Thread Subject: Setting up linear multiple regression matrix

I have
A=[1 X; 0 X];
b=[Y;Z];
where X, Y and Z are vectors and I want to do x=A\b to find two
coefficients x1 and x2. I am finding it hard to arrange the vectors in
the matrix form for the required regression.
Any help please ?

On Jul 18, 2:03=A0am, fas <faisalmu...@gmail.com> wrote:
> I have
> A=3D[1 X; 0 X];

X must be a row vector

> b=3D[Y;Z];
> where X, Y and Z are vectors

It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]

size(A) =3D [ 2 n+1 ]
size(b) =3D [ 2 n ]

=3D=3D> size(A\b) =3D [ n+1 n]

> and I want to do x=3DA\b to find two
> coefficients x1 and x2.

It does not compute.

>I am finding it hard to arrange the vectors in
> the matrix form for the required regression.
> Any help please ?

Begin by using less confusing notation;
e.g., X,Y,Z --> U,Y,Z

Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.

It looks like you are just trying to solve A*x=3Db, given A and b.

This is not a regression problem.

Hope this helps.

Greg

On Jul 18, 7:58 pm, Greg Heath <he...@alumni.brown.edu> wrote:
> On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > I have
> > A=[1 X; 0 X];
>
> X must be a row vector
>
> > b=[Y;Z];
> > where X, Y and Z are vectors
>
> It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]
>
> size(A) = [ 2 n+1 ]
> size(b) = [ 2 n ]
>
> ==> size(A\b) = [ n+1 n]
>
> > and I want to do x=A\b to find two
> > coefficients x1 and x2.
>
> It does not compute.
>
> >I am finding it hard to arrange the vectors in
> > the matrix form for the required regression.
> > Any help please ?
>
> Begin by using less confusing notation;
> e.g., X,Y,Z --> U,Y,Z
>
> Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.
>
> It looks like you are just trying to solve A*x=b, given A and b.
>
> This is not a regression problem.
>
> Hope this helps.
>
> Greg
My A matrix is like that
A=
[1 X1;
 0 X1;
1 X2;
0 X2;
....
1 Xn;
0 Xn]
b=
[Y1;
Z1;
Y2;
Z2;
..
Yn;
Zn]

and finally
x=[a;b]
If I manually supply few vectors values for X,Y,Z I do get a& b.
like
x=A\b;
but my only problem is I do not want to enter the vector values may be
repmat or some other command may help me. I have tried but did not
have success :(

On Jul 18, 7:40=A0am, fas <faisalmu...@gmail.com> wrote:
> On Jul 18, 7:58 pm, Greg Heath <he...@alumni.brown.edu> wrote:
>
>
>
> > On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > > I have
> > > A=3D[1 X; 0 X];
>
> > X must be a row vector
>
> > > b=3D[Y;Z];
> > > where X, Y and Z are vectors
>
> > It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]
>
> > size(A) =3D [ 2 =A0n+1 ]
> > size(b) =3D [ 2 =A0n ]
>
> > =3D=3D> size(A\b) =3D [ n+1 n]
>
> > > and I want to do x=3DA\b to find two
> > > coefficients x1 and x2.
>
> > It does not compute.
>
> > >I am finding it hard to arrange the vectors in
> > > the matrix form for the required regression.
> > > Any help please ?
>
> > Begin by using less confusing notation;
> > e.g., X,Y,Z --> U,Y,Z
>
> > Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.
>
> > It looks like you are just trying to solve A*x=3Db, given A and b.
>
> > This is not a regression problem.
>
> > Hope this helps.
>
> > Greg
>
> My A matrix is like that
> A=3D
> [1 =A0 X1;
> =A00 =A0 X1;
> 1 =A0 X2;
> 0 =A0 X2;
> ....
> 1 =A0Xn;
> 0 =A0Xn]
> b=3D
> [Y1;
> Z1;
> Y2;
> Z2;
> ..
> Yn;
> Zn]
>
> and finally
> x=3D[a;b]
> If I manually supply few vectors values for X,Y,Z I do get a& b.
> like
> x=3DA\b;
> but my only problem is I do not want to enter the vector values may be
> repmat or some other command may help me. I have tried but did not
> have success

Look up row permutation matrices and apply them to

[ ones(n,1) X ; zeros(n,1) X ]

and

[ Y; Z]

Hope this helps.

