def compute(self):
signal = self.get_input("Input").get_array()
ptx = self.get_input("X")
pty = self.get_input("Y")
ptz = self.get_input("Z")
lof = self.get_input("Low Freq")
hif = self.get_input("High Freq")
sigx = signal[ptz,pty,:]
sigy = signal[ptz,:,ptx]
sigz = signal[:,pty,ptx]
tx = st.st(sigx, lof, hif)
ty = st.st(sigy, lof, hif)
tz = st.st(sigz, lof, hif)
tx = tx * tx.conjugate()
ty = ty * ty.conjugate()
tz = tz * tz.conjugate()
out_ar = tx.real + ty.real + tz.real
out = NDArray()
out.set_array(out_ar)
self.set_output("Output", out)
def compute(self):
signal = self.getInputFromPort("Input").get_array()
ptx = self.getInputFromPort("X")
pty = self.getInputFromPort("Y")
ptz = self.getInputFromPort("Z")
lof = self.getInputFromPort("Low Freq")
hif = self.getInputFromPort("High Freq")
sigx = signal[ptz, pty, :]
sigy = signal[ptz, :, ptx]
sigz = signal[:, pty, ptx]
tx = st.st(sigx, lof, hif)
ty = st.st(sigy, lof, hif)
tz = st.st(sigz, lof, hif)
tx = tx * tx.conjugate()
ty = ty * ty.conjugate()
tz = tz * tz.conjugate()
out_ar = tx.real + ty.real + tz.real
out = NDArray()
out.set_array(out_ar)
self.setResult("Output", out)
def compute(self):
signal = self.getInputFromPort("Input").get_array()
lof = self.getInputFromPort("Low Freq")
hif = self.getInputFromPort("High Freq")
num_pts = signal.size
min_s = signal.min()
max_s = signal.max()
d = max_s - min_s
print "Accumulating over " + str(num_pts) + " points"
histo = numpy.zeros((512, hif - lof + 1))
print "Histo: ", histo.shape
dist = numpy.zeros(512)
for z in range(signal.shape[2]):
for y in range(signal.shape[1]):
for x in range(signal.shape[0]):
sigx = signal[z, y, :]
sigy = signal[z, :, x]
tx = st.st(sigx, lof, hif)
ty = st.st(sigy, lof, hif)
sigz = signal[:, y, z]
tz = st.st(sigz, lof, hif)
tz = tz[:, x].squeeze()
tz = tz * tz.conjugate()
tx = tx[:, z].squeeze()
ty = ty[:, y].squeeze()
tx = tx * tx.conjugate()
ty = ty * ty.conjugate()
ar = tx.real + ty.real + tz.real
ar = ar / ar.sum()
# ar = ar.sum(axis=1)
# print "ar: ", ar.shape
# ar.shape = (ar.shape[0],1)
scalar = signal[z, y, x]
try:
bin = int((scalar - min_s) / d * 511.)
# dist[bin] += 1
# print bin, scalar, ar
sigma = self.forceGetInputFromPort("Sigma")
if sigma:
ar = scipy.signal.gaussian(ar.size, sigma) * ar
histo[bin, :] += ar
except:
print "Cannot assign to bin: " + str(
bin) + ", scalar: " + str(scalar)
print "location = ", x, y, z
raise ModuleError("Cannot assign to bin: " + str(bin) +
", scalar: " + str(scalar))
# print "done with y = ", y
print "done with z = ", z
out = NDArray()
out.set_array(histo) # / dist)
self.setResult("Output", out)
def compute(self):
signal = self.get_input("Input").get_array()
lof = self.get_input("Low Freq")
hif = self.get_input("High Freq")
num_pts = signal.size
min_s = signal.min()
max_s = signal.max()
d = max_s - min_s
print "Accumulating over " + str(num_pts) + " points"
histo = numpy.zeros((512,hif-lof+1))
print "Histo: ",histo.shape
dist = numpy.zeros(512)
for z in range(signal.shape[2]):
for y in range(signal.shape[1]):
for x in range(signal.shape[0]):
sigx = signal[z,y,:]
sigy = signal[z,:,x]
tx = st.st(sigx, lof, hif)
ty = st.st(sigy, lof, hif)
sigz = signal[:,y,z]
tz = st.st(sigz, lof, hif)
tz = tz[:,x].squeeze()
tz = tz * tz.conjugate()
tx = tx[:,z].squeeze()
ty = ty[:,y].squeeze()
tx = tx * tx.conjugate()
ty = ty * ty.conjugate()
ar = tx.real + ty.real + tz.real
ar = ar / ar.sum()
# ar = ar.sum(axis=1)
# print "ar: ", ar.shape
# ar.shape = (ar.shape[0],1)
scalar = signal[z,y,x]
try:
bin = int((scalar - min_s) / d * 511.)
