def plot_coord_mapping(mapper, sheet, style='b-'):
"""
Plot a coordinate mapping for a sheet.
Given a CoordinateMapperFn (as for a CFProjection) and a sheet
of the projection, plot a grid showing where the sheet's units
are mapped.
"""
from pylab import plot, hold, ishold
xs = sheet.sheet_rows()
ys = sheet.sheet_cols()
hold_on = ishold()
if not hold_on:
plot()
hold(True)
for y in ys:
pts = [mapper(x, y) for x in xs]
plot([u for u, v in pts], [v for u, v in pts], style)
for x in xs:
pts = [mapper(x, y) for y in ys]
plot([u for u, v in pts], [v for u, v in pts], style)
hold(hold_on)
def plot_coord_mapping(mapper,sheet,style='b-'):
"""
Plot a coordinate mapping for a sheet.
Given a CoordinateMapperFn (as for a CFProjection) and a sheet
of the projection, plot a grid showing where the sheet's units
are mapped.
"""
from pylab import plot,hold,ishold
xs = sheet.sheet_rows()
ys = sheet.sheet_cols()
hold_on = ishold()
if not hold_on:
plot()
hold(True)
for y in ys:
pts = [mapper(x,y) for x in xs]
plot([u for u,v in pts],
[v for u,v in pts],
style)
for x in xs:
pts = [mapper(x,y) for y in ys]
plot([u for u,v in pts],
[v for u,v in pts],
style)
hold(hold_on)
def plot_regression(x,y,smoothing=.3):
fit=sm.nonparametric.lowess(y,x,frac=smoothing)
df=(fit[:,1]-y)**2
fit_var=sm.nonparametric.lowess(df,x,frac=smoothing)
isheld = pl.ishold()
pl.hold(1)
pl.plot(fit[:,0],fit[:,1])
pl.fill_between(fit_var[:,0],fit[:,1]-1*pl.sqrt(fit_var[:,1]),fit[:,1]+1*pl.sqrt(fit_var[:,1]),color=((0,0,.99,.2),))
pl.plot(x,y,'.')
pl.hold(isheld)
def plot(self, *args, **kwargs):
from pylab import plot, ioff, ion, show, ishold, cla
ioff()
if kwargs.get('hold')==0 or not ishold():
cla()
kwargs['hold']=1
for i,w in enumerate(self.iterwhiskers()):
plot( w.x + 0.1*i, w.y + 0.1*i , *args, **kwargs)
ion()
show()
def plot_regression(x, y, smoothing=.3):
fit = sm.nonparametric.lowess(y, x, frac=smoothing)
df = (fit[:, 1] - y)**2
fit_var = sm.nonparametric.lowess(df, x, frac=smoothing)
isheld = pl.ishold()
pl.hold(1)
pl.plot(fit[:, 0], fit[:, 1])
pl.fill_between(fit_var[:, 0],
fit[:, 1] - 1 * pl.sqrt(fit_var[:, 1]),
fit[:, 1] + 1 * pl.sqrt(fit_var[:, 1]),
color=((0, 0, .99, .2), ))
pl.plot(x, y, '.')
pl.hold(isheld)
def plotPZ(H, color='b', markersize=5, showlist=False):
"""Plot the poles and zeros of a transfer function.
**Parameters:**
H : transfer function
Any supported transfer function representation,
eg num/den, zpk, lti...
color : Any matplotlib-compatible color descr, optional
For example, 'r' for 'red' or '#000080' for 'navy'.
You can also specify separately poles and zeros, in a tuple.
markersize : scalar, optional
The markers size in points.
showlist : boolean, optional
Superimpose a list of the poles and zeros on the plot.
.. plot::
import pylab as plt
from deltasigma import synthesizeNTF, plotPZ
order = 5
osr = 32
f0 = 0.
