Plotting and Output - MATLAB Video Lecture | MATLAB Programming for Numerical Computation - Software Development

hello and welcome to matlab programming for
numerical computations
we are at the end of module 1 this module
we are covering introduction to m atlab programming
in lecture 1.5 we are going to cover plotting
and output using matlab ok
ok we have seen various forms of of output
in the first 4 lectures of this particular
module and what we have seen is that when
we do not end of particular line with the
semicolon the variables will echo on this
screen ok that is one of the way of displaying
on the screen the
other way that we had used in the previous
lecture was to use the command called disp
or display ok so that is the displaying on
the screen that we are going to cover in this
lecture i am also going to cover how to plot
the data using what is known as the plot command
ok for more help on plotting we can go to
matlab website called using basic plotting
functions the link for which is given over
here
so let us now focus of the attention to displaying
on the screen and these are the various examples
that we have taken on how to display on the
screen the first one is when you give a command
b equal to 1 2 7 1 with a semicolon there
will not be any echo but if you do not give
this trailing semicolon this particular result
will be displayed on the screen this is what
we have seen in lecture 1.1 as well as multiple
times
the other way to display is using the command
disp display it will going to it is going
to display the contains of this variable b
ok on the screen
the third way is to use oh displ display a
more more advanced version of of it and display
can be used in order to display certain texts
such as disp hello world will display this
particular text on the screen ok and that
idea can be used to make a more beautiful
output so let us go at matlab and look at
this ok
ya ok we have this b equal to 1 7 say 1 3
close this and press enter i am going to give
get this as an echo ok so this is what we
have seen multiple times same thing if i am
going give this b if this is going to display
the contents of b but it is not going to give
the initial part that is b equal to part that
we see what here when I will click on this
b and press enter this is what I am going
to see ok like wise if i give this hello world
it is going to display that is string as it
is ok so display the string hello world ok
if we recall what we had done in the previous
lecture using my factorial this was what i
had shown as aware to display the factorial
value ok what does that do let we just copy
this ok and paste toward here and let us go
over each on this ok so this uses basically
the same rules as we do of with respect 2
brackets the innermost bracket is what is
going to be executed first so this is the
innermost bracket and let us look at that
let us removed rest of the stuff and let us
look at this
this is the innermost bracket so this particular
___ is a string that says factorial value
colon space and this is a command with says
num2str myfact ok so let us look at what numb2str
does and for that we will do help numb2str
ok numb2str converts a number into a string
so let us look at what say numb2 let us say
myfact equal to 6 factorial so we can using
____ 1 to 6 and that gives the value myfact
as 720 because i did not end this command
with semicolon I got the result
myfact equal to 720 ok what happens if i give
let us we just clear the screen clc num2str
myfact if I give this command let us we saw
what happens ok what happens is again ans
equal to 720 so how this this ans differ from
myfact let us look at the work space for here
ans that you see of here is as a string that
we know that it substring because it
has the apostrophe is slash sign in the front
and back which means this is not a number
720 but it is consists of 3 characters first
character is a 7 second character is 2 and
third character is 0 ok so that is the difference
between ans and myfact ok let us look again
at that particular display command control
c and control v the display command and let
us look at the innermost bracket of the display
command that we had done earlier so now we
have the square bracket which has one part
of the string and then we are catenating the
other part of the string ok so let us a similar
thigh again let us say part 1 that is the
first part and we say part 2 and let us see
what happens ok what we should get is the
words part space 1 part space 2 there is no
space between 1 and p of the second part that
is what result we expect press enter and that
is exactly what we get ok now we replays
part 2 with this ans value is 720 and we were
to repalys part 1 with factorial value equal
to this what we are going to get this factorial
value colon space ok and 720 ok that is also
in slashes because this is a string when i
press enter I am going to get factorial value720
ok so what i want to do is replays that 720
with myfact if i do this i
just replace it with myfact what i am going
to get is i am trying to take a string and
next string i am trying to put a number ok
when I try to do that what i get is i do not
get anything over here because that number
is not converted into ask key characters 720
i am just getting factorial value colon followed
by some kind of a character that you probably
cannot see _____ ok so instead what we need
to do is
used the num2str command to convert 720 into
720 as 3 characters and when i do that I am
going to get factorial value colon 720 ok
now i did not want this ans to display to
be displayed like this in order to do that
I am going to give command with says disp
dis sorry disp and in circular brackets and
give this I am going to get factorial value
720 without this ans equal to factorial value
720 i will just clear the screen and type
again when i give this disp factorial value
colon numb2str myfact and i press enter this
is just displayed as is on the screen so this
is what disp
function is going to do this ok so a more
beautiful can be created using disp and using
numb2str ok sometimes we want to type out
more complex things we want to output more
