MATLAB Tutorial: Using Arrays Video Lecture | MATLAB Programming for Numerical Computation - Software Development

hello and welcome to matlab programming for
numerical computations course we are in module
1 which is introduction to matlab programming
ah today we are going to ah revisit lecture
1 point 2 where we had discussed some of the
array operation in matlab we are going to
take 1 simple example to look at how the array
operations can be fairly pow powerful tool
in matlab so the example
that we are going to take basically on marks
that are earned by 6 students in 4 different
courses the courses are mathematics programming
thermodynamics and mechanics and the marks
that are obtained by the 6 students are listed
over here we are going to undergo certain
computations that we did ah in the previous
lectures ah we are going to revisit them with
this specific example
so the computation that we are going to do
is first we will create a matrix called allmarks
which will contain the marks for the first
3 courses the 3 courses are math programming
and thermodynamics for all of the 6 students
and then when the mechanics marks come in
from the teachers for mechanics we are going
to add those marks or append those marks to
the matrix that we are formed ah if you recall
what we said in the in the previous lecture
ah basically this is going to be a matix which
has 6 rows and 4 columns and therefore is
going to be 6 by 4 matix after we have appended
the mechanics marks
once we have done at appending the marks for
the mechanics course we are going to do several
computations ah first is going to be the scaling
the marks for the various for the mechanics
course we are going to extract the marks of
chetan ah and give it to him as well as calculate
his total marks ah 2 of our students deepak
and farah ah are the best students so we are
going to extract the marks for the first 3
courses for these 2 students we are going
to calculate average marks and we are going
to scale all the marks out of 10
and we are going to use 1 of the matrix fundaes
for this ah in matrix multiplication so if
you have matrix of this sort ah a b c d e
f so we have 3 rows and 2 columns and we multiply
this with a diagonal matrix of this form ah
we are post multiplying with the diagonal
matrix what is going to happen
over here is that the number 2 is going to
multiply with the first row and the number
0 point 1 sorry first column and the number
0 point 1 is going to multiply with the ah
second column and this is the result that
we are going to get ah you can just simply
do this matrix multiplication and see this
for yourself so ah a
multiply by 2 plus b multiply by 0 is going
to be 2a a multiply by 0 plus b multiply by
point 1 is going to be 0 point 1b so on and
so for okay so if we want to scale all the
marks out of 10 this is the kind of computation
that we need to do remember that at this stage
the marks for the 3 lecturers
are going to be out of 100 where as eventually
the marks for mechanics
is going to be out of 50 so thats what we
are going to do in matlab so let go to matlab
to do this array operations
okay ah so rather than typing out all the
stuff i have already created a file which
calculates the marks for 3 cour courses for
all the 6 students and we also given mechanics
marks in another vector called mechmarks okay
so lets type allmarks sorry lets
type mark list and when we execute this we
are going to get allmarks and mechmarks as
the 2 vectors so lets type allMarks okay so
these are the marks for the 6 students in
the ah 3 courses and mechmarks are the less
are the marks for all the 6 students in mechanics
course okay now what want we to do is we want
to append mechanics marks to allMarks array
so i will do this allMarks equal to allMarks
comma mechmarks okay i am going to get an
error over here but lets lets try this out
and lets see what happens the error that we
get is the error using horizontal catenation
that means what we are trying to do is we
are trying to put ah 1 by 6 array besides
at ah 6 by 3 array which is something that
we cannot do so we have this particular box
over here and we want to put this box next
to it that is something thats not possible
in matlab what we need to do is we need to
transpose this particular array and once we
transpose that array
we are going to put it next to the allMarks
array so lets try and do that and in order
to do that i will just clear the screen first
okay transposing mechmarks is the command
for that is mechmarks dash thats going to
transpose the mechmarks which is going to
result in a 6 by 1 array 6 by 1 array we can
catenated with a 6 by 3 array and thats going
to result in a 6 by 4 array okay so we can
try do that we are now going to get our allMarks
as the marks for 6 students in the 4 courses
and this is what we wanted as the result of
this first computation step at the end of
the first computation step we wanted to append
the marks for the mechanics course whenever
ah to the allMarks array whenever we receive
okay the next thing that we want to do is
we want to scale the marks for mechanics by
ah 2 marks out of 50 instead of marks out
of 100 so in that case what we need to do
is mechmarks equal to mechmarks multiplied
by 0 point 5
thats going to ah basically scale the marks
