## Continuing with graphing

### Plotting a function

# In[1]:

def simple_plot_data(fn, xlow, xhigh, xstep=1, yscale=1, yoffset=0) :
    """This function cooks up data points for a very obnoxious looking graph of the function."""
    
    retval = []
    x = xlow
    while x < xhigh + xstep :
        y = fn(x)
        retval.append((x, (y + yoffset) * yscale))
        x += xstep
    return retval


# To try it out :

# In[2]:

simple_plot_data(lambda x : x*x, 0, 10)


# Out[2]:

#     [(0, 0),
#      (1, 1),
#      (2, 4),
#      (3, 9),
#      (4, 16),
#      (5, 25),
#      (6, 36),
#      (7, 49),
#      (8, 64),
#      (9, 81),
#      (10, 100)]

# In[3]:

simple_plot_data(fn=lambda x : x*x*x, xlow=-10, xhigh=10, xstep=2, yscale=0.04, yoffset=1000)


# Out[3]:

#     [(-10, 0.0),
#      (-8, 19.52),
#      (-6, 31.36),
#      (-4, 37.44),
#      (-2, 39.68),
#      (0, 40.0),
#      (2, 40.32),
#      (4, 42.56),
#      (6, 48.64),
#      (8, 60.480000000000004),
#      (10, 80.0)]

# In[4]:

def simple_plot(fn, xlow, xhigh, xstep=1, yscale=1, yoffset=0, debug=0) :
    data_pts = simple_plot_data(fn, xlow, xhigh, xstep, yscale, yoffset)
    if debug > 0 :
        print "simple_plot :",
        print data_pts
    # to print the x-axis
    y_is_0 = yoffset * yscale
    if debug > 0 :
        print "simple_plot : y_is_0 = %d" % y_is_0
    # list to store the lines
    plot_list = []
    for (x, y) in data_pts :
        # String to store the line
        str_line = ""
        for i in range(max(int(y_is_0)+1, int(y)+1)) : 
            # The +1 is so that those points do get included
            if i == int(y) or i == y_is_0 :
                str_line += "*"
            else :
                str_line += " "
            if debug > 0 :
                print "simple_plot : %s" % str_line
        plot_list.append(str_line)
    return plot_list


# Let us test this

# In[5]:

for line in simple_plot(lambda x : x*x*x, -100, 100, xstep=10, yscale=.00004,yoffset=1000000) :
    print line
    


# Out[5]:

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

# In[6]:

import math
for line in simple_plot(math.sin, -math.pi, math.pi, math.pi/10, yscale=20, yoffset=1.5) :
    print line


# Out[6]:

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

### Plotting loci

# Suppose you want to plot the solutions to the equation, say $x^2 + y^2 = 1$. First we shall convert any such equation to an equation of the form $f(x, y) = 0$. In this case, $f(x, y) = x^2 + y^2 - 1$.

# In[7]:

screen = []
xlen = 25
ylen = 40


# In[8]:

def init_screen() :
    """Initiates the screen. One can also use this to clear the screen. One should use this everytime one changes the size of the screen."""
    global screen
    global xlen
    global ylen
    
    screen = []
    for i in range(xlen) :
        screen.append([])
        for j in range(ylen) :
            screen[i].append(' ')
        # print screen
        # print "************************************************************"


# In[9]:

init_screen()
print screen


# Out[9]:

#     [[' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '], [' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ']]
# 

# In[10]:

def print_screen() :
    firstline = True
    rule = " "
    for line in screen :
        line_str = "|"
        for char in line :
            line_str += char
            if firstline :
                rule += "-"
        line_str += "|"
        if firstline :
            print rule
            firstline = False
        print line_str
    print rule


# In[11]:

init_screen()
print_screen()


# Out[11]:

#      ----------------------------------------
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#      ----------------------------------------
# 

# In[12]:

def print_error(function, warning_type, warning_string) :
    """warning_types : w, e, i"""
    can_cont = 1
    warning_dict = [("w", "Warning"),                    ("e", "Error"),                    ("i", "Info")]
    warning_fullform = ""
    for (s, term) in warning_dict :
        if s == warning_type :
            warning_fullform = term
    if warning_fullform == "" :
        print "Error : print_error : Invalid error type."
    print "%s : %s : %s" % (warning_fullform, function, warning_string)
    if warning_type == "w" or warning_type == "i" :
        can_cont = 0
    return can_cont


# In[13]:

def plot(x, y) :
    global screen
    
    cont = 0
    if x < 0 or x >= xlen :
        cont += print_error(plot, "e", "x out of range")
    if y < 0 or y >= ylen :
        cont += print_error(plot, "e", "y out of range")
    if cont == 0 :
        screen[x][y] = "*"


