So what we have are special
reports computing that

are to be given by the very years a Ph D.

candidate at University of Florida
in their C.I.S. the department and

specialised in US forests major
exactly the methods of accuracy

than today will be talking about what
patients for a rejection is worth.

That's really super.

Thank you.

I would like the time from
somebody to first for

giving me this opportunity to talk here.

I'll be talking about some
blocking whether it's

the bit I would be talking about to
whether it's one of the band reduction

that there is a spa single
value decomposition.

The common theme between both of
them less both of them benefit

greatly by the locking that's the basic
idea what I'm going to get it.

But before we go into the actual method.

Let me talk about.

What this whole Prop problem A.T.M.
What because I see people from different.

Background here some from dead analytics
and some from the high performance

computing and so this is a diagram
I borrowed from Bruce and

it's from a conference in two thousand and
three.

So when you consider these two
power A.V.O.'s computer science

in terms of the algorithms of computer
science and computer science it's out of.

What is in the intersection and.

That is coming to a real
scientific computing

a lot of people are familiar with this and
then I want to give this talk and

they want to put sparse
static methods there.

I was curious pared to place by static
methods I see Jason smiling at me at night

because there are just parts of sparse
static methods that are actually.

Not just that it doesn't fit
exactly in the center and

probably should just pull it a little
bit into the combinational science

a little bit more because there
are some memory guys but.

Viral which may be one of
the conversation from the combination of

science perspective.

But at least in the sense
of this stark we can put

the whole thing the parts that matter it's
into the intersection they're OK with us.

We're going to just look at a product
look at two problems in the time and

our real sense.

So that's the idea and inspire others

can if US are being so
inspired that that's one of the goals

we generally work on that three
main goals Oneness the performance.

In terms of time we look at
the flops as our great idea

as a as our my trip and that can you do
you are that candle can do other flops.

So that's one of the Caribbean and
how close to the system theoretical

peak can you get and
there are some problems later.

You could just drop this too and
then say can you go any faster.

So that's in terms of
time in terms of space.

We always do symbolic analysis to
reduce the feeling of power for

people who don't come from sparse.

I was first made its all good times.

So it offered the feel is
basically any zero that turns into

non-zero as you do your factorizations

whether the stroller ski L U R S
sparseness really doesn't matter.

So if you are a ZERO done
seem to Nancy fall into

while you're doing the factorization
we call it as a fifth.

So you read play the videos to
fill your play to predict the full

doing a symbolic analysis ahead
of time and the symbolic analysis

more like we try to do the exact
replay to find the exact structure.

Most of the time.

If you can find the exact
structure at least can you get by.

And so so

that you can allocate your data structure
right out of your actual factorization.

And the third thing is what I
like about this field is you just

don't write algorithms and say OK fine
great you actually write software and

then release it so that people can.

So the software is
available robust software

they collect back scallop back and
back and be all of them so.

These are the three main goals
in spots that are with us.

So with that picture in mind what is
the problem you're dealing with here.

So imagine you are an investor and you
have a lot of one markets decomposition.

OK.

So what will that be as media.

So let it be is really.

Because it's the Swiss Army knife as
they call it of the decompositions.

It's not my job I heard it somewhere so.

So you give an air you try to find
a single value decomposition.

You say movie transports and
that where works

far in most cases and
then you do it in most cases doesn't it.

What's in most cases.

Sometimes it's too costly for
you to do it or you don't do.

So how do you compute a sweetie.

So I am going to talk about development
of this darkness with spice that matters.

OK So in that whether it's your
computer Q.R. factorization.

Then you take the are you do buy
diagonally star which I'm going to talk

about and then you have you go from a by
diagonal to diagonal really developed.

OK they do a bit better than us.

So the second bullet is
the one they start is

concerned about going from a sparse
upper playing lower our to a by diagram.

But actually it's a complex proud.

It's slightly canvas problem
than the problem here.

Lestrade follow a simple problem before
that the problem the simpler problem is

given a which is a bat I
assume is a bad month next.

You have to go from a bad amount of store
by dialing a map it's using our target and

nations that are an advanced
nations the most commonly used

given stations are planned
protections as they have

recently God I prefer I still use even for
patients.

Most of the time but yeah the talk.

Here is in the current way it's it's
called Plan for patients when relations.

So you go from the band
Maddux to abidingly

Magic's using either give inspirations
are cultural or transformations.

These are two options.

OK So what are the methods
to do this then I actually

did it with just one matter that had been
done in one thousand nine hundred sixty.

I think by these two guys who disorder.

I think I pronounce his name

correctly I don't know if there
is any Germans in that room.

And Saif it's wrong and swats So
these are the two guys who developed

it to nine hundred sixty and that got
them pretty much still works fine.

So it's basically take one entry
I'll just show you a brief

idea of the algorithm in the next life.

So take one entry reduce it using
a plain rotation just fill.

Down the mattocks today to the end
of the Maddox so that is the idea so

they did it in nine hundred sixty and

after that there has been only two
different modifications to it.

One by a lead back in a linear Kaufman
did it and that's basically for

better computers so she did it for better
computers and it still works well for

her in our machines so
that isn't a look back you does.

Something close to blocking but
it's not exactly block a little and

the next is we are told bots and
they did for using last three so

that they try to do as
many of the operations.

