MATLAB Central Newsreader - Interpolation of matrix

Interpolation of matrix

Ben — Thu, 08 Nov 2007 14:30:22 -0500

Hi there,

I'm trying to perform some operations on a matrix - I have a 20x20
matrix that I've got to remove some rows from the top, and re-generate
lines at the bottom to leave the matrix the same size as it was.

So, say I have a 10x10 matrix, I remove the top row. What I now want to
do is generate a row between the row at the bottom, and the one above
it, that I can put in to keep it 10x10.

I've looked at interp2, and it sort of seems to do what I want, e.g
running interp2(Matrix) gives me a 19x19 matrix with an interpolated row
between each. Is there any way to point interp2 at a matrix, with row
vector 9, and get it to return a 1x10 matrix containing the interpolated
row between row vectors 9 and 10, that I can just add to the first matrix?

I believe interp2 can sort-of do this, using Xi and Yi, but that appears
to be more related to generating an interpolated value from two data
points, not two rows?

Anyone have any advice?

Thanks,

Ben

Re: Interpolation of matrix

PB — Thu, 08 Nov 2007 21:04:18 -0500

Den Thu, 08 Nov 2007 14:30:22 +0000 skrev Ben:

> Hi there,
>
> I'm trying to perform some operations on a matrix - I have a 20x20
> matrix that I've got to remove some rows from the top, and re-generate
> lines at the bottom to leave the matrix the same size as it was.
>
> So, say I have a 10x10 matrix, I remove the top row. What I now want to
> do is generate a row between the row at the bottom, and the one above
> it, that I can put in to keep it 10x10.
>
> I've looked at interp2, and it sort of seems to do what I want, e.g
> running interp2(Matrix) gives me a 19x19 matrix with an interpolated row
> between each. Is there any way to point interp2 at a matrix, with row
> vector 9, and get it to return a 1x10 matrix containing the interpolated
> row between row vectors 9 and 10, that I can just add to the first
> matrix?
>
> I believe interp2 can sort-of do this, using Xi and Yi, but that appears
> to be more related to generating an interpolated value from two data
> points, not two rows?
>
> Anyone have any advice?
>
> Thanks,
>
> Ben

Does this help?

a=magic(3);
a(:,3)=[] % remove last row
ix=1:0.5:2;
[xi,yi]=meshgrid(ix)
y=interp2(a,xi,yi)

/PB

Re: Interpolation of matrix

Ben — Fri, 09 Nov 2007 10:45:38 -0500

PB wrote:
> Den Thu, 08 Nov 2007 14:30:22 +0000 skrev Ben:
>
>> Hi there,
>>
>> I'm trying to perform some operations on a matrix - I have a 20x20
>> matrix that I've got to remove some rows from the top, and re-generate
>> lines at the bottom to leave the matrix the same size as it was.
>>
>> So, say I have a 10x10 matrix, I remove the top row. What I now want to
>> do is generate a row between the row at the bottom, and the one above
>> it, that I can put in to keep it 10x10.
>>
>> I've looked at interp2, and it sort of seems to do what I want, e.g
>> running interp2(Matrix) gives me a 19x19 matrix with an interpolated row
>> between each. Is there any way to point interp2 at a matrix, with row
>> vector 9, and get it to return a 1x10 matrix containing the interpolated
>> row between row vectors 9 and 10, that I can just add to the first
>> matrix?
>>
>> I believe interp2 can sort-of do this, using Xi and Yi, but that appears
>> to be more related to generating an interpolated value from two data
>> points, not two rows?
>>
>> Anyone have any advice?
>>
>> Thanks,
>>
>> Ben
>
> Does this help?
>
> a=magic(3);
> a(:,3)=[] % remove last row
> ix=1:0.5:2;
> [xi,yi]=meshgrid(ix)
> y=interp2(a,xi,yi)
>
>
> /PB

Thanks, but your a= line actually removes the last column and not the
last row...

I changed it to remove the last column, but the final result bears no
resemblance to the original square I'm not sure how the meshgrid of ix
interacts with the interpolation, which is what I think is causing the
wrong results as I changed it from column to row...?

