%pylab inline
rcParams['figure.figsize'] = (10, 4) #wide graphs by default
from __future__ import print_function
from __future__ import division

samps = normal(scale=2.0, size= 10000)
samps.var()

samps.std(), samps.std()**2

a = rand(100)
b = rand(100)
cov(a,b)

a = rand(100)* 100
b = rand(100) * 100
cov(a,b)

a = rand(100000)* 100
b = rand(100000) * 100
cov(a,b)

var(a), var(b)

a = rand(100)
b = rand(100)
c = rand(100)
cov(a + (2*c),b + (2*c))

a = rand(100000)
b = rand(100000)
c = rand(100000)
cov(a + (2*c),b + (2*c))

a = rand(100)
b = rand(100)
d = sin(linspace(0, 2*pi*7, 100))
plot(a+d)
plot(b+d)

cov(a + d,b + d)

plot(a+d + 2)
plot(-2*(b+d))
cov(a + d + 2,-2*(b+d))

plot(a + (d*3))
plot(-(b + (d*3)))

cov(a + (d*3),-(b + (d*3)))

sig1 = sin(linspace(0, 100*2*pi, 44100))
sig2 = sin(linspace(0.1, 0.1 + (100*2*pi), 44100))
plot(sig1)
plot(sig2)
xlim((0, 1000))

lags, c, lines, line = xcorr(sig1, sig2, maxlags=500, usevlines=False);
grid()

lags, c, lines, line = xcorr(sig1, sig2, maxlags=50, usevlines=False);
grid()

len(c)

plot(c)

argmax(c)

cc_index = lags[argmax(c)]
print(cc_index)

plot(lags, c)
vlines(cc_index, 0.5, 1.09, color='r', lw=2)
text(cc_index + 1, 1.05, 'CC peak', color='r')
grid()

sr = 44100
f = 100.0
Ps = sr/f
Ps # period in number of samples

cc_index

cc_index/Ps

2 * pi * cc_index/Ps

2 * pi * (cc_index + 1)/Ps

noise1 = random.random(44100) - 0.5
noise2 = random.random(44100) - 0.5

lags, c, lines, line = xcorr(noise1, noise2, maxlags=500, usevlines=False);
grid()

noise1 = normal(size=44100)
noise2 = normal(size=44100)

lags, c, lines, line = xcorr(noise1, noise2, maxlags=500, usevlines=False);
grid()

a = (rand(44100)*2) - 1
plot(a)

b = sin(linspace(0, 2*pi*200, 44100))*0.3
plot(a+b)

c = (rand(44100)*2) - 1
d = sin(linspace(0.7, 0.7 + (2*pi*200), 44100))*0.3
plot(c+d)

plot(c+d)
xlim(0,1000)

lags, c, lines, line = xcorr(a+b, c+d, maxlags=500);

m = argmax(c[500:600]) + 500

lags[m]

sr = 44100
f = 200.0
Ps = sr/f
Ps # period in number of samples

lags[m]/Ps

(lags[m]/Ps) * 2 * pi

lags, c, lines, line = acorr(a + b, maxlags=500);

plot(c[501:])
vlines(220.5, -0.15, 0.15)

from scipy.io import wavfile

sr, in_sig = wavfile.read('cars.wav')

win_size = 1024
hop = 256

cc_lags = 0.001*sr # 1 ms max lag

rccf = []
win_start = arange(0, in_sig.shape[0] - win_size, hop)
for start in win_start:
    win = in_sig[start: start+win_size].astype(float)
    lags, c, lines, line = xcorr(win[:,0], win[:,1], maxlags=cc_lags)
    rccf.append(c)


imshow(array(rccf).T, aspect='auto')

plot(in_sig)

sr, in_sig = wavfile.read('superstition.wav')

!aplay superstition.wav

plot(in_sig)

in_sig.shape

lags,c, lines, line = acorr(in_sig[:100000,0].astype(double), maxlags= 50000);

i = imread('galileo.png')
imshow(i)

plot(i[:,:,3].T);

i.shape

i.dtype

i = sum(i[:,:,:-1], axis=2)/3.0
imshow(i)
colorbar()

i.shape

imshow(i)
colorbar()

imshow(i, cmap=cm.gray)
colorbar()

i = where(i > 0.9, 0, 1)
imshow(i, cmap='gray')
colorbar()

o = imread('o.png')
imshow(o)
colorbar()

o = o.astype(float).sum(axis=-1)/3
o = where(o > 0.9, 0, 1)
imshow(o, cmap=cm.gray, interpolation='nearest')

from scipy.signal import correlate2d
cc = correlate2d(i, o)
imshow(cc)
colorbar()
gcf().set_figheight(8)

imshow(cc, cmap=cm.gray)
colorbar()
gcf().set_figheight(8)

imshow(where(cc > 200, 1, 0), interpolation='nearest', cmap=cm.gray)
colorbar()
gcf().set_figheight(8)

imshow(where(cc > 300, 1, 0), interpolation='nearest', cmap=cm.gray)
colorbar()
gcf().set_figheight(8)

from scipy.ndimage.filters import maximum_filter

imshow(maximum_filter(cc, (10,10)))
gcf().set_figheight(8)

subplot(121)
imshow(maximum_filter(cc, (50,50)))
subplot(122)
imshow(i, cmap=cm.gray)
gcf().set_figheight(8)

mf = maximum_filter(cc, (50,50))

argmax(mf)

unravel_index(argmax(mf), mf.shape)

argmax(cc)

unravel_index(argmax(cc), cc.shape)