Possible when you bring it from memory
to cash the one we disadvantage of this

one is not this is not a Black Berry give
them the L A back a little the other one

is optimized for cash but that takes
a lot lot of work space than it's

actually quite So the goal for
us is to get the board of the Worlds.

OK.

OK So apart from these two
there is this all a matter of.

Doing one memory at a time.

OK so

they're doing one entry at a time the fill
you are going to get is one scale or.

The really big one entry.

If you fit and
you get one skill to fill it just so

that it's not what's required
a thought you just need one skill

in the back little more work
space out of any one space.

If we had to box a lot more space.

The thing is what's the idea
was what space doesn't matter.

You're going no compensated
with the flops.

We may well be using Blaster use.

OK So the our goal is can
we do scale of a lot of

the flops lower the workspace requirement
and use cash in a better way and

blocking that's it and not just blocking
doing blocking with some sort of

pipeline thing I'll just show you
what it is so that is a goal.

I have once lay on just
the basics bear with me.

OK So
if this is what agreements rotation us.

OK so you pick the two entries.

You just want to reduce that
entry the theory to C.D.O. So

you find a mattress G. that he wants for
patients and so that's basically

the C.M.S. or the cause and saying
if you are the angle and liberation.

OK So that's the basic
definition of introduction.

So I think I want what happens when you
operate this rotation to a sparse vector.

OK.

I feel like this going to be sparse it.

Not parsing the ban case but

if you have if your rep read
that happens to be sparse.

Nancy the bottom.

After you apply this is going to
be the union of the manual but

not the previous thing to it.

Look at the.

If you operate between two actors the
National Guard is going to be the unit.

So it's going to be cut.

It's costly in terms of Phil.

So keep in mind that small note will come
to that when we come to this process with

the acting and this is the method I was
talking about from one hundred sixty S..

This is there are two methods one as

they consider this entry one
here pointer sort of things.

So and So this anyone here OK.

We want to reduce that entry one.

So we find a rotation.

I call the column rotation because it's
going to be within two columns and

then apply the rotation to this column
that reduces the entry one to zero but

it causes a field in the bullet
here down here in the sub diagram.

Then consider these two entries
find a new rotation and

operate between these two rows.

It reduces this will happen and
creates a new good.

OK so the choice is down the field
down to the entire map and

then go back to the next entry up here so

this is a very simple algorithm
one one for the time scale I feel

no problems at all when the thing is
it's a skeleton and the two methods.

The first method will reduce the entries
mob to three and four of eight

reduces one draw at a time and before it
goes to the next entries in the next row.

The second method marks
entries zero two three and

four after it made zero it is going
to reduce entries to three and four.

So it's going to reduce the diagnosis
there basically is what worked well but

what would that mean medically stable so
it doesn't cause problems and there.

In terms of the amount of work they are
kind of laid off by a so this is the most

people and that the most costly one where
the dumbest of the number of patients.

This is going to the diagonal reduction.

I'm going to call this dying of
election and we'll call this voter.

So the diagonal direction the number of
rotations is almost it's probably going to

do twice more so when you're going to
are play the rotations and you want to

accumulate all the patients in you when
you want to you want V. not just the Sigma

you're going to do much more work in
the diagonal election than in that order.

OK let's keep in mind.

This point the basics and
then we'll come back to later.

OK So from there.

How we're going to do blocking itself.

OK so you can see that there isn't that so
and so a small block R.B.C.

BLOCK I want on our base to block
which you want to reduce and one step.

Instead of doing one entry or one step.

So those entries are like
zero zero plus if you have so

that all plus entries are the ones I'm
going to produce if you look at it.

These are the one really possible entries
you can do you can reduce as a block to

get OK So
because anything else you end up costing

a full of all the day we want one so
this is the structure you have to

do you have produce a battleground
sort of structure and so

you pick the structure you pick R.B.C.
entries of that structure then you once

you pick the structure then we what we do
is we try to find blocks in the matter.

On the part of these
corporations are going to pick.

When we when you do the chase.

OK you are going to sit.

Be very dramatic scene two blocks so
that it's easier for.

I'll go behind what differentiates one
block to the other one in just them but.

Hold on for a moment.

OK So the very dramatic the whole matter
is in two different types of blocks and

then do the choosing it looks like there
are more than one field here but not all

of them are percent at the same time it's
still going to be one scalar field there.

OK so
it's going to be one scale at a time so

divide the Vatican two blocks and
consider the first one.

OK I call it the yes block because it's
the seat that's going to probably give you

a little patience you want.

So once you have the you have the C.
block.

Then there is a C. block.

If you look at the c block what type of
what Asians are going to be in the C.

block one of the collaborations.

We're going up play a bunch of
givens relations on the columns and

the R R Block here.

There are going to be only voter patience.

Even in this step and see that one step
after reducing our we see entries and

chasing down the field in this step.

The C. block is going to have
only collaborations the art

rock is going to have only two auditions.

This is another C. block here.

OK so
the Maddux is sort of divided into its.

Chance.

OK so now it's easier to look
at the whole problem and

say that was how I'm going to
do the action in each block and

still I haven't talked about how I'm going
to restrict the film to one scale or

because if you do all the six entries
together you will end up with a tremble of

feel OK it's usually like
a household a sort of if you

take these three entries and
I played a houseful of acquisition.

