$(40$ points$)$ Create a source file named fmlxxxx$\_$proj$3\_$vector.c$.$ In this file create a set of functions that

process a single dimension array $($vector$)$ of doubles of arbitrary length for each operation listed below.

Make sure you don't have any printf statements in this file!

$5\mathrm{.}1.$ Add $($element by element$)$ two vectors of doubles. Name this function vect$\_$add$().$

$5\mathrm{.}2.$ Subtract $($element by element$)$ two vectors of doubles. Name this function vect$\_$sub$().$

$5\mathrm{.}3.$ Multiply $($element by element$)$ two vectors. Name this function vect$\_$prod$().$

$5\mathrm{.}4.$ Compute and return the dot product of two vectors. Name this function vect$\_$dot$\_$prod$().$ The dot

product operation is the result of taking two vectors $($single dimension arrays$)$ and multiplying

corresponding element by element and then adding up the sum of all the products. For example, if I

have $2$ vectors of length $3$ that have the following values $\{$l$,2,3\}$ and $\{3,2,$ l$\}$ the dot product of these

two vectors is: $1*3+2*2+3*1=10$

$5\mathrm{.}5.$ Compute and return the mean of a single vector. Name this function vect$\_$mean$().$

$5\mathrm{.}6.$ Compute and return the median of a single vector. Name this function vect$\_$median$().$ First sort

the array. If the length of the sorted array is odd, then the median is the middle element. If the

length is even, the median is the average of the middle two elements. You can use the bubble sort

algorithm covered in class, provided by the book.

$5\mathrm{.}7.$ Compute and return the maximum element of a vector. Name this function vect$\_$max$().$

$5\mathrm{.}8.$ Compute and return the minimum element of a vector. Name this function vect$\_$min$().$

$5\mathrm{.}9.$ Write a function that reverses the elements in a given array. This function will change the original

array, passed by reference. Name this function vect$\_$reverse$().$

$5\mathrm{.}10.$ The header for fmlxxxx$\_$proj$3\_$vector.h should contain the following function prototypes. Notice that

for the first three functions, the result is stored in array ans$[],$ it is not "returned".

void vect$\_$add$($ const double x$[],$ const double y$[],$ double ans$[],$ unsigned length $)$;

void vect$\_$sub$($ const double x$[],$ const double y$[],$ double ans$[],$ unsigned length $)$;

void vect$\_$prod$($const double x$[],$ const double y$[],$ double ans$[],$ unsigned length$)$;

double vect$\_$dot$\_$prod$($ const double x$[],$ const double y$[],$ unsigned length $)$;

double vect$\_$mean$($ const double x$[],$ unsigned length $)$;

double vect$\_$median$($ const double x$[],$ unsigned length $)$;

double vect$\_$max$($ const double x$[],$ unsigned length $)$;

double vect$\_$min$($ const double x$[],$ unsigned length $)$;

void vect$\_$reverse$($ double x$[],$ unsigned length $)$;

Notice that a template header file is provided for you on myCourses $($cabeee$\_$proj$3\_$vector.h$).$

Rename the template to fmlxxxx$\_$proj$3\_$vector.h$,$ and make sure that you change the macros

$($#define$$s$)$ once your code is compiling properly. For example, change:

#define VECT$\_$ADD$\_$WORKING FALSE

to this:

#define VECT$\_$ADD$\_$WORKING TRUE

once the vect$\_$add$()$ function is working properly.

$5\mathrm{.}11.(20$ points$)$ Create a $2$nd source file and name it fmlxxxx$\_$proj$3\_$vectortest.c$.$ In the main$()$ of this file

create an array of the values of a sine wave. Include the math.h header to use the sin floating point

function. The function sin takes an argument of radians $($not degrees$).$ Make your array $721$

elements and initialize each element with $10*$ sin$(2*3\mathrm{.}1416*($i$/360\mathrm{.}0))$ where i is the array index

from $0-720.$ When done properly, the array should contain approximately $2$ complete sine wave

cycles. Similarly, create an array of $721$ elements only this time initialize it with a cosine function

with amplitude $5.$ Have the program process and compute the following $($in the order given$)$; display

the title of the action and answers on the screen by using printf statements:

$5\mathrm{.}11\mathrm{.}1.$ The maximum value of the cos and sin array added together. $($first add cos and sin arrays,

THEN find the maximum of that resulting array$).$

$5\mathrm{.}11\mathrm{.}2.$ The mean value of the sin array

$5\mathrm{.}11\mathrm{.}3.$ The mean value of the element by element product of the sin and cos$.$

$5\mathrm{.}11\mathrm{.}4.$ The median value of the cos array.

$5\mathrm{.}11\mathrm{.}5.$ The dot product of the cos and sin array.

$5\mathrm{.}11\mathrm{.}6.$ The dot product of a reversed cos array with a sin array