def y(t, v0):
    g = 9.81
    return v0*t - 0.5*g*t**2

def y(t):
    g = 9.81
    return v0*t - 0.5*g*t**2

class Y:
    def __init__(self, v0):
        self.v0 = v0
        self.g = 9.81

    def value(self, t):
        return self.v0*t - 0.5*self.g*t**2

y = Y(v0=3)            # create instance (object)
v = y.value(0.1)       # compute function value

y = Y(v0=3)

    def __init__(self, v0):
        self.v0 = v0
        self.g = 9.81

print y.v0
print y.g

def value(self, t):
    return self.v0*t - 0.5*self.g*t**2

v = y.value(t=0.1)

Y.value(y, t=0.1)

return y.v0*t - 0.5*y.g*t**2

def make_table(f, tstop, n):
    for t in linspace(0, tstop, n):
        print t, f(t)

def g(t):
    return sin(t)*exp(-t)

table(g, 2*pi, 101)         # send ordinary function

y = Y(6.5)
table(y.value, 2*pi, 101)   # send class method

class MyFunc:
    def __init__(self, p0, p1, p2, ..., pn):
        self.p0 = p0
        self.p1 = p1
        ...
        self.pn = pn

    def value(self, x):
        return ...

class VelocityProfile:
    def __init__(self, beta, mu0, n, R):
        self.beta, self.mu0, self.n, self.R = \
        beta, mu0, n, R

    def value(self, r):
        beta, mu0, n, R = \
        self.beta, self.mu0, self.n, self.R
        n = float(n)  # ensure float divisions
        v = (beta/(2.0*mu0))**(1/n)*(n/(n+1))*\
            (R**(1+1/n) - r**(1+1/n))
        return v

v = VelocityProfile(R=1, beta=0.06, mu0=0.02, n=0.1)
print v.value(r=0.1)

class MyClass:
    def __init__(self, p1, p2):
        self.attr1 = p1
        self.attr2 = p2

    def method1(self, arg):
        # can init new attribute outside constructor:
        self.attr3 = arg
        return self.attr1 + self.attr2 + self.attr3

    def method2(self):
        print 'Hello!'

m = MyClass(4, 10)
print m.method1(-2)
m.method2()

y = Y(3)

Y.__init__(y, 3)   # class prefix Y. is like a module prefix

self.v0 = v0

y.v0 = 3

v = y.value(2)

v = Y.value(y, 2)

class SelfExplorer:
    """Class for computing a*x."""
    def __init__(self, a):
        self.a = a
        print 'init: a=%g, id(self)=%d' % (self.a, id(self))

    def value(self, x):
        print 'value: a=%g, id(self)=%d' % (self.a, id(self))
        return self.a*x

s1 = SelfExplorer(1)

id(s1)

s2 = SelfExplorer(2)

id(s2)

s1.value(4)

SelfExplorer.value(s1, 4)

s2.value(5)

SelfExplorer.value(s2, 5)

y = Y(3)

Y.__init__(y, 3)   # class prefix Y. is like a module prefix

self.v0 = v0

y.v0 = 3

v = y.value(2)

v = Y.value(y, 2)

class SelfExplorer:
    """Class for computing a*x."""
    def __init__(self, a):
        self.a = a
        print 'init: a=%g, id(self)=%d' % (self.a, id(self))

    def value(self, x):
        print 'value: a=%g, id(self)=%d' % (self.a, id(self))
        return self.a*x

s1 = SelfExplorer(1)

id(s1)

s2 = SelfExplorer(2)

id(s2)

s1.value(4)

SelfExplorer.value(s1, 4)

s2.value(5)