complex things on the screen and for that
we want to use the function fpintf the syntax
is fprinf is a similar to what we follow in
c ok however in this particular lecture series
we are not going to cover fpintf for all our
purposes in this particular lecture series
the disp function is going to be sufficient
however for the ___ of completeness i have
given more advanced output using fprintf
ok so that covers the outputting on the screen
part let us now look at how to plot ok so
we will consider the example of the ball thrown
vertically upwards we will plot location versus
time we will lable the axes and we will go
the more other features of plotting ok
so let us go back to matlab and the function
that we are going to use for plot is a function
called plot so let us look at help for this
help plot and this is what we are going to
get okay for now let us ignore the overloaded
method part that is not of a concern for us
right now that is go right at the top and
what does plot do plot linear plot plot x
comma y plots vector y versus vector x if
x or y
is a matrix then the vector is plotted against
rows or columns of the matrix whichever line
up okay so plot is a very very powerful way
of plotting things okay so plot x comma y
is going to plot y as a function of x okay
let us take that example that we had done
a couple of lectures earlier which is of ball
being throwing vertically upwards this was
the script that we had used for the ball that
was being thrown vertically upwards okay when
run this particular script what we got was
we are getting this display at multiple times
okay
recall what we have just done a couple of
minutes back when we talked about the disp
command and when we used this disp command
using multiple num2str the result that we
are going to get is as we can show in the
screen okay at various times we are getting
the values of the location where the ball
is okay so now what we want to do is we want
to capture all of these in 2 vectors let us
called the 2 vectors time and location so
time equal to let us make the blank vector
location equal again to a blank vector okay
for let us actually put as time equal to 0
and location is equal to 0 because that is
what we have starting with it okay and at
end of this we will put t sorry time equal
to time semicolon t what that is going to
do is at each time this y _____ the new value
of time t is going to be catenated to this
time vector and likewise we will do location
is equal to location y okay and finally we
want to plot this and we will give the command
plot time comma location enter semicolon save
this okay
and we execute this and we will clear the
screen first and we will just execute ball
vertical and this is going to plot okay so
this is the trajectory of that particular
ball as the ball goes from time 0 to time
4 okay now what we want to do is we want to
label these two axis the x axis is time and
y axis is location we do that the x axis we
will label it by using the command x label
time and time was in seconds enter and y label
is location and location was in meters okay
and let us go to again that figure again and
now we this has been local label time and
it has been label location now let us say
that what want to say increase the font size
of this way to that just click
on this arrow right click click on font and
we will be able to increase the font size
to 14 likewise we will increase the font size
again to 14 and we can do this with the access
as well we click on font and make the font
size 14 and we will get this particular figure
and now we have the font size increased to
14 okay now there are options to change the
way of this particular line that was displayed
and also the way to do that again is using
the plot command so okay
again this we can be done with plot command
and the way to do is plot time comma location
comma give matlab how to plot this and for
example we wanted a dash line which is red
in color we will give dash dash r that will
plot a red dash line okay let us go and see
this okay and what we now have is a red dash
line as seen over here now instead if we wanted
to have dash dot line which is green in color
we will change it to dash dot g that will
plot a line that is green dash dot in color
okay instead now if we wanted in addition
to that we also wanted let
us say to plot circles at the end of it a
blue color line with circles far at the various
locations we will do dash b followed by o
and o will tell matlab that each data point
we want to have a marker that is circled press
this enter and let us see what happens at
each data point we now this circled plot it
as we seen over here we can also change the
size or thickness of this line again by right
clicking this line styles we have different
styles of lines as well as line
width we can change this let us say the line
width of 2.0 again this markers we can change
the markers to two different types of markers
as we can have plus sign, circle star square
diamond and so on so if we wanted a star we
can press this and we will get star and so
on okay so these are multiple ways of one
plotting and manipulating the plot okay now
let us say we wanted to plot multiple things
on the same plot how we can do that so for
that lets us have a value of x let us say
x equal to 0 to 5 in steps of 1 okay and let
us say now we want to took
plot sin x and cos x so all we need to do
plot x comma sin x comma dash b that will
be blue color line and x comma cos x comma
dash r sorry let us say dash dash r that will
be the red dash line when we will do that
this is what we are going to get okay i actually
made a mistake when i type x i did x in the
steps of 1 that is reason why we got plot
in that particular manner if i had x equal
to 0 to 0.15 and then I give the plot command
and let us see what happens and we now
get a smoother plot okay now we have this
particular blue line and this red line both
of them are plotted on the same plot okay
so the way to do this when we have multiple
x and y vectors we can have them comma separated
and we will be getting multiple plots okay
another way to do this is also define a matrix
let us say
equal to sin x colon cos x okay let us type
