%lsmagic

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

%timeit np.linalg.eigvals(np.random.rand(100,100))

%%timeit a = np.random.rand(100, 100)
np.linalg.eigvals(a)

%%capture capt
from __future__ import print_function
import sys
print('Hello stdout')
print('and stderr', file=sys.stderr)

capt.stdout, capt.stderr

capt.show()

%%writefile foo.py
print('Hello world')

%run foo

%%script python
import sys
print 'hello from Python %s' % sys.version

%%script python3
import sys
print('hello from Python: %s' % sys.version)

%%ruby
puts "Hello from Ruby #{RUBY_VERSION}"

%%bash
echo "hello from $BASH"

%%script ./lnum.py
my first line
my second
more

%%bash
echo "hi, stdout"
echo "hello, stderr" >&2


%%bash --out output --err error
echo "hi, stdout"
echo "hello, stderr" >&2

print(error)
print(output)

%%ruby --bg --out ruby_lines
for n in 1...10
    sleep 1
    puts "line #{n}"
    STDOUT.flush
end

ruby_lines

print(ruby_lines.read())

%load_ext cythonmagic

%%cython_pyximport foo
def f(x):
    return 4.0*x

f(10)

%%cython
cimport cython
from libc.math cimport exp, sqrt, pow, log, erf

@cython.cdivision(True)
cdef double std_norm_cdf(double x) nogil:
    return 0.5*(1+erf(x/sqrt(2.0)))

@cython.cdivision(True)
def black_scholes(double s, double k, double t, double v,
                 double rf, double div, double cp):
    """Price an option using the Black-Scholes model.
    
    s : initial stock price
    k : strike price
    t : expiration time
    v : volatility
    rf : risk-free rate
    div : dividend
    cp : +1/-1 for call/put
    """
    cdef double d1, d2, optprice
    with nogil:
        d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))
        d2 = d1 - v*sqrt(t)
        optprice = cp*s*exp(-div*t)*std_norm_cdf(cp*d1) - \
            cp*k*exp(-rf*t)*std_norm_cdf(cp*d2)
    return optprice

black_scholes(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)

%timeit black_scholes(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)

%%cython -lm
from libc.math cimport sin
print 'sin(1)=', sin(1)

%load_ext rmagic

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

X = np.array([0,1,2,3,4])
Y = np.array([3,5,4,6,7])
plt.scatter(X, Y)

%Rpush X Y
%R lm(Y~X)$coef

%R resid(lm(Y~X)); coef(lm(X~Y))

b = %R a=resid(lm(Y~X))
%Rpull a
print(a)
assert id(b.data) == id(a.data)
%R -o a

from __future__ import print_function
v1 = %R plot(X,Y); print(summary(lm(Y~X))); vv=mean(X)*mean(Y)
print('v1 is:', v1)
v2 = %R mean(X)*mean(Y)
print('v2 is:', v2)

%%R -i X,Y -o XYcoef
XYlm = lm(Y~X)
XYcoef = coef(XYlm)
print(summary(XYlm))
par(mfrow=c(2,2))
plot(XYlm)

%load_ext octavemagic

x = %octave [1 2; 3 4];
x

a = [1, 2, 3]

%octave_push a
%octave a = a * 2;
%octave_pull a
a

%%octave -i x -o y
y = x + 3;

y

%%octave -f svg

p = [12 -2.5 -8 -0.1 8];
x = 0:0.01:1;

polyout(p, 'x')
plot(x, polyval(p, x));

%%octave -s 500,500

# butterworth filter, order 2, cutoff pi/2 radians
b = [0.292893218813452  0.585786437626905  0.292893218813452];
a = [1  0  0.171572875253810];
freqz(b, a, 32);

%%octave -s 600,200 -f png

subplot(121);
[x, y] = meshgrid(0:0.1:3);
r = sin(x - 0.5).^2 + cos(y - 0.5).^2;
surf(x, y, r);

subplot(122);
sombrero()