%matplotlib inline

from scitools.std import *
x0 = 100                      # initial amount
p = 5                         # interest rate
N = 4                         # number of years
index_set = range(N+1)
x = zeros(len(index_set))

# Solution:
x[0] = x0
for n in index_set[1:]:
    x[n] = x[n-1] + (p/100.0)*x[n-1]
print x
plot(index_set, x, 'ro', xlabel='years', ylabel='amount')

x_old = x0
for n in index_set[1:]:
    x_new = x_old + (p/100.)*x_old
    x_old = x_new  # x_new becomes x_old at next step

import datetime
date1 = datetime.date(2007, 8, 3)  # Aug 3, 2007
date2 = datetime.date(2008, 8, 4)  # Aug 4, 2008
diff = date2 - date1
print diff.days

from scitools.std import *
x0 = 100                           # initial amount
p = 5                              # annual interest rate
r = p/360.0                        # daily interest rate
import datetime
date1 = datetime.date(2007, 8, 3)
date2 = datetime.date(2011, 8, 3)
diff = date2 - date1
N = diff.days
index_set = range(N+1)
x = zeros(len(index_set))

# Solution:
x[0] = x0
for n in index_set[1:]:
    x[n] = x[n-1] + (r/100.0)*x[n-1]
print x
plot(index_set, x, 'ro', xlabel='days', ylabel='amount')

p = zeros(len(index_set))
# fill p[n] for n in index_set (might be non-trivial...)

r = p/360.0                      # daily interest rate
x = zeros(len(index_set))

x[0] = x0
for n in index_set[1:]:
    x[n] = x[n-1] + (r[n-1]/100.0)*x[n-1]

N = int(sys.argv[1])
from numpy import zeros
x = zeros(N+1, int)
x[0] = 1
x[1] = 1
for n in range(2, N+1):
    x[n] = x[n-1] + x[n-2]
    print n, x[n]

2 2
3 3
4 5
5 8
6 13
...
45 1836311903
Warning: overflow encountered in long_scalars
46 -1323752223

import sys
N = int(sys.argv[1])
xnm1 = 1                           # "x_n minus 1"
xnm2 = 1                           # "x_n minus 2"
n = 2
while n <= N:
    xn = xnm1 + xnm2
    print 'x_%d = %d' % (n, xn)
    xnm2 = xnm1
    xnm1 = xn
    n += 1

x_2 = 2
x_3 = 3
...
x_198 = 173402521172797813159685037284371942044301
x_199 = 280571172992510140037611932413038677189525
x_200 = 453973694165307953197296969697410619233826

x[n] = x[n-1] + p/100.0)*x[n-1]

x[n] = x[n-1] + (rho/100.0)*x[n-1]*(1 - x[n-1]/float(M))

def Newton(f, x, dfdx, epsilon=1.0E-7, max_n=100):
    n = 0
    while abs(f(x)) > epsilon and n <= max_n:
        x = x - f(x)/dfdx(x)
        n += 1
    return x, n, f(x)

def Newton(f, x, dfdx, epsilon=1.0E-7, max_n=100,
           store=False):
    f_value = f(x)
    n = 0
    if store: info = [(x, f_value)]
    while abs(f_value) > epsilon and n <= max_n:
        x = x - float(f_value)/dfdx(x)
        n += 1
        f_value = f(x)
        if store: info.append((x, f_value))
    if store:
        return x, info
    else:
        return x, n, f_value

from math import sin, cos, exp, pi
import sys

def g(x):
    return exp(-0.1*x**2)*sin(pi/2*x)

def dg(x):
    return -2*0.1*x*exp(-0.1*x**2)*sin(pi/2*x) + \
           pi/2*exp(-0.1*x**2)*cos(pi/2*x)

x0 = float(sys.argv[1])
x, info = Newton(g, x0, dg, store=True)
print 'Computed zero:', x

# Print the evolution of the difference equation
# (i.e., the search for the root)
for i in range(len(info)):
    print 'Iteration %3d: f(%g)=%g' % (i, info[i][0], info[i][1])

zero: 1.999999999768449
Iteration  0: f(1.7)=0.340044
Iteration  1: f(1.99215)=0.00828786
Iteration  2: f(1.99998)=2.53347e-05
Iteration  3: f(2)=2.43808e-10

zero: 42.49723316011362
Iteration  0: f(3)=-0.40657
Iteration  1: f(4.66667)=0.0981146
Iteration  2: f(42.4972)=-2.59037e-79

import numpy
def note(frequency, length, amplitude=1,
         sample_rate=44100):
    time_points = numpy.linspace(0, length,
                                 length*sample_rate)
    data = numpy.sin(2*numpy.pi*frequency*time_points)
    data = amplitude*data
    return data

data = note(440, 2)
data = data.astype(numpy.int16)
max_amplitude = 2**15 - 1
data = max_amplitude*data
import scitools.sound
scitools.sound.write(data, 'Atone.wav')
scitools.sound.play('Atone.wav')

# echo: e[n] = beta*s[n] + (1-beta)*s[n-b]

def add_echo(data, beta=0.8, delay=0.002,
             sample_rate=44100):
    newdata = data.copy()
    shift = int(delay*sample_rate)  # b (math symbol)
    for i in xrange(shift, len(data)):
        newdata[i] = beta*data[i] + (1-beta)*data[i-shift]
    return newdata

data = scitools.sound.read(filename)
data = data.astype(float)
data = add_echo(data, beta=0.6)
data = data.astype(int16)
scitools.sound.play(data)

# put data1, data2, ... after each other in a new array:
data = numpy.concatenate((data1, data2, data3, ...))

E1 = note(164.81, .5)
G = note(392, .5)
B = note(493.88, .5)
E2 = note(659.26, .5)
intro = numpy.concatenate((E1, G, B, E2, B, G))
...
song = numpy.concatenate((intro, intro, ...))
scitools.sound.play(song)
scitools.sound.write(song, 'tmp.wav')

index_set = <array of n-values: 0, 1, ..., N>
x = zeros(N+1)
x[0] = x0
for n in index_set[1:]:
    x[n] = <formula involving x[n-1]>

for n in index_set[1:]:
    x[n] = <formula involving x[n-1]>
    y[n] = <formula involving y[n-1] and x[n]>