SelfExplorer.value(s2, 5)

class Account:
    def __init__(self, name, account_number, initial_amount):
        self.name = name
        self.no = account_number
        self.balance = initial_amount

    def deposit(self, amount):
        self.balance += amount

    def withdraw(self, amount):
        self.balance -= amount

    def dump(self):
        s = '%s, %s, balance: %s' % \
            (self.name, self.no, self.balance)
        print s

a1 = Account('John Olsson', '19371554951', 20000)
a2 = Account('Liz Olsson',  '19371564761', 20000)
a1.deposit(1000)
a1.withdraw(4000)
a2.withdraw(10500)
a1.withdraw(3500)
print "a1's balance:", a1.balance

a1.dump()

a2.dump()

class AccountP:
    def __init__(self, name, account_number, initial_amount):
        self._name = name
        self._no = account_number
        self._balance = initial_amount

    def deposit(self, amount):
        self._balance += amount

    def withdraw(self, amount):
        self._balance -= amount

    def get_balance(self):    # NEW - read balance value
        return self._balance

    def dump(self):
        s = '%s, %s, balance: %s' % \
            (self._name, self._no, self._balance)
        print s

a1 = AccountP('John Olsson', '19371554951', 20000)
a1.withdraw(4000)

print a1._balance      # it works, but a convention is broken

print a1.get_balance() # correct way of viewing the balance

a1._no = '19371554955' # this is a "serious crime"!

 class Person:
    def __init__(self, name,
                 mobile_phone=None, office_phone=None,
                 private_phone=None, email=None):
        self.name = name
        self.mobile = mobile_phone
        self.office = office_phone
        self.private = private_phone
        self.email = email

    def add_mobile_phone(self, number):
        self.mobile = number

    def add_office_phone(self, number):
        self.office = number

    def add_private_phone(self, number):
        self.private = number

    def add_email(self, address):
        self.email = address

 class Person:
    ...
    def dump(self):
        s = self.name + '\n'
        if self.mobile is not None:
            s += 'mobile phone:   %s\n' % self.mobile
        if self.office is not None:
            s += 'office phone:   %s\n' % self.office
        if self.private is not None:
            s += 'private phone:  %s\n' % self.private
        if self.email is not None:
            s += 'email address:  %s\n' % self.email
        print s

p1 = Person('Hans Petter Langtangen', email='hpl@simula.no')
p1.add_office_phone('67828283'),
p2 = Person('Aslak Tveito', office_phone='67828282')
p2.add_email('aslak@simula.no')
phone_book = [p1, p2]                           # list
phone_book = {'Langtangen': p1, 'Tveito': p2}   # better
for p in phone_book:
    p.dump()

class Circle:
    def __init__(self, x0, y0, R):
        self.x0, self.y0, self.R = x0, y0, R

    def area(self):
        return pi*self.R**2

    def circumference(self):
        return 2*pi*self.R

c = Circle(2, -1, 5)
print 'A circle with radius %g at (%g, %g) has area %g' % \
      (c.R, c.x0, c.y0, c.area())

def test_Circle():
    R = 2.5
    c = Circle(7.4, -8.1, R)

    from math import pi
    expected_area = pi*R**2
    computed_area = c.area()
    diff = abs(expected_area - computed_area)
    tol = 1E-14
    assert diff < tol, 'bug in Circle.area, diff=%s' % diff

    expected_circumference = 2*pi*R
    computed_circumference = c.circumference()
    diff = abs(expected_circumference - computed_circumference)
    assert diff < tol, 'bug in Circle.circumference, diff=%s' % diff

class MyClass:
    def __init__(self, a, b):
    ...

p1 = MyClass(2, 5)
p2 = MyClass(-1, 10)

p3 = p1 + p2
p4 = p1 - p2
p5 = p1*p2
p6 = p1**7 + 4*p3

def __init__(self, ...)
def __call__(self, ...)
def __add__(self, other)

