + 1/dtheta[:,1:]) ) )
# compute theta gradients at exterior points
if p.mod(theta[0,0],2*p.pi) == p.mod(theta[0,-1],2*p.pi):
# use weighted central differences to compute gradient if periodic boundary
dpsidtheta[:,[0,-1]] = p.tile(((p.diff(psi[:,:2],axis=1) / dtheta[:,0]**2 +
p.diff(psi[:,-2:],axis=1) / dtheta[:,-1]**2) /
(1/dtheta[:,0] + 1/dtheta[:-1]) ), (1,2) )
else:
# use one-sided difference to compute gradient if not a periodic boundary
dpsidtheta[:,-1] = (p.diff(psi[:,-2:],axis=1).T / dtheta[:,-1])
dpsidtheta[:,0] = (p.diff(psi[:,:2],axis=1).T / dtheta[:,0])
return dpsidtheta
def classify(self, x):
d = self.X - tile(x.reshape(self.n,1), self.N);
dsq = sum(d*d,0)
# Get N nearest neighbors
minindex = np.argsort(dsq)[0:self.k]
# Group sum by value
return Counter(self.c[minindex]).most_common()[0][0]
def flica_reorder(output_dir, nmod):
data_dir = os.path.join(output_dir, '')
X = []
for i in range(0, nmod):
X.append(np.load(data_dir + '/flica_X' + str(i + 1) + '.npy'))
M = np.load(data_dir + '/flica_result.npz')
K = len(X)
R = M['H'].shape[1]
for k in range(0, K):
#M.X{k} * diag(M.W{k}.*sqrt( M.H.^2 * makesize(M.lambda{k},[R 1]) * M.DD(k))')]; %#ok<AGROW>
if np.matrix(M['lambda1'][k]).shape[0] == R:
tmp = np.dot(np.square(M['H']), M['lambda1'][k])
else:
tmp = np.dot(np.square(M['H']), tile(M['lambda1'][k], [R, 1]))
tmp2 = np.sqrt(np.dot(tmp, M['DD'][k]))
tmp3 = np.diag(np.multiply(M['W'][k], tmp2))
tmp4 = np.dot(X[k], np.diag(tmp3))
if k == 0:
Xcat = copy.deepcopy(tmp4)
else:
Xcat = np.concatenate((Xcat, tmp4))
weight = np.sum(np.square(Xcat), 0)
order = np.argsort(weight)
order = order[::-1]
weight = weight[order]
np.save(data_dir + 'new_order.npy', order)
np.save(data_dir + 'new_weight.npy', weight)
return order
def feature_scale(M,
normalize=False,
dbscale=False,
norm=False,
bels=False):
"""
::
Perform mutually-orthogonal scaling operations, otherwise return identity:
normalize [False]
dbscale [False]
norm [False]
"""
if not (normalize or dbscale or norm or bels):
return M
else:
X = M.copy() # don't alter the original
if norm:
X = X / pylab.tile(pylab.sqrt((X * X).sum(0)), (X.shape[0], 1))
if normalize:
X = adb.normalize(X)
if dbscale or bels:
X = pylab.log10(X)
if dbscale:
X = 20 * X
return X
def main():
mu = pl.array([[0], [12], [24], [36]])
Sigma = pl.array([[3.01602775, 1.02746769, -3.60224613, -2.08792829],
[1.02746769, 5.65146472, -3.98616664, 0.48723704],
[-3.60224613, -3.98616664, 13.04508284, -1.59255406],
[-2.08792829, 0.48723704, -1.59255406, 8.28742469]])
# The data matrix is created for above mu and Sigma.
d, U = pl.eig(Sigma)
L = pl.diagflat(d)
A = pl.dot(U, pl.sqrt(L))
X = pl.randn(4, 1000)
# Y is the data matrix of random samples.
Y = pl.dot(A, X) + pl.tile(mu, 1000)
pl.figure(1)
pl.clf()
pl.plot(X[0], Y[1], '+', color='#0000FF', label='i=0,j=1')
pl.plot(X[0], Y[2], '+', color='#FF0000', label='i=0,j=2')
pl.plot(X[0], Y[3], '+', color='#00FF00', label='i=0,j=3')
pl.plot(X[1], Y[0], 'x', color='#FFFF00', label='i=1,j=0')
pl.plot(X[1], Y[2], 'x', color='#00FFFF', label='i=1,j=2')
pl.plot(X[1], Y[3], 'x', color='#444444', label='i=1,j=3')
pl.plot(X[2], Y[0], '.', color='#774411', label='i=2,j=0')
pl.plot(X[2], Y[1], '.', color='#222222', label='i=2,j=1')
pl.plot(X[2], Y[3], '.', color='#AAAAAA', label='i=2,j=3')
pl.plot(X[3], Y[0], '+', color='#FFAA22', label='i=3,j=0')
pl.plot(X[3], Y[1], '+', color='#22AAFF', label='i=3,j=1')
pl.plot(X[3], Y[2], '+', color='#FFDD00', label='i=3,j=2')
pl.legend()
pl.savefig('fig21.png')
def plot():
( ml_idxs,
ml_lengths,
ml_lanes,
or_idxs,
capacity,
w,
ff,
j,
Time,
Lengths,
XLengths,
Lanes,
density,
flow,
velocity,
queues,
dt,
n,
m
) = scen_output.load()
rho_crit = pylab.array([fm / vff for fm, vff in zip(capacity, ff)]) * 1000.0
rho_max = pylab.array(j) * 1000.0
norm_density = density / pylab.tile(rho_crit, (m, 1)).transpose()
norm_density_max = density / pylab.tile(rho_max, (m, 1)).transpose()
norm_flow = flow / (pylab.tile(capacity, (m,1)).transpose() * 3600.0)
nplots = 2
mplots = 4
g = [0]
def plot_grid(data, title):
g[0] += 1
pylab.subplot(nplots, mplots, g[0])
pylab.pcolormesh(Time, XLengths, data)
pylab.colorbar()
pylab.title(title)
pylab.xlabel("Time (hours)")
pylab.ylabel("Offset (km)")
plot_grid(density, "Mainline Density (veh / km-lane)")
plot_grid(queues, "Onramps (veh)")
plot_grid(flow, "Flow (veh / hour / lane)")
plot_grid(velocity, "Velocity (km / hr)")
plot_grid(norm_density, "Ratio over Critical Mainline")
plot_grid(norm_density_max, "Ratio over Max Mainline")
plot_grid(norm_flow, "Ratio over Capacity Flow")
pylab.show()
def raytrace (self, uv, lam=1):
uvMat = np.atleast_2d (uv)
if uvMat.shape[0] == 1:
uvMat = uvMat.T
npts = uvMat.shape[1]
invPx = self.pinvP.dot (homogeneous.homogenize (uvMat))
XLambda = invPx + pl.tile (lam*homogeneous.homogenize (self.C), (npts, 1)).T
return homogeneous.dehomogenize (XLambda)
def translate_back(outputs,threshold=0.7,pos=0):
"""Translate back. Thresholds on class 0, then assigns
the maximum class to each region."""