# In[14]:

init_screen()
for i in range(29) :
    plot(i, 2*i)
print_screen()


# Out[14]:

#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : x out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : x out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : x out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#     Error : <function plot at 0x1ba0488> : x out of range
#     Error : <function plot at 0x1ba0488> : y out of range
#      ----------------------------------------
#     |*                                       |
#     |  *                                     |
#     |    *                                   |
#     |      *                                 |
#     |        *                               |
#     |          *                             |
#     |            *                           |
#     |              *                         |
#     |                *                       |
#     |                  *                     |
#     |                    *                   |
#     |                      *                 |
#     |                        *               |
#     |                          *             |
#     |                            *           |
#     |                              *         |
#     |                                *       |
#     |                                  *     |
#     |                                    *   |
#     |                                      * |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#      ----------------------------------------
# 

# In[15]:

def clever_plot(x, y, origx=xlen-1, origy=0) :
    cont = 0
    x = int(x)
    y = int(y)
    array_x = origx - y
    array_y = origy + x
    if array_x < 0 or array_x > xlen - 1 :
        cont += print_error(clever_plot, "e", "x out of range")
    if array_y < 0 or array_y > ylen - 1 :
        cont += print_error(clever_plot, "e", "y out of range")
    if cont == 0 :
        plot(array_x, array_y)


# In[16]:

for i in range(50) :
    clever_plot(i, i)
print_screen()


# Out[16]:

#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#     Error : <function clever_plot at 0x1ba02a8> : x out of range
#     Error : <function clever_plot at 0x1ba02a8> : y out of range
#      ----------------------------------------
#     |*                       *               |
#     |  *                    *                |
#     |    *                 *                 |
#     |      *              *                  |
#     |        *           *                   |
#     |          *        *                    |
#     |            *     *                     |
#     |              *  *                      |
#     |                *                       |
#     |               *  *                     |
#     |              *     *                   |
#     |             *        *                 |
#     |            *           *               |
#     |           *              *             |
#     |          *                 *           |
#     |         *                    *         |
#     |        *                       *       |
#     |       *                          *     |
#     |      *                             *   |
#     |     *                                * |
#     |    *                                   |
#     |   *                                    |
#     |  *                                     |
#     | *                                      |
#     |*                                       |
#      ----------------------------------------
# 

# In[17]:

init_screen()
for i in range(-5,5) :
    clever_plot(i, 1-i, xlen/2, ylen/2)
print_screen()


# Out[17]:

#      ----------------------------------------
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |               *                        |
#     |                *                       |
#     |                 *                      |
#     |                  *                     |
#     |                   *                    |
#     |                    *                   |
#     |                     *                  |
#     |                      *                 |
#     |                       *                |
#     |                        *               |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#      ----------------------------------------
# 

# In[18]:

def fn_plot(fn, xlow, xhigh, ylow, yhigh, error=.001) :
    init_screen()
    xscale = float(xhigh - xlow) / ylen
    yscale = float(yhigh - ylow) / xlen
    for i in range(ylen) :
        for j in range(xlen) :
            x = (xlow + i * xscale)
            y = (ylow + j * yscale)
            if abs(fn(x, y)) < error :
                clever_plot(i, j)
    print_screen()
    


# In[19]:

def circle (x, y) :
    return x*x + y*y - 1
fn_plot(circle, -2, 2, -2, 2, .122)


# Out[19]:

#      ----------------------------------------
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                  *****                 |
#     |               **       **              |
#     |             **           **            |
#     |            *               *           |
#     |           *                 *          |
#     |          *                   *         |
#     |          *                   *         |
#     |          *                   *         |
#     |          *                   *         |
#     |           *                 *          |
#     |            *               *           |
#     |             **           **            |
#     |               **       **              |
#     |                  *****                 |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#      ----------------------------------------
# 

# In[20]:

def parabola (x, y) :
    return (x*x - 4*y)
fn_plot(parabola, -10, 10, -1, 5, .6)


# Out[20]:

#      ----------------------------------------
#     |                                        |
#     |                                        |
#     |                                        |
#     |            *               *           |
#     |                                        |
#     |                                        |
#     |                                        |
#     |             *             *            |
#     |                                        |
#     |                                        |
#     |              *           *             |
#     |              *           *             |
#     |                                        |
#     |               *         *              |
#     |                                        |
#     |                                        |
#     |                *       *               |
#     |                 *     *                |
#     |                 *     *                |
#     |                  ** **                 |
#     |                   ***                  |
#     |                                        |
#     |                                        |
#     |                                        |
#     |                                        |
#      ----------------------------------------
#