Greg

On Jul 19, 2:56 am, Greg Heath <he...@alumni.brown.edu> wrote:
> On Jul 18, 7:40 am, fas <faisalmu...@gmail.com> wrote:
>
>
>
> > On Jul 18, 7:58 pm, Greg Heath <he...@alumni.brown.edu> wrote:
>
> > > On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > I have
> > > > A=[1 X; 0 X];
>
> > > X must be a row vector
>
> > > > b=[Y;Z];
> > > > where X, Y and Z are vectors
>
> > > It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]
>
> > > size(A) = [ 2 n+1 ]
> > > size(b) = [ 2 n ]
>
> > > ==> size(A\b) = [ n+1 n]
>
> > > > and I want to do x=A\b to find two
> > > > coefficients x1 and x2.
>
> > > It does not compute.
>
> > > >I am finding it hard to arrange the vectors in
> > > > the matrix form for the required regression.
> > > > Any help please ?
>
> > > Begin by using less confusing notation;
> > > e.g., X,Y,Z --> U,Y,Z
>
> > > Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.
>
> > > It looks like you are just trying to solve A*x=b, given A and b.
>
> > > This is not a regression problem.
>
> > > Hope this helps.
>
> > > Greg
>
> > My A matrix is like that
> > A=
> > [1 X1;
> > 0 X1;
> > 1 X2;
> > 0 X2;
> > ....
> > 1 Xn;
> > 0 Xn]
> > b=
> > [Y1;
> > Z1;
> > Y2;
> > Z2;
> > ..
> > Yn;
> > Zn]
>
> > and finally
> > x=[a;b]
> > If I manually supply few vectors values for X,Y,Z I do get a& b.
> > like
> > x=A\b;
> > but my only problem is I do not want to enter the vector values may be
> > repmat or some other command may help me. I have tried but did not
> > have success
>
> Look up row permutation matrices and apply them to
>
> [ ones(n,1) X ; zeros(n,1) X ]
>
> and
>
> [ Y; Z]
>
> Hope this helps.
>
> Greg

Hi Greg
I gave the format for my A matrix, as such its not created and I have
to create my A and b matrices. I have only given their format. Can you
help me a bit further ?

On Jul 21, 1:05=A0am, fas <faisalmu...@gmail.com> wrote:
> On Jul 19, 2:56 am,Greg Heath<he...@alumni.brown.edu> wrote:
>
>
>
>
>
> > On Jul 18, 7:40 am, fas <faisalmu...@gmail.com> wrote:
>
> > > On Jul 18, 7:58 pm,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > > On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > > I have
> > > > > A=3D[1 X; 0 X];
>
> > > > X must be a row vector
>
> > > > > b=3D[Y;Z];
> > > > > where X, Y and Z are vectors
>
> > > > It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]
>
> > > > size(A) =3D [ 2 =A0n+1 ]
> > > > size(b) =3D [ 2 =A0n ]
>
> > > > =3D=3D> size(A\b) =3D [ n+1 n]
>
> > > > > and I want to do x=3DA\b to find two
> > > > > coefficients x1 and x2.
>
> > > > It does not compute.
>
> > > > >I am finding it hard to arrange the vectors in
> > > > > the matrix form for the required regression.
> > > > > Any help please ?
>
> > > > Begin by using less confusing notation;
> > > > e.g., X,Y,Z --> U,Y,Z
>
> > > > Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.
>
> > > > It looks like you are just trying to solve A*x=3Db, given A and b.
>
> > > > This is not a regression problem.
>
> > > > Hope this helps.
>
> > > > Greg
>
> > > My A matrix is like that
> > > A=3D
> > > [1 =A0 X1;
> > > =A00 =A0 X1;
> > > 1 =A0 X2;
> > > 0 =A0 X2;
> > > ....
> > > 1 =A0Xn;
> > > 0 =A0Xn]
> > > b=3D
> > > [Y1;
> > > Z1;
> > > Y2;
> > > Z2;
> > > ..
> > > Yn;
> > > Zn]
>
> > > and finally
> > > x=3D[a;b]
> > > If I manually supply few vectors values for X,Y,Z I do get a& b.
> > > like
> > > x=3DA\b;
> > > but my only problem is I do not want to enter the vector values may b=
e
> > > repmat or some other command may help me. I have tried but did not
> > > have success
>
> > Look up row permutation matrices and apply them to
>
> > [ ones(n,1) X ; zeros(n,1) X ]
>
> > and
>
> > [ Y; Z]
>
> > Hope this helps.
>
> > Greg
>
> Hi Greg
> I gave the format for my A matrix, as such its not created and I have
> to create my A and b matrices. I have only given their format. Can you
> help me a bit further ?