# print outputs
labels,n = measurements.label(outputs[:,0]<threshold)
mask = tile(labels.reshape(-1,1), (1,outputs.shape[1]))
maxima = measurements.maximum_position(outputs,mask,arange(1,amax(mask)+1))
if pos: return maxima
return [c for (r,c) in maxima]
def raytrace(self, uv, lam=1):
uvMat = np.atleast_2d(uv)
if uvMat.shape[0] == 1:
uvMat = uvMat.T
npts = uvMat.shape[1]
invPx = self.pinvP.dot(homogeneous.homogenize(uvMat))
XLambda = invPx + pl.tile(lam * homogeneous.homogenize(self.C),
(npts, 1)).T
return homogeneous.dehomogenize(XLambda)
def translate_back(outputs,threshold=0.7,pos=0):
"""Translate back. Thresholds on class 0, then assigns
the maximum class to each region."""
# print outputs
labels,n = measurements.label(outputs[:,0]<threshold)
mask = tile(labels.reshape(-1,1), (1,outputs.shape[1]))
maxima = measurements.maximum_position(outputs,mask,arange(1,amax(mask)+1))
if pos: return maxima
return [c for (r,c) in maxima]
def translate_back(outputs, threshold=0.7, pos=0):
labels, n = measurements.label(outputs[:, 0] < threshold)
mask = tile(labels.reshape(-1, 1), (1, outputs.shape[1]))
maxima = measurements.maximum_position(outputs, mask,
arange(1,
amax(mask) + 1))
if pos == 1:
return maxima
if pos == 2:
return [(c, outputs[r, c]) for (r, c) in maxima]
return [c for (r, c) in maxima]
def mi(x,y, bins=11):
"""Given two arrays x and y of equal length, return their mutual information in bits
"""
Hxy, xe, ye = pylab.histogram2d(x,y,bins=bins)
Hx = Hxy.sum(axis=1)
Hy = Hxy.sum(axis=0)
Pxy = Hxy/float(x.size)
Px = Hx/float(x.size)
Py = Hy/float(x.size)
pxy = Pxy.ravel()
px = Px.repeat(Py.size)
py = pylab.tile(Py, Px.size)
idx = pylab.find((pxy > 0) & (px > 0) & (py > 0))
return (pxy[idx]*pylab.log2(pxy[idx]/(px[idx]*py[idx]))).sum()
def classify(self, x, k):
d = self.X - tile(x.reshape(self.n,1), self.N)
# Occurrence of a class
occd = {}
for i in range(k):
dsq = sum(d*d,0)
minindex = argmin(dsq)
if self.c[minindex] in occd:
occd[self.c[minindex]] += 1
else:
occd[self.c[minindex]] = 1
# Prevent next iter giving this index again
d[:, minindex] = self.max + 1
# Return the name of the class that occurred most
return max(occd.iteritems(), key=operator.itemgetter(1))[0]
def feature_scale(M, normalize=False, dbscale=False, norm=False, bels=False):
"""
Perform mutually-orthogonal scaling operations, otherwise return identity:
normalize [False]
dbscale [False]
norm [False]
"""
if not (normalize or dbscale or norm or bels):
return M
else:
X = M.copy() # don't alter the original
if norm:
X = X / P.tile(P.sqrt((X * X).sum(0)), (X.shape[0], 1))
if normalize:
X = _normalize(X)
if dbscale or bels:
X = P.log10(P.clip(X, 0.0001, X.max()))
if dbscale:
X = 20 * X
return X
def mutual_information(x,y, bins=11): """Given two arrays x and y of equal length, return their mutual information in bits >>> N = 10000 >>> xi = pylab.randn(N) >>> xi[pylab.find(xi>0)] = 1 >>> xi[pylab.find(xi<=0)] = 0 >>> yi = xi >>> print round(mutual_information(xi, yi, 1000),2) #One bit of info 1.0 >>> N = 10000 >>> xi = pylab.uniform(size=N) >>> yi = pylab.floor(xi*8) >>> print round(mutual_information(xi, yi, 1000),2) #Three bits of info 3.0 >>> N = 100000 >>> xi = pylab.randn(N) >>> yi = pylab.randn(N) >>> print round(mutual_information(xi, yi),2) #Should be zero given enough data and not too sparse binning 0.0 """ Hxy, xe, ye = pylab.histogram2d(x,y,bins=bins) Hx = Hxy.sum(axis=1) Hy = Hxy.sum(axis=0) Pxy = Hxy/float(x.size) Px = Hx/float(x.size) Py = Hy/float(x.size) pxy = Pxy.ravel() px = Px.repeat(Py.size) py = pylab.tile(Py, Px.size) idx = pylab.find((pxy > 0) & (px > 0) & (py > 0)) mi = (pxy[idx]*pylab.log2(pxy[idx]/(px[idx]*py[idx]))).sum() return mi
def mutual_information(x, y, bins=11):
"""Given two arrays x and y of equal length, return their mutual information in bits
>>> N = 10000
>>> xi = pylab.randn(N)
>>> xi[pylab.find(xi>0)] = 1
>>> xi[pylab.find(xi<=0)] = 0
>>> yi = xi
>>> print round(mutual_information(xi, yi, 1000),2) #One bit of info
1.0
>>> N = 10000
>>> xi = pylab.uniform(size=N)
>>> yi = pylab.floor(xi*8)
>>> print round(mutual_information(xi, yi, 1000),2) #Three bits of info
3.0
>>> N = 100000
>>> xi = pylab.randn(N)
>>> yi = pylab.randn(N)
>>> print round(mutual_information(xi, yi),2) #Should be zero given enough data and not too sparse binning
0.0
"""
Hxy, xe, ye = pylab.histogram2d(x, y, bins=bins)
Hx = Hxy.sum(axis=1)
Hy = Hxy.sum(axis=0)
Pxy = Hxy / float(x.size)
Px = Hx / float(x.size)
Py = Hy / float(x.size)
pxy = Pxy.ravel()
px = Px.repeat(Py.size)
py = pylab.tile(Py, Px.size)
idx = pylab.find((pxy > 0) & (px > 0) & (py > 0))
mi = (pxy[idx] * pylab.log2(pxy[idx] / (px[idx] * py[idx]))).sum()
return mi
def feature_scale(M, normalize=False, dbscale=False, norm=False, bels=False):
"""
::
Perform mutually-orthogonal scaling operations, otherwise return identity:
normalize [False]
dbscale [False]
norm [False]
"""
if not (normalize or dbscale or norm or bels):
return M
else:
X = M.copy() # don't alter the original
if norm:
X = X / P.tile(P.sqrt((X*X).sum(0)),(X.shape[0],1))
if normalize:
X = _normalize(X)
if dbscale or bels:
X = P.log10(P.clip(X,0.0001,X.max()))
if dbscale:
X = 20*X
return X
def __init__(self, X, c):
self.n, self.N = X.shape
self.X = X
self.mu = empty((3, self.n))
self.cov = empty((3, self.n, self.n))
self.P = empty(3)
cond = zeros(self.N)
for i in range(0, 3):
cond = cond + 1.0
indices = where(c == cond)
# Xa bevat alle elementen uit X waar de klasse gelijk van is aan i + 1.0
Xa = [X[:, b] for b in indices]
# Bovenstaande pakt de xjes in een extra array, dit willen we niet
Xa = Xa[0]
Na = shape(Xa)[1]
self.mu[i] = mean(Xa, axis=1)
# Tile smeert mu uit zodat we mu kunnen aftrekken van de X matrix
self.cov[i] = cov(Xa - tile(self.mu[i].T, Na).reshape(self.n, Na))
# De kans op deze klasse
self.P[i] = (Na * 1.0) / self.N
def _grad_phi(psi, xxx_todo_changeme):
"""
Compute the 1D gradient of a scalar field in the phi direction on a unit-
radius spherical shell. Assumes psi is a 2D array with phi changing along
axis 0. We use central differences for interior points, one-sided differences
for exterior points, and address simple periodic boundaries.