You'll get a triangle of them.

That's the most common thing.

So we're going to rest in the Philly
instances of doing that sort of the angle

of if you're going to restrict the skill
of it that's by doing the pipeline

that is in the next day so I assume
you're going to do the blocking thing.

Once you test this block.

Go ahead and find the next block of it and

this is some idea sort of
leads to a band of action.

First you reduce the entire band Mandrax
to a band batiks as small a band mattress

of band with one with is the number of
bags in the back of the of band with art.

If you can.

If the number of rows in the block is our
number of columns in the block is C..

OK so it's our way.

C. block.

If you started with
the are like bandwidth key and

you have an R.B.C. block at thirty two a
thirty two block you reduce the math books

to thirty two by ignorance first and
then do wonder what the time.

OK so you have a three hundred
by a band what you start with

thirty two bit thirty two blocks and then
you bring from three hundred bandwidth to

a plan with a thirty two and
then do one better little box.

OK So it's it's a two step process.

The reason why we're doing that as because
take a look at this innovation right.

If we try to do another block here I'm
going to get more than one thing here in

the the videos which I just
created are going to get filled.

OK So that's the idea.

So you divide this whole
thing into blocks and

now how are you going to do
the operations in the blocks.

OK So this is a C. block consider
this one as the seed BLOCK OK so

I have I have to reduce three entries.

This is the only place that I am going
to go now I'm straight on that's OK

everywhere else.

I'm going to go straight on
axis as much as possible.

So I want to take three entries and
I'm going to reduce them.

OK So do you want you to do the result.

Three given for patients.

I'm going to make create treatments for
Asians and of course apply them and

make them zeroes then take
the next row up a play

the three given three patients which
are just created from the first row and

create three new given
circumference G forty five and six.

OK That concludes my C. block.

Once I'm done with my C. block.

Now I have six given sufficient stored.

If you think.

What I have done this.

Instead of creating a town
Wrangler block of fill.

I've increased the wall space
by the size of the block.

OK so I have to store
the given situation somewhere.

So I'm still I'm going to store
these three six Givens for patients.

Now I'm going to use them down
the metrics in different lots of care.

So how I'm going to do it in each block is
going to give us the performance people.

So think of this column block now
I have six given three patients.

I would operate on a big chunk of columns.

I can take a column.

I've played a little patient.

So here I have just two entries
in the column I can apply.

That addition ten and eleven and the next
thing I do is play pull in thirteen so

this column is in memory for me.

And I do fourteen and fifteen.

So this column is in memory for me.

So from the rotation in the first
row ever played all of them to this.

And the next six rotations I replace
it with the column block again.

So I have.

From what I have seen this and
they are block receipts in the memory.

Mostly the blocks are small enough to
reset the entire block is small enough

to be saving my money.

Most of it but at least the column
they say it's in memory.

So I'm not.

I won't be very bad.

OK.

And think about drop actions.

Previously I used to do
non straight on ISIS.

So in the terms of scalar I used to go
between wrote one draw at a time but

even that all operations
I can take one column and

the place say all the six were
patients to the one column.

We now might know me or operate
sions have become column operations.

I can take one column I play all
the six operations for that column.

So I think it's the one thing
is if you look at the numbers I

don't know that it's possible it is
sixty four sixty four and sixty six.

So I am going against the memory and
there are certain compiler.

But you don't like I
think son was one of them

which is not able to research got to me
for this sixty four sixty five sixty six.

So the compiler's like.

They're able to figure that I'm going
the other way around in memory because

it is stored this entry stored
below the center this is a column.

It's a column.

Storage.

And the fill in the diagonal blocks
are actually a little complex to shorten

the figures it's in the paper but
the basic idea is this you

create a full you create one full and
use it immediately with at all.

Before your play any other quotation.

OK if that there is a fill
from column A culmination kid

we immediately reduce it
with that automation and

then play the culmination K.
plus one that's the basic idea.

So you create it because this
block I'm talking about.

OK.

Is this what I'm talking
about this is a field log.

This is the field of this is a diagram
of so here I apply this what Asian

create this fill immediately reduce it
with it or a patient pipeline and here.

OK I'll play this for

Patient column a very use it without
authorization immediately pipelining.

OK but the way I'm explaining it.

I'm showing it.

The rotation.

I'm going to do non straight on Access but

I can do it without going on
straight on axis OK I can do for.

It's a slightly more
difficult thing to explain.

You can look at the picture but
the ideas then use this fill.

Before you apply the sort.

Ation here before you clear distance so

that if the meter fail to see
a scalar instead of doing a plan.

So be limited to fill a wider non-trade
one axis and we did the blocking so

it would help the performance so that
is a performance for against any pack.

This is a Against this is against.

If we are this be our tool box.

This is a blast three OK I'm
competing against last three and

this is the number flops I'm doing and Y.
axis is basically a lot skate so it's

the top is four if you can do it from the
back if I'm biting one of them or four.

So it's almost four times faster than hell
about what would end faster than S.B.

are we as we have used the last three and
be used as much more memory.

They say they're just giving the same
amount of memory as the input by Maddox So

what our number of Nancy doesn't improve
by medics give me the same amount

of force base.