http://en.wikipedia.org/wiki/Permutation_matrix

Hope this helps.

Greg

On Jul 22, 3:12 am, Greg Heath <he...@alumni.brown.edu> wrote:
> On Jul 21, 1:05 am, fas <faisalmu...@gmail.com> wrote:
>
>
>
> > On Jul 19, 2:56 am,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > On Jul 18, 7:40 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > On Jul 18, 7:58 pm,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > > > On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > > > I have
> > > > > > A=[1 X; 0 X];
>
> > > > > X must be a row vector
>
> > > > > > b=[Y;Z];
> > > > > > where X, Y and Z are vectors
>
> > > > > It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]
>
> > > > > size(A) = [ 2 n+1 ]
> > > > > size(b) = [ 2 n ]
>
> > > > > ==> size(A\b) = [ n+1 n]
>
> > > > > > and I want to do x=A\b to find two
> > > > > > coefficients x1 and x2.
>
> > > > > It does not compute.
>
> > > > > >I am finding it hard to arrange the vectors in
> > > > > > the matrix form for the required regression.
> > > > > > Any help please ?
>
> > > > > Begin by using less confusing notation;
> > > > > e.g., X,Y,Z --> U,Y,Z
>
> > > > > Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.
>
> > > > > It looks like you are just trying to solve A*x=b, given A and b.
>
> > > > > This is not a regression problem.
>
> > > > > Hope this helps.
>
> > > > > Greg
>
> > > > My A matrix is like that
> > > > A=
> > > > [1 X1;
> > > > 0 X1;
> > > > 1 X2;
> > > > 0 X2;
> > > > ....
> > > > 1 Xn;
> > > > 0 Xn]
> > > > b=
> > > > [Y1;
> > > > Z1;
> > > > Y2;
> > > > Z2;
> > > > ..
> > > > Yn;
> > > > Zn]
>
> > > > and finally
> > > > x=[a;b]
> > > > If I manually supply few vectors values for X,Y,Z I do get a& b.
> > > > like
> > > > x=A\b;
> > > > but my only problem is I do not want to enter the vector values may be
> > > > repmat or some other command may help me. I have tried but did not
> > > > have success
>
> > > Look up row permutation matrices and apply them to
>
> > > [ ones(n,1) X ; zeros(n,1) X ]
>
> > > and
>
> > > [ Y; Z]
>
> > > Hope this helps.
>
> > > Greg
>
> > Hi Greg
> > I gave the format for my A matrix, as such its not created and I have
> > to create my A and b matrices. I have only given their format. Can you
> > help me a bit further ?
>
> http://en.wikipedia.org/wiki/Permutation_matrix
>
> Hope this helps.
>
> Greg