our out of 50 instead of out of 100 okay because
this is the scalar multiplication with the
vector we can actually do this and this is
not going
to be a problem and we are going to get mechanic
the marks in mechanics out of 50 so this is
going to be the marks in mechanics out of
50 okay and now what we want to do is we want
to now replace the last column with ah the
actual scaled marks okay so how do we access
the last column allMarks last column is going
to be the fourth column okay so its going
to be the 1 to 6 all the rows comma all comma
fourth column okay so this is going to access
basically the last column and all the rows
in that column so the rows is going to be
the first a element in the reference
and the column is going to be the second element
in that reference okay if we type this lets
see what we are going to get we are just going
to extract that particular column okay so
when we type this this is what is we are going
to extract okay what we want to do is not
extract but assign the the mech mechmarks
ah that were shown over here that is what
we want to assign to that particular array
so
what we are going to do is allMarks colon
comma 4 remember if we just use this colon
without any numbers ah on either side in an
array notation that means the entire column
all the rows in a particular column so that
is going to be equal to mechMarks prime because
we want to transpose that multiplied by 0
point 5 okay and when we do that we are going
to get allMarks as seen over here okay now
the reason why we are getting this in not
an integer form but a real number form
is because we have 2 marks over here 36 point
5 and 45 point 5 which are real numbers if
this was a programming language such as mat
as such as c plus plus we would have to define
allMarks as a real number vector or real number
array which is something we dont need to do
in matlab so matlab is a higher level programming
language that itself takes care of all this
conversion from integers into double procession
double procession into integer and so on and
so forth of all these numbers are by default
defined
as doubled position numbers in matlab so we
dont really worry about defining or predefining
any of the arrays in matlab okay the next
thing was to extract the marks of chetan chetan
so we have i have name the 6 students as a
b c d e f so that ah its just easier for us
to know to extract or to find what particular
ah row that
particular student belongs to so chetan is
row number 3 so we wanted to extract the marks
for chetan so ah i will say chetan marks equal
to allMarks okay we want
to extract row number 3 now so row number
3 and and all the columns from that row number
3 so we can say 1 colon 4 so because we have
colon we have 4 marks or i can just put colon
over here because we want that entire row
okay when i do that i am able to extract the
marks for chetan okay so these are the marks
for chetan now i wanted also to calculate
the total marks for chetan all i need to do
is to use the command sum chetan marks okay
and i am going to get the marks sum of the
total marks for chetan which is 224 point
5 okay so that is what i am going to get get
over here now what i wanted to do is for deepak
and farah i wanted to get their marks okay
for the first 3 courses only the deepak is
in row number 4 farah is in row number 6 and
i wanted column number 1 2 and 3 okay how
do i do that is i will clear the screen over
here allMarks okay i wanted rows row numbers
4 and 6 so in square
brackets i will put rows number 4 and 6 okay
then separated by comma and i will put all
the columns that i need and the columns that
i needed are 1 2 and 3 when i pu put that
i and type enter i am going to get the marks
of the deepak and farah in the 3 courses so
i will just type allMarks again so that we
can confirm what we have gotten so the marks
for deepak are over here which we have gotten
in the first row marks for farah are over
here which we have gotten in the second okay
so this is how
we are able to extract a sub array from any
array or matrix in matlab okay so now let
us oh next step that we wanted to do lets
go over and find out okay next what we wanted
to do is to calculate average marks obtained
in each of the 4 courses okay and the way
to compute average is in matlab is using the
command mean so lets ah lets do help mean
okay and it is lets read s equal to mean x
is the mean value of element x if x is a vector
okay for matrices s is a row vector containing
mean values of each column okay so what that
means is that if we have the vector for
example chetan marks chetan marks was a vector
if we do mean chetan marks we are going to
get the average of marks of chetan okay in
all the 4 courses okay instead what we wanted
to do is we wanted to get the mean in each
column of all the 6 rows in each columns of
all the 6 students in column number 1 likewise
all the 6 students in column no 2 3 and 4
that is exactly what the command mean does
if it operates on an array
which means that it is going to mean over
the first dimension the first dimension is
the row dimension is going to mean the first
guy with the second guy with the third guy
with the fourth guy with the 5th guy and the
6th guy in the column number 1 it is going
to repeat the same operation for column number
