len(dir())

%pylab inline

len(dir())

%pylab inline
import mpl_toolkits.mplot3d
t=linspace(-9,9,dtype='i')
x,y=meshgrid(t,t)
gca(projection='3d').plot_surface(x,y,x*x^y)

#Jupyter
%pylab inline
import pandas as pd
rnd=np.random.random
t=arange(10)
f=pd.DataFrame(dict(a=t, b=t+rnd(10), c=rnd(10)))
subplot(221);plot(f.a,f.b,'.')
subplot(222);plot(f.a,f.c,'mo:')
subplot(223);plot(f.b,f.a,'^-')
subplot(224);plot(f.b,f.c,'rv--')
f

#Jupyter #pandas #matplotlib
%pylab inline
import seaborn
style.use('seaborn-poster') #pretty

rnd = random.random
t = arange(99) * .1
f = pd.DataFrame(dict(a=t, b=t+rnd(99), c=rnd(99)+rnd(99)+rnd(99)))
f.boxplot()
f.hist()
f.plot()

#Jupyter #pandas
%pylab inline
import seaborn
style.use('seaborn-poster')
import pandas as pd
rnd = random.random
u = arange(6)
g = pd.DataFrame(dict(b=u+rnd(6), c=rnd(6)), index=list('ABCDEF'))
print(g.b)
print(g.ix['C'])
xlim(0, 6)

for r in g.itertuples():
    text(r.b, r.c, r.Index)

g

list(g.b)

g.index

%%time
#Jupyter
%pylab inline
import seaborn
style.use('seaborn-poster')
rc('figure', figsize=(13,10))

z = c = linspace(-2, 0.5, 1400) + linspace(-1j, 1j, 1400)[:, None]
for i in range(32): z = z**2 + c
imshow(abs(z) < 2, extent=[c.real.min(), c.real.max(), c.imag.min(), c.imag.max()])

c.imag

(newaxis, newaxis)

#Jupyter #DSP
%pylab inline
import seaborn
style.use('seaborn-poster') #pretty
x = linspace(0, 2*pi, 99)
env = bartlett(len(x))
subplot(311)
stem(x, sin(8*x)*env, 'b', 'bo')
stem(x, cos(9*x)*env*2, 'r:', 'r.')

#Jupyter #Python #matplotlib
%pylab inline
import seaborn
style.use('seaborn-poster') #pretty
rcParams['lines.linewidth'] = 0.5

x = arange(1, 64)
f = x * (x-48)**2 - 4096
plot(x, f, label='$\phi$')
plot(x, x * 100, label='$100x$') # 2nd func

m = f.argmax()
axvline(x[m])
text(x[m] + .5, f[m] + 300, 'max')

n = f.argmin()
axvline(x[n])
annotate('min', (x[n], f[n]), textcoords='offset pixels', xytext=(-100,0), arrowprops=dict(arrowstyle='->'), va='center')

legend()
gca().set_xscale('log')

matshow(bitwise_and.outer(x, x), cmap=cm.seismic) # plot #2. seaborn default is grayscale
colorbar()

%pylab inline
import seaborn
style.use('seaborn-poster')
import sympy
sympy.init_printing()
x = sympy.symbols('x')

y = (x-1)*(x-2)*(x-5)
d = y.diff().simplify()
sympy.plotting.plot(y, d, d.integrate(), (x, -1, 7))
y, y.expand(), d, sympy.solve(d), y.integrate().factor()

import sympy
sympy.init_printing()
x = sympy.symbols('x')

(((x-16)*(x-48)).integrate()).factor()

#Jupyter #Sympy #Numpy #matplotlib
%pylab inline
import seaborn
style.use('seaborn-poster')
import sympy
sympy.init_printing()

x = sympy.symbols('x')
y = x*(x-4)*(x-3) - 3
yp = y.diff()
ypp = yp.diff()

# sympy.plotting can't axvline, so lambdify to plot with numpy
yf, ypf, yppf = [sympy.lambdify(x, f, 'numpy') for f in [y, yp, ypp]]
xs = linspace(0, 5)
plot(xs, zip(yf(xs), ypf(xs), yppf(xs)))

es = sympy.solve(yp) + sympy.solve(ypp)
for e in es:
    axvline(e)

y, yp, yp.simplify(), es

plot(xs, stack((yf(xs), ypf(xs), yppf(xs)), -1))

#Jupyter #DSP #FFT #matplotlib #FM
%pylab inline
import seaborn
style.use('seaborn-poster')

# omit 6π sample, avoid leakage
t = linspace(0, 6*pi, 193)[:-1]

# FM synth, -60dB noise
f = sin(t + cos(3*t)/4 + cos(2*t)/4) + random.random(len(t))/999
subplot(2, 1, 1); xlim(t.min(), t.max()); plot(t, f)
# PSD
subplot(2, 1, 2).set_yscale('log'); xticks(arange(0, 101, 3)); stem(abs(fft.fft(f))[:len(f)//2]**2)

#Jupyter #matplotlib
%pylab inline
import seaborn
style.use('seaborn-poster')

# meshgrid alternative
x = tile(linspace(-1, 1), [50, 1])  
# make circles round
gca().set_aspect(1)
# use non-grayscale background; set_facecolor in matplotlib ≥2.0
# seaborn-poster grayscale colormap is murder for contour plots
gca().set_axis_bgcolor('#3fcfef') 
# paraboloid
contour(x, x.T, x**2 + x.T**2)
colorbar()

#Jupyter #matplotlib
%pylab inline
import seaborn
style.use('seaborn-poster')

f = random.random((6, 99)).sum(axis=0)
subplot(411); tick_params(labelbottom=False); h = hist(f, 20)
subplot(412, sharex=gca()); tick_params(labelbottom=False, labelleft=False); boxplot(f, vert=False)
subplot(212, sharex=gca()); plot(h[1][1:], h[0].cumsum(), 'wo-'); ylabel('cdf')
f.sort(); plot(f, arange(len(f)), ':')
xlim(.5, 5.5)
h

#Jupyter #matplotlib #SVG
%pylab inline
import mpl_toolkits.mplot3d
from scipy.signal import convolve2d
import seaborn
style.use('seaborn-poster')
%config InlineBackend.figure_format = 'svg' # or 'pdf'; default 'png'
x = linspace(-10, 10, 20)
y = x[:, None]
rs = x**2 + y**2
f = sin(rs*6)/rs
w = random.random((60, 60)) > .996
g = convolve2d(f, w)
gx, gy = indices(g.shape)
gca(projection='3d').contour(gx, gy, g)
t = linspace(-1, 1, 99)
plot(30*(1+sin(9*t)*t), 30*(1+cos(9*t)*t), t)
matshow(g)

from scipy.signal import convolve2d
m = zeros((60, 60))
m[random.randint(0, m.shape[0], 10), random.randint(0, m.shape[0], 10)] = random.random(10) - .5
matshow(convolve2d(m, f))