I think I havn't been clear about my question.
What I want is to create a matrix of the form
A=
 [1 X1;
  0 X1;
 1 X2;
 0 X2;
.. 1 Xn;
 0 Xn]
from a vector X where X=X1,X2...Xn

secondly a vector b=
 [Y1;
Z1;
Y2;
 Z2;
 ..
Yn;
Zn]

from two vector Y and Z. I am afraid I am still unable to code it :(

On Jul 22, 2:17=A0am, fas <faisalmu...@gmail.com> wrote:
> On Jul 22, 3:12 am, Greg Heath <he...@alumni.brown.edu> wrote:
>
>
>
>
>
> > On Jul 21, 1:05 am, fas <faisalmu...@gmail.com> wrote:
>
> > > On Jul 19, 2:56 am,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > > On Jul 18, 7:40 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > > On Jul 18, 7:58 pm,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > > > > On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > > > > I have
> > > > > > > A=3D[1 X; 0 X];
>
> > > > > > X must be a row vector
>
> > > > > > > b=3D[Y;Z];
> > > > > > > where X, Y and Z are vectors
>
> > > > > > It looks like you want X,Y,Z to have the same dimensions .. [ 1=
 n]
>
> > > > > > size(A) =3D [ 2 =A0n+1 ]
> > > > > > size(b) =3D [ 2 =A0n ]
>
> > > > > > =3D=3D> size(A\b) =3D [ n+1 n]
>
> > > > > > > and I want to do x=3DA\b to find two
> > > > > > > coefficients x1 and x2.
>
> > > > > > It does not compute.
>
> > > > > > >I am finding it hard to arrange the vectors in
> > > > > > > the matrix form for the required regression.
> > > > > > > Any help please ?
>
> > > > > > Begin by using less confusing notation;
> > > > > > e.g., X,Y,Z --> U,Y,Z
>
> > > > > > Next, explicitly state the dimensions of ALL variables U,Y,Z,A,=
b,x.
>
> > > > > > It looks like you are just trying to solve A*x=3Db, given A and=
 b.
>
> > > > > > This is not a regression problem.
>
> > > > > > Hope this helps.
>
> > > > > > Greg
>
> > > > > My A matrix is like that
> > > > > A=3D
> > > > > [1 =A0 X1;
> > > > > =A00 =A0 X1;
> > > > > 1 =A0 X2;
> > > > > 0 =A0 X2;
> > > > > ....
> > > > > 1 =A0Xn;
> > > > > 0 =A0Xn]
> > > > > b=3D
> > > > > [Y1;
> > > > > Z1;
> > > > > Y2;
> > > > > Z2;
> > > > > ..
> > > > > Yn;
> > > > > Zn]
>
> > > > > and finally
> > > > > x=3D[a;b]
> > > > > If I manually supply few vectors values for X,Y,Z I do get a& b.
> > > > > like
> > > > > x=3DA\b;
> > > > > but my only problem is I do not want to enter the vector values m=
ay be
> > > > > repmat or some other command may help me. I have tried but did no=
t
> > > > > have success
>
> > > > Look up row permutation matrices and apply them to
>
> > > > [ ones(n,1) X ; zeros(n,1) X ]
>
> > > > and
>
> > > > [ Y; Z]
>
> > > > Hope this helps.
>
> > > > Greg
>
> > > Hi Greg
> > > I gave the format for my A matrix, as such its not created and I have
> > > to create my A and b matrices. I have only given their format. Can yo=
u
> > > help me a bit further ?
>
> >http://en.wikipedia.org/wiki/Permutation_matrix
>
> > Hope this helps.
>
> > Greg
>
> I think I havn't been clear about my question.
> What I want is to create a matrix of the form
> A=3D
> =A0[1 =A0 X1;
> =A0 0 =A0 X1;
> =A01 =A0 X2;
> =A00 =A0 X2;
> .. 1 =A0Xn;
> =A00 =A0Xn]
> from a vector X where X=3DX1,X2...Xn
>
> secondly a vector b=3D
> =A0[Y1;
> Z1;
> Y2;
> =A0Z2;
> =A0..
> Yn;
> Zn]
>
> from two vector Y and Z. I am afraid I am still unable to code it

A =3D P1*[ ones(n,1) X ; zeros(n,1) X ];

b =3D P2* [ Y; Z];

where P1 and P2 are row permutation matrices.

http://en.wikipedia.org/wiki/Permutation_matrix

Hope you understand it now.

