Advanced Fortran Programming 006 Complex numbers and related intrinsic

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 looking at some applications and how
to use complex numbers in Fortran now
you guys know must have been knowing
that there are few data types available
in Fortran like real numbers integers in
the air numbers in a single position
they're given by real really underscore
type eight kind eight real kind eighth
and the ninth for kind eight and all and
even down pressure numbers at all and
you also saw that there are logical
numbers
I mean logical the statements and
logical values also okay characters from
strings array of characters and arrays
and all okay just like that you also
have a new statement callers complex
generative callers complex now what this
does is this is used for storing complex
numbers which are both real part as well
as your imaginary part I just have a
small program right over here I'll walk
you guys through I define three complex
variables a B and D instead of a
conventional C I represented as can be
nothing more and what I did here is that
I assigned B 2 B 3 comma 4 what does
this mean is that B is a complex number
whose value is 3 plus 4j or 3 plus 4i
well 3 is the real part and 4 as the
imaginary part coefficient of the
imaginary part simple as that
now this is the notation in which you
have to define a complex number alright
suppose if this part is a real part like
that all I have to do is put the put the
decimal down put the period and start
writing the decimal part this will part
of it similarly both had by default come
a complex statement assume complex
statement assumes the values to be real
so by default it assumes to be real so
even if you give an integer kind of an
input like this they'll take it as a
real number each and every both
but as soon as imagine anybody's taken
as a real number so so that's how it is
okay now I define three formats here now
farmer 10 is used for printing the
number complex number so the asking for
append still in the user to print the
complex number until the complex number
one or two or like that and then read
this format this format is used for
reading the data from the user
especially the complex number format
this 15 is used for printing it in a
specified format we'll come to that now
what I do here is then using this format
10 Palmerton
I'm printing and telling the user to
enter the first complex number and using
farmer 20 I'm reading the first complex
number similarly I'm getting the second
printing this a tilling user to gave the
second complex number reading the second
complex number and without any
formatting I'm printing how the printing
the complex number D and now I am
printing the complex number a and
complex never be in separate lines using
this format 15 here what it the numbers
will it will be like this the complex
number one is within brackets the
numbers in the part the real part and
imaginary part the according to
according to in the correct places
like that blueprint and here I just use
the print statements just to print the
standard multiplication operations like
addition subtraction multiplication and
division of complex numbers here what I
did is that I mean the key I've
indicated the real numbers how to find
the real part of the complex number
imaginary part of the complex number the
complex conjugate of the mile
I mean complex canada of the comple
complex-- number and then the absolute
value or the modulus of the complex
number i define them using these
functions over here real real gives the
real part imaginary part con con con GJ
c 1j g whichever you call it okay this
function returns the complex conjugate
of the number you entered and this
function returns the modulus operation
wearin it squares the real part and
squares the imaginary part
adds these two and it takes the square
root of this sum and it turns it so it's
their absolute value and then here okay
this division the division of eight the
division of complex numbers a by B what
we do generally is that we multiply and
divide the conjugate of the denominator
conjugate of the denominator the
denominator okay
for a division like a a divided by B
especially if the numbers are complex
and then that is preceded so that the in
the denominator we don't have a complex
number of you don't have a complex
number the denominator that's how we do
and that is what I've written over here
the division of a by B a and B by comma
Phi functions is a stock on jg b divided
by B star con jg b jg.b okay see so
we'll see how this statement over here
and this statement differs alright and
that's all i have for this program now
let's see let's run this since is a
simple program I can use genie itself to
compile build and run this so fi to
compile f9 to build and I fight execute
ok the terminal shows up here and there
are a few things you have to tell since
you have written the farm at over here
in this form what do you have to suppose
if you just type a value and press enter
it will not take the imaginary part will
just take the value as it is okay and it
will just go to the next number so if I
were to type enter again that's it it
just goes and because of this file
because of this thing if you guys just
come perilously comparing our program
this statements printed over here D
prints nicely okay but no formatting is
given here D gets printed in a standard
complex number formatting without the ie
but within Pratt with as a pad as a pair
complex numbers get printed as a pair
now what does this does is that when the
comp here and complex number this line
and come okay let me keep this both in
common complex number is printed it's
printed with a spine triple zero I mean
double zero double zero 4 comma 0 and B
sprinted as w0w 0 5 comma 0 but this is
not what we entered its we entered 4 & 5
here this reason is because of the
farmer thing we deduced while saving the
values and that has to be taken into
consideration okay
when you enter a farm and you have to
give the peanuts impeded the symbol and
all to make sure the formatting was
right and that's the thing and this
addition subtraction stuff we look at we
look at it with the proper data all
right now this being done
let me just execute this again okay now
this time let me be smart enough and
that four point five I can give a space
all a comma now I'll give space and the
next step the next value look eight
point nine okay now it's throwing
another why it's because that space
cannot be taken obvious I think it
cannot be taken if I were to execute
this again we get this again now instead
of space like me type 4 comma 5 like 4 /
4 point 5 comma 8.9 and it accepts so
imagine so when you write this kind of
formatting give a comma that's important
if you are entering multiple values
Thomas better thousand space alright and
7 point 8 comma 6.30 yeah Thomas six
point six point three okay presenter
there it does everything it does
everything what we said okay these
printed nicely the top the complex
number one is 4 point 5 comma eight
point nine these trailing zeros is
because of a formatting we use nothing
more okay number one and two I got
printed sum of a and B is 12 point three
comma five point it's actually 16 if my
let's see the let's see 8 8 plus 6 is 14
15 point so it's 15 point 2 there might
be there might be you know these are
just memory allocation issues
but have been not much of a big not much
of a big big sense not much of a big
deal okay guys it just printed number
properly this might be this might be
because of you know far matting issues
nothing more when you guys give them
formatting there there are some
adjustments than to the number to print
it but the value remains the same while
some adjustments are made done at the
background new copy and then they get
printed over here so may get some major
issues like that and then the difference
between E and E is this that's fine if
you guys want the mathematics out it
would be it would be the same to be fine
the product is also pride will be a same
just like how we do in the nominal
complex multiplication stuff and the
division happens like that okay we look
at we look at how the we look at the
last line you guys look at it the last
line look at the looking at this answer
over here
the last line answer over here well
they're the same is it more or less more
or less did the same the last few digits
might vary because of precision and all
we kept we kept this to be real the real
value complex numbers of type four and
four so in the last few digits you might
have some inaccuracy but other overall
the answer remains more or less the same
at least in the first few significant
digits are correct now if we just
increase if we just increase the
precision then this this will be fine
and now let's look at the beast lines
the imaginary the c-in-c
okay okay I just don't see but anyway
it's actually be the real part of this D
numbers three and it's printed over here
the imaginary part is actually for this
sketch fretted over here the conjugate
of 3 comma 4 is actually 3 comma minus 4
which is printed here which is nice and
then absolute of C is 5 which is
actually the modulus which is actually 3
square plus 4 square the square root of
3 square plus 4 square so it's PI and
it's perfectly fine well that's all I
have for you guys in this tutorial and
this is the basics of complex numbers
and how to use them in Fortran ok thank
you guys for watching and see you guys
next to the island
you guys able to understand this this is
how it will go on for all that for all
the other complex complex numbers and
operations also so see you guys