# Python syntax
y = Y(4)
print y(2)
z = Y(6)
print y + z

# What's actually going on
Y.__init__(y, 4)
print Y.__call__(y, 2)
Y.__init__(z, 6)
print Y.__add__(y, z)

class Y:
    def __init__(self, v0):
        self.v0 = v0
        self.g = 9.81

    def __call__(self, t):
        return self.v0*t - 0.5*self.g*t**2

y = Y(3)
v = y(0.1) # same as v = y.__call__(0.1) or Y.__call__(y, 0.1)

class MyFunc:
    def __init__(self, p0, p1, p2, ..., pn):
        self.p0 = p0
        self.p1 = p1
        ...
        self.pn = pn

    def __call__(self, x):
        return ...

def f(x):
    return x**3

dfdx = Derivative(f)

print dfdx(2)   # computes 3*x**2 for x=2

class Derivative:
    def __init__(self, f, h=1E-5):
        self.f = f
        self.h = float(h)

    def __call__(self, x):
        f, h = self.f, self.h      # make short forms
        return (f(x+h) - f(x))/h

from math import *
df = Derivative(sin)
x = pi
df(x)

cos(x)  # exact

def g(t):
    return t**3

dg = Derivative(g)
t = 1
dg(t)  # compare with 3 (exact)

def Newton(f, xstart, dfdx, epsilon=1E-6):
    ...
    return x, no_of_iterations, f(x)

def f(x):
    return 100000*(x - 0.9)**2 * (x - 1.1)**3

df = Derivative(f)
xstart = 1.01
Newton(f, xstart, df, epsilon=1E-5)

def test_Derivative():
    # The formula is exact for linear functions, regardless of h
    f = lambda x: a*x + b
    a = 3.5; b = 8
    dfdx = Derivative(f, h=0.5)
    diff = abs(dfdx(4.5) - a)
    assert diff < 1E-14, 'bug in class Derivative, diff=%s' % diff

f = lambda x: a*x + b

def f(x):
    return a*x + b

f = lambda x: a*x + b
a = 3.5; b = 8
dfdx = Derivative(f, h=0.5)
dfdx(4.5)

>>> from sympy import *
>>> def g(t):
...     return t**3
...
>>> t = Symbol('t')
>>> dgdt = diff(g(t), t)           # compute g'(t)
>>> dgdt
3*t**2

>>> # Turn sympy expression dgdt into Python function dg(t)
>>> dg = lambdify([t], dgdt)
>>> dg(1)
3

import sympy as sp

class Derivative_sympy:
    def __init__(self, f):
        # f: Python f(x)
        x = sp.Symbol('x')
        sympy_f = f(x)
        sympy_dfdx = sp.diff(sympy_f, x)
        self.__call__ = sp.lambdify([x], sympy_dfdx)

def g(t):
   return t**3

def h(y):
   return sp.sin(y)

dg = Derivative_sympy(g)
dh = Derivative_sympy(h)
dg(1)   # 3*1**2 = 3

from math import pi
dh(pi)  # cos(pi) = -1

def f(x):
    return exp(-x**2)*sin(10*x)

a = 0; n = 200
F = Integral(f, a, n)
x = 1.2
print F(x)

def trapezoidal(f, a, x, n):
    h = (x-a)/float(n)
    I = 0.5*f(a)
    for i in range(1, n):
        I += f(a + i*h)
    I += 0.5*f(x)
    I *= h
    return I

class Integral:
    def __init__(self, f, a, n=100):
        self.f, self.a, self.n = f, a, n

    def __call__(self, x):
        return trapezoidal(self.f, self.a, x, self.n)

def test_Integral():
    f = lambda x: 2*x + 5
    F = lambda x: x**2 + 5*x - (a**2 + 5*a)
    a = 2
    dfdx = Integralf, a, n=4)
    x = 6
    diff = abs(I(x) - (F(x) - F(a)))
    assert diff < 1E-15, 'bug in class Integral, diff=%s' % diff

class Y:
    ...
    def __call__(self, t):
        return self.v0*t - 0.5*self.g*t**2

    def __str__(self):
        return 'v0*t - 0.5*g*t**2; v0=%g' % self.v0

y = Y(1.5)
y(0.2)

print y

p1 = Polynomial([1, -1])
print p1

p2 = Polynomial([0, 1, 0, 0, -6, -1])
p3 = p1 + p2
print p3.coeff

print p3

p2.differentiate()
print p2

class Polynomial:
    def __init__(self, coefficients):
        self.coeff = coefficients

    def __call__(self, x):
        s = 0
        for i in range(len(self.coeff)):
            s += self.coeff[i]*x**i
        return s

class Polynomial:
    ...

