%pylab inline

from __future__ import print_function
from deltasigma import *
from IPython.core.display import Image

# skip this, this is just to display nice tables.
from itertools import izip_longest
class Table(list):
    def _repr_html_(self):
        html = ["<table>"]
        for row in self:
            html.append("<tr>")
            for col in row:
                try:
                    float(col)
                    html.append("<td>%.6f</td>" % col)
                except(ValueError):
                    html.append("<td><b>%s</b></td>" % col)
            html.append("</tr>")
        html.append("</table>")
        return ''.join(html)

order = 5
R = 42
opt = 1
H = synthesizeNTF(order, R, opt)

print(pretty_lti(H))

figure(figsize=(10, 5))
plotPZ(H, showlist=True)
title('NTF');

Image(url='http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png', retina=True)

a, g, b, c = realizeNTF(H)

b = np.concatenate((b[0].reshape((1, )), np.zeros((b.shape[0] - 1, ))), axis=0)

t = Table()
ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']
t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', 
          'Feed-in', 'Interstage'])
t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])
[t.append(x) for x in izip_longest(ilabels, a.tolist(), g.tolist(), b.tolist(), c.tolist(), fillvalue="")]
t

ABCD = stuffABCD(a, g, b, c);
u = np.linspace(0, 0.6, 30);
N = 1e4; 
T = np.ones((1, N))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
    ui = u[i]
    v, xn, xmax, _ = simulateDSM(ui*T, ABCD);
    maxima[:, i] = np.squeeze(xmax)
    if any(xmax > 1e2):
        umax = ui;
        u = u[:i+1];
        maxima = maxima[:, :i]
        break;
# save the maxima
prescale_maxima = np.copy(maxima)
print('The state maxima have been evaluated through simulation.')

for i in range(order):
    semilogy(u, maxima[i, :],'o-')
    if not i:
        hold(True)
grid(True)
xlabel('DC input')
ylabel('Peak value')
title('Simulated State Maxima')
xlim([0, 0.6]) 
ylim([1e-4, 10]);

ABCDs, umax, _ = scaleABCD(ABCD, N_sim=1e5)
as_, gs, bs, cs = mapABCD(ABCDs)
print('\nScaled modulator, umax = %.2f\n' % umax)

t = Table()
ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']
t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', 
          'Feed-in', 'Interstage'])
t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])
[t.append(x) for x in izip_longest(ilabels, as_.tolist(), gs.tolist(), bs.tolist(), cs.tolist(), fillvalue="")]
t

u = np.linspace(0, umax, 30)
N = 1e4
T = np.ones((N,))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
    ui = u[i]
    v, xn, xmax, _ = simulateDSM(ui*T, ABCDs)
    maxima[:, i] = xmax.squeeze()
    if any(xmax > 1e2):
        umax = ui;
        u = u[:i]
        maxima = maxima[:, :i]
        break
print('The state maxima have been re-evaluated through simulation.')
print("The maximum input was found to be %.6f" % umax)

for i in range(order):
    semilogy(u, maxima[i, :], 'o-')
    if not i:
        hold(True)
grid(True)
ylabel('Peak value')
xlabel('DC input')
xlim([0, 0.6])
ylim([4e-2, 4]);

#%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py
%load_ext version_information
%reload_ext version_information

%version_information numpy, scipy, matplotlib, deltasigma