#!/usr/bin/env python
# coding: utf-8

# # 2.18 Programming for Geoscientists class test - example paper based on 2012 2.18 exam

# #Test instructions
# 
# * This test contains **5** questions each of which should be answered.
# * Write your program in a Python cell just under each question.
# * You can write an explanation of your solution as comments in your code.
# * In each case your solution program must fulfil all of the instructions - please check the instructions carefully and double check that your program fulfils all of the given instructions.
# * Save your work regularly.
# * At the end of the test you should email your IPython notebook document (i.e. this document) to [Gerard J. Gorman](http://www.imperial.ac.uk/people/g.gorman) at g.gorman@imperial.ac.uk

# **1.** Ignore this question from 2012 as it deals with material we have not discussed this year.

# **2.** Write a program, that creates a *list* $t$ with 6 values, 0.1, 0.2, ..., 0.6. Compute a corresponding *list* $y$ of $y(t)$ values using the formula:
# $$y(t) = v_0t − gt^2,$$
# where $v_0=6.0$ and $g=9.8$.
# 
# * Store these two lists, t and y, in a new list t1.
# * Write out a table with a column of t and a column of y values by traversing the data in the nested t1 list.
# * You may use list or NumPy array for t and y.
# * Print out a table header with the column names ’t’ and ’y’.
# * For printing the table, iterate the nested list t1, do not access the previously computed t and y lists directly.
# * Print out the table t1 using format specifiers so that the columns are aligned.

# In[1]:


t = [0.1*i for i in range(1, 7)]
v0 = 6.0
g = 9.8
y = [v0*ti-g*ti**2 for ti in t]
t1 = []
for ti, yi in zip(t, y):
    t1.append([ti, yi])
    
print "%8s%8s"%("t", "y")
for pair in t1:
        print "%8g%8g"%(pair[0], pair[1])


# **3.** The factorial of n, written as n!, is defined as:
# $$n! = n(n − 1)(n − 2)...2\cdot1,$$
# with the special cases
# $$1! = 1, 0! = 1.$$
# For example, $4! = 4\cdot3\cdot2\cdot1 = 24$, and $2! = 2\cdot1 = 2$.
# 
# * Write a function fact(n) that returns $n!$. You **must** not use the *fact* function from the math module.
# * Return 1 immediately if $x$ is 1 or 0, otherwise use a loop to compute $n!$.
# * The function must be called *fact* and take a single argument called n.
# * The software should check that the supplied value is a non-negative integer. If it is not, raise a ValueError exception.

# In[2]:


def fact(n):
    if type(n) != int:
        raise ValueError("value must be of type int")
    if n < 0:
        raise ValueError("value must be positive")
    if n<2:
            return 1
    product = 1
    for i in range(1, n+1):
        product *= i
    return product

# Let's show that it works
for i in range(5):
    print "%d! = %d"%(i, fact(i))


# **4.** A table of temperatures and densities, in units of degrees ($C$) and $kg/m^3$, are given in the file *data/density\_air.dat*
# Write a program that reads in the data from file into a list for temperature (first column) and density (second column) and plots the variation of density against temperature.
# 
# * The input file contains blank lines and lines starting with a ’#’, which you must ignore when reading in the data.
# * You may use list or NumPy array for temperature and density.
# * Plot the variation of density against temperature.
# * Label the x axis "Temperature (Celsius)" and the y axis "Density ($kg/m^3$)".
# * Use the plot title "Density of air at different temperatures, at 1 atm pressure".
# * Display a legend with the label ’Air’.

# In[3]:


get_ipython().run_line_magic('pylab', 'inline')
from pylab import *

file = open("data/density_air.dat")
tlist = []
dlist = []
for line in file:
    words = line.split()
    if len(words) != 2:
        continue
    try:
        t = float(words[0])
        d = float(words[1])
    except:
        continue
    tlist.append(t)
    dlist.append(d)
tarray = array(tlist)
darray = array(dlist)

plot(tarray, darray)
xlabel("Temperature (Celsius)")
ylabel("Density ($kg/m^3$)")
title("Density of air at different temperatures, at 1 atm pressure")
legend(("Air", ))


# **5.** Based on the data in the file *data/constants.txt*, make a dictionary where the keys are the names of the physical constant and the values are a tuple containing the numerical value and the units.
# 
# * Use a Python dictionary to store the data.
# * All numerical values should be of type float.
# * Print out the dictionary without any formatting.

# In[4]:


file = open("data/constants.txt", "r")
constants = {}
for line in file:
    try:
        name = line[0:27].strip()
        
        words = line[27:].split()
        value = float(words[0])
        units = words[1]
    except:
        continue
    
    constants[name] = (value, units)

print constants


# In[4]: