Fortran Programming Tutorials (Revised) : 026 : Array operations; Changing Index Video Lecture | Introduction to Fortran Programming (Basic Level) - Database Management

hello guys my name is Aaron and welcome
to my channel this series is a series of
tutorials on Fortran programming now in
the last tutorial and in the previous
tutorials we kind of used some array
operations and all array operations and
we calculated some we calculated the
Fibonacci series and we kind of played
along with it and in the last tutorial
we looked at some farm and
specifications to write and I mean the
simple formal specifications to write
and read from the right into files and
read data from files okay
in this tutorial we will be looking into
more of arrays using trigonometric I
mean more of arrays and we'll be
reducing some array operations at all
okay and and for to give an explanation
for that together get an example for
that sorry to have an example for that
you'll be trying to verify the trek
nominee currently here now most of you
guys who know most of you guys must know
me knowing the true dimetric equations
here and this is actually sine square X
of plus cos square X equals 1 secant
square X minus tan square x equals 1 and
cosecant square X minus tau cot square x
equals 1 now in the in our program we'll
be calculating these values and then we
will be trying to prove them prove these
identities right okay further firstly
what we need is that we need a real
number real number and instead of making
it allocatable we make it we'll make it
static this time so that way you know
you know how many things are going on so
before that I need an integer integer
and this has to be needed increment
increment integer I and then an integer
and the value N and this n has to be to
start with I'm setting this to be let's
say hundred they're setting this to be
hundred okay
now yeah now what I need is a real
number is real real away which has three
values which has some values like X sine
X Y me cos x okay secant X tan X okay
cos he connects and then cart X okay D
all of them are dimensional dimensions
and specifically I didn't mention this
in the last two tutorials regarding
arrays and then this tutor in this to
this to delay I'll mentioned that you
can change the indices of the race by
default
Fortran arrays take one us the beginning
index but in the fourth being Fortran
you'll have the permission or allowance
or the license to you know change
indices now for this program I'm making
the indices to be from the varying from
0 to 0 to n meaning these arrays will be
each of them will have about 101 real
values and for accuracy reasons I make
this kind
I'm a kiss real real arrays to have I
make these arrays of kind eight parent
these are real number real arrays which
store eight up to eight values said up
to eight bytes means the story's value
takes 8 by 8 into 8 bytes of memory okay
no I just keep the line-break on and the
intonation type is spaces so that is
fine so I just put an and and bring this
to the other line okay okay now this
being done now I need what what all do I
need yeah I need this the value of pi'
for this what I can do is
like type parameter sorry parameter to
bring a constant to bring a constant and
I can write PI to be like this has to be
a double colon PI to be you know 3.14159
something okay but this can be done but
I prefer our else you can write the / 15
decimals of accuracy otherwise there's a
simple way which I kind of which I found
it interesting so what we do is that you
know I can write to into a sign to into
a sign of 1.0 now what does this do is
that say sigh I mean a sign finds the a
sign finds the inverse inverse trig now
it's the inverse trigonometric function
it finds an angle you know that sine 90
degrees is 1 okay which is the 90
degrees is actually PI by 2 radians so
the a sign will give us PI by 2 a sign
of 1 will give us PI by 2 radians and if
I multiply by 2 we'll get the value of
pi so we'll be using pi here as it is
and since way I won't be 1 PI to be a
parameter or a constant throughout this
wave function we use the parameter
keyword and now let's calculate X now do
okay I just need one more free l equals
real this is an increment increment this
this should be equal to 2 okay I'll set
I'll define it here increment equals 2
into pi divided by you know real of a
okay so real love yen so the elephant so
fine this will do what did the word what
it does is it just it just calculates it
just finds an increment to sorry he just
divides the entire pipe entire range to
from zero to two pi into N equals n
equal segments now what I do before we
find the value of sine x cos x secant X
tan X cosecant X and context we need to
feed
do statement to set the value of x now
do i equals 0 to n okay and the end do
here and x of i will be eat will be
equal to will be equal to I into
increment okay this will be I into
increment now this bit is being done
okay
this what is this is it will calculate
the value of x for each and every hmm
for each and every time until the last
increment and all and this will this
will be taken care of okay
and now finally not finally we will look
at will cat ate sine X sine X this is
actually it can be calculated very
simply it is nothing but the sine
function of X so instead of doing a do
loop where and I have to instead of
passing a do loop where and you know
sine X of I instead of sine X of I
equals sine of X of I like this okay
where and I have to run a do loop and
calculate the value of sine X of I 101
times at each and every point all you
can do
all I can do is that you know the Isle
of Wight insert this this is actually a
poor way yes Mikey this is actually poor
implementation this is actually a poor
implementation and instead of that we
can use the inbuilt intrinsic function
also this does not this will take care
of you know sine function cos function
tan function at all me I mean this this