# dist[bin] += 1
# print bin, scalar, ar
sigma = self.force_get_input("Sigma")
if sigma:
ar = scipy.signal.gaussian(ar.size, sigma) * ar
histo[bin,:] += ar
except:
print "Cannot assign to bin: " + str(bin) +", scalar: " +str(scalar)
print "location = ", x, y, z
raise ModuleError("Cannot assign to bin: " + str(bin) +", scalar: " +str(scalar))
# print "done with y = ", y
print "done with z = ", z
out = NDArray()
out.set_array(histo)# / dist)
self.set_output("Output", out)
def funhv(Mv,Mn,Me,fi,ff,fmm):
stV,t,f=st(Mv.transpose(),fi,ff,fmm)# S-transform de V
stN,t,f=st(Mn.transpose(),fi,ff,fmm)# S-transform de N
stE,t,f=st(Me.transpose(),fi,ff,fmm)# S-transform de E
a = np.absolute(stN)
b = np.absolute(stE)
c = np.absolute(stV)
a = np.power(a,2)
b = np.power(b,2)
hv = np.power((a+b)/2,0.5)
hv = hv/c
return hv.T
def compute(self):
vol = self.getInputFromPort("Input").get_array()
lof = self.getInputFromPort("Low Freq")
hif = self.getInputFromPort("Hi Freq")
sigma = self.forceGetInputFromPort("Sigma")
out_vol = numpy.zeros(vol.shape)
(slices, rows, cols) = vol.shape
for z in range(slices):
t = time.time()
for y in range(rows):
for x in range(cols):
# grab our 3 rays
xray = vol[z, y, :].squeeze()
yray = vol[z, :, x].squeeze()
zray = vol[:, y, x].squeeze()
# Transform each ray
xt = st.st(xray, lof, hif)
yt = st.st(yray, lof, hif)
zt = st.st(zray, lof, hif)
# Grab the point at all valid scales
xpt = xt[:, x]
ypt = yt[:, y]
zpt = zt[:, z]
# Take the magnitude
xpt = xpt * xpt.conjugate()
ypt = ypt * ypt.conjugate()
zpt = zpt * zpt.conjugate()
scale_vec = xpt.real + ypt.real + zpt.real
if sigma:
scale_vec = scale_vec * scipy.signal.gaussian(
scale_vec.shape[0], sigma)
scale = scale_vec.argmax()
out_vol[x, y, z] = scale
print "done z = ", z
print "took: ", (time.time() - t) * 1000.
out = NDArray()
out.set_array(out_vol)
self.setResult("Output", out)
def compute(self):
vol = self.get_input("Input").get_array()
lof = self.get_input("Low Freq")
hif = self.get_input("Hi Freq")
sigma = self.force_get_input("Sigma")
out_vol = numpy.zeros(vol.shape)
(slices,rows,cols) = vol.shape
for z in range(slices):
t = time.time()
for y in range(rows):
for x in range(cols):
# grab our 3 rays
xray = vol[z,y,:].squeeze()
yray = vol[z,:,x].squeeze()
zray = vol[:,y,x].squeeze()
# Transform each ray
xt = st.st(xray,lof,hif)
yt = st.st(yray,lof,hif)
zt = st.st(zray,lof,hif)
# Grab the point at all valid scales
xpt = xt[:,x]
ypt = yt[:,y]
zpt = zt[:,z]
# Take the magnitude
xpt = xpt * xpt.conjugate()
ypt = ypt * ypt.conjugate()
zpt = zpt * zpt.conjugate()
scale_vec = xpt.real + ypt.real + zpt.real
if sigma:
scale_vec = scale_vec * scipy.signal.gaussian(scale_vec.shape[0], sigma)
scale = scale_vec.argmax()
out_vol[x,y,z] = scale
print "done z = ", z
print "took: ", (time.time() - t) * 1000.
