Julia Programming Language for Scientific Computing
University of Konstanz, SS 2015

EXERCISE SHEET 3

Read the Julia Language Documentation,
Sections 1.7 to 1.8: Strings and Functions
until Monday, April 27, and
Sections 1.9 to 1.10: Control Flow and Scope of Variables
until Thursday, April 30.

Solve the following exercises by filling in the details (JULIA code only).
Submit by email to dietmar.saupe@uni-konstanz.de by Thursday, April 30, 12 noon.

These exercises were suggested by Thomas Sargent, John Stachurski. However, find your own solutions!

Exercise 1

Part 1: 
Given two numeric arrays or tuples x_vals and y_vals of equal length, compute their inner product using zip()

Part 2: 
Using a comprehension, count the number of even numbers in 0,...,99
Hint: x % 2 returns 0 if x is even, 1 otherwise

Part 3: 
Using a comprehension, take pairs = ((2, 5), (4, 2), (9, 8), (12, 10)) and count the number of pairs (a, b) such that both a and b are even

Exercise 2

Consider the polynomial

(1) p(x)=a0+a1*x+a2*x2+⋯+an*xn
Using enumerate() in your loop, write a function p such that p(x, coeff) computes the value in (1) given a point x and an array of coefficients coeff

Exercise 3

Write a function that takes a string as an argument and returns the number of capital letters in the string
Hint: uppercase("foo") returns "FOO"

Exercise 4

The Julia libraries include functions for interpolation and approximation.
Nevertheless, let’s write our own function approximation routine as an exercise.
In particular, write a function linapprox that takes as arguments

	A function f mapping some interval [a,b] into ℝ
	two scalars a and b providing the limits of this interval
	An integer n determining the number of grid points
	A number x satisfying a <= x <= b
	and returns the piecewise linear interpolation of f at x, based on n evenly spaced grid points a = point[1] < point[2] < ... < point[n] = b
Aim for clarity, not efficiency

Exercise 5

The following data lists US cities and their populations

new york: 8244910
los angeles: 3819702
chicago: 2707120
houston: 2145146
philadelphia: 1536471
phoenix: 1469471
san antonio: 1359758
san diego: 1326179
dallas: 1223229

Copy this text into a text file called us_cities.txt and save it in your present working directory.
That is, save it in the location Julia returns when you call pwd().
Write a program to calculate total population across these cities.

Hints:

If f is a file object then eachline(f) provides an iterable that steps you through the lines in the file.
int("100") converts the string "100" into an integer.