Advanced Fortran Programming : 016 : Introduction to BLAS and LAPACK 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 an advanced Fortran
programming now before I start with this
tutorial this is kind of you know an
optional tutorial I actually tried to
mint because one of my senior in my
department and he's a good friend of
mine too
he kind of suggested me today saying
that hey Aaron
since you're working with Fortran and
there are a lot of for no mathematical
packages as a little Fortran I mean
build with Fortran why don't you just
give a tutorial on that so that you know
people might be you get used to it in
the future
well I thought about that and I felt
since this is an advanced tutorial
series and many of you guys you might
find this really useful you know I
thought of touching upon that turning
today's topic
so as a result I kind of came up with
the program today just some time ago and
I was just looking through some looking
through some stuff in the Internet
just to see how this can be done okay
for those of you guys who don't know
what lapack who don't know what's going
on here
today I will be explaining guys how to
integrate some four famous mathematical
packages like class la pack and several
other packages meant for scientific
computation okay now see la pack
sometimes called as linear algebra
package package is a set of it's a
collection of subroutines and functions
developed by there are several people in
the past you are doing some very basic
linear algebra operations suppose you
want to find the sum find the solution
to a set of simultaneous equations if
you want to do that it's not writing
your own code just like what we did last
time in the Gauss elimination example
instead of doing like that okay la pack
has a lot of subroutines inside of it
which it can be used and if you want to
you know something called as an Lu
decomposition find the eigenvalues of a
matrix if you want to find any kind in a
condition number of the matrix or you
know norm of a matrix if you want to do
some kind of linear algebra based on
and you know kinda based on that and
similar to that and all its you don't
have to necessarily sit and write all
the code okay we got that kind of
writing code that I takes away a lot of
time and you don't have to use that lapa
cause all the la paga is all the
information you want okay and if you
guys just search in the internet lapack
okay by the way I'm using a different
system here because the screen is wider
here so I can know Vallely
let's check thoroughly let me show you
both if you guys just a blob back and
the Internet
okay the first thing in the first thing
you'll get is this the link to net-lib
that Oregon okay click that and it says
linear algebra package and if you guys
notice it's a very big list over here
what's more interesting well what's
important is that these are like history
on how it developed and how would God
modified and all yeah you can read it
you can read this at your own pace but
what's important is that it's a free
package completely completely free
package and then it comes under you know
some kind of general public license so
it can be used in a test machine is
three point five you can get that or
else if you want to you know other thing
you want to run this through internet or
something what you can do just ask
install a pack in Ubuntu or something
like that you know if I my place nearby
and in my place okay this I got this
link maybe in your search it meant you
may get something similar what do you do
is that I just got this webpage Peron
it's and I think it's an Indian
Institute of Science in a fish it's a
institution in India okay there this I
think this asked of astrophysics
Department myself or somebody there gave
an introduction as to how to install
them through terminal in Ubuntu what do
you do is they just type all these
comments and run type all these comments
and click enter automatically this these
will install the required packages to
run blast and lapack okay glasses
I mean glasses some kind of a
prerequisite for lapa that's what I
remember
okay so if you want to install a path
glass has to be installed by default and
the reason why people prefer in a pack
is there's a explaining guys la patte
wiki pedia we go to lapack Wikipedia
okay now that we keep it here if you
guys notice this la path where is
actually made in Fortran 77 and it's the
first C language they use separately
okay you know many love any plug or any
language is used some you can if you
want the good details of what it's all
over here and you can have a look at it
and many computer languages like MATLAB
MATLAB and I'm Python of Python the
octave they all are built upon it they
all have been they all are you know
build on top of it so let's see love
back Nakia right great
they might take yeah the glass and
lapack actually they are used for the
aiming they are they actually under run
underneath la pack armadillo limp and
GNU octave mathematica matlab and
vampire not know these are these
packages actually under the hood loose
you slap a canned glass for all the
computational process okay enough of me
you know enough of me rambling about
these let's run let's have a look have a
quick tutorial on how to run this okay
now what I have here just have a small
program over here okay let me type down
the top
program to solve system of linear
simultaneous equations system of
simultaneous simultaneous equations okay
now this program start this problem
started with the name saw one okay I
said that I said N equals three thereby
I have three two one dimension variables
of length 3 namely X and P 3 by 3 matrix
a and some integers I in for LD LD be
and n are H's and then I have a pivoting
matrix and integer pivoting matrix I
pick okay
I'll explain you guys why this is okay
and we using this reshape command I kind
of stored one answer over here let me
show you that system of simultaneous
linear equations if you go to a system
of simultaneous equations and Vicki okay
there's this example this is an example
over here I'm using the same example
over here I'm just copying all the
copying all the right-hand side values
and the reshape here in the column vise
no for Tyrannis column contiguous so I'm
writing the those values here and then
the left hand side here the right hand
side of this B matrix and then my
sending b2x
okay now this value n rh s equals 1