out = NDArray()
out.set_array(out_vol)
self.set_output("Output", out)
def compute(self):
in_ar = self.getInputFromPort("Input").get_array()
lo_f = self.getInputFromPort("Low Freq")
hi_f = self.getInputFromPort("High Freq")
num_f = hi_f - lo_f + 1
(slices, rows, cols) = in_ar.shape
out_ar = numpy.zeros((num_f, slices, rows, cols))
for s in range(slices):
for r in range(rows):
sig = in_ar[s, r, :]
t = st.st(sig, lo_f, hi_f)
t = t.conjugate() * t
t = t.real
for f in range(t.shape[0]):
out_ar[f, s, r, :] = t[f, :]
print "done dim 1"
for s in range(slices):
for c in range(cols):
sig = in_ar[s, :, c]
t = st.st(sig, lo_f, hi_f)
t = t.conjugate() * t
t = t.real
for f in range(t.shape[0]):
out_ar[f, s, :, c] += t[f, :]
print "done dim 2"
for r in range(rows):
for c in range(cols):
sig = in_ar[:, r, c]
t = st.st(sig, lo_f, hi_f)
t = t.conjugate() * t
t = t.real
for f in range(t.shape[0]):
out_ar[f, :, r, c] += t[f, :]
print "done dim 3"
# out_ar = out_ar * out_ar.conjugate()
out = NDArray()
out.set_array(out_ar)
self.setResult("Output", out)
def compute(self):
in_ar = self.get_input("Input").get_array()
lo_f = self.get_input("Low Freq")
hi_f = self.get_input("High Freq")
num_f = hi_f - lo_f + 1
(slices, rows, cols) = in_ar.shape
out_ar = numpy.zeros((num_f, slices, rows, cols))
for s in range(slices):
for r in range(rows):
sig = in_ar[s,r,:]
t = st.st(sig,lo_f,hi_f)
t = t.conjugate() * t
t = t.real
for f in range(t.shape[0]):
out_ar[f,s,r,:] = t[f,:]
print "done dim 1"
for s in range(slices):
for c in range(cols):
sig = in_ar[s,:,c]
t = st.st(sig,lo_f,hi_f)
t = t.conjugate() * t
t = t.real
for f in range(t.shape[0]):
out_ar[f,s,:,c] += t[f,:]
print "done dim 2"
for r in range(rows):
for c in range(cols):
sig = in_ar[:,r,c]
t = st.st(sig,lo_f,hi_f)
t = t.conjugate() * t
t = t.real
for f in range(t.shape[0]):
out_ar[f,:,r,c] += t[f,:]
print "done dim 3"
# out_ar = out_ar * out_ar.conjugate()
out = NDArray()
out.set_array(out_ar)
self.set_output("Output", out)
def mtst(K, tapers, x, lo, hi): N = len(x) K2 = float(K * K) s = 0. n = 0. for k in range(K): X = st(tapers[k] * x, lo, hi) mu = 1. - k * k / K2 s += mu * abs(X)**2 n += mu s *= N / n return s
def mtst(K, tapers, x, lo, hi):
N = len(x)
K2 = float(K * K)
s = 0.
n = 0.
for k in range(K):
X = st(tapers[k] * x, lo, hi)
mu = 1. - k * k / K2
s += mu * abs(X)**2
n += mu
s *= N / n
return s
def compute(self):
trial_ar = self.getInputFromPort("Single Trials").get_array()
print "trial_ar.shape = ", trial_ar.shape
self.lof = self.getInputFromPort("Low Freq")
self.hif = self.getInputFromPort("High Freq")
sensor_list = self.forceGetInputListFromPort("Sensors")
if len(trial_ar.shape) != 3:
raise ModuleError("Cannot process input with rank not 3")
(trials, sensors, sig_len) = trial_ar.shape
if sensor_list == None:
sensor_list = numpy.arange(sensors)
else:
sensor_list = numpy.array(sensor_list)
# Compute the TFR for a single sensor across all trials
freq_range = self.hif - self.lof
out_ar = numpy.zeros(
(sensor_list.shape[0], sig_len, freq_range + 1, freq_range + 1))
print "sensor list = ", sensor_list
# For each sensor to consider, extract the signal array
for i in range(sensor_list.shape[0]):
tmp_sig = trial_ar[:, sensor_list[i], :].squeeze()
# For each trial, extract the signal
for j in range(trials):
sig = tmp_sig[j, :].squeeze()
tfr = st.st(sig, self.lof, self.hif)
# Compute the phase for the Time-freq plane
p = numpy.arctan2(tfr.real, tfr.imag)
# the ordering of p is: (freqs,times) = p.shape
dphi_ar = numpy.array(0. - 1.j * self.make_delta_phi(p.real))
dphi_ar = numpy.exp(dphi_ar)
out_ar[i, :, :, :] += dphi_ar
print "Trial " + str(j) + " done processing..."