Greg

On Jul 22, 9:27 pm, Greg Heath <he...@alumni.brown.edu> wrote:
> On Jul 22, 2:17 am, fas <faisalmu...@gmail.com> wrote:
>
>
>
> > On Jul 22, 3:12 am, Greg Heath <he...@alumni.brown.edu> wrote:
>
> > > On Jul 21, 1:05 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > On Jul 19, 2:56 am,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > > > On Jul 18, 7:40 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > > > On Jul 18, 7:58 pm,Greg Heath<he...@alumni.brown.edu> wrote:
>
> > > > > > > On Jul 18, 2:03 am, fas <faisalmu...@gmail.com> wrote:
>
> > > > > > > > I have
> > > > > > > > A=[1 X; 0 X];
>
> > > > > > > X must be a row vector
>
> > > > > > > > b=[Y;Z];
> > > > > > > > where X, Y and Z are vectors
>
> > > > > > > It looks like you want X,Y,Z to have the same dimensions .. [ 1 n]
>
> > > > > > > size(A) = [ 2 n+1 ]
> > > > > > > size(b) = [ 2 n ]
>
> > > > > > > ==> size(A\b) = [ n+1 n]
>
> > > > > > > > and I want to do x=A\b to find two
> > > > > > > > coefficients x1 and x2.
>
> > > > > > > It does not compute.
>
> > > > > > > >I am finding it hard to arrange the vectors in
> > > > > > > > the matrix form for the required regression.
> > > > > > > > Any help please ?
>
> > > > > > > Begin by using less confusing notation;
> > > > > > > e.g., X,Y,Z --> U,Y,Z
>
> > > > > > > Next, explicitly state the dimensions of ALL variables U,Y,Z,A,b,x.
>
> > > > > > > It looks like you are just trying to solve A*x=b, given A and b.
>
> > > > > > > This is not a regression problem.
>
> > > > > > > Hope this helps.
>
> > > > > > > Greg
>
> > > > > > My A matrix is like that
> > > > > > A=
> > > > > > [1 X1;
> > > > > > 0 X1;
> > > > > > 1 X2;
> > > > > > 0 X2;
> > > > > > ....
> > > > > > 1 Xn;
> > > > > > 0 Xn]
> > > > > > b=
> > > > > > [Y1;
> > > > > > Z1;
> > > > > > Y2;
> > > > > > Z2;
> > > > > > ..
> > > > > > Yn;
> > > > > > Zn]
>
> > > > > > and finally
> > > > > > x=[a;b]
> > > > > > If I manually supply few vectors values for X,Y,Z I do get a& b.
> > > > > > like
> > > > > > x=A\b;
> > > > > > but my only problem is I do not want to enter the vector values may be
> > > > > > repmat or some other command may help me. I have tried but did not
> > > > > > have success
>
> > > > > Look up row permutation matrices and apply them to
>
> > > > > [ ones(n,1) X ; zeros(n,1) X ]
>
> > > > > and
>
> > > > > [ Y; Z]
>
> > > > > Hope this helps.
>
> > > > > Greg
>
> > > > Hi Greg
> > > > I gave the format for my A matrix, as such its not created and I have
> > > > to create my A and b matrices. I have only given their format. Can you
> > > > help me a bit further ?
>
> > >http://en.wikipedia.org/wiki/Permutation_matrix
>
> > > Hope this helps.
>
> > > Greg
>
> > I think I havn't been clear about my question.
> > What I want is to create a matrix of the form
> > A=
> > [1 X1;
> > 0 X1;
> > 1 X2;
> > 0 X2;
> > .. 1 Xn;
> > 0 Xn]
> > from a vector X where X=X1,X2...Xn
>
> > secondly a vector b=
> > [Y1;
> > Z1;
> > Y2;
> > Z2;
> > ..
> > Yn;
> > Zn]
>
> > from two vector Y and Z. I am afraid I am still unable to code it
>
> A = P1*[ ones(n,1) X ; zeros(n,1) X ];
>
> b = P2* [ Y; Z];
>
> where P1 and P2 are row permutation matrices.
>
> http://en.wikipedia.org/wiki/Permutation_matrix
>
> Hope you understand it now.
>
> Greg

I have come to realize that constructing P1 and P2 is as time
consuming as putting the values manually, if I am not wrong ?