I give them that uses
much more work space and

I use thirty two way to work space in
about uses out of the on work space.

But yeah it's much slower.

OK and that this is just
requiring the buy diagonal.

OK I'm not going to arbitrate I'm
not accumulating the difference for

patients yet.

And this is that our performance for
people who are interested in front of us.

I am.

This is run on a two point six to go.

Hertz M.B. machine.

So I'm able to get a bigger flop and
it is quite stable and because.

This basically there is a slight glob but

it was like Hundred make of a drop or
something.

And this is how I perform for
different block sizes up there.

I think.

Drawing a line will hear
what I've been crazy.

So I just left it as a scatter plot.

So that the.

The X. axis again here is flops
the way axis is the blocking time for

say a circle is a block I'm considering
they enter your role as a block and

the squire my blocks a is
a sixty four by sixty four.

OK.

And the Y. axis is basically the blocks
ace which is the default box I chose.

OK so I choose the default block so

it's based on if it just less
than ten by ten I do so.

Of blocks of eight eight by eight and

the place is smaller than the issues
of lots of people with every bill.

I do a pretty good job of
choosing the boxes here.

OK there's only one case when I lay
there is a middle point here like.

The block in fact because of and

even if you didn't use the blocks it's got
a CLI OK unless you are going to do some

really cool stand there was your
block your only off by ten percent.

So the blocking pretty much works like
even if you choose a bad block so

it will be only off by ten percent.

But we're faster by like three or
four times.

So it's fine.

OK So we have done this case.

Now can we do the update.

Can we accumulate all dissertations
the events relations and identi matter.

So that you find you want to be not just
Sigma but you also find that you want to

be OK So OK finding that the simpler
it just takes that operation.

Multiply it of five into matters and

pretty soon it is going
to become full you want.

We're going to become full and OK so
you feel you want to do instead

of doing that you want to keep track of
the structure of you want to be self.

OK Can you explain the zero's you start
with and I didn't imagine it's right.

So the first two patients here
is to eliminate that N.P.C.

too so if you are play that entry
all you have to do is do poop.

Operations here instead of doing
that entire zero of columns.

OK And the second the number two here.

If you are going to do three of them.

Three operations here instead
of doing the entire thing.

OK So can you eat exploit
the structure of you want to be

that is a question of when you are playing
that we once were patients to.

And I didn't imagine a dunce are they what
is the easiest algorithm you can think of

is having an out of an array and the index
of where the last non-zero was after.

And you want to be OK so YOU YOU MORE THAN
That's so there is to start with I like

for what one two three four five six two
and OK and then you keep increasing it.

So if you have another N.R.
it's a very simple problem.

The thing is we want to do it at the scale
that we don't want to come out of another.

OK so if you are play the first two or

patients this is going to
be the structure in you.

OK So
what happens if you do one more that.

If you don't use the third in three and
four twenty.

That is going to be the structure for
the entry that is going to structure.

OK This is from the chase.

OK so once you will use this and
they are wrong.

The number zero one two five
hundred here's all the entries.

This is going to be
the structure of the you and

you can see that it's a block diagram
structure of the every block.

It's a hasn't been a structure.

OK.
Every Brothers has or has.

So now you know the structure.

Now if you start reducing this endless
open less than a mob go plus the next row.

The structure this going to be this.

OK if you can not do
that you got a huge fill

in the lot Wrangler part of
the upper time of the part.

It just increased by one super diagonal.

OK so

it is going to part is going to increase
by one super diagonal for every row.

So you're going to get
a lot of improvement there.

And then the lot on your part is
going to feel quite fast leap but

still you'll get some improvement here.

OK because to fill the entire lawyer to
handle a part you have to do you know or

care if you have to reduce you know or
care who was here.

OK as long as you reduce an order chaos
you will gain something in terms of

reducing the number of operations so that
is to update you on be and this is a very

simple case OK I took one draw at the time
but out of luck in fact I can be anything.

The ideal blocking I used was.

Thirty two bit article.

OK so if you do I think about a tree
this is what my structure looks

like after reducing this one two
three four five six seven eight nine.

This is my structure.

And that is my structure after reducing
this next chunk of three inches and

we can still track it OK.

It's just like it's a very
simple over them but

I CAN YOU JUST KEEP THIS is if you look
at it it looks like a funny structure.

But it's actually it's actually a lot lot
hasn't work with a small plan bill or

chunk of family that is zeroes here and

these are actually it's a Care lot hasn't
been the case from the number of columns.

OK so
the the number of columns here is three.

So it's a clear lower hasn't been
mavericks with a small plan will jump of

the list so
every block is going to be a lot has and

will that language chunk of seals and
you can.

And once you know that one.

Then how these two play
Lord who hasn't worked.

Magic seemed like this is what
this brings you to destruction.

So all you need this to
keep track of the key.

And then just for scale if you are able.

You'll be able to track
the entire structure of this so

that you reduce the number of floating
point operations required to a play that

all patients to identity methods.

OK so

this reduces the floating mind operations
and that is the performance improvement.

Or a lead pipe and this is a leap.

As we are beginning to bluster
the biggest one that's an impact.

OK.

You look back you saw something
similar to what they did.

OK but not exactly similar they
use they don't use blocking so

they're stuck to this different but
they have something similar.