Re: Interpolation of matrix

John D'Errico — Fri, 09 Nov 2007 11:28:08 -0500

Ben <bw.games_n0spam@gmail.nospam.com> wrote in message <mTWYi.
10525$ib1.5678@newsfe3-win.ntli.net>...
> PB wrote:
> > Den Thu, 08 Nov 2007 14:30:22 +0000 skrev Ben:
> >
> >> Hi there,
> >>
> >> I'm trying to perform some operations on a matrix - I have a 20x20
> >> matrix that I've got to remove some rows from the top, and re-
generate
> >> lines at the bottom to leave the matrix the same size as it was.
> >>
> >> So, say I have a 10x10 matrix, I remove the top row. What I now want
to
> >> do is generate a row between the row at the bottom, and the one above
> >> it, that I can put in to keep it 10x10.
> >>
> >> I've looked at interp2, and it sort of seems to do what I want, e.g
> >> running interp2(Matrix) gives me a 19x19 matrix with an interpolated
row
> >> between each. Is there any way to point interp2 at a matrix, with row
> >> vector 9, and get it to return a 1x10 matrix containing the interpolated
> >> row between row vectors 9 and 10, that I can just add to the first
> >> matrix?
> >>
> >> I believe interp2 can sort-of do this, using Xi and Yi, but that appears
> >> to be more related to generating an interpolated value from two data
> >> points, not two rows?
> >>
> >> Anyone have any advice?
> >>
> >> Thanks,
> >>
> >> Ben
> >
> > Does this help?
> >
> > a=magic(3);
> > a(:,3)=[] % remove last row
> > ix=1:0.5:2;
> > [xi,yi]=meshgrid(ix)
> > y=interp2(a,xi,yi)
> >
> >
> > /PB
>
> Thanks, but your a= line actually removes the last column and not the
> last row...
>
> I changed it to remove the last column, but the final result bears no
> resemblance to the original square I'm not sure how the meshgrid of ix
> interacts with the interpolation, which is what I think is causing the
> wrong results as I changed it from column to row...?
>

When you remove information by deleting a row
from a magic square, an interpolant will not know
that the square was a magic one. Also, PB made
a mistake in his example.

a=magic(3);
a(3,:)=[]; % remove last row
ix=1:0.5:2;
iy = 1:3;
[xi,yi]=meshgrid(ix,iy);
y=interp2(a,yi,xi)';

a =
     8 1 6
     3 5 7

y =
            8 1 6
          5.5 3 6.5
            3 5 7

Note the transpose at the end!

HOWEVER. dropping the last row of an array,
then inserting a new one internally to make
up for it by interpolation will not generally
make sense to me. But its your data.

HTH,
John

Re: Interpolation of matrix

Ben — Fri, 09 Nov 2007 16:35:17 -0500

John D'Errico wrote:
> Ben <bw.games_n0spam@gmail.nospam.com> wrote in message <mTWYi.
> 10525$ib1.5678@newsfe3-win.ntli.net>...
>> PB wrote:
>>> Den Thu, 08 Nov 2007 14:30:22 +0000 skrev Ben:
>>>
>>>> Hi there,
>>>>
>>>> I'm trying to perform some operations on a matrix - I have a 20x20
>>>> matrix that I've got to remove some rows from the top, and re-
> generate
>>>> lines at the bottom to leave the matrix the same size as it was.
>>>>
>>>> So, say I have a 10x10 matrix, I remove the top row. What I now want
> to
>>>> do is generate a row between the row at the bottom, and the one above
>>>> it, that I can put in to keep it 10x10.
>>>>
>>>> I've looked at interp2, and it sort of seems to do what I want, e.g
>>>> running interp2(Matrix) gives me a 19x19 matrix with an interpolated
> row
>>>> between each. Is there any way to point interp2 at a matrix, with row
>>>> vector 9, and get it to return a 1x10 matrix containing the interpolated
>>>> row between row vectors 9 and 10, that I can just add to the first
>>>> matrix?
>>>>
>>>> I believe interp2 can sort-of do this, using Xi and Yi, but that appears
>>>> to be more related to generating an interpolated value from two data
>>>> points, not two rows?
>>>>
>>>> Anyone have any advice?
>>>>
>>>> Thanks,
>>>>
>>>> Ben
>>> Does this help?
>>>
>>> a=magic(3);
>>> a(:,3)=[] % remove last row
>>> ix=1:0.5:2;
>>> [xi,yi]=meshgrid(ix)
>>> y=interp2(a,xi,yi)
>>>
>>>
>>> /PB
>> Thanks, but your a= line actually removes the last column and not the
>> last row...
>>
>> I changed it to remove the last column, but the final result bears no
>> resemblance to the original square I'm not sure how the meshgrid of ix
>> interacts with the interpolation, which is what I think is causing the
>> wrong results as I changed it from column to row...?
>>
>
> When you remove information by deleting a row
> from a magic square, an interpolant will not know
> that the square was a magic one. Also, PB made
> a mistake in his example.
>
> a=magic(3);
> a(3,:)=[]; % remove last row
> ix=1:0.5:2;
> iy = 1:3;
> [xi,yi]=meshgrid(ix,iy);
> y=interp2(a,yi,xi)';
>
>
> a =
> 8 1 6
> 3 5 7
>
> y =
> 8 1 6
> 5.5 3 6.5
> 3 5 7
>
> Note the transpose at the end!
>
> HOWEVER. dropping the last row of an array,
> then inserting a new one internally to make
> up for it by interpolation will not generally
> make sense to me. But its your data.
>
> HTH,
> John
>
>

Thanks for the feedback.

I think I was a bit unclear, sorry.

What I want to do, is remove the top row of an array.
Then I want to interpolate at the bottom of the array and create an
interpolated row between the last row, and the row previous to that, to
leave the array the same size as it was before, and the data is roughly
the same.
This has the effect of shifting the previous centre row of the array up
by one, without dramatically affecting my data, which is what I want.

Any ideas?

Thanks,

Ben