    def __add__(self, other):
        # return self + other

        # start with the longest list and add in the other:
        if len(self.coeff) > len(other.coeff):
            coeffsum = self.coeff[:]  # copy!
            for i in range(len(other.coeff)):
                coeffsum[i] += other.coeff[i]
        else:
            coeffsum = other.coeff[:] # copy!
            for i in range(len(self.coeff)):
                coeffsum[i] += self.coeff[i]
        return Polynomial(coeffsum)

class Polynomial:
    ...
    def __mul__(self, other):
        M = len(self.coeff) - 1
        N = len(other.coeff) - 1
        coeff = [0]*(M+N+1)  # or zeros(M+N+1)
        for i in range(0, M+1):
            for j in range(0, N+1):
                coeff[i+j] += self.coeff[i]*other.coeff[j]
        return Polynomial(coeff)

class Polynomial:
    ...
    def differentiate(self):    # change self
        for i in range(1, len(self.coeff)):
            self.coeff[i-1] = i*self.coeff[i]
        del self.coeff[-1]

    def derivative(self):       # return new polynomial
        dpdx = Polynomial(self.coeff[:])  # copy
        dpdx.differentiate()
        return dpdx

class Polynomial:
    ...
    def __str__(self):
        s = ''
        for i in range(0, len(self.coeff)):
            if self.coeff[i] != 0:
                s += ' + %g*x^%d' % (self.coeff[i], i)
        # fix layout (lots of special cases):
        s = s.replace('+ -', '- ')
        s = s.replace(' 1*', ' ')
        s = s.replace('x^0', '1')
        s = s.replace('x^1 ', 'x ')
        s = s.replace('x^1', 'x')
        if s[0:3] == ' + ':  # remove initial +
            s = s[3:]
        if s[0:3] == ' - ':  # fix spaces for initial -
            s = '-' + s[3:]
        return s

p1 = Polynomial([1, -1])
print p1

p2 = Polynomial([0, 1, 0, 0, -6, -1])
p3 = p1 + p2
print p3.coeff

p2.differentiate()
print p2

c = a + b    #  c = a.__add__(b)

c = a - b    #  c = a.__sub__(b)

c = a*b      #  c = a.__mul__(b)

c = a/b      #  c = a.__div__(b)

c = a**e     #  c = a.__pow__(e)

a == b       #  a.__eq__(b)

a != b       #  a.__ne__(b)

a < b        #  a.__lt__(b)

a <= b       #  a.__le__(b)

a > b        #  a.__gt__(b)

a >= b       #  a.__ge__(b)

u = Vec2D(0,1)
v = Vec2D(1,0)
print u + v

a = u + v
w = Vec2D(1,1)
a == w

print u - v

print u*v

 class Vec2D:
    def __init__(self, x, y):
        self.x = x;  self.y = y

    def __add__(self, other):
        return Vec2D(self.x+other.x, self.y+other.y)

    def __sub__(self, other):
        return Vec2D(self.x-other.x, self.y-other.y)

    def __mul__(self, other):
        return self.x*other.x + self.y*other.y

    def __abs__(self):
        return math.sqrt(self.x**2 + self.y**2)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __str__(self):
        return '(%g, %g)' % (self.x, self.y)

    def __ne__(self, other):
        return not self.__eq__(other)  # reuse __eq__

class MyClass:
    def __init__(self, a, b):
        self.a, self.b = a, b

    def __str__(self):
        """Return string with pretty print."""
        return 'a=%s, b=%s' % (self.a, self.b)

    def __repr__(self):
        """Return string such that eval(s) recreates self."""
        return 'MyClass(%s, %s)' % (self.a, self.b)

m = MyClass(1, 5)
print m      # calls m.__str__()

str(m)       # calls m.__str__()

s = repr(m)  # calls m.__repr__()
s

m2 = eval(s) # same as m2 = MyClass(1, 5)
m2           # calls m.__repr__()

class Y:
    """Class for function y(t; v0, g) = v0*t - 0.5*g*t**2."""