kind of method will calculate for all of
it and laid it all it has to do the sine
function has to be the bad value that
you be put in it has to be an array even
if it's a single value it doesn't matter
no does this this is one of the other
simplest array operation that can be
done and for cos x cos x what he can do
is just type COS of x i simplest that
for tan x okay all you can do is that we
can either use tan tan of x okay which
is perfectly valid okay so I just
which just write this is also valid okay
what I'm going to do is I'm going to
comment this out I'm going to write tan
X tan X equals sine X by Cossacks okay
and now this being said now we can also
find no Cosi Cosi can think you can find
seek and X and I think there are little
I think you know I think if you had to
slightly modify the contents or check in
the internet we be the position to find
the secant X tan secant X cosecant X in
context but we stick to our basic
trigonometry now cosecant X cosecant X
is equal to 1 the 1.0 divided by sine X
sine X ok that's all you need yeah I
don't have to put in a loop and do that
again this is sufficient and then car C
connects
seek an X okay equals 1.0 the 1.0
divided by cos x x and then cart x
equals 1 0 divided by tan x as simple as
that now let's take care of that let's
take care of the identities for this
let's now before we do before we do all
this let's let's compare how the values
looks like so do i equals 0 to n again
and do okay now let's print it print I
keep a farm at say 15 15 I come sorry X
of I comma Y sine X Fi okay and here
we'll define the format we define the
loop also but instead of defining the
format each and every time 101 times in
this loop since I in this 100 okay
let's define it once how outside farm at
and that lets open let's open this up
and it's going to be an int it's going
to be an integer so this is going to be
a float okay
the sign-off okay and this is going to
be F with let's say let's give a value
of up to say v like say eight eight
eight fields let's give a ten field that
four decimal places you know okay the
sign of this value yes we give a call
and give a space and then right yes
ten point four this will do okay let's
print this out all the values now let me
do this here we just click LS you have
this trigger trigger and us underscore
idendeaf ninety now T for time okay and
then drag ninety trick the underscore
f9f ninety then - oh and then trick okay
you don't need an exit you don't need
add our text extension also this will
also work just click enter
okay it should have a constant shape I
should have a constant shape
hmm
the end can okay okay fine fine fine
okay now I get it
what is saying is that is kind of a
variable but it should not change with
respect to you know that's respect to
you know the change conditions so what I
do is that I just change this reduce
this up integer parameter and then click
n hopefully if if my April hunch is
right it should work yeah it works and
if I were to look this up now we get a
function call we got an X again we call
this trick we just open this up yeah
perfect
yeah perfect it just calculates all the
values of trigonometric function and the
hundred values one hundred values per
nice nice and nice and smooth nice and
sound now this doesn't make a proper
sense to us so what we will do is that
we will use this pi and convert this
into radians and have a look at it okay
now instead of this X I Waterloo is that
I divide I divide this by PI okay while
printing the values I divide this by PI
and multiply this by 360 now if this
and we might have to add a era constant
had a little addition here okay so to
make two barristers degrees this
conversion will print it in degrees so I
just run this file again no problem and
if I were to execute this you can get
this click enter yeah they do it works
it works fine it was fine okay okay I
just forgot there's no small correction
this is not this should not be 360 there
should be 180 because the degrees and
angle can be degrees and radians or the
degree conversion says that it should be
180 okay so no problem you just figure
that we'll just take this out again say
run this run this again yeah now it's
now it's working fine perfect okay now
what no what we can do is that we just
gave only four let's see do we read
anything no this is this is fine this
this this will work out fine now our
sine function is perfect because you can
see in the sine function value it starts
from zero the sine function unless it's
like a function that goes up the reaches
zero and then goes negative reaches are
positive reaches in a negative one and
then goes back to zero between zero and
between zero and you know 360 so now
because of even split even split up the
angles are proper here the angles are
properly here so we have lot this is
good for us okay now if you look at the
values they are continuously and
constantly increasing they reach a hit
the reach that the vacuum of maximum
value of one at SCI ninety which is
perfect and then they start decreasing
and when your angle is just 180 180 the
value is zero we ignore the negative
sign because it might not be in a
position when it is you know like this
in this bad
matters more and then and then it
Devender it continuously decreases and
which is the minimum value of -1 and
when the angle is at 270 degrees and
finally when it reaches 360 he reaches
zero again so as simple as that
the values turn out to be perfect Holly
just turned out to be perfect now I'll
stop this video here in in the next two
in the next tutorial next video we will
continue with these we will continue
will continue with this I'll remove this
I just comment out this print statement
and really rate is in the same way we
calculate these values and print them
and you know and we'll check these
trigonometric I will check these
trigonometric identities
similarly okay thank you guys for
watching then please do subscribe and
see you guys later