They explain to exploit
the structure of you and me.

So the performance
improvement is slightly late.

It's.

Like at most.

I'm two times faster than a lap and
two times I came faster.

And it's be are even with plastic.

And this is the case.

This is for for
a short all of them or for.

Symmetry cases this is for
than similarities and

symmetry get to be our toolbox it
stands for symmetry band reduction.

So they don't have an answer
to the elevator constant and

symmetry case and
the number here is on the darkest night.

OK So this is one tonight.

So I am close to nine times
eight of my and faster with

the our data if you want to be this
is just finding the buy back any US.

OK.

So our.

I hope we convinced you that
the blocking in the pipeline works for

a block branded action case.

OK Let's take a look at how it does for

the sparse case next year
the next is a sparse part of it.

The thing about sparse problem is OK so
this is

think of this as sparse are OK This is
like a fabricated one which I so that.

I created so that I can show out
that the items and procedures.

OK And this is going to be
a distraction I am going to use.

I've already filled up
quite a bit of that.

OK So that is going to be May.

I call that a scaling profile.

Actually my advice and came up with a ton.

OK So the idea is this you first and
then the definition

of scaling profile lists the biting of
A list all ways that in the scale and

perfectly OK because you're going to find
the byte like that if an entry is there

all the in piece below to build a diagram
of it that's like a skyscraper.

And you're looking at the scaling
I'm a slope something of a so

everything is a Consider
each column as a skyscraper.

You can have.

What is a level three.

We don't level two like.

Level three percent Level two is person so
and

then please present all
the entries below this person.

So that's a scale in profile are OK so

I'm this is going to be Main Street
their structure to store the Mavericks

operate on and that is a mounting
structure welcome for the definition.

So the mountain restructure is going.

It's actually nice to prove things for
just a temporary other ways

it's basically useless because
what I'm saying is you've been in

please percent of all the entry below
that feel the diagonal is present and

all the entries to the left
of it to the bag nice person.

OK So think of it like like a lot.

Your viewing a landscape of mountains
OK these are like three mountains here.

One two and three and
then there's a bunch of rubble.

So there are three mountains.

OK So that's the mountain we provide this.

This is useful to prove theorems.

This is the one that us
that we called it was on.

So that's the scaling profile
of the sparse mat metrics our

scallion profile of are in
the mountain we profile.

OK.

So once we have this this profile is
defined I defined something called

a conifer OK so
there Connor is a column key the.

This is the actual definition with just.

OK let's look at I'll just describe
to you in words what it is

a con is a column value
few What do you tip.

You will get one fill in the sub and
one of their

OK you want to get Phil anywhere in
the in the statement of I'm not but

I'm not going to talk about the sparse
matrix itself OK all the things that I'm

going to say are on the scale and
profile of our from here.

OK so if I do want to
patient of those two columns.

I'm going to get one fill in this about of
him so that is how I define the candidate

and these are the three corners in
this matter in this even matters.

Ok this.

Scan of this column is a corner
because if I had predicted.

And I always thought it column
key with column Q. minus one.

If you haven't seen it and never do
that operation by the way and keep us.

Always good clear and clean minus
one because if you do it with care.

Plus one you're the Phyllis
sort of are OK.

The film is about the day
I always want to blow.

OK.

So I do care and came minus one and
this one fill in the sabbatical and

then Bush is exactly like the band is only
thing is I have to I cannot do it for

any column here.

OK so you feel I'm going to do say this.

Consider this X. here OK.

The brown big X..

I'm going to do would add operation with
the column next to consider column key and

it would with column K. plus one island
up to feels here and one down there so

I end up with a difference but
I always want to limit the field to one

subject me and so I'm going to do what I
have defined the corner in such a way that

the fill column Q.
Secondly if column K. and came in.

If you wanted column Q. and K.
minus one that is going to be one

fill in the subtitle of payments one so
that that is what the definition.

Basically that's OK So
you define the counter and

the column Connor's definition.

Also I make sure that we have
this nice properties of F.

the by dogmatics won't
have any conscious of it.

So the idea becomes you have
a mattress with a bunch of

Connor's you have to go to
a mattress with no conscious of it.

So you take a bunch of corners reduce the
Congress from a lot of corners you have

to go the more corners there.

That is out of them.

That is a problem at least.

OK so you've got them there is a common.

OK So the next property is we have defined
it in such a way that if there is a con or

there minus one is not a kind
of a plus one is not on so

that it's easy to rotate between us.

OK So this is how we define the Congress.

There are two more properties
of Commerce water.

Consider this next one in the second one.

OK.

This is a condo because I can prove it.

I can find a human body from these between
these two entries exactly like I did for

the bandit from the court date between
those two columns and find this about him.

OK until the last one.

OK I can't find the given situation but
then people who left offices actually feel

I don't need to find a new
information what I like and

do is against Rob these two columns
are king and the swap is basically

a special form of for patience basically
I didn't read that either way.

So I didn't give it a property.

So you're going to basically swap it.

So so that this column comes
here this column comes in.

It's basically if you want for
patients but it's a swap.

OK so I can do it.

Actually I can do it in memory
without any trouble and

good ones the last words of the diagonal
into the old offer to the what space.

So you define the commerce in this way and

then look at all three contests and say
that which one do you want to reduce now.

