gibson:teaching:spring-2016:math445:lab5

Matlab vocabulary for this lab

for fprintf function mean std * length size rand randn

**Problem 1:** Write a **for** loop that will print statements of the form

1 times pi is 3.1416 2 times pi is 6.2832

for the numbers 1 through 10.

**Problem 2:** If is a temperature in Farenheit, then is the same temperature in Celsius. Write a function `farenheit2celsius`

that takes a Farenheit temperature as input, converts it to Celsius, prints a statement of the form `20 Farenheit is -6.6667 Celsius.`

, and returns the Celsius value as its output.

**Problem 3:** Write a **for** loop that uses the above function to print a list of statements

-10 Farenheit is -23.3333 Celsius. 0 Farenheit is -17.7778 Celsius.

for Farenheit temperatures from -10 to 100, in steps of 10.

Challenge: Get the text to line up nicely using field-width specifiers in fprintf!

**Problem 4:** Write a function `average`

that takes an input vector and returns as output the average (mean) value of its elements, according to the formula

where is the number of elements in .
Test your function by comparing its output to the output of the built-in Matlab function **mean** on a random vector of length 100 whose elements are uniformly distributed between 0 and 1.

**Problem 5:** Write a function `deviation`

that takes an input vector and returns the standard deviation of its elements, according to the formula

where is the average the elements of , and is the number of elements in .
Test your function by comparing its output to the output of the built-in Matlab function **std** on a random vector of length 100 whose elements are in a normal (Gaussian) distribution about .

**Problem 6:** The formula for matrix-vector multiplication is

In this formula, is an matrix, is an -dimensional column vector, and is an -dimensional column vector.

Write a function `matvecmult`

that takes a matrix and a vector as inputs, computes according to that formula, and returns the vector . Compare your `matvecmult`

to Matlab's built-in matrix-vector multiplication operator `*`

on a random matrix and a random 4d column vector.

**Problem 7:** The formula for matrix-matrix multiplication of an matrix and an, matrix is

The product is an matrix.

Write a function `matmatmult`

that takes a matrix and a vector as inputs, computes according to that formula, and returns the matrix . Compare your `matmatmult`

to Matlab's built-in matrix-vector multiplication operator `*`

on a random matrix and a random matrix B.

gibson/teaching/spring-2016/math445/lab5.txt · Last modified: 2016/02/18 08:36 by gibson