print "out_ar done with all trials"
out_ar[i, :, :, :] /= float(trials)
out_ar[i, :, :, :] = out_ar[i, :, :, :] * out_ar[
i, :, :, :].conjugate()
out_ar[i, :, :, :] = out_ar[i, :, :, :].real
print "min,max,mean = ", out_ar[i].min(), out_ar[i].max(
), out_ar[i].mean()
out = NDArray()
out.set_array(out_ar)
self.setResult("Output", out)
def svt(X, tau):
"""
Singular value thresholding operator
Syntax: Xs = svt(X, tau)
Inputs:
:param X: The input matrix
:param tau: The input shrinkage parameter
Output:
Xs is the result of applying singular value thresholding to X
"""
U, S, Vt = la.svd(X, full_matrices=False)
Xs = np.dot(U * st(S, tau), Vt)
return Xs
def compute(self):
trial_ar = self.get_input("Single Trials").get_array()
print "trial_ar.shape = ", trial_ar.shape
self.lof = self.get_input("Low Freq")
self.hif = self.get_input("High Freq")
sensor_list = self.force_get_input_list("Sensors")
if len(trial_ar.shape) != 3:
raise ModuleError("Cannot process input with rank not 3")
(trials, sensors, sig_len) = trial_ar.shape
if sensor_list == None:
sensor_list = numpy.arange(sensors)
else:
sensor_list = numpy.array(sensor_list)
# Compute the TFR for a single sensor across all trials
freq_range = self.hif - self.lof
out_ar = numpy.zeros((sensor_list.shape[0], sig_len, freq_range+1, freq_range+1))
print "sensor list = ", sensor_list
# For each sensor to consider, extract the signal array
for i in range(sensor_list.shape[0]):
tmp_sig = trial_ar[:,sensor_list[i],:].squeeze()
# For each trial, extract the signal
for j in range(trials):
sig = tmp_sig[j,:].squeeze()
tfr = st.st(sig, self.lof, self.hif)
# Compute the phase for the Time-freq plane
p = numpy.arctan2(tfr.real, tfr.imag)
# the ordering of p is: (freqs,times) = p.shape
dphi_ar = numpy.array(0.-1.j*self.make_delta_phi(p.real))
dphi_ar = numpy.exp(dphi_ar)
out_ar[i,:,:,:] += dphi_ar
print "Trial " + str(j) + " done processing..."
print "out_ar done with all trials"
out_ar[i,:,:,:] /= float(trials)
out_ar[i,:,:,:] = out_ar[i,:,:,:] * out_ar[i,:,:,:].conjugate()
out_ar[i,:,:,:] = out_ar[i,:,:,:].real
print "min,max,mean = ", out_ar[i].min(), out_ar[i].max(), out_ar[i].mean()
out = NDArray()
out.set_array(out_ar)
self.set_output("Output", out)
def compute(self):
t = time.time()
signals = self.getInputFromPort("Signals").get_array()
lof = self.getInputFromPort("Low Freq")
hif = self.getInputFromPort("Hi Freq")
if len(signals.shape) == 1:
signals.shape = (1, signals.shape[0])
outl = []
for i in xrange(signals.shape[0]):
sig_ar = signals[i]
x = st.st(sig_ar, lof, hif)
outl.append(x)
out_ar = numpy.array(outl).squeeze()
print "c time = ", (time.time() - t) * 1000.
out = NDArray()
out.set_array(out_ar)
self.setResult("Output", out)
def compute(self):
t = time.time()
signals = self.get_input("Signals").get_array()
lof = self.get_input("Low Freq")
hif = self.get_input("Hi Freq")
if len(signals.shape) == 1:
signals.shape = (1, signals.shape[0])
outl = []
for i in xrange(signals.shape[0]):
sig_ar = signals[i]
x = st.st(sig_ar, lof, hif)
outl.append(x)
out_ar = numpy.array(outl).squeeze()
print "c time = ", (time.time() - t) * 1000.