Hinf = 1.5
ntf = synthesizeNTF(order, osr, 2, Hinf, f0)
plt.figure(figsize=(8, 6))
plotPZ(ntf, color=('r', 'b'), showlist=True)
plt.title("NTF singularities")
plt.show()
"""
# Parts of the code come from 'pydsm'
#
# Original copyright notices:
#
# For pydsm
# Copyright (c) 2012, Sergio Callegari
# All rights reserved.
#
# For Richard Schreier's Delta Sigma toolbox
# Copyright (c) 2009, Richard Schreier
z, p, _ = _get_zpk(H)
p = np.real_if_close(np.round(p, 5))
z = np.real_if_close(np.round(z, 5))
pole_fmt = {'marker': 'x', 'markersize': markersize}
zero_fmt = {'marker': 'o', 'markersize': markersize}
if isinstance(color, list) or isinstance(color, tuple):
pole_fmt['color'] = color[0]
zero_fmt['color'] = color[1]
else:
pole_fmt['color'] = color
zero_fmt['color'] = color
hold_status = plt.ishold()
plt.grid(True)
# Plot x and o for poles and zeros, respectively
plt.plot(p.real, p.imag, linestyle='None', **pole_fmt)
plt.hold(True)
if len(z) > 0:
plt.plot(z.real, z.imag, linestyle='None', **zero_fmt)
# Draw unit circle, real axis and imag axis
circle = np.exp(2j * np.pi * np.linspace(0, 1, 100))
plt.plot(circle.real, circle.imag)
ax = plt.gca()
ax.set_autoscale_on(False)
if showlist:
ax = plt.gca()
x1, x2, y1, y2 = ax.axis()
x2 = np.round((x2 - x1) * 1.48 + x1, 1)
ax.axis((x1, x2, y1, y2))
markers = []
descr = []
ps = p[p.imag >= 0]
for pi in ps:
markers += [plt.Line2D((), (), linestyle='None', **pole_fmt)]
if np.allclose(pi.imag, 0, atol=1e-5):
descr += ['%+.4f' % pi.real]
else:
descr += ['%+.4f+/-j%.4f' % (pi.real, pi.imag)]
if len(z) > 0:
for zi in z[z.imag >= 0]:
markers += [plt.Line2D((), (), linestyle='None', **zero_fmt)]
if zi.imag == 0:
descr += ['%+.4f' % zi.real]
else:
descr += ['%+.4f +/-j%.4f' % (zi.real, zi.imag)]
plt.legend(markers,
descr,
title="Poles (x) and zeros (o)",
ncol=1,
loc='best',
handlelength=.55,
prop={'size': 10})
else:
plt.xlim((-1.1, 1.1))
plt.ylim((-1.1, 1.1))
plt.gca().set_aspect('equal')
# plt.axes().set_aspect('equal', 'datalim')
plt.ylabel('Imag')
plt.xlabel('Real')
if not hold_status:
plt.hold(False)
def peakSNR(snr, amp):
"""Find the snr peak by fitting a smooth curve to the top end of the SNR
vs input amplitude data.
The curve fitted is y = ax + b/(x-c).
Parameters:
snr: ndarray
amp: ndarray
Returns:
peak_snr, peak_amp
Notes:
* Both amp and snr are expressed in dB.
* The two arrays snr and amp should have the same size.
"""
# Delete garbage data
for check in (np.isinf, np.isnan):
i = check(snr)
snr = np.delete(snr, np.where(i))
amp = np.delete(amp, np.where(i))
# sanitize inputs
for x in (snr, amp):
if not hasattr(x, 'ndim'):
x = np.array(x)
if len(x.shape) > 1 and np.prod(x.shape) != max(x.shape):
raise ValueError("snr and amp should be vectors (ndim=1)" +
"snr.shape: %s, amp.shape: %s" % (snr.shape, amp.shape))
x = x.squeeze
# All good
max_snr = np.max(snr)
i = np.flatnonzero(snr > max_snr - 10)
min_i = np.min(i)
max_i = np.max(i)
j = np.flatnonzero(snr[min_i:max_i + 1] < max_snr - 15)
if j:
max_i = min_i + np.min(j) - 2
i = np.arange(min_i, max_i + 1)
snr = 10.0**(snr[i]/20)
amp = 10.0**(amp[i]/20)
#n = max(i.shape) # unused variable, REP?
c = np.max(amp)*1.05
# fit y = ax + b/(x-c) to the data
A = np.hstack((amp.reshape(-1, 1), 1.0/(amp.reshape(-1, 1) - c)))
ab = np.linalg.lstsq(A, snr.reshape((-1, 1)))[0]
peak_amp = c - np.sqrt(ab[1, 0]/ab[0, 0])
peak_snr = np.dot(np.array([[peak_amp, 1./(peak_amp-c)]]), ab) #None check mcode
peak_snr = dbv(peak_snr)
peak_amp = dbv(peak_amp)
if _debug:
import pylab as plt
pred = np.dot(A, ab)
hold = plt.ishold()
plt.hold(True)
plt.plot(dbv(amp), dbv(pred), '-', color='b')
plt.hold(hold)
return peak_snr, peak_amp
def peakSNR(snr, amp):
"""Find the SNR peak by fitting the SNR curve.