size of y okay so y has 2 rows and 51 columns
that basically means we have the first row
is sin of x and second row is cos of x and
let say when we do plot x comma y we are going
to get plot of the 2 lines and 2 lines will
be plotted
using a default way of plotting and default
is the first line going to be blue dash and
second line is going to be a green dash okay
so this is the default way of plotting using
matrices rather than using vectors okay so
you can plot multiple lines on the same plot
and let say now we wanted to plot third line
over here but if let say what happens if we
do plot x comma say sin x plus cos x okay
what we will see this we will get only one
single line and that is because when we
do two that the previous plot gets overwritten
and that is why we are getting a single line
as seen over here okay if we do not want the
previous plot to get overwritten we need to
use the command hold on so let see how that
works of close that plot let me plot x comma
y again as before okay so these are the two
lines blue and green lines now if i do not
want to erase that plot i will give command
hold space on okay and now when I plot x comma
sin x plus cos x this is what i am
going to get let me go to this file again
okay so these were the original 2 lines in
blue and green color and this is third line
that get got plotted in blue color now let
say we wanted we actually wanted to plot this
in red color what we will do just click on
this and delete this particular line okay
and plot this say using dash dash or that
will give me a red dash line on this figure
okay so this is the way you can use the plotting
commands okay so what we have done this we
have look plotting location versus time we
have looked at way to label the axis, we have
to look certain other
plotting options and we have seen how to plot
multiple lines using matrices as well as how
to plot multiple lines using hold on the final
thing is how to plot loglog plot so far that
again we have to go to mat log and we do not
know how to plot a loglog plot so let us just
do help log and see whether we can find out
how to plot loglog plot okay at the end close
to the end of the help we will see see also
okay and
see also we will give you commands that are
related to plot so there are plottools semilo
x semilog y loglog and so on so far and log
log is probably the one that we need to use
so let us just click on loglog and look at
that help lo log is nothing but a log log
scale plot log log you works in exact same
way as plot except the scales are logarithmic
okay so let say I do loglog x comma and y
I am going to have x and sin x and cos x on
loglog plot and this is how I am going to
get okay so what is the funny things that
is happen door here so okay remember sin x
and cos x have negative values what we happened
when we plotted using a loglog is that the
negative data that was ignored during the
plotting so only the positive data were plotted
in the loglog plot okay so what we have covered
is the basic plotting functions we have covered
how to label the plot we have covered how
to plot multiple lines how to use hold on
in order to keep the previous lines we have
looked at how to change the phones for axis
labels as well as the axis titles we have
also look at plotting loglog plots in the
same way we can plot semilog plot using either
semilog x or semilog y command okay with that
we come to end of this particular lecture
also to the end of this module before I end
I will quickly recap in the next minute or
so what we covered in this module for what
we covered in this module was introduction
to matlab programming we looked at matlab
basics familiarized ourselves with matlab-
command window and matlab editor we looked
at variables scalars vectors and arrays and
became comfortable using array operations
okay we also looked at both scalar as well
as matrix operations a multiplied by b using
a star b as well as a dot star b where that
was an element by element multiplication so
these so both of these types of mathematical
operations we covered we also covered trigonometric
operations covered operations such as some
prod come some come prod and so on so
for so why range of operations we have covered
in lecture 1.2 we have also look at arrays
and use arrays unlock the potential of matlab
compared array operations versus elemental
operations and use arrays for more efficiently
using matlab let we finally go to quick example
for doing this let us consider the example
of factorial okay the better way of calculating
the factorial as we had seen rather than having
all these number of lines we can place all
of this with just a prod command my fact equal
to prod 1 colon n that is exactly going to
do what what the entire function with the
loop was going to do so I
have replaced that entire loop with this prod
command and when I execute this that is myfactorial
i get the exact same result but in unmore
efficient way okay so this was something that
is one of the most important features of matlab
that it was able to work with arrays and we
will need to be comfortably working with arrays
to unlock the full potential of matlab of
course this is going to come with lot of practice
us to get more and more using the matlab you
will find we are using arrays in much more
efficient way we then used look at execution
control looked at for loop and while loop
if then statements is
something that we have not exactly covered
but essentially if then statements are used
when we want to compare certain condition
if that condition is met certain commands
or executive if it is not met then certain
other commands and if there is statement or
executed again if you do help if we will get
how to use the if then commands and then we
looked at matlab scripts and functions we
also in detail covered when to use scripts
versus functions when to use functions and
finally we will add plotting in outputting
in matlab okay so that we come to the end
of the first week we come to the end of module
1 and the next module we are going to cover
errors, error analysis and approximations
and using numerical techniques so thank you
and see you next week bye.