OK So there are a bunch of corners.

The problem becomes what is the best going
to do reduce OK things we don't know

a lot of IF OK from here.

We know this is the best going
to reduce the thing is and

you give me a lot of
comments I really don't.

So we have to find out with asking where
come up with a scheme where we find

the lake.

We have to make some assumptions OK so.

I'm going to assume that that I was kind
of is the best part of why I am going

to do this is that's what's true art.

If you give me a bad Mattocks I'll
be always reducing the but

in the bad mind the the current
definition works for the bad taste to.

OK that's a nice thing
you take about medics and

you mean I believe these definitions and
do work exactly the same way

you do to reduce the same injuries
the squad the shortest method to reduce.

OK so I'm going to take the I'm going to
find the rightmost on that in such a way

that the law just gave out which case
a condom is my right most on what I saw

on the street and there is this is the one
that's going to be when I was gone and

I'm going to read you start.

Why I'm going to produce it because
I have some nice property stored.

OK.

You look hard when you looked at it in
terms of the mountain you will see this

was one moment and this was another
moment on this was the last moment.

And after that they said there was
some rubble there is no mountain.

OK So the basic idea.

If this is the right mosque
on them anything that late

offered will not have any
moments we can pull and

I define a moment unless it's sort of
like you can see from the pointing right.

It's just a bunch of columns
of the same top of us.

OK so you're bunch of
columns of the same top pros.

So the idea.

So this is what it says to the eight
operate more scanner that won't be

a bunch of corners with the same top was
the top pros will be one automatically

increasing in memory.

You're increasing.

OK you get the increasing in between.

So OK So that is one nice property
there is no mountain top off

because if you have a moment
to consider this entry.

If you wanted this you have a mountain
here you are going to feel you're going to

Jaycee Dugard not because they're
OK to have the M.P.'s are going for

I don't want that I want.

You for you provided this I get some
Bagnall Philetus if I don't want them and

they're planted here.

I want you for there is a mountain
that I'm going to get all of it.

So one nice property.

The other is basically a corollary
of the what I said just saying

because there are no mountains there.

The skyline and mount and
we were basically the same.

OK To the right.

So even if we operate on a scale in my
tracks I can think of it like I'm open.

It's OK so I have the nice property.

And the third one and
it is the actual proof.

What I'm going to say is how much more.

Stick the statement than before.

If I do this I get one sub bag and
feel I'm going to chase it.

I will not get more than one
thing I make a deal for but

I won't get more than one for OK I've any
point in the chase and we can prove it.

OK I'm not going to prove here but
it's it's not very easy.

It's not it's not very tough.

You can think of it late you can say that
I'm going to get more than one file and

prove that there is a moment there.

OK.

Just a contradiction.

So once you do that then
the algorithm becomes really simple

you have a bunch of corners.

Go From got both all the columns
collect all the columns

in a stack start on the right
most corner where you

stick on a just a full you managed
to get only one full of it which

is probably not useable even they're
OK if you're not sure if it's not just

about if it's a simple continue with your
sublists else we're going to be all right.

Most content.

OK so you all you have to
maintain a stack of entries and

always reduce the rate most
gonna keep producing OK so

it's a very simple algorithm nice
properties the what anything else.

What are the problems.

OK The process was very nice.

I would give them a very simple one.

The and

the memory requirements are easy because
every fill every entry will cost one fill.

So we're making some progress or at least
staying the same and we have a nice

public property of the conses it's
not blocked it's not by plane and

you just going to do the diagonal
direction with that which

is doing a lot more
information than we quickly.

OK.

Part of me.

No I'm not using the last three at all.

No I'm not used this algorithm at least
doesn't he was rushed to get out and

I am not using blustery anyone actually.

No you can in the bank order I
don't use last year at all and

my you just may block chord but
even within the blocks it's and

very much like it will have been mama
Secord it's not using the last three.

So I mean it's able to be blast three
because it's using the tash that it

leads using the investing that
it's not using blasting no.

This algorithm is totally bad for
blaster you OK this is just one.

It's chasing one element about.

OK so obvious.

So.

That is about right.

Most elegant work or if we're not play the
leftmost going out of there you can easily

see that leftmost kind of is going to
create two fields year and a chase.

OK so I add a constraint to it.

I say that the leftmost
corner is not any corner but

any valid counter and they say that
a valid can other is the one that is going

to create a one stop Bagnall feel and
one feel when a chest of F..

So this them corner that is marked yellow
is a valid kind of a because it is going

to create a fill in this.

If you may call it some sort of a crisis.

So I think it's going to clear Phil what
you think is going to create this funny.

Fearless we are used to seeing
feels at the end of the columns.

OK A or end of the horse.

The thing is it's going to
get in the middle of the road

in the middle of two columns of it.

That's the problem.

I'm not going to go
into detail about this.

The thing is it's back in the it is

actually doing doesn't
work very well because.

We're not able to prove that the next
great left more scanner is in about

closed door so
I'm not able to block it out so

far blocking because the left there is
one left most going to hear the next left

what's going to be any one of the odd it
can be actually that it was can we can

prove the rightmost can't
it's always alert valid.