A smooth curve is fitted to the top end of the SNR vs input amplitude
data with Legendre's least-squares method.
The curve fitted to the data is:
.. math::
y = ax + \\frac{b}{x - c}
**Parameters:**
snr : 1D ndarray or array-like
Signal to Noise Ratio array, expressed in decibels (dB).
amp : 1D ndarray or array-like
Amplitude array, expressed in decibels (dB).
The two arrays ``snr`` and ``amp`` should have the same size.
**Returns:**
(peak_snr, peak_amp) : tuple
The peak SNR value and its corresponding amplitude,
expressed in dB.
"""
# sanitize inputs
snr = np.atleast_1d(np.asarray(snr))
amp = np.atleast_1d(np.asarray(amp))
# Delete garbage data
for check in (np.isinf, np.isnan):
i = check(snr)
snr = np.delete(snr, np.where(i))
amp = np.delete(amp, np.where(i))
for x in (snr, amp):
if len(x.shape) > 1 and np.prod(x.shape) != max(x.shape):
raise ValueError("snr and amp should be vectors (ndim=1)" +
"snr.shape: %s, amp.shape: %s" % (snr.shape, amp.shape))
# All good
max_snr = np.max(snr)
i = np.flatnonzero(snr > max_snr - 10)
min_i = np.min(i)
max_i = np.max(i)
j = np.flatnonzero(snr[min_i:max_i + 1] < max_snr - 15)
if j:
max_i = min_i + np.min(j) - 2
i = np.arange(min_i, max_i + 1)
snr = 10.0**(snr[i]/20)
amp = 10.0**(amp[i]/20)
#n = max(i.shape) # unused variable, REP?
c = np.max(amp)*1.05
# fit y = ax + b/(x-c) to the data
A = np.hstack((amp.reshape(-1, 1), 1.0/(amp.reshape(-1, 1) - c)))
ab = np.linalg.lstsq(A, snr.reshape((-1, 1)))[0]
peak_amp = c - np.sqrt(ab[1, 0]/ab[0, 0])
peak_snr = np.dot(np.array([[peak_amp, 1./(peak_amp-c)]]), ab) #None check mcode
peak_snr = dbv(peak_snr)
peak_amp = dbv(peak_amp)
if _debug:
import pylab as plt
pred = np.dot(A, ab)
hold = plt.ishold()
plt.hold(True)
plt.plot(dbv(amp), dbv(pred), '-', color='b')
plt.hold(hold)
return peak_snr, peak_amp
def plotPZ(H, color='b', markersize=5, showlist=False):
"""Plot the poles and zeros of a transfer function.
**Parameters:**
H : transfer function
Any supported transfer function representation,
eg num/den, zpk, lti...
color : Any matplotlib-compatible color descr, optional
For example, 'r' for 'red' or '#000080' for 'navy'.
You can also specify separately poles and zeros, in a tuple.
markersize : scalar, optional
The markers size in points.
showlist : boolean, optional
Superimpose a list of the poles and zeros on the plot.
.. plot::
import pylab as plt
from deltasigma import synthesizeNTF, plotPZ
order = 5
osr = 32
f0 = 0.
Hinf = 1.5
ntf = synthesizeNTF(order, osr, 2, Hinf, f0)
plt.figure(figsize=(8, 6))
plotPZ(ntf, color=('r', 'b'), showlist=True)
plt.title("NTF singularities")
plt.show()
"""