    def __init__(self, v0):
        """Store parameters."""
        self.v0 = v0
        self.g = 9.81

    def __call__(self, t):
        """Evaluate function."""
        return self.v0*t - 0.5*self.g*t**2

    def __str__(self):
        """Pretty print."""
        return 'v0*t - 0.5*g*t**2; v0=%g' % self.v0

    def __repr__(self):
        """Print code for regenerating this instance."""
        return 'Y(%s)' % self.v0

u = Complex(2,-1)
v = Complex(1)     # zero imaginary part
w = u + v
print w

w != u

u*v

u < v

print w + 4

print 4 - w

class Complex:
    def __init__(self, real, imag=0.0):
        self.real = real
        self.imag = imag

    def __add__(self, other):
        return Complex(self.real + other.real,
                       self.imag + other.imag)

    def __sub__(self, other):
        return Complex(self.real - other.real,
                       self.imag - other.imag)

    def __mul__(self, other):
        return Complex(self.real*other.real - self.imag*other.imag,
                       self.imag*other.real + self.real*other.imag)

    def __div__(self, other):
        ar, ai, br, bi = self.real, self.imag, \
                         other.real, other.imag # short forms
        r = float(br**2 + bi**2)
        return Complex((ar*br+ai*bi)/r, (ai*br-ar*bi)/r)

    def __abs__(self):
        return sqrt(self.real**2 + self.imag**2)

    def __neg__(self):   # defines -c (c is Complex)
        return Complex(-self.real, -self.imag)

    def __eq__(self, other):
        return self.real == other.real and \
               self.imag == other.imag

    def __ne__(self, other):
        return not self.__eq__(other)

    def __str__(self):
        return '(%g, %g)' % (self.real, self.imag)

    def __repr__(self):
        return 'Complex' + str(self)

    def __pow__(self, power):
        raise NotImplementedError(
          'self**power is not yet impl. for Complex')

u = Complex(1, 2)
w = u + 4.5

class Complex:
    ...
    def __add__(self, other):
        if isinstance(other, (float,int)):
            other = Complex(other)
        return Complex(self.real + other.real,
                       self.imag + other.imag)

# or

    def __add__(self, other):
        if isinstance(other, (float,int)):
            return Complex(self.real + other, self.imag)
        else:
            return Complex(self.real + other.real,
                           self.imag + other.imag)

u = Complex(1, 2)
w = 4.5 + u

class Complex:
    ...
    def __radd__(self, other):
        """Rturn other + self."""
        # other + self = self + other:
        return self.__add__(other)

class Complex:
    ...
    def __sub__(self, other):
        if isinstance(other, (float,int)):
            other = Complex(other)
        return Complex(self.real - other.real,
                       self.imag - other.imag)

    def __rsub__(self, other):
        if isinstance(other, (float,int)):
            other = Complex(other)
        return other.__sub__(self)

 class A:
    """A class for demo purposes."""
    def __init__(self, value):
        self.v = value

a = A([1,2])
print a.__dict__  # all attributes

dir(a)            # what's in object a?

a.__doc__         # programmer's documentation of A

a.myvar = 10            # add new attribute (!)
a.__dict__

dir(a)

b = A(-1)
b.__dict__              # b has no myvar attribute

dir(b)