So once there is there are no valid going
to here we always come to that it must be

so that is a problem with this mother
valve we try to do something there and

then find that there is no valid can or
gamble actually that I was gone so

it's actually not working well OK I
just wanted to put it there so

that just give a brief idea.

So can we do blocking on this.

OK.

Almost time to hear.

Five or ten minutes.

OK OK So we try to do blocking here.

OK So this is the basic idea
you have the scanner here.

The rightmost corner we
can prove that it isn't

OK I'm going back to
the Mountain View from the skyline.

OK.

This is a Mountain View Maddux OK.

No that's short crazes any more.

And I might exist for three moments I
think in Mountain View we can prove that

if there is the in the rightmost
corner consider this kind of.

OK I'm in the top row of the king
consider the column top row.

K. plus one.

OK consider this column if
top of peer is I.E. bro I.

Consider the column I plus one.

OK we can prove that any corner from I
placed one to N. because you know I want.

OK.

The first proof was saying but

it was counted because you are one for
now I am saying this.

If column Q Is the rate most current I can
go up to Lee who I which is the top of

here and go to the column I get
this is the column one and any can

have within this whole block because you
are one field and again it's because

it is always going to go to the rubble and
the rubble is zero or one of it.

So I'm going to say that any
corner here is going to do it.

And then.

Now I can do block in here.

OK so I said this whole thing is.

Sibel But what I'm going to do is I'm
going to reduce one mountain at a time.

OK.
Instead of producing one

car at a time I'm going to consider this
and they are mountain as one big chunk.

Now I can do my blocking
the one we think this

might mean the size of the mountain
is now where you will.

OK it's basically
depending on the mattress.

So my block size has to be really dynamic.

So I give a block sister
to the way that we go.

It finds that I was gonna try to expand
the process with a little bit of you

don't you just buy off able
to find the right away.

There you go and

go to Asians it's fine if it's not
what I would as it is able to find so

it's going to be entirely different
in the structure of the mattress.

So that's the idea and

the thing as if you look at the initial
mountain This entry is not there.

One two one three and

these are from the mountain but
the fourteenth is actually from the club.

So it's not just reduced amount but

also we have to improve
the few entries in the room.

So this works.

The only thing is modern it was too high.

OK.
Can this be converted into coiling OK I

just have two slates for the sky and
I'll go to the performance.

First the problem here is you if you
do this thing that doesn't work for

the sky line us the the proof way
to give you the idea that any call

column from this corner to
the end we clearly don't want

this will create probably two fields
because there is this chunk right here.

There will be a full to the left
of that eight most economists and

restructured OK So
we really don't want to do that.

So we're going to increase
the constraint a little bit

by saying that the top
row of any kind of sick.

This is our seed blog the word unity block
which we talk about in the band adoption

something to think of it a legacy blog
from the battery action is that shot just

going of the other top row of any column
is going to be constrained point.

Ok to find.

A color here.

OK so I cannot go beyond I
cannot get enough sleep here.

That is the basic idea of it so
start on the right most on it go.

The block in such a fashion that you have
to have you cannot have a feel here.

OK so you.

And then you.

You can use your blocking and by planning
schemes for that's the basic idea.

Now you can operate on a scale and OK so

if you do that you'll actually
get instead of four rotations

in the previous on in your case we could
read a difference here and in the sky

in case that because of the scaling you
can help people going to sit in the block.

So you then you have the choice of
Husing any candidate in this block in

Mountain View there is always one con
of once you find the mountain of it.

And then the scale and
if there are multiple corners.

So you are used to the leftmost
going on within the rightmost So

you find the rightmost mountain
go right most cannot go a block.

They just to the left most quantum.

Because it's sort of actually simpler and
mice.

OK but you can do any kind
of within this block and

you can do the blocking and
pipelining them.

OK Within this.

And then go to the next moment and

were brought in by playing
with the next moment.

Good luck.

OK so it's really using one mountain at
a time and another nice thing about us.

You can see that I actually took
the bad markets which are used and

actually deleted a few entries.

Well it's easy.

OK So this has a nice band structure but
there is this nice.

So can you use.

OK before going to that
the performance numbers for this.

OK.

OK So this is the thing that happens when
you come up with a performance numbers and

then we'll tonight in the last day.

OK So excuse me for but
I'll try to explain to you.

This is the flops.

I'm sorry this is not
the flubs label here is wrong.

This is an art and this is basically.

One and I'm comparing it against
an eternity with sweetie.

OK I'm able to find all
the single about us.

OK I'm going to compute compare it
against a need to read it as we decode

the one anything else might
I'm going to say that

if you look at all
the similar values I'm fast.

OK so I'm going to hold up.

OK I'm not going to
come patter comparable.

OK.
It was with the slope.

You if you require one of two similar
values your read of yesterday is fast.

I'm not going to compare the case.

OK so I'm going to leave that to you just
the in-between that is interesting to us.

OK So this is the in-between but.

So you feel young is
say three thousand and

the axis are basically
N over five hundred.

If you asked Are you the very best really
three thousand or five hundred or single.

Yes OK And
over five hundred single about us.

I mean you ask me all the single
events then I can by the time.

OK So take the case of plus
Right it's an hour hundred

you ask you to reverse
really thirty single ovens.

OK And you ask me all the single of
a little history thousands of lives.