# Parts of the code come from 'pydsm'
#
# Original copyright notices:
#
# For pydsm
# Copyright (c) 2012, Sergio Callegari
# All rights reserved.
#
# For Richard Schreier's Delta Sigma toolbox
# Copyright (c) 2009, Richard Schreier
z, p, _ = _get_zpk(H)
p = np.real_if_close(np.round(p, 5))
z = np.real_if_close(np.round(z, 5))
pole_fmt = {'marker': 'x', 'markersize': markersize}
zero_fmt = {'marker': 'o', 'markersize': markersize}
if isinstance(color, list) or isinstance(color, tuple):
pole_fmt['color'] = color[0]
zero_fmt['color'] = color[1]
else:
pole_fmt['color'] = color
zero_fmt['color'] = color
hold_status = plt.ishold()
plt.grid(True)
# Plot x and o for poles and zeros, respectively
plt.plot(p.real, p.imag, linestyle='None', **pole_fmt)
plt.hold(True)
if len(z) > 0:
plt.plot(z.real, z.imag, linestyle='None', **zero_fmt)
# Draw unit circle, real axis and imag axis
circle = np.exp(2j*np.pi*np.linspace(0, 1, 100))
plt.plot(circle.real, circle.imag)
ax = plt.gca()
ax.set_autoscale_on(False)
if showlist:
ax = plt.gca()
x1, x2, y1, y2 = ax.axis()
x2 = np.round((x2 - x1)*1.48 + x1, 1)
ax.axis((x1, x2, y1, y2))
markers = []
descr = []
ps = p[p.imag >= 0]
for pi in ps:
markers += [plt.Line2D((), (), linestyle='None', **pole_fmt)]
if np.allclose(pi.imag, 0, atol=1e-5):
descr += ['%+.4f' % pi.real]
else:
descr += ['%+.4f+/-j%.4f' % (pi.real, pi.imag)]
if len(z) > 0:
for zi in z[z.imag >= 0]:
markers += [plt.Line2D((), (), linestyle='None', **zero_fmt)]
if zi.imag == 0:
descr += ['%+.4f' % zi.real]
else:
descr += ['%+.4f +/-j%.4f' % (zi.real, zi.imag)]
plt.legend(markers, descr, title="Poles (x) and zeros (o)", ncol=1, loc='best',
handlelength=.55, prop={'size':10})
else:
plt.xlim((-1.1, 1.1))
plt.ylim((-1.1, 1.1))
plt.gca().set_aspect('equal')
# plt.axes().set_aspect('equal', 'datalim')
plt.ylabel('Imag')
plt.xlabel('Real')
if not hold_status:
plt.hold(False)
def peakSNR(snr, amp):
"""Find the SNR peak by fitting the SNR curve.
A smooth curve is fitted to the top end of the SNR vs input amplitude
data with Legendre's least-squares method.
The curve fitted to the data is:
.. math::
y = ax + \\frac{b}{x - c}
**Parameters:**
snr : 1D ndarray or array-like
Signal to Noise Ratio array, expressed in decibels (dB).
amp : 1D ndarray or array-like
Amplitude array, expressed in decibels (dB).
The two arrays ``snr`` and ``amp`` should have the same size.
**Returns:**
(peak_snr, peak_amp) : tuple
The peak SNR value and its corresponding amplitude,
expressed in dB.
"""
# sanitize inputs
snr = np.atleast_1d(np.asarray(snr))
amp = np.atleast_1d(np.asarray(amp))
# Delete garbage data
for check in (np.isinf, np.isnan):
i = check(snr)
snr = np.delete(snr, np.where(i))
amp = np.delete(amp, np.where(i))
for x in (snr, amp):
if len(x.shape) > 1 and np.prod(x.shape) != max(x.shape):
raise ValueError("snr and amp should be vectors (ndim=1)" +
"snr.shape: %s, amp.shape: %s" %
(snr.shape, amp.shape))
# All good
max_snr = np.max(snr)
i = np.flatnonzero(snr > max_snr - 10)
min_i = np.min(i)
max_i = np.max(i)
j = np.flatnonzero(snr[min_i:max_i + 1] < max_snr - 15)
if j:
max_i = min_i + np.min(j) - 2
i = np.arange(min_i, max_i + 1)
snr = 10.0**(snr[i] / 20)
amp = 10.0**(amp[i] / 20)
#n = max(i.shape) # unused variable, REP?
c = np.max(amp) * 1.05
# fit y = ax + b/(x-c) to the data
A = np.hstack((amp.reshape(-1, 1), 1.0 / (amp.reshape(-1, 1) - c)))
ab = np.linalg.lstsq(A, snr.reshape((-1, 1)))[0]
peak_amp = c - np.sqrt(ab[1, 0] / ab[0, 0])
peak_snr = np.dot(np.array([[peak_amp, 1. / (peak_amp - c)]]),
ab) #None check mcode
peak_snr = dbv(peak_snr)
peak_amp = dbv(peak_amp)
if _debug:
import pylab as plt
pred = np.dot(A, ab)
hold = plt.ishold()
plt.hold(True)
plt.plot(dbv(amp), dbv(pred), '-', color='b')
plt.hold(hold)
return peak_snr, peak_amp