2 and repeat the same operation for column
number 3 and repeating the same operation
for column number 4 also so
lets try that mean of allMarks when i type
that and i press enter this is what i am going
to get so this is the mean of all the students
in the first course thats math course so the
mean the average marks in mathematics is 53
point 5 average marks in computer is 52 point
2 average marks in the third course is 61
thermodynamics and the average marks in mechanics
is 31 point 3 for all the 6 students
okay now let us say we wanted to get the sum
of marks for each student we can do some lets
do help sum over here okay and what we see
over here in 1of the things in the help section
is s equal to sum x comma dimension sums along
the dimension dim okay so lets go back to
the allMarks array over here so what we wanted
to do is we wanted to sum over all the columns
sum over column 1 plus column 2 plus column
3 plus column 4 okay so column is this second
dimension row is the first dimension column
is the second dimension
recall when we said allMarks i comma j i was
the row j was the column so i is the first
dimension row is the first dimension j is
the second dimension column is the second
dimension so we wanted to sum over each and
every column so we want to use the command
sum allMarks comma 2 okay that is going to
sum over the columns for allMarks so we will
get the sum of marks
the total marks each and every students okay
and when we do that we are going to get so
first guy is in total marks for amith and
the second guy is the total marks for bhavna
the third 1 is total marks for chetan so on
and so forth so we can see these are the total
marks for each student okay so this is what
we obtained the final thing that we wanted
to do was to scale the marks out of 10 okay
okay recall the first 3 guys are marks out
of 100 and the last guy is marks out of 50
so
remember the matrix operation that we wanted
to do the same matrix operations now
we need to do with a 6 by 4 matrix that is
matrix of 6 students and 4 lectures we wanted
to scale it to 1 tenth 1 tenth 1 tenth and
1 fifth okay because the mechanics marks is
out of 50 and not out of 100 so we what we
want to do is to create a diagonal matrix
of 4 rows and 4 columns first guy is 0 point
1 second guy is 0 point 1 third guy is 0 point
1 and the last guy is 0 point 2 because we
want to scale out of 50 to out of 10 okay
so how do we create that lets go back to our
matlab
and we will create this using a command called
diag which creates a diagonal ah matrix so
0 point 1 comma 0 point 1 comma 0 point 1
comma 0 point 2 when i give this okay and
press enter this is the matrix that i am going
to get and what i need to do is to post multiply
by allMarks with this particular matrix okay
so this allMarks multiplied by this is
going to give me scale if i pre multiply i
am ah trying to multiply a 4 by 4 array with
a 6 by 4 array 4 by 4 and 6 by 4 are not commutative
under pre multiplication so let me try this
a and s multiplied by allMarks and lets see
what i get i should get an error okay error
using star inner matrix dimensions must agree
that means the number of columns of the first
guy should be equal to number of rows of
the second guy number of columns are 4 for
our a and s but number of rows for allMarks
were 6 so this is not commutative under multiplication
but anyway this is not what we wanted what
we wanted to do was a post multiplication
i just showed you what type of errors you
can expect and what that
error really means okay so if i do allMarks
multiplied by a and s this is what i am going
to get now the marks are scaled out of 10
instead of out of 100 100 100 50 they are
now each of them are out of 10 okay again
if you we combine the 2 commands we can combine
them saying allMarks multiplied by diag okay
0 point 1 comma 0 point 1 comma 0 point 1
comma 0 point 2 square bracket closed round
bracket closed okay diag has 1 ah vector
that is an argument so there is only 1 single
argument to the command diag and that argument
is a vector which has 4 elements okay so note
this that within the circular brackets i have
created a square bracket okay so this is going
to create a vector containing point 1 point
1 point 1 point 2 and that vector is a single
argument to my diag command when i do that
i am going to get the same result
okay and if i wanted to store this in a vector
called lets say scaled marks all i have to
do is i go up key when i press up key the
previous command is visible to me and now
i say scaled marks equal to allMarks multiplied
by diag okay when i do that and press enter
i am to going to get scaled marks okay so
with this we come to the end
of the recap for lecture 1 point 2
so what ah i have tried to do in this particular
lecture is take a simple example and go over
some of the array operations that we did in
the previous lecture okay ah so as you can
see the column notations how to refer to a
particular row to a particular ah column something
that we have seen and the final thing that
we have seen is how to use some of the array
operations such as sum mean so on and so forth
okay so thank you for listening to this lecture
1 ah 1 dash 2b and i will see you in the next
lecture where we are going to cover ah how
to use for and while loops thank you