out = NDArray()
out.set_array(out_ar)
self.set_output("Output", out)
def compute(self):
vol = self.get_input("Input").get_array()
lof = self.get_input("Low Freq")
hif = self.get_input("Hi Freq")
max_vol = numpy.zeros(vol.shape)
grav_vol = numpy.zeros(vol.shape)
(slices,rows,cols) = vol.shape
for z in range(slices):
tr = time.time()
for y in range(rows):
ray = vol[z,y,:].squeeze()
t = st.st(ray, lof, hif)
for x in range(cols):
scales = t[:,x].squeeze()
scales = scales * scales.conjugate()
max_vol[x,y,z] = float(scales.argmax())
grav = 0.
for i in range(scales.shape[0]):
v = scales[i]
f = lof + i
grav += float(v) * float(f)
grav_vol[x,y,z] = grav
print "done z = ", z
print "took: ", (time.time() - tr) * 1000.
grav_vol = grav_vol - grav_vol.min()
grav_vol = grav_vol / grav_vol.max()
grav_vol = grav_vol * float(hif - lof)
grav_vol = grav_vol + lof
max_out = NDArray()
max_out.set_array(max_vol)
grav_out = NDArray()
grav_out.set_array(grav_vol)
self.set_output("Max Output", max_out)
self.set_output("Grav Output", grav_out)
def compute(self):
vol = self.getInputFromPort("Input").get_array()
lof = self.getInputFromPort("Low Freq")
hif = self.getInputFromPort("Hi Freq")
max_vol = numpy.zeros(vol.shape)
grav_vol = numpy.zeros(vol.shape)
(slices, rows, cols) = vol.shape
for z in range(slices):
tr = time.time()
for y in range(rows):
ray = vol[z, y, :].squeeze()
t = st.st(ray, lof, hif)
for x in range(cols):
scales = t[:, x].squeeze()
scales = scales * scales.conjugate()
max_vol[x, y, z] = float(scales.argmax())
grav = 0.
for i in range(scales.shape[0]):
v = scales[i]
f = lof + i
grav += float(v) * float(f)
grav_vol[x, y, z] = grav
print "done z = ", z
print "took: ", (time.time() - tr) * 1000.
grav_vol = grav_vol - grav_vol.min()
grav_vol = grav_vol / grav_vol.max()
grav_vol = grav_vol * float(hif - lof)
grav_vol = grav_vol + lof
max_out = NDArray()
max_out.set_array(max_vol)
grav_out = NDArray()
grav_out.set_array(grav_vol)
self.setResult("Max Output", max_out)
self.setResult("Grav Output", grav_out)
def pcp(Y):
"""
Principal Component Pursuit solved with ADMM
Syntax: L, S = pcp(Y)
Inputs:
:param Y: A matrix of size [D, N]
Ouputs:
L: The low rank matrix with size [D, N]
S: The sparse matrix with size [D, N]
"""
### Parameters that we'll use
D, N = np.shape(Y)
normY = norm(Y, ord='fro')
### Algorithm parameters
lam = 1 / sqrt(max(D, N))
rho = 10 * lam
tol = 1e-4
maxIter = 1000
### Initialize the variables of optimization
L = zeros([D, N])
S = zeros([D, N])
Z = zeros([D, N])
### ADMM Iterations
for ii in range(maxIter):
L = svt((Y - S + (1 / rho) * Z), 1 / rho)
S = st((Y - L + (1 / rho) * Z), lam / rho)
Z = Z + rho * (Y - L - S)
## Calculate error and output at each iteration:
err = norm(Y - L - S, ord='fro')
if err < tol:
break
return L, S
def compute(self):
vol = self.get_input("Input").get_array()
lof = self.get_input("Low Freq")
hif = self.get_input("Hi Freq")
sigma = self.force_get_input("Sigma")
max_vol = numpy.zeros(vol.shape)
grav_vol = numpy.zeros(vol.shape)
(slices,rows,cols) = vol.shape
for z in range(slices):
t = time.time()
for y in range(rows):
for x in range(cols):
# grab our 3 rays
xray = vol[z,y,:].squeeze()
yray = vol[z,:,x].squeeze()
zray = vol[:,y,x].squeeze()
# Transform each ray
xt = st.st(xray,lof,hif)
yt = st.st(yray,lof,hif)
zt = st.st(zray,lof,hif)
# Grab the point at all valid scales
xpt = xt[:,x]
ypt = yt[:,y]
zpt = zt[:,z]
# Take the magnitude
xpt = xpt * xpt.conjugate()
ypt = ypt * ypt.conjugate()
zpt = zpt * zpt.conjugate()
scale_vec = xpt.real + ypt.real + zpt.real
if sigma:
scale_vec = scale_vec * scipy.signal.gaussian(scale_vec.shape[0], sigma)
scale = scale_vec.argmax()
max_vol[x,y,z] = scale
# scale_vec =
# scale_vec = scale_vec / scale_vec.sum()
grav = 0
for s in range(scale_vec.shape[0]):
v = scale_vec[s]
f = lof + s
grav += float(f) * float(v)
# grav = grav / float(scale_vec.shape[0])
grav_vol[x,y,z] = grav
print "done z = ", z
print "took: ", (time.time() - t) * 1000.
