## Scope of variables, Tabulating a function, lambda functions

### Scope of variables

# Let us study scopes of variables to a slight more detail.

# The LGB rule : Python searches for variable names in the following order : 
# 
# 1. First it looks at the local variable names.
# 
# 2. Then it searches for the variale in the list of global variables.
# 
# 3. Finally it tries to see if there is some builtin function having the same name.

# In[1]:

# An example from the book :
print "builtin sum = ", sum # Here no local or global variable is defined, so it takes the inbuilt sum.
sum = 12            # Assigning 12 to sum. This is a global variable for this code.
print "global sum = ", sum

# To see local variables we have to define a function :
def somefn(n) :
    sum = n + 1   # Here it is a local variable. The global variable is untouched.
    print "local sum = ", sum
    return sum

print "whuch sum am I?", sum
sum = somefn(4)
print "New global sum = ", sum
somefn(12)
print "Global sum = ", sum


# Out[1]:

#     builtin sum =  <built-in function sum>
#     global sum =  12
#     whuch sum am I? 12
#     local sum =  5
#     New global sum =  5
#     local sum =  13
#     Global sum =  5
# 

# In[2]:

del sum


# Look at what the keyword global does

# In[3]:

# An example from the book :
print "builtin sum = ", sum # Here no local or global variable is defined, so it takes the inbuilt sum.
sum = 12            # Assigning 12 to sum. This is a global variable for this code.
print "global sum = ", sum

# To see local variables we have to define a function :
def somefn(n) :
    global sum
    sum = n + 1   # Here it is a local variable. The global variable is untouched.
    print "local sum = ", sum
    return sum

print "whuch sum am I?", sum
sum = somefn(4)
print "New global sum = ", sum
somefn(12)
print "global sum = ", sum


# Out[3]:

#     builtin sum =  <built-in function sum>
#     global sum =  12
#     whuch sum am I? 12
#     local sum =  5
#     New global sum =  5
#     local sum =  13
#     global sum =  13
# 

# Can functions access a global variable without using the keyword global? (Or of what use is a global variable if you cannot access it everywhere?)
# 
# The answer is that you can access it everywhere. Without using global you cannot modify it. Here is an example

# In[4]:

globvar = 4

def fun_just_accessing_globvar (n) :
    x = globvar
    print "fun_just_accessing_globvar: 1 : ", x
    x = n
    print "fun_just_accessing_globvar: 2 : ", x
    return globvar

def fun_using_loc_var_globvar (n) :
    globvar = n
    print "fun_using_loc_var_globvar :", globvar
    return globvar

def fun_modifying_globvar (n) :
    global globvar
    print "fun_modifying_globvar: 1 : ", globvar
    globvar = n
    print "fun_modifying_globvar: 2 : ", globvar
    return globvar

fun_just_accessing_globvar(100)
print "After fun_just_accessing_globvar, globvar =", globvar

fun_modifying_globvar(200)
print "After fun_modifying_globvar, globvar =", globvar

fun_using_loc_var_globvar(30)
print "After fun_using_loc_var_globvar, globvar =", globvar

fun_just_accessing_globvar(300)
print "After fun_just_accessing_globvar, globvar =", globvar

fun_modifying_globvar(300)
print "After fun_modifying_globvar, globvar =", globvar


# Out[4]:

#     fun_just_accessing_globvar: 1 :  4
#     fun_just_accessing_globvar: 2 :  100
#     After fun_just_accessing_globvar, globvar = 4
#     fun_modifying_globvar: 1 :  4
#     fun_modifying_globvar: 2 :  200
#     After fun_modifying_globvar, globvar = 200
#     fun_using_loc_var_globvar : 30
#     After fun_using_loc_var_globvar, globvar = 200
#     fun_just_accessing_globvar: 1 :  200
#     fun_just_accessing_globvar: 2 :  300
#     After fun_just_accessing_globvar, globvar = 200
#     fun_modifying_globvar: 1 :  200
#     fun_modifying_globvar: 2 :  300
#     After fun_modifying_globvar, globvar = 300
# 

# Exercise : Understand the output above by printing/copying tha above program and marking the globvar's occuring there as local or global.

