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.