"""
(phi,theta) = xxx_todo_changeme
dphi = p.diff(phi,axis=0)
dtheta = p.diff(theta,axis=1)
# pre-allocate output grid
dpsidphi = p.zeros(phi.shape)
# use weighted central differences to compute gradient on the interior
dpsidphi[1:-1,:] = (((p.diff(psi[:-1,:],axis=0) / dphi[:-1,:]**2 +
p.diff(psi[1:,:],axis=0) / dphi[1:,:]**2) /
(1/dphi[:-1,:] + 1/dphi[1:,:]) ) *
1./p.sin(theta[1:-1,:]) )
# compute phi gradients at exterior points
if p.mod(phi[0,0],2*p.pi) == p.mod(phi[-1,0],2*p.pi):
# use weighted central differences to compute gradient if periodic boundary
dpsidphi[[0,-1],:] = p.tile(((p.diff(psi[:2,:],axis=0) / dphi[0,:]**2 +
p.diff(psi[-2:,:],axis=0) / dphi[-1,:]**2) /
(1/dphi[0,:] + 1/dphi[-1,:]) ) *
1./p.sin(theta[0,:]), (2,1) )
else:
# use one-sided difference to compute gradient if not a periodic boundary
dpsidphi[-1,:] = (p.diff(psi[-2:,:],axis=0) / dphi[-1,:] / p.sin(theta[-1,:]) )
dpsidphi[0,:] = (p.diff(psi[:2,:],axis=0) / dphi[0,:] / p.sin(theta[0,:]) )
return dpsidphi
import pylab as plt
n = 1000
mu = [[0],
[0],
[0],
[0]]
Sigma = [[3.01602775, 1.02746769, -3.60224613, -2.08792829],
[1.02746769, 5.65146472, -3.98616664, 0.48723704],
[-3.60224613, -3.98616664, 13.04508284, -1.59255406],
[-2.08792829, 0.48723704, -1.59255406, 8.28742469]]
d, U = plt.eig(Sigma) # Sigma = U L Ut
L = plt.diagflat(d)
A = plt.dot(U, plt.sqrt(L)) # Required transform matrix.
X = plt.randn(4, n) # 4*n matrix with each element ~ N(0,1)
# 4*n each column vector ~N(mu,Sigma), random draws from distribution.
Y = plt.dot(A, X) + plt.tile(mu, n)
Ybar = [[avg] for avg in plt.mean(Y, 1)] # Mean along the 1 axis.
Yzm = Y - plt.tile(Ybar, n) # Subtract mean from each column.
# Estimator for covariance matrix.
S = plt.dot(Yzm, plt.transpose(Yzm)) / n - 1
print(Ybar, S)
def classify(self, x):
d = self.X - tile(x.reshape(self.n, 1), self.N)
dsq = sum(d*d, 0)
neighbours = self.c[argpartition(dsq, self.k)[:self.k]]
most_common = argmax(bincount(neighbours.astype(int)))
return most_common
def classify(self, x): d = self.X - tile(x.reshape(self.n,1), self.N) dsq = sum(d*d,0) minindex = argmin(dsq) return self.c[minindex]
def CreateFrames(path='./', run='',
t0='', t1='',
hemisphere='north', geoGrid=False,
ignoreBinary=False, binaryType='pkl',
configFile=None):
"""
Compute deltaBs hemispheric grid given LFM-MIX output files in path.
Computes:
pngFiles - a list of PNG filenames, each corresponding to a snapshot in
time of LFM-MIX ground deltaB vector fields
NOTE: while the output is a list of filenames, the function
generates binary pkl/mat files that can be read in by
other software for further analysis.
FIXME: southern hemisphere summary plots are presented from a
point of view below the south pole, looking up. Likewise
for the data files. This is not technically a right-handed
frame of reference, so any analysis of southern hemisphere
data must rotate fields 180 degrees about the X axis, or
0 longitude, 0 latitude line. This odd data file convention
is consistent with how southern hemisphere data is stored
in MIX files, but there is a strong argument to just store
everything assuming the same (northern) POV, and rotate
to a southern POV for display purposes only; this will
require significant work.
Requires:
Nothing, all inputs are optional
Optional:
path - path to data directory holding LFM and MIX model output files
(default is current directory)
run - output filename prefix identifying LFM-MIX run (i.e., the part
of the filename prior to [mhd|mix]_yyyy-mm-ddTHH-MM-SSZ.hdf)
(default is any mhd|mix files in path)
t0 - datetime object specifying the earliest of available time step
to include in the extraction
(default is earliest available)
t1 - datetime object specfiying the latest of available time step
to include in the extraction
(default is last available)
hemisphere - specify 'north' or 'south' hemisphere
(default is 'north')
geoGrid - if True, assume observatory coordinates are in geographic
coordinates rather than solar magnetic; same for outputs
(default is False)
ignoreBinary - if True, ignore any pre-computed binary files and re-
compute everything from scratch; NOTE: individual binary files
will be ignored anyway if they are incompatible with specified
inputs, but this option avoids reading the binary file entirely.
(default is False)
binaryType - binary type to generate, NOT to read in...routine looks for
PKL files first, then mat files, then proceeds to re-compute
if neither are available.
(default is 'pkl')
configFile - specifies plotting config file; if None, default config file
is path/figs/north|south/deltaBSum.config; if this doesn't
exist, create new one with default config parameters.