So you can see that a lot
of exercise feels so

and because the standard of my fondest and
of hours ago I'm not doing very bad.

OK When they in the time they do it's
really compute thirty single values.

I'm computing all assimilates So
if you want to find their best but

come and
you want more than single value for it.

It was me it was a matter
of this is obvious.

Yes OK.

If you want.

We'll make fifty single of our lives.

Sure OK And over fifty and
over twenty five.

I know it's all here.

OK And over five hundred hundred.

It's all OK and over five hundred of them.

So these those and
by two thousand and five and so

the that's the reason why this is here OK.

So the kids obviously later
somewhere around say for this fight.

So this is an interesting problem.

You want for in over a hundred three
thousand the medics Ace I don't do it

often seven hundred I guess.

So forty thousand seven hundred.

If you ask you mean you know or

five hundred single while
you're still I'm doing this.

I'm able to find all three thousand seven
hundred single values when the utility

method is able to find you know if I
had some of them so that's the idea.

So that's what basically brought and
this method is this is the most block

left corner matter where I have graphs for
each of them but this is the best so far.

And the other problems
which I haven't discussed.

OK Is symbolic factorization for this.

I didn't discuss symbolic AI positions on.

But even look at this problem say
you start with a column K. and

you're going down a few columns OK and
you're going to think of column clearly

we can think of it as a graph problem and
as a part of arson.

OK And

the graph is a special graph I can talk
to you if you want if you're interested.

We're able to show that if
you can do a simple symbolic

act with Asian with a graph that was and
one thing is the graph.

It's not a two graph it's a funny.

It's basically a set of parts.

It's not a graph.

It's it's a like a bunch of sequence.

OK so we're able to do that.

I don't doubt I would agree there and
the court actually uses

that if they showed you the next this
can lead to a cure factorization.

And we do in our ng for that you have that
this is the thing as the are doing is to

reduce the number of non-zero is in
our But are not all also equal for

me I.E. later special are used to R.
is closer to about my picks.

I like it a lot you feel the are saying
if the archives really young entries.

OK.

The top row is full.

OK you can see the skyline.

I'll tell you this like a fully
operational about in terms of scale it so

in terms of scale and
it's really really bad.

So not all are all our side
equals what can you find in our

Can we find in our living for
the Q R factorisation that is helping us

protection our drinks dust but
not really well.

So we're working on lotteries for.

Can we integrate this whole thing
with a band of them can we.

If you just give me a band Mattocks
while you do all this stuff just

then you do that.

Doing that I do that.

OK I actually do
the performance of a cell.

So I showed you used to that idea.

The one thing is I just look
at the other end time I try to

find an approximate bandwidth.

So approximate band with this
on three hundred then I just.

It's call in economy three
hundred Anything you need to

call an old three hundred is a con of
the thing below that it's not a condom.

So I use the magic's two or
three hundred bandwidth and

then call the bank all of it which is much
faster than doing all the simple stuff.

So those are some of the issues
I didn't talk about.

So in conclusion.

We talked about a bandolier them which
is I don't go to name names Foster we

dubbed a border sparser CD which
has some nice whistles thing

as you need to have big and
it is quite comedy do with it.

Of sparse is released when you think you
need to if you want some decent number

of think about it if you want to want to
sing live as if it doesn't and I have

the software online for the band the band
called it is online only thing is it's for

evaluation purposes for now because the
university is working the licensing thing.

But yeah you can use it for.

All your purposes and the sky name
cordis if you want to they can give it

to you want it in this it's I didn't put
it up in the website because it's not

quite production for the I want this
to be fully It's not a court order.

It's not for me and

work with Matt with have been Davis' if
you sideways at the end and she got so.

You know all of them has
to thank you thank you.

OK.

Yes yes and no no.

The thing is I I didn't like it but
I did this whole problem we know

very that it's sort of
like a pilot to look

at problems that are traditionally
using Blaster yelled at them's but

will be better too wide and
then use something simpler.

I think it's up something to spar score.

So that's one thing the next is
up from want to talk to people.

OK it's not up it's not for
production for daily use but

the thing is when you actually
develop an application.

You want to find the key to stop.

Rather you want to see the spectrum and

say I have to stop here OK
to find the cure yourself.

You know to find all the single values.

So even for that one.

Piers you were not able to do it but
if you do it.

So if you do all the single values I
don't even sure the numbers even even on

the tests are honestly because the spiral.

It really is really really really slow
if you ask about singularities So

what we will actually do is they're
doing two hundred single values.

OK two hundred is not working.

Maybe to fifteen.

So you're doing it so on this.

I think this would be
useful in that sense.

Yeah I thought about it but
actually it's in the future.

What's actually it's not in
the homes of you not in terms

of if anywhere close to the.

Production value or something like I
say I have some implementation might

more of a multi-core sort of or
plan of battle work.

Because if you look at the Elop.

Cord.
It's actually developed.

It was actually developed out of a braced
machine to create a place machines and.

What they have done can even be done with

can that can be enhanced with
the algorithm they're from.

I can take a look back
at what they did there.

And even use it on my blog court.

The thing is up.

I've thought a word for

them in the multi-core sense not in dumps
of battle sense but not a production very

version they have must sort of
like the Matlab sort of things

and all thank you thank you.

Thank you.

Thank you.