Advanced Fortran Programming : 003 : Re-visiting Modules with Statistical functions Video Lecture | Introduction to Fortran Programming (AdvancedLevel) - Database Management

hello guys my name is Aaron and welcome
to my channel this series is a series of
tutorials on advanced Fortran
programming now in this tutorial we'll
be will be looking at one application
program okay this is completely related
to statistics and this might be useful
for you know any people who are we who
wanted to use have some number crunching
related programs and off okay okay I
come to the point
this program is an application program
wherein you calculate the mean standard
deviation variance of the given data
sets and other than that we'll be
calculating the covariance and
correlation of between two data sets
okay and all these data sets are
actually one-dimensional meaning you
just meaning they're like one set of
data having a one set of data other set
of data which I have not do not have any
complications in between them kind of a
there and okay that's how it is it's not
like a big matrix kind of a stuff and
all this data will be well that will be
available as 1d array so that's how it
goes okay
I have written a small program over here
I'll walk you guys through as to what
i'm doing here i'm using i'm using a
module called us stat and I mean a
called a stat underscore funks and I
think is not this this module is
something I wrote just before just
before okay
this module contains all the statistical
functions that statistical functions
which does the mean variance standard
deviation covariance and then
correlation and then one subroutine to
print on that one D matrix just like
this subroutine is exactly the same
subroutine we saw in the in the previous
program where previous one
doing some array operations in that
match match one module it's the same in
the same separate areas kind of copy
pasted and explain how this module works
step by step okay
to include that module okay the more you
let me start underscore funks same as a
file name here okay yeah I mean
imploding they're importing that module
using this command use and then I'm
defining a parameter N equals five
okay and then okay actually I don't need
these two integers for this calculation
okay I need these two integers for these
calculations okay and then what I do is
that I've defined
eight variables here eight variables
here mean D 1 star state f DB 1 bar b1
koves underscore b12 and then mean B to
stir s theta B to carve our v2 and car
underscore b12 mean V 1 is the mean of
the data set 1 this is the standard
deviation of the data set 1 this is the
variance of data set 1 this is the mean
of the data set to this is a standard
deviation of data set 2 this is the
variance of data set 2 and this is the
this is the car covariance between this
data to data sets and this is the
correlation between the two data sets
okay and these two are one dimensional
array of size n given here these are the
two data sets
Valek Valse 1 and Val's 2 okay I said
valves want to be 48 49 50 51 52 and the
walls to to be 34 56 78 34 and 31 ok and
then I said the mean of valves 1 equals
mean is equal to mean one mean one of
Valve's 1 comma n similarly the mean of
V 2 is given by this function in this
format now I'll explain you guys how
mean one comes in this mean one is
actually a function I wrote to calculate
the mean of all
values alright okay and this is how it
goes in this stat underscore funk this
is the first function it's a real live
function of kind eight kind eight it
takes the value n as the integer and
then defines defines the size of the
incoming variable incoming matrix and a
matrix X and then mean one is nothing
but sum of all the entries of value X
you know we just like the function we
used last time so if are a function we
used last time okay
it's sum of all the entries of values
all the entries in the matrix X divided
by the real value real number of real
off the number of integer n okay since
the reason is the reason I put this in
real is because n is integer you know in
some compilers what happens is that this
division my turn BIC might become an
integer division so we're in one I don't
want that to happen just as a precaution
I'm converting that into real value and
then this is n into a real value and
using that over here so this returns act
this actually returns the average of the
1d arrays okay and now this is actually
now this line is actually a reputation
of this but it does for the second where
data sit okay and now this function c d
e f one calculates a standard deviation
of one dimensional variables this is the
mean of one develops this is the
standard deviation of one dimension
variables okay i'm passing the data set
valves 1 comma in here here i've a
supposed to come in a accordingly set
them here okay now let's see how this
standard e st double bond works okay
that function is here that function is
let's see yeah that function is here
what it does is the order does is that
it takes the value n a cancer and uses
it to set the value of x and then what
it does is that it initially inside it
it calls the function y VARs underscore
one and it passes the variables x and n
inside okay and this function will
return the variance of this value of x
okay and that variance this brought here
into the standard a way in the standard
deviation function and that variance is
take square I mean the square of that
variance square root of the variance is
done in this come in this line and the
square root of the variance the standard
deviation so that is being done over
here and then we go and then this out
this option comes over here so this
option this function actually calls
another function inside itself to do the
job okay and now the next line next line
we calculate the variance of this
function radians are the data sets using
this function and I'll and here yeah
also we saw how variance works okay now
I'll explain you guys how the variance
works it's on the top what it does is it
takes the value n and sets it to define
the size of the matrix X and I define an
integer I okay and what this I does what
I do with a this I is that I can I
calculate the mean of this this may be a
little complicated sentence to explain
okay so I'll just comment this out
comment align and explain you guys out
so suppose if you have a variable like X
2 which is actually square of all the
entries okay this can be written as i1
is 2 n okay is that being the case if
you want to write this okay you can
write like this
now what did this does is that this is a
one dimension this is a single line okay
this is a single line allocation of X X
squares X I X X X squares for all the
values for instance X if X Y if X is
like 1 2 3 4 5 X X to build like 1 4 9
16 25 and so on okay
what I did is that instead of allocating
a static memory X to a variable with X -
okay what I did is I didn't and it's not
doing that I just passed this right hand
side over here as
the argument itself so this function
calculates uses the mean function that
we defined above and in for that very
for the passing x2 it instead of passing
this entire stuff it just passes the X
square you calculates X square and
passes it okay and then here it
calculates the mean of X X okay and then
the what it does is that this takes the
difference of it takes them finds the
mean and squares it and here it takes
the mean of X squares okay and the data
center and subtract these two and this
this difference of expect they call it
mean of squares minus square of means