# Another example : 

# In[5]:

x = 100

def print_glob_x () :
    print "print_glob_x : Global x = ", x
    

def fn_loc_x (n) :
    x = n
    print "fn_loc_x : Local x : ", x
    print_glob_x()
    
def fn_glob_x (n) :
    global x
    x = n
    print "fn_glob_x : Local x : ", x
    print_glob_x()

print "Global x = ", x
fn_loc_x(200)
print "Global x = ", x
fn_glob_x(200)
print "Global x = ", x


# Out[5]:

#     Global x =  100
#     fn_loc_x : Local x :  200
#     print_glob_x : Global x =  100
#     Global x =  100
#     fn_glob_x : Local x :  200
#     print_glob_x : Global x =  200
#     Global x =  200
# 

# Informal exercise : Experiment with variables as much as you can

### Tabulating functions

# In python one can pass functions to other functions, just as one passes variables

# In[6]:

def tabulate(fn, x_lo, x_hi, step) :
    a = x_lo
    while a <= x_hi :
        print "%f\t\t%f" %(a, fn(a))
        a += step


# In[7]:

def square(x) :
    return x * x


# In[8]:

tabulate(square, 0, 10, 1)


# Out[8]:

#     0.000000		0.000000
#     1.000000		1.000000
#     2.000000		4.000000
#     3.000000		9.000000
#     4.000000		16.000000
#     5.000000		25.000000
#     6.000000		36.000000
#     7.000000		49.000000
#     8.000000		64.000000
#     9.000000		81.000000
#     10.000000		100.000000
# 

### Lambda functions

# In[9]:

tabulate(lambda y : y*y, 0, 10, 1)


# Out[9]:

#     0.000000		0.000000
#     1.000000		1.000000
#     2.000000		4.000000
#     3.000000		9.000000
#     4.000000		16.000000
#     5.000000		25.000000
#     6.000000		36.000000
#     7.000000		49.000000
#     8.000000		64.000000
#     9.000000		81.000000
#     10.000000		100.000000
# 

### Most basic plotting

# In[10]:

def very_simple_plot(f, xlow, xhigh, xscale, yscale, yoffset) :
    number_of_lines = int(float(xhigh - xlow)/xscale)
    if number_of_lines < 0 :
        temp = xlow
        xlow = xhigh
        xhigh = temp
        
    for i in range(number_of_lines) :
        xi = xlow + i * xscale
        yi = (yoffset + f(xi)) * yscale
        ith_line = ""
        for j in range(int(yi) - 1) :
            ith_line += " "
        ith_line += "*"
        print ith_line


# In[11]:

very_simple_plot(lambda x : x*x, 0, 1, .1, 50, 0)


# Out[11]:

#     *
#     *
#      *
#        *
#            *
#                *
#                      *
#                            *
#                                    *
#                                            *
# 

# In[12]:

from math import sin


# In[13]:

very_simple_plot(sin, 0, 14, .2, 10, 2)


# Out[13]:

#                        *
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# In[14]:

def very_simple_plot_with_x_axis(f, xlow, xhigh, xscale, yscale, yoffset) :
    number_of_lines = int(float(xhigh - xlow)/xscale)
    if number_of_lines < 0 :
        temp = xlow
        xlow = xhigh
        xhigh = temp
        
    for i in range(number_of_lines) :
        xi = xlow + i * xscale
        yi = (yoffset + f(xi)) * yscale
        ith_line = ""
        # x-axis is y = 0 :
        if yoffset * yscale < int(yi) :
            for j in range(1, int(yi)) :
                if j == yoffset * yscale :
                    ith_line += "*"
                else :
                    ith_line += " "
            ith_line += "*"
        else :
            for j in range(1, yoffset * yscale) :
                if j == int(yi) :
                    ith_line += "*"
                else :
                    ith_line += " "
            ith_line += "*"
        print ith_line


# In[15]:

very_simple_plot_with_x_axis(sin, 0, 14, .2, 20, 2)


# Out[15]:

#                                            *
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