"""
assert( (hemisphere == 'north') | (hemisphere == 'south') )
hemiSelect = {'north': 'North', 'south': 'South'}[hemisphere]
# Make sure the output directory exisits if not make it
dirname = os.path.join(path, 'figs', hemisphere)
if not os.path.exists(dirname):
os.makedirs( dirname )
print(('Rendering ' + hemiSelect + 'ern hemisphere, storing frames at ' + dirname))
#Now check to make sure the MIX files are correct
dMIX = pyLTR.Models.MIX(path, run)
modelVars = dMIX.getVarNames()
for v in ['Grid X', 'Grid Y',
'Potential North [V]', 'Potential South [V]',
'FAC North [A/m^2]', 'FAC South [A/m^2]',
'Pedersen conductance North [S]', 'Pedersen conductance South [S]',
'Hall conductance North [S]', 'Hall conductance South [S]']:
assert( v in modelVars )
timeRange = dMIX.getTimeRange()
#Now check to make sure the LFM files are correct
dLFM = pyLTR.Models.LFM(path, run)
modelVars = dLFM.getVarNames()
for v in ['X_grid', 'Y_grid', 'Z_grid',
'bx_', 'by_', 'bz_']:
assert( v in modelVars )
# check that LFM output timeRanges are exactly the same as MIX output timeRanges
trLFM = dLFM.getTimeRange()
# _roundTime() rounds to nearest minute by default, which should suffice here
# NOTE: we do NOT change the time stamps at all, just make sure they match
# to a 1-minute tolerance
if list(map(_roundTime, timeRange)) != list(map(_roundTime, trLFM)):
raise Exception(('Mismatched MIX and LFM output files'))
if len(timeRange) == 0:
raise Exception(('No data files found. Are you pointing to the correct run directory?'))
## Original code defaulted to entire data set if the user-supplied time range
## fell outside of the available data, almost certainly not a desired result.
## Now if the user requests a time range that falls completely outside of the
## available data, and exception is raised.
##index0 = 0
##if t0:
## for i,t in enumerate(timeRange):
## if t0 >= t:
## index0 = i
##
###index1 = len(timeRange)-1
##index1 = len(timeRange) # we were skipping the last valid time step
##if t1:
## for i,t in enumerate(timeRange):
## if t1 >= t:
## #index1 = i
## index1 = i + 1 # we were skipping the last valid time step
if t0:
if t1 and t1 < timeRange[0]: # upper time stamp below lowest available time stamp
raise Exception('Requested time range falls outside available data')
if t0 > timeRange[-1]: # lower time stamp above highest available time stamp
raise Exception('Requested time range falls outside available data')
for i,t in enumerate(timeRange):
if t0 >= t:
index0 = i
else:
index0 = 0
if t1:
if t0 and t0 > timeRange[-1]: # lower time stamp above highest available time stamp
raise Exception('Requested time range falls outside available data')
if t1 < timeRange[0]: # upper time stamp below lowest available time stamp
raise Exception('Requested time range falls outside available data')
for i,t in enumerate(timeRange):
if t1 >= t:
index1 = i+1
else:
index1 = len(timeRange)
if index1 > index0:
print(( 'Extracting LFM and MIX quantities for time series over %d time steps.' % (index1-index0) ))
else:
raise Exception('Requested time range is invalid')
# Output a status bar displaying how far along the computation is.
progress = pyLTR.StatusBar(0, index1-index0)
progress.start()
# Pre-compute r and theta
x = dMIX.read('Grid X', timeRange[index0])
xdict={'data':x*6500e3,'name':'X','units':r'm'}
y = dMIX.read('Grid Y', timeRange[index0])
ydict={'data':y*6500e3,'name':'Y','units':r'm'}
theta=n.arctan2(y,x)
theta[theta<0]=theta[theta<0]+2*n.pi
# plotting routines now rotate local noon to point up
#theta=theta+n.pi/2 # to put noon up
r=n.sqrt(x**2+y**2)
# plotting routines now expect longitude and colatitude, in radians, stored in dictionaries
longitude = {'data':theta,'name':r'\phi','units':r'rad'}
colatitude = {'data':n.arcsin(r),'name':r'\theta','units':r'rad'}
# Deal with the plot options
if (configFile == None and os.path.exists(os.path.join(dirname,'deltaBSum.config')) ):
configFile = os.path.join(dirname,'deltaBSum.config')
if configFile == None:
# scalar radial magnetic pertubations
dBradialTotOpts={'min':-100,'max':100,'colormap':'jet'}
dBradialIonOpts={'min':-100,'max':100,'colormap':'jet'}
dBradialFACOpts={'min':-100,'max':100,'colormap':'jet'}
dBradialMagOpts={'min':-100,'max':100,'colormap':'jet'}
# 2D vector horizontal perturbations
dBhvecTotOpts={'width':.0025,'scale':1e3,'pivot':'middle'}
dBhvecIonOpts={'width':.0025,'scale':1e3,'pivot':'middle'}
dBhvecFACOpts={'width':.0025,'scale':1e3,'pivot':'middle'}
dBhvecMagOpts={'width':.0025,'scale':1e3,'pivot':'middle'}
# place all config dictionaries in one big dictionary
optsObject = {'dBradialTot':dBradialTotOpts,
'dBradialIon':dBradialIonOpts,
'dBradialFAC':dBradialFACOpts,
'dBradialMag':dBradialMagOpts,
'dBhvecTot':dBhvecTotOpts,
'dBhvecIon':dBhvecIonOpts,
'dBhvecFAC':dBhvecFACOpts,
'dBhvecMag':dBhvecMagOpts,
'altPole':altPoleOpts}
configFilename=os.path.join(dirname,'deltaBSum.config')
print(("Writing plot config file at " + configFilename))
f=open(configFilename,'w')
f.write(pyLTR.yaml.safe_dump(optsObject,default_flow_style=False))
f.close()
else:
f=open(configFile,'r')
optsDict=pyLTR.yaml.safe_load(f.read())
f.close()
if ('dBradialTot' in optsDict):
dBradialTotOpts = optsDict['dBradialTot']
else:
dBradialTotOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBradialIon' in optsDict):
dBradialIonOpts = optsDict['dBradialIon']
else:
dBradialIonOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBradialFAC' in optsDict):
dBradialFACOpts = optsDict['dBradialFAC']
else:
dBradialFACOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBradialMag' in optsDict):
dBradialMagOpts = optsDict['dBradialMag']
else:
dBradialMagOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBhvecTot' in optsDict):
dBhvecTotOpts = optsDict['dBhvecTot']
else:
dBhvecTotOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBhvecIon' in optsDict):
dBhvecIonOpts = optsDict['dBhvecIon']
else:
dBhvecIonOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBhvecFAC' in optsDict):
dBhvecFACOpts = optsDict['dBhvecFAC']
else:
dBhvecFACOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('dBhvecMag' in optsDict):
dBhvecMagOpts = optsDict['dBhvecMag']
else:
dBhvecMagOpts={'min':-100.,'max':100.,'colormap':'jet'}
if ('altPole' in optsDict):
altPoleOpts = optsDict['altPole']
else:
altPoleOpts = {'poleMarker1':'x', 'poleMarker2':'x',
'poleSize1':7, 'poleSize2':5,
'poleWidth1':3, 'poleWidth2':1,
'poleColor1':'blue', 'poleColor2':'white'}
# initialize output list
pngFilenames = []
for i,time in enumerate(timeRange[index0:index1]):
try:
try:
# ignore binary file even if one exists
if ignoreBinary:
raise Exception
# look for a .pkl file that already holds all the data required for
# subsequent plots before recalculating all the derived data...if
# this fails, look for a .mat file, if this fails, fall through to
# recalculate all summary data
filePrefix = os.path.join(path,'figs',hemisphere)
# this is a possible race condition, but try/except just doesn't do what I want
if os.path.exists(os.path.join(filePrefix,
'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.pkl'%
(time.year,time.month,time.day,
time.hour,time.minute,time.second))):
binFilename = os.path.join(filePrefix,
'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.pkl'%
(time.year,time.month,time.day,
time.hour,time.minute,time.second))
fh=open(binFilename,'rb')
allDict = pickle.load(fh)
fh.close()
elif os.path.exists(os.path.join(filePrefix,
'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.mat'%
(time.year,time.month,time.day,
time.hour,time.minute,time.second))):
binFilename = os.path.join(filePrefix,
'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.mat'%
(time.year,time.month,time.day,
time.hour,time.minute,time.second))
fh=open(binFilename,'rb')
allDict = sio.loadmat(fh, squeeze_me=True)
fh.close()
else:
print(('No binary file found, recalculating '+
'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ'%
(time.year,time.month,time.day,time.hour,time.minute,time.second)+
'...'))