okay it's actually called as variance
and that is what I what is done over
here
suppose if you guys don't understand a
bit just suppose if you guys did not
don't understand this okay just look at
the code again and maybe you can write
this in a piece of paper and explain
maybe the piece of paper just compiled
it might compare this up you will find
it fine okay and that's what the very
variance function does what a raelians
function this is that cause the main
function inside to get the variance and
standard deviation does is that after
finding the mean okay
it calls the variance function which in
turn calls the mean function
so once the mean functions are done the
radience calculates and the radiance
returns one value and then that variance
is just an additional here so it's like
- it's like here if this is the lab on
wall level one call where variance will
be a level two call and that mean will
be a level three curve so you have three
levels of function calls over here okay
and then okay what we lose that we
calculate the covariance of these two my
values in this line
now how this covariance works is this
over here
what it does this what does the
covariance mean is that it actually is
the simple this function takes the value
of N and n and defines the sizes of x
and y okay and I need an integer just
like how we did
the variance variance now what
covariance does is that the form of
covariance is like this it takes the
mean of excite the XS star Y I of all
the values of I okay just like what we
did over here here we calculate X square
now what it does is that the covariance
by definition is actually the mean of X
prime mean of XY minus mean of x times
mean of Y so that's what it does this
one this line this part calculates the
mean of X Y because this by definite
this this statement is actually the this
statement is actually ex-wife meaning
each and every value of x corresponding
to the value of I is multiplied to get
the value of x y and that does take an
mean over here and then you have mean of
X calculator here and we know Y
calculated here I'd write this in two
separate lines because it's crossing the
margin limit so anyway so this
calculates the mean of X Y the
Seattleite the mean of X this catalyst
the mean of Y so ultimately this guy
class of covariance of X covariance
between these two variables
and this is and this is like this is
simple nothing much and then finally the
last function okay
last function correlation between these
two data sets it's given by this
function car underscore one two no car
underscore one two is simple it's a
little tricky this requires this
requires a little more careful
concentration okay it defines the value
and it gets the value and and uses that
to define the variables x and y and then
what car underscore does sister it
calculates the covariance of the data
sets x and y okay and it calculates the
standard deviation of X and calculates
the standard deviation of y separately
and what it does is that it multiplies
the standard deviation of X and mass on
I deviation of y and this product is
kept Tacitus is kept in the denominator
that I saw the numerator you have asked
of a covariance of one well so
covariance of a inside the correlation
to variable data says it said it's
nothing but the covariance of x and y
divided by the standard is the product
of the standard deviations of x and y so
that is what is being done over here and
then finally and finally to print the
data sets I'm using this subroutine
print underscore print underscore Matt
one okay and this subroutine is a
nothing's it's exactly similar it's
exactly the same subroutine that we used
last time in one of the previous
tutorials to print the print the 1d
matters 1d arrays and Stephane 1d arrays
has stuff in the form of a column matrix
and that's it and with that this module
is over this module is over and this
file is over and what I'm doing is that
I'm just printing all the mean variance
standard deviation of all the data sets
just like that
nothing more okay and now any including
the covariance and correlation and
nothing more this is fairly
straightforward and then I'm writing I
wrote a shell script over here and I
made some modifications to it unlike the
previous a shell script I've included
something over the top over here okay
these two are actually comments if you
start anything with the hash tag hash
even if it even if it's a tag it's fine
okay okay even pizza even it's a hash
it's fine okay what it does is that but
if you start something with a hash then
that that line becomes a comment okay
similarly the same as here but this is
not a comment rather that is a
preprocessor directive to tell the shell
file to go to go to which place to do
all the job at all okay this is not much
important this these are just in degree
suggests no extra information okay to
make sure that you know this LS and
stuff does not make a kind of confuses
confuses I wrote some I wrote a few
statements here you'd echo what does
echo command does is it just prints a
string just like the print statement in
Fortran echo is tough for printing
statement
I'm using that to print printing print
what option is to tell us what I option
is what action is actually going on so
this will print this will trim the so
nothing but we are removing all the mod
files object files an executable file
serums printing that I'm comparing this
compiling the module file here okay and
then printing that I'm comparing the
main file here and printing that and I'm
a compiled and building executable and
printing and I'm blending that and
running it printing that simple as that
now let's that's the clear the screen
okay
no this found this four files are in
this folder statistics I click that less
clear
okay now what I do is that bash Star
Search okay run this it does all the job
nicely okay to give you guys a feel of
what's going on now this is the clear
after clear this entire black spaces
because of clear
I would listed the files it it prints
that echo statement it removes all the
dark mod files object files and exe
files okay it compiles a file and a
compass a model file to produce
mod funk mad file and an object file it
compels the main function to produce a
no main main up main object file and
then it appropriate to Princeton and
builds an executable to make an
executable out of it and it runs the
executable and that way we get value set
one well I said to mean of value set one
variance of the value set one standard
deviation of value set one and then the
mean a very mean of Cilicia to variance
of their values of two standard
deviation the correlation between
covariance between these two and the
correlation between these two well
that's all I have for you guys in this
tutorial thank you guys so thank you
guys for watching and I'll see you guys
the next tutorial with a little more
advanced topic hope you guys learn
something over here and the reason why I
included this video is simple many of
you guys must be really confused as to
how to write a module and also I thought
I'll just revisit a topic so that it
becomes so that if you guys become a
little comfortable with it and that's
nothing more and this function this
module will be I think if you guys are
working on hardcore statistics and stuff
this might be this module might be
really help really helpful if you guys
want to work with Fortran especially for
your job and that's all I have for you
guys in this tutorial thank you guys for
watching and I'll see you guys next
tutorial with even another example bye