%matplotlib inline


class Gravity:
    """Gravity force between two objects."""
    def __init__(self, m, M):
        self.m = m
        self.M = M
        self.G = 6.67428E-11 # gravity constant

    def force(self, r):
        G, m, M = self.G, self.m, self.M
        return G*m*M/r**2

    def visualize(self, r_start, r_stop, n=100):
        from scitools.std import plot, linspace
        r = linspace(r_start, r_stop, n)
        g = self.force(r)
        title='m=%g, M=%g' % (self.m, self.M)
        plot(r, g, title=title)

mass_moon = 7.35E+22
mass_earth = 5.97E+24

# make instance of class Gravity:
gravity = Gravity(mass_moon, mass_earth)

r = 3.85E+8  # earth-moon distance in meters
Fg = gravity.force(r)   # call class method

class IntervalMath:
    def __init__(self, lower, upper):
        self.lo = float(lower)
        self.up = float(upper)

    def __add__(self, other):
        a, b, c, d = self.lo, self.up, other.lo, other.up
        return IntervalMath(a + c, b + d)

    def __sub__(self, other):
        a, b, c, d = self.lo, self.up, other.lo, other.up
        return IntervalMath(a - d, b - c)

    def __mul__(self, other):
        a, b, c, d = self.lo, self.up, other.lo, other.up
        return IntervalMath(min(a*c, a*d, b*c, b*d),
                            max(a*c, a*d, b*c, b*d))

    def __div__(self, other):
        a, b, c, d = self.lo, self.up, other.lo, other.up
        if c*d <= 0: return None
        return IntervalMath(min(a/c, a/d, b/c, b/d),
                            max(a/c, a/d, b/c, b/d))
    def __str__(self):
        return '[%g, %g]' % (self.lo, self.up)

I = IntervalMath   # abbreviate
a = I(-3,-2)
b = I(4,5)

expr = 'a+b', 'a-b', 'a*b', 'a/b'   # test expressions
for e in expr:
    print e, '=', eval(e)

a+b = [1, 3]
a-b = [-8, -6]
a*b = [-15, -8]
a/b = [-0.75, -0.4]

a = I(4,5)
q = 2
b = a*q

class IntervalArithmetics:
    ...
    def __mul__(self, other):
        if isinstance(other, (int, float)):      # NEW
            other = IntervalMath(other, other)   # NEW
        a, b, c, d = self.lo, self.up, other.lo, other.up
        return IntervalMath(min(a*c, a*d, b*c, b*d),
                            max(a*c, a*d, b*c, b*d))

class IntervalArithmetics:
    ...
    def __rmul__(self, other):
        if isinstance(other, (int, float)):
            other = IntervalMath(other, other)
        return other*self

    def __pow__(self, exponent):
        if isinstance(exponent, int):
            p = 1
            if exponent > 0:
                for i in range(exponent):
                    p = p*self
            elif exponent < 0:
                for i in range(-exponent):
                    p = p*self
                p = 1/p
            else:   # exponent == 0
                p = IntervalMath(1, 1)
            return p
        else:
            raise TypeError('exponent must int')

a = IntervalMath(5,7)
float(a)

class IntervalArithmetics:
    ...
    def __float__(self):
        return 0.5*(self.lo + self.up)

class IntervalArithmetics:
    ...
    def __str__(self):
        return '[%g, %g]' % (self.lo, self.up)

    def __repr__(self):
        return '%s(%g, %g)' % \
          (self.__class__.__name__, self.lo, self.up)

g = 9.81
y_0 = I(0.99, 1.01)
Tm = 0.45                 # mean T
T = I(Tm*0.95, Tm*1.05)   # 10% uncertainty
print T

g = 2*y_0*T**(-2)
g

# computing with mean values:
T = float(T)
y = 1
g = 2*y_0*T**(-2)
print '%.2f' % g

R = I(6*0.9, 6*1.1)   # 20 % error
V = (4./3)*pi*R**3
V

print V

print float(V)

# compute with mean values:
R = float(R)
V = (4./3)*pi*R**3
print V