raise Exception
# ignore binary file if the coordinate system is not consistent with geoGrid
if ((geoGrid and allDict['coordinates'] != 'Geographic') or
(not(geoGrid) and allDict['coordinates'] != 'Solar Magnetic')):
raise Exception
phi_dict,theta_dict,rho_dict = allDict['dB_obs']
phi = phi_dict['data'] * 1. # '*1' forces array of floats, NOT objects
theta = theta_dict['data'] * 1. # '*1' forces array of floats, NOT objects
rho = rho_dict['data'] * 1. # '*1' forces array of floats, NOT objects
if geoGrid:
phi_geo = phi
theta_geo = theta
rho_geo = rho
dBphi_ion_dict,dBtheta_ion_dict,dBrho_ion_dict = allDict['dB_ion']
dBphi_ion = dBphi_ion_dict['data'] / 1e9 # convert to Tesla
dBtheta_ion = dBtheta_ion_dict['data'] / 1e9 # convert to Tesla
dBrho_ion = dBrho_ion_dict['data'] / 1e9 # convert to Tesla
dBphi_fac_dict,dBtheta_fac_dict,dBrho_fac_dict = allDict['dB_fac']
dBphi_fac = dBphi_fac_dict['data'] / 1e9 # convert to Tesla
dBtheta_fac = dBtheta_fac_dict['data'] / 1e9 # convert to Tesla
dBrho_fac = dBrho_fac_dict['data'] / 1e9 # convert to Tesla
dBphi_mag_dict,dBtheta_mag_dict,dBrho_mag_dict = allDict['dB_mag']
dBphi_mag = dBphi_mag_dict['data'] / 1e9 # convert to Tesla
dBtheta_mag = dBtheta_mag_dict['data'] / 1e9 # convert to Tesla
dBrho_mag = dBrho_mag_dict['data'] / 1e9 # convert to Tesla
except:
# first read the MIX data
vals=dMIX.read('Potential '+hemiSelect+' [V]',time)/1000.0
psi_dict={'data':vals,'name':r'$\Phi$','units':r'kV'}
vals=dMIX.read('Pedersen conductance '+hemiSelect+' [S]',time)
sigmap_dict={'data':vals,'name':r'$\Sigma_{P}$','units':r'S'}
vals=dMIX.read('Hall conductance '+hemiSelect+' [S]',time)
sigmah_dict={'data':vals,'name':r'$\Sigma_{H}$','units':r'S'}
vals=dMIX.read('FAC '+hemiSelect+' [A/m^2]',time)
fac_dict={'data':vals*1e6,'name':r'$J_\parallel$','units':r'$\mu A/m^2$'}
# then compute the electric field vectors
((phi_dict,theta_dict),
(ephi_dict,etheta_dict)) = pyLTR.Physics.MIXCalcs.efieldDict(
xdict, ydict, psi_dict, ri=6500e3)
# then compute total, Pedersen, and Hall current vectors
if hemisphere=='north':
((Jphi_dict,Jtheta_dict),
(Jpedphi_dict,Jpedtheta_dict),
(Jhallphi_dict,Jhalltheta_dict)) = pyLTR.Physics.MIXCalcs.jphithetaDict(
(ephi_dict,etheta_dict), sigmap_dict, sigmah_dict, colatitude['data'])
else:
((Jphi_dict,Jtheta_dict),
(Jpedphi_dict,Jpedtheta_dict),
(Jhallphi_dict,Jhalltheta_dict)) = pyLTR.Physics.MIXCalcs.jphithetaDict(
(ephi_dict,etheta_dict), sigmap_dict, sigmah_dict, n.pi-colatitude['data'])
# then generate the SSECS, starting with min/max bounds of ionosphere
# segments
phi = phi_dict['data']
theta = theta_dict['data']
# caclulate MIX grid cell boundaries in phi and theta
rion_min = [None] * 3 # initialize empty 3 list
rion_min[0] = p.zeros(phi.shape)
rion_min[0][1:,:] = phi[1:,:] - p.diff(phi, axis=0)/2.
rion_min[0][0,:] = phi[0,:] - p.diff(phi[0:2,:], axis=0).squeeze()/2.
rion_min[1] = p.zeros(theta.shape)
rion_min[1][:,1:] = theta[:,1:] - p.diff(theta, axis=1)/2.
rion_min[1][:,0] = theta[:,0] - p.diff(theta[:,0:2], axis=1).squeeze()/2.
rion_min[2] = p.zeros(theta.shape)
rion_min[2][:,:] = 6500.e3
rion_max = [None] * 3 # initialize empty 3 list
rion_max[0] = p.zeros(phi.shape)
rion_max[0][:-1,:] = phi[:-1,:] + p.diff(phi, axis=0)/2.
rion_max[0][-1,:] = phi[-1,:] + p.diff(phi[-2:,:], axis=0).squeeze()/2.
rion_max[1] = p.zeros(theta.shape)
rion_max[1][:,:-1] = theta[:,:-1] + p.diff(theta, axis=1)/2.
rion_max[1][:,-1] = theta[:,-1] + p.diff(theta[:,-2:], axis=1).squeeze()/2.