>> > I think I havn't been clear about my question.
>> > What I want is to create a matrix of the form
>> > A=
>> > [1 X1;
>> > 0 X1;
>> > 1 X2;
>> > 0 X2;
>> > .. 1 Xn;
>> > 0 Xn]
>> > from a vector X where X=X1,X2...Xn
>>
>> > secondly a vector b=
>> > [Y1;
>> > Z1;
>> > Y2;
>> > Z2;
>> > ..
>> > Yn;
>> > Zn]
>>
>> > from two vector Y and Z. I am afraid I am still unable to code it

I have not followed this until now, but it seems like you want to do the
following:

x = (1:5)'; y = 10*x; z = 100*x;
col1 = repmat([1;0],5,1); % column of alternating 1 and 0
col2 = [x'; x']; col2 = col2(:); % column of x values repeated twice
a = [col1 col2]
b = [y'; z']; % matrix with y in row 1, z in row 2
b = b(:) % column of interleaved y and z

-- Tom

On Jul 23, 11:20 pm, "Tom Lane" <tl...@mathworks.com> wrote:
> >> > I think I havn't been clear about my question.
> >> > What I want is to create a matrix of the form
> >> > A=
> >> > [1 X1;
> >> > 0 X1;
> >> > 1 X2;
> >> > 0 X2;
> >> > .. 1 Xn;
> >> > 0 Xn]
> >> > from a vector X where X=X1,X2...Xn
>
> >> > secondly a vector b=
> >> > [Y1;
> >> > Z1;
> >> > Y2;
> >> > Z2;
> >> > ..
> >> > Yn;
> >> > Zn]
>
> >> > from two vector Y and Z. I am afraid I am still unable to code it
>
> I have not followed this until now, but it seems like you want to do the
> following:
>
> x = (1:5)'; y = 10*x; z = 100*x;
> col1 = repmat([1;0],5,1); % column of alternating 1 and 0
> col2 = [x'; x']; col2 = col2(:); % column of x values repeated twice
> a = [col1 col2]
> b = [y'; z']; % matrix with y in row 1, z in row 2
> b = b(:) % column of interleaved y and z
>
> -- Tom

Thanks Tom. This is exactly what I want.

On Jul 23, 9:20=A0am, "Tom Lane" <tl...@mathworks.com> wrote:
> >> > I think I havn't been clear about my question.
> >> > What I want is to create a matrix of the form
> >> > A=3D
> >> > =A0[1 =A0 X1;
> >> > =A0 0 =A0 X1;
> >> > =A01 =A0 X2;
> >> > =A00 =A0 X2;
> >> > .. 1 =A0Xn;
> >> > =A00 =A0Xn]
> >> > from a vector X where X=3DX1,X2...Xn
>
> >> > secondly a vector b=3D
> >> > =A0[Y1;
> >> > Z1;
> >> > Y2;
> >> > =A0Z2;
> >> > =A0..
> >> > Yn;
> >> > Zn]
>
> >> > from two vector Y and Z. I am afraid I am still unable to code it
>
> I have not followed this until now, but it seems like you want to do the
> following:
>
> x =3D (1:5)'; y =3D 10*x; z =3D 100*x;
> col1 =3D repmat([1;0],5,1); =A0 % column of alternating 1 and 0
> col2 =3D [x'; x']; col2 =3D col2(:); =A0 % column of x values repeated tw=
ice
> a =3D [col1 col2]
> b =3D [y'; z']; =A0% matrix with y in row 1, z in row 2
> b =3D b(:) =A0% column of interleaved y and z

Nice use of (:)!

Greg