indicating that the number of right-hand
sides will be the number of terms number
of you know columns in B is actually 1
it's an indication and LD l da means the
leading dimension of it I mean the
number of the largest dimension is a and
the LD B stands for the largest
dimension B since we are having an N by
n system that is actually n may be in
somewhere sometimes in certain parts
certain times you may get a non Li you
may get the equations larger number with
you may get more equations with less
variables or something of that sort know
this this is just quick checks to do it
and here's the main part this comes this
subroutine DGE
BGE sv is actually for solving the
linear system of life simultaneous
linear equations in the back there
assume there are multiple versions of it
like if you want to go detail okay there
is this if you guys there's this users
guide users guide in this page HTML
version of the user's guide and if you
guys look at it there'd be like so many
pages over here you could just have look
at how to use that at all okay if you
just go to next next next they'll give
you all the things like what to do let
me just check previous yeah okay there's
a naming convention over here what does
it mean something
so this come this is actually I'll walk
you guys through B stands for the the
names are of these functions and
subroutines are written in this format X
double Y triple Z format and explained
the first letter X stands for X stands
for like this s means reals and demons
double precision since we're using kind
equals eight it's a double precision
function which returns double Christian
values next to let us why why has the
meaning that's a meaning and if you guys
look at look at this back list over here
the table over here de means for general
so it's either answer metric in some
case rectangular matrix so G stands for
that and the last three digits has a
specific name and I think it's given in
section 2.4 if you just go to that
section let's see like that so if I were
to click that further to click that you
know there'll be a lot of things over
here and if you guys check to check this
out I mean there's a lot of you know
page pages over here we just want linked
linked to the other and stuff okay what
what it is simply says is that this SV
is for solving a system of simultaneous
equations so it's a this four
subroutines
double-precision general rectangular
contain general rectangular matrix
solve
subroutine for solving linear equations
so and this n stands for the order of
the matrix n Rho stands for the number
of right-hand sides a stands for the
matrix coefficient matrix a Lda stands
for the leading dimension of a the IPM
is actually a matrix for some pivoting
it requires it you need not be assigned
initialized with anyone it has to be
done yeah X has to be the right hand
side which gets ultimately converted to
your ultimately converter converter to
your solution l DB is the same we saw
and it was just indication just a
variable to say what's going on over
here
suppose it is info zero or something
that I said will be correct if the fit
is less than one it sure it shows that
some problem could be there and if it's
not greater than one its it will show
some other value indicate some other in
the early said indicating that you know
the solution did not come out properly
or not something of that sort and I'm
using the print statement over here to
get the values okay now how to compile
how to compare and build all this is
militia a small shell script over here
okay small shell script over here okay
let me go to that I'm deleting all the
object files executable files and mod
files here and this I think I don't need
this file I think I don't need this
fight I was just checking or something
okay first what do you need is that you
just have to compile this file now
pagano's query X 2 dot X 95 that's fine
now if you compile this you will get an
object file and this is this you have to
include this flag very important very
very important what what is this flag
does is that it just tells to the
compiler okay there are some files in
this folder link it this my capital L
flag is used for linking the files and
ok and then once this is done okay you
have to indicate that we will be using
la Park and glass for running all this
functions so you have to give addition
these two flags in addition to the
object files then you guys do this what
we'll get is that you will get the file
called as a dot out and if you want to
rename that file what do you do is then
this is the shell command called as MB
uses MB and what it
then when you try to type this this
output this executable error out gets
converted into a lapack underscore e^x
dot exe and then we run the exe over
here I've tested this now this shell
script is actually executable so what I
do is that this file is ready this file
is ready let's take a check it out you
guys look at this solution this is the
solution for this final equation set
there's 1 minus 2 minus 2 so we should
get something you should get X as per
this part we should get X 1 to be 1 X 2
to be minus 2 and X 2 X 2 X 3 to be
minus 3 minus 2 okay
now let's check this out building this
from Genie ok execute nice perfect if
you guys look at this the solutions are
exact and they know this way you don't
have to you know write your own code you
can just after little search you can
just work your way out and you know call
the subroutines that are available a
pack and lacA can blast for your for
your operations like suppose if you mean
this is very easy in a sense it there
these are flexible these packages and
subroutines are flexible enough to
include a very large number of I realize
enough complications and odd which might
be no it's you might encounter in your
future encounter in your work so this is
what really really was the try okay now
this is just a sample tutorial this is
an example with a line may not be I mean
I may not be not delving into lapack
much but it's definitely recommended for
people and if you if you guys are you
know seriously working with Fortran for
your job then lopaka s-- iraq an attack
is highly recommended for others who
want to do you know wanted to give a try
that's always always worth the time you
want to work with photon itself for your
job it's your call
okay that's all I fire you guys in this
tutorial thank you guys for watching and
I'll see you guys next time bye