rion_max[2] = p.zeros(theta.shape)
rion_max[2][:,:] = p.Inf
# generate SSECS for ionospheric currents only
(rv_ion,
Jv_ion,
dv_ion) = pyLTR.Physics.SSECS.ssecs_sphere([rion_min[0],rion_min[1],rion_min[2]],
[rion_max[0],rion_max[1],rion_min[2]],
(Jphi_dict['data']/1e6,
Jtheta_dict['data']/1e6),
10, False)
# generate SSECS inside LFM inner boundary
(rv_IBin,
Jv_IBin,
dv_IBin) = pyLTR.Physics.SSECS.ssecs_sphere([rion_min[0],rion_min[1],rion_min[2]],
[rion_max[0],rion_max[1],2.5*rion_min[2]],
(Jphi_dict['data']/1e6,
Jtheta_dict['data']/1e6),
10, False)
# do NOT attempt to generate SSECS for FACs alone...this isn't possible
# with existing code; However, the deltaB from FACs is the difference
# between deltaBs calculated from the two SSECS above
# generate SSECS outside LFM inner boundary
# (this is serving as a proxy for magnetosphere currents for now)
(rv_mag,
Jv_mag,
dv_mag) = pyLTR.Physics.SSECS.ssecs_sphere([rion_min[0],rion_min[1],2.5*rion_min[2]],
[rion_max[0],rion_max[1],rion_min[2]],
(Jphi_dict['data']/1e6,
Jtheta_dict['data']/1e6),
10, False)
# extract currents from MHD data
# NOTE: LFM time stamps are not necessarily the same as MIX, so it
# is necessary to use the LFM's timeRange list (i.e., trLFM)
x=dLFM.read('X_grid', trLFM[index0:index1][i]) # this is in cm
y=dLFM.read('Y_grid', trLFM[index0:index1][i]) # this is in cm
z=dLFM.read('Z_grid', trLFM[index0:index1][i]) # this is in cm
Bx=dLFM.read('bx_', trLFM[index0:index1][i]) # this is in G
By=dLFM.read('by_', trLFM[index0:index1][i]) # this is in G
Bz=dLFM.read('bz_', trLFM[index0:index1][i]) # this is in G
hgrid=pyLTR.Grids.HexahedralGrid(x,y,z)
xB,yB,zB=hgrid.cellCenters()
hgridcc=pyLTR.Grids.HexahedralGrid(xB,yB,zB) # B is at cell centers
Jx,Jy,Jz = pyLTR.Physics.LFMCurrent(hgridcc,Bx,By,Bz,rion=1) # ...should be A/m^2 given default input units
xJ,yJ,zJ = hgridcc.cellCenters() # ...and J is at the centers of these cells
xJ = xJ/100 # ...and the coordinates should be in meters for BS.py
yJ = yJ/100 # ...and the coordinates should be in meters for BS.py
zJ = zJ/100 # ...and the coordinates should be in meters for BS.py
ldV = hgridcc.cellVolume()/(100**3) # ...and we need dV in m^3 for BS.py
if hemisphere=='south':
# it's easier to rotate the LFM grid than convert the MIX coordinates
# for southern hemisphere output
yJ = -yJ
zJ = -zJ
Jy = -Jy
Jz = -Jz
#
# This is a little ugly...Quad (and Oct) resolution LFM runs use
# MIX grids that are different resoltions than Single and Double
# runs; not surprising, but I was slow to figure this out. Anyway,
# we need to visualize and cross-validate on similar grids, thus
# the following kludge ('kludge' because the better answer is to
# specify a useful grid without any reference to the MIX grid).
#
if phi.size == 181*27:
pass
elif phi.size == 361*48:
phi = phi[::2,[0,1,2,3,4]+list(range(5,48,2))]
theta = theta[::2,[0,1,2,3,4]+list(range(5,48,2))]
else:
raise Exception('Unrecognized MIX grid dimensions')
# calculate deltaBs on a grid that decimates MIX grid by 2/3, and removes
# the lowest 3 colatitutdes
phi = phi[::3,3:]
theta = theta[::3,3:]
rho = p.tile(6378e3,phi.shape)
if geoGrid:
phi_geo = phi
theta_geo = theta
rho_geo = rho
x,y,z = pyLTR.transform.SPHtoCAR(phi,theta,rho)
x,y,z = pyLTR.transform.GEOtoSM(x,y,z,time)
phi,theta,rho = pyLTR.transform.CARtoSPH(x,y,z)
# deltaB for ionospheric currents
(dBphi_ion,
dBtheta_ion,
dBrho_ion) = pyLTR.Physics.BS.bs_sphere(rv_ion,
Jv_ion,
dv_ion,
(phi,theta,rho))
# deltaB for currents inside IB
(dBphi_IBin,
dBtheta_IBin,
dBrho_IBin) = pyLTR.Physics.BS.bs_sphere(rv_IBin,
Jv_IBin,
dv_IBin,
(phi,theta,rho))
# difference between dB*_IBin and dB*_ion is the FAC inside IB
dBphi_fac = dBphi_IBin - dBphi_ion
dBtheta_fac = dBtheta_IBin - dBtheta_ion
dBrho_fac = dBrho_IBin - dBrho_ion
# deltaB from magnetospheric currents
# convert cartesian positions and vectors to spherical
lphi,ltheta,lrho,lJphi,lJtheta,lJrho=pyLTR.transform.CARtoSPH(xJ,yJ,zJ,Jx,Jy,Jz)
(dBphi_mag,
dBtheta_mag,
dBrho_mag) = pyLTR.Physics.BS.bs_sphere((lphi,ltheta,lrho),
(lJphi,lJtheta,lJrho),
ldV,
(phi,theta,rho))
if geoGrid:
# rotate ionospheric contribution from SM to GEO coordinates; leave
# position vectors unchanged for subsequent rotations
x,y,z,dx,dy,dz = pyLTR.transform.SPHtoCAR(phi,theta,rho,dBphi_ion,dBtheta_ion,dBrho_ion)
x,y,z = pyLTR.transform.SMtoGEO(x,y,z,time)
dx,dy,dz = pyLTR.transform.SMtoGEO(dx,dy,dz,time)
_, _, _, dBphi_ion, dBtheta_ion, dBrho_ion = pyLTR.transform.CARtoSPH(x,y,z,dx,dy,dz)
# rotate FAC contribution from SM to GEO coordinates leave
# position vectors unchanged for subsequent rotations
x,y,z,dx,dy,dz = pyLTR.transform.SPHtoCAR(phi,theta,rho,dBphi_fac,dBtheta_fac,dBrho_fac)
x,y,z = pyLTR.transform.SMtoGEO(x,y,z,time)
dx,dy,dz = pyLTR.transform.SMtoGEO(dx,dy,dz,time)
_, _, _, dBphi_fac, dBtheta_fac, dBrho_fac = pyLTR.transform.CARtoSPH(x,y,z,dx,dy,dz)
# rotate magnetospheric contribution from SM to GEO coordinates
x,y,z,dx,dy,dz = pyLTR.transform.SPHtoCAR(phi,theta,rho,dBphi_mag,dBtheta_mag,dBrho_mag)
x,y,z = pyLTR.transform.SMtoGEO(x,y,z,time)
dx,dy,dz = pyLTR.transform.SMtoGEO(dx,dy,dz,time)
_, _, _, dBphi_mag, dBtheta_mag, dBrho_mag = pyLTR.transform.CARtoSPH(x,y,z,dx,dy,dz)
phi = phi_geo
theta = theta_geo
rho = rho_geo
#
# end of [re]processing 'except' block
#
# (re)create grid dictionary for subsequent plots and pickling
toPickle={}
if hemisphere=='south':
toPickle['pov'] = 'south'
else:
toPickle['pov'] = 'north'
if geoGrid:
toPickle['coordinates'] = 'Geographic'
# get geographic coordinates of sm pole
x,y,z = pyLTR.transform.SPHtoCAR(0,0,1)
x,y,z = pyLTR.transform.SMtoGEO(x,y,z,time)
poleCoords = pyLTR.transform.CARtoSPH(x,y,z)
else:
toPickle['coordinates'] = 'Solar Magnetic'
## # get sm coordinates of geographic pole
## x,y,z = pyLTR.transform.SPHtoCAR(0,0,1)
## x,y,z = pyLTR.transform.GEOtoSM(x,y,z,time)
## poleCoords = pyLTR.transform.CARtoSPH(x,y,z)
## now that MapPlot is being used, and until it can properly
## plot in centered SM coordinates, we want to just plot the
## magnetic pole;
poleCoords = (0, 0, 1)
phi_dict = {'data':phi,'name':r'$\phi$','units':r'rad'}
theta_dict = {'data':theta,'name':r'$\theta$','units':r'rad'}
rho_dict = {'data':rho,'name':r'$\rho$','units':r'm'}
toPickle['dB_obs'] = (phi_dict,theta_dict,rho_dict)