grav_vol = grav_vol - grav_vol.min()
grav_vol = grav_vol / grav_vol.max()
grav_vol = grav_vol * float(hif - lof)
grav_vol = grav_vol + lof
max_out = NDArray()
max_out.set_array(max_vol)
grav_out = NDArray()
grav_out.set_array(grav_vol)
self.set_output("Max Output", max_out)
self.set_output("Grav Output", grav_out)
def compute(self):
vol = self.getInputFromPort("Input").get_array()
lof = self.getInputFromPort("Low Freq")
hif = self.getInputFromPort("Hi Freq")
sigma = self.forceGetInputFromPort("Sigma")
max_vol = numpy.zeros(vol.shape)
grav_vol = numpy.zeros(vol.shape)
(slices, rows, cols) = vol.shape
for z in range(slices):
t = time.time()
for y in range(rows):
for x in range(cols):
# grab our 3 rays
xray = vol[z, y, :].squeeze()
yray = vol[z, :, x].squeeze()
zray = vol[:, y, x].squeeze()
# Transform each ray
xt = st.st(xray, lof, hif)
yt = st.st(yray, lof, hif)
zt = st.st(zray, lof, hif)
# Grab the point at all valid scales
xpt = xt[:, x]
ypt = yt[:, y]
zpt = zt[:, z]
# Take the magnitude
xpt = xpt * xpt.conjugate()
ypt = ypt * ypt.conjugate()
zpt = zpt * zpt.conjugate()
scale_vec = xpt.real + ypt.real + zpt.real
if sigma:
scale_vec = scale_vec * scipy.signal.gaussian(
scale_vec.shape[0], sigma)
scale = scale_vec.argmax()
max_vol[x, y, z] = scale
# scale_vec =
# scale_vec = scale_vec / scale_vec.sum()
grav = 0
for s in range(scale_vec.shape[0]):
v = scale_vec[s]
f = lof + s
grav += float(f) * float(v)
# grav = grav / float(scale_vec.shape[0])
grav_vol[x, y, z] = grav
print "done z = ", z
print "took: ", (time.time() - t) * 1000.
grav_vol = grav_vol - grav_vol.min()
grav_vol = grav_vol / grav_vol.max()
grav_vol = grav_vol * float(hif - lof)
grav_vol = grav_vol + lof
max_out = NDArray()
max_out.set_array(max_vol)
grav_out = NDArray()
grav_out.set_array(grav_vol)
self.setResult("Max Output", max_out)
self.setResult("Grav Output", grav_out)
import numpy as np
import matplotlib.pyplot as plt
from svt import svt
from st import st
m = 100
n = 50
## test st
x = np.ones(n)
y = np.linspace(-1,1,m)
tau = 0.5
# generate matrix and threshold
A = np.outer(x, y)
As = st(A, tau)
# display results
plt.figure()
plt.imshow(A, extent=[-1,1,0,n], aspect='auto')
plt.clim(-1,1)
plt.set_cmap('gray')
plt.colorbar()
plt.title('original matrix')
plt.show()
plt.figure()
plt.imshow(As, extent=[-1,1,0,n], aspect='auto')
plt.clim(-1,1)
plt.set_cmap('gray')
plt.colorbar()