#####################################################################
##
## FIXME: move plots from this function into if __name__ == '__main__'
## section like deltaBTimeSeries.py; plots will then only be
## generated if user requests it, and this function may be
## called as part of a module...
## But note: one reason the plots are generated inside this
## function is that a long time series of gridded
## data becomes unmanageable memory-wise fairly
## quickly...think this through carefully. -EJR
##
#####################################################################
# Now onto the plots
tt=time.timetuple()
p.figure(1,figsize=(28,6))
p.figtext(0.5,0.92,'Ground '+'$\Delta{\mathbf{B}}$'+' - '+hemiSelect+
'\n%4d-%02d-%02d %02d:%02d:%02d' %
(tt.tm_year,tt.tm_mon,tt.tm_mday,
tt.tm_hour,tt.tm_min,tt.tm_sec),
fontsize=14,multialignment='center')
# plot total deltaB
ax=p.subplot(141)
# temporary dictionaries
dBphi_dict = {'data':(dBphi_ion + dBphi_fac + dBphi_mag)*1e9,'name':r'$\Delta \mathrm{B}_{\phi}$','units':'nT'}
dBtheta_dict = {'data':(dBtheta_ion + dBtheta_fac + dBtheta_mag)*1e9,'name':r'$\Delta \mathrm{B}_{\theta}$','units':'nT'}
dBrho_dict = {'data':(dBrho_ion + dBrho_fac + dBrho_mag)*1e9,'name':r'$\Delta \mathrm{B}_{\rho}$','units':'nT'}
bm = pyLTR.Graphics.MapPlot.QuiverPlotDict(phi_dict,theta_dict,
dBrho_dict,(dBphi_dict, dBtheta_dict),
dtUTC=time, coordSystem=toPickle['coordinates'],
plotOpts1=dBradialTotOpts,
plotOpts2=dBhvecTotOpts,
points=[(poleCoords[0],poleCoords[1])],
userAxes=ax, northPOV=hemisphere=='north')
to=p.text(.05, .95, r"$\Delta \mathbf{B}_{\mathrm{Total}}$",
fontsize=14, transform=ax.transAxes)
# plot ionospheric deltaB
ax=p.subplot(142)
# temporary dictionaries
dBphi_dict = {'data':(dBphi_ion)*1e9,'name':r'$\Delta \mathrm{B}_{\phi}$','units':'nT'}
dBtheta_dict = {'data':(dBtheta_ion)*1e9,'name':r'$\Delta \mathrm{B}_{\theta}$','units':'nT'}
dBrho_dict = {'data':(dBrho_ion)*1e9,'name':r'$\Delta \mathrm{B}_{\rho}$','units':'nT'}
bm = pyLTR.Graphics.MapPlot.QuiverPlotDict(phi_dict,theta_dict,
dBrho_dict,(dBphi_dict, dBtheta_dict),
dtUTC=time, coordSystem=toPickle['coordinates'],
plotOpts1=dBradialIonOpts,
plotOpts2=dBhvecIonOpts,
points=[(poleCoords[0],poleCoords[1])],
userAxes=ax, northPOV=hemisphere=='north')
to=p.text(.05, .95, r"$\Delta \mathbf{B}_{\mathrm{ion}}$",
fontsize=14, transform=ax.transAxes)
# for subsequent pickling
toPickle['dB_ion'] = (dBphi_dict,dBtheta_dict,dBrho_dict)
# plot FAC deltaB
ax=p.subplot(143)
# temporary dictionaries
dBphi_dict = {'data':(dBphi_fac)*1e9,'name':r'$\Delta \mathrm{B}_{\phi}$','units':'nT'}
dBtheta_dict = {'data':(dBtheta_fac)*1e9,'name':r'$\Delta \mathrm{B}_{\theta}$','units':'nT'}
dBrho_dict = {'data':(dBrho_fac)*1e9,'name':r'$\Delta \mathrm{B}_{\rho}$','units':'nT'}
bm = pyLTR.Graphics.MapPlot.QuiverPlotDict(phi_dict,theta_dict,
dBrho_dict,(dBphi_dict, dBtheta_dict),
dtUTC=time, coordSystem=toPickle['coordinates'],
plotOpts1=dBradialFACOpts,
plotOpts2=dBhvecFACOpts,
points=[(poleCoords[0],poleCoords[1])],
userAxes=ax, northPOV=hemisphere=='north')
to=p.text(.05, .95, r"$\Delta \mathbf{B}_{\mathrm{fac}}$",
fontsize=14, transform=ax.transAxes)
# for subsequent pickling
toPickle['dB_fac'] = (dBphi_dict,dBtheta_dict,dBrho_dict)
# plot magnetospheric deltaB
ax=p.subplot(144)
# temporary dictionaries
dBphi_dict = {'data':(dBphi_mag)*1e9,r'name':'$\Delta \mathrm{B}_{\phi}$','units':'nT'}
dBtheta_dict = {'data':(dBtheta_mag)*1e9,r'name':'$\Delta \mathrm{B}_{\theta}$','units':'nT'}
dBrho_dict = {'data':(dBrho_mag)*1e9,'name':r'$\Delta \mathrm{B}_{\rho}$','units':'nT'}
bm = pyLTR.Graphics.MapPlot.QuiverPlotDict(phi_dict,theta_dict,
dBrho_dict,(dBphi_dict, dBtheta_dict),
dtUTC=time, coordSystem=toPickle['coordinates'],
plotOpts1=dBradialMagOpts,
plotOpts2=dBhvecMagOpts,
points=[(poleCoords[0],poleCoords[1])],
userAxes=ax, northPOV=hemisphere=='north')
to=p.text(.05, .95, r"$\Delta \mathbf{B}_{\mathrm{mag}}$",
fontsize=14, transform=ax.transAxes)
# for subsequent pickling
toPickle['dB_mag'] = (dBphi_dict,dBtheta_dict,dBrho_dict)
#savefigName = os.path.join(path,'figs',hemisphere,'frame_deltaB_%05d.png'%i)
filePrefix = os.path.join(path,'figs',hemisphere)
pngFilename = os.path.join(filePrefix,'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.png'%
(time.year,time.month,time.day,time.hour,time.minute,time.second))
p.savefig(pngFilename,dpi=150)
p.clf()
if binaryType.lower() == 'pkl' or binaryType.lower() == '.pkl' or binaryType.lower() == 'pickle':
# --- Dump a pickle!
pklFilename = os.path.join(filePrefix,'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.pkl'%
(time.year,time.month,time.day,time.hour,time.minute,time.second))
fh = open(pklFilename, 'wb')
pickle.dump(toPickle, fh, protocol=2)
fh.close()
elif binaryType.lower() == 'mat' or binaryType.lower() == '.mat' or binaryType.lower() == 'matlab':
# --- Dump a .mat file!
matFilename = os.path.join(filePrefix,'frame_deltaB_%04d-%02d-%02dT%02d-%02d-%02dZ.mat'%
(time.year,time.month,time.day,time.hour,time.minute,time.second))
sio.savemat(matFilename, toPickle)
elif binaryType.lower() == 'none':
pass
else:
print(('Unrecognized binary type '+binaryType+' requested'))
raise Exception
progress.increment()
except KeyboardInterrupt:
# Exit when the user hits CTRL+C.
progress.stop()
progress.join()
print('Exiting.')
import sys
sys.exit(0)
except:
# Cleanup progress bar if something bad happened.
progress.stop()
progress.join()
raise
# append pngFilename to list of fully qualified filenames
pngFilenames.append(pngFilename)
progress.stop()
progress.join()
#return os.path.join(path,'figs',hemisphere)
return pngFilenames
def main():
mu = pl.array([[2], [8], [16], [32]])
Sigma = pl.array([[3.01602775, 1.02746769, -3.60224613, -2.08792829],
[1.02746769, 5.65146472, -3.98616664, 0.48723704],
[-3.60224613, -3.98616664, 13.04508284, -1.59255406],
[-2.08792829, 0.48723704, -1.59255406, 8.28742469]])
d, U = pl.eig(Sigma)
L = pl.diagflat(d)
A = pl.dot(U, pl.sqrt(L))
N = []
mu_deviations = []
Sigma_deviations = []
# First part of the exercise.
# This loop is used to get different sizes of N.
for i in range(1, 40):
means = pl.array([])
covariances = pl.array([])
N.append(50 * i)
# From this loop, the average is taken to get an accurate measurement.
for _ in range(1, 200):
X = pl.randn(4, 50 * i)
Y = pl.dot(A, X) + pl.tile(mu, 50 * i)
mean = pl.mean(Y, axis=1)
covariance = pl.cov(Y)
covariance = covariance.reshape((1, 16))
if (len(means) == 0 and len(covariances) == 0):
means = mean
covariances = covariance
else:
means = pl.vstack((means, mean))
covariances = pl.vstack((covariances, covariance))
mu_deviations.append(pl.mean(pl.std(covariances, axis=0)))
Sigma_deviations.append(pl.mean(pl.std(means, axis=0)))
pl.figure(1)
pl.clf()
pl.title('The average deviation, over 200 times,\n of the mean\
and covariance matrix for a given N')
pl.xlabel('N')
pl.ylabel('average deviation')
pl.plot(N, mu_deviations, label='average mean deviation')
pl.plot(N, Sigma_deviations, label='average covariance deviation')
pl.legend()
pl.savefig('fig22.png')
# Second part of the exercise.
covariances = pl.array([])
# Over the loop is iterated to create a data matrix of the covariances of
# the data matrices obtained from the multivariate normal distribution.
# The covariance from this data matrix of covariances is shown.
for _ in range(1, 200):
X = pl.randn(4, 1000)
Y = pl.dot(A, X) + pl.tile(mu, 1000)
covariance = pl.cov(Y)
if (len(covariances) == 0):
covariances = covariance
else:
covariances = pl.hstack((covariances, covariance))
covariance_data = pl.cov(covariances)
print(covariance_data)
n = 1000
mu = [[0],
[0],
[0],
[0]]
Sigma = [[3.01602775, 1.02746769, -3.60224613, -2.08792829],
[1.02746769, 5.65146472, -3.98616664, 0.48723704],
[-3.60224613, -3.98616664, 13.04508284, -1.59255406],
[-2.08792829, 0.48723704, -1.59255406, 8.28742469]]
d, U = plt.eig(Sigma) # Sigma = U L Ut
L = plt.diagflat(d)
A = plt.dot(U, plt.sqrt(L)) # required transform matrix
X = plt.randn(4, n) # 4xn matrix with each element ~ N(0,1)
Y = plt.dot(A, X) + plt.tile(mu, n) # 4xn each column vector ~N(mu,Sigma)
f, axarr = plt.subplots(4, 4, sharex=True, sharey=True)
for i in range(0, len(Y)):
for j in range(0, len(Y)):
if(i == j):
axarr[i][j].set_title(str(i) + ',' + str(j))
axarr[i][j].axis('off')
continue
axarr[i][j].plot(Y[i], Y[j], 'xg')
axarr[i][j].set_title(str(i) + ',' + str(j))
plt.setp([a.get_xticklabels() for a in axarr[0, :]], visible=False)
plt.setp([a.get_yticklabels() for a in axarr[:, 1]], visible=False)
plt.tight_layout()
# calculate ionospheric components of SSECS from MIX data
(rv_MIX_iono, Jv_MIX_iono, dv_MIX_iono) = pyLTR.Physics.SSECS.ssecs_sphere(
[rion_min_MIX[0], rion_min_MIX[1], rion_min_MIX[2]],
[rion_max_MIX[0], rion_max_MIX[1], rion_min_MIX[2]],
(Jphi_MIX_dict['data'] / 1e6, Jtheta_MIX_dict['data'] / 1e6), 10, False)
# calculate non-ionospheric component of SSECS from MIX data
(rv_MIX_faceq, Jv_MIX_faceq, dv_MIX_faceq) = pyLTR.Physics.SSECS.ssecs_sphere(
[rion_min_MIX[0], rion_min_MIX[1], rion_min_MIX[2] + 1],
[rion_max_MIX[0], rion_max_MIX[1], rion_min_MIX[2]],
(Jphi_MIX_dict['data'] / 1e6, Jtheta_MIX_dict['data'] / 1e6), 10, False)
# calculate deltaB for total SSECS
(dBphi_MIX_total,
dBtheta_MIX_total, dBrho_MIX_total) = pyLTR.Physics.BS.bs_sphere(
rv_MIX_total, Jv_MIX_total, dv_MIX_total,
(phi_MIX, theta_MIX, p.tile(6378e3, phi_MIX.shape)))
# convert into nanoTeslas
dBphi_MIX_total_dict = {
'data': dBphi_MIX_total * 1e9,
'name': r'$dB_\phi$',
'units': r'nT'
}
dBtheta_MIX_total_dict = {
'data': dBtheta_MIX_total * 1e9,
'name': r'$dB_\theta$',
'units': r'nT'
}
dBrho_MIX_total_dict = {
'data': dBrho_MIX_total * 1e9,
'name': r'$dB_\rho$',
'units': r'nT'