Loop for nested matrix multiplication

Hello guys,

My problem is the following.

I have two matrices: a 155*3 matrix and a 465*3 matrix. I have to multiply each 1x3 row (from the 155*3 matrix) with each consecutive 3x3 matrix from the 465*3 matrix.

Now the loop I tried did not work out and I just can't get my thought's around it.

Here's my code:

m = size(A,2);
n = B(D:E);
D = B(1,:);
E = B(1:3,:); 
C = zeros(m,n);
for ii = 1:m
    for jj = 1:n
         C(ii,jj) = sum(A(ii,:).*B(:,jj).');
    end
end

Where matrix A is the 155*3 matrix and matrix B is the 465*3 matrix.

Any suggestions how to adjust the loop?

Thanks a million.

Kevin

[the cyclist]

This code will not get past the line

n = B(D:E)

unless D and E were already define previously. Can you post the entire code?

What do you want the shape of the final output to be? 155*3?

Is this a school assignment?

[Kevin van Berkel]

Hi Cyclist,

thank you for your response.

I tried to define D and E as integers but did not work out.

my code looks like this now:

d = [19261103; 20121231];  
ddte = datenum(num2str(d),'yyyymmdd');
ndte = (ddte(1):ddte(2))';
t = weekday(ndte);
ndte = ndte(t ~= 1 & t ~= 7);
yourdata = [date,mkt,hml,mom]; 
[yy,mm,dd] = datevec(yourdata(:,1));
ymd = [yy,mm,dd];
im = mm == 11 & dd >= 3;
ii = strfind([~im(1),im(:)'],[0 1]);
sb = zeros(numel(ndte),1);
sb(ii) = 1;
sbc = cumsum(sb);
t = sbc > 0 & sbc ~= max(sbc);
sbb = sbc(t);
sb1 = find(sb(t));
wdta = yourdata(t,:);
[r, c] = ndgrid(sbb,1:size(wdta,2)-1);
out1 = accumarray([r(:) c(:)],reshape(wdta(:,2:4),[],1),[],@mean);
means = [ymd(ii(1:end-1),:),out1] ;

d = [19261103; 20121231];  
ddte = datenum(num2str(d),'yyyymmdd');
ndte = (ddte(1):ddte(2))';
t = weekday(ndte);
ndte = ndte(t ~= 1 & t ~= 7);
yourdata = [date,mkt,hml,mom];
[yy,mm,dd] = datevec(yourdata(:,1));
ymd = [yy,mm,dd];
im = mm == 11 & dd >= 3;
ii = strfind([~im(1),im(:)'],[0 1]);
sb = zeros(size(yourdata,1),1);
sb(ii) = 1;
sbc = cumsum(sb);
t = sbc > 0 & sbc ~= max(sbc);
sb1 = diff(find([sb(t);1]));
wdta = yourdata(t,:);
s = size(wdta,2) - 1;
ydcell = mat2cell(wdta(:,2:end),sb1,s);
invcov = cellfun(@(x)cov(x)\eye(s),ydcell,'un',0);

*m = size(A,2);
D = B(1,:);
E = B(1:3,:); 
n = B(D:E);
C = zeros(m,n);
for ii = 1:m
  for jj = 1:n
       C(ii,jj) = sum(B(ii,:).*A(:,jj).');
  end
end*

Where the latter part is where I got stuck.

This is no school assignment but I need to determine portfolio weights to do further research. I am quite new to matlab so still have to get familiar with certain parts of it..

Thanks anyway for your help!

The final shape should indeed be 155*3!

Answer 1

[Andrei Bobrov]

eg:

A = randi(4,155,3);
B = randi(8,455,3);% your matrices A and B

one variant;

s = size(A);
C = zeros(s);
for j1 = 1:s(1)
    C(j1,:) = A(j1,:)*B((j1-1)*s(2)+1:j1*s(2),:);
end

other variant

s = size(A);
C = zeros(s);
for j1 = 1:s(1)
    C(j1,:) = B((j1-1)*s(2)+1:j1*s(2),:)*A(j1,:)';
end

Answer 2

[Matt J]

Here's a way with very short loops, using my DOWNSAMPN utility below

a=reshape(A.',[],1);
C=bsxfun(@times,a,B);
C=downsampn(C,[3,1]);

function M=downsampn(M,bindims)
%DOWNSAMPN - simple tool for downsampling n-dimensional nonsparse arrays
%
%  M=downsampn(M,bindims)
%
%in:
%
% M: an array
% bindims: a vector of integer binning dimensions
%
%out:
%
% M: the downsized array

nn=length(bindims);

[sz{1:nn}]=size(M); %M is the original array
sz=[sz{:}];

newdims=sz./bindims;

args=num2cell([bindims;newdims]);

M=reshape(M,args{:});

for ii=1:nn

   M=mean(M,2*ii-1);

end

M=reshape(M,newdims);

[Matt J]

Kevin van Berkel Commented:

Hello Matt,

Thank you for your response.

I tried your code but Matlab yields some errors. The first error is that the

function M=downsampn(M,bindims) is wrong. Matlab does not know what to do with the "function" part. The next error I get is:

Error using bsxfun Non-singleton dimensions of the two input arrays must match each other.

Error in mult (line 2) C=bsxfun(@times,a,B);.

Do you have any clue how to resolve this?

Cheers.

[Matt J]

function M=downsampn(M,bindims) is wrong. Matlab does not know what to do with the "function" part.

You were supposed to put the code for downsampn in its own mfile. If that's not the problem, I need to see copy/pastes of the error messages.

Error using bsxfun Non-singleton dimensions of the two input arrays must match each other.

I don't receive this error. In all likelihood, it means that A is not 155x3 or B is not 465x3 like you posted. Here is the output of WHOS when I run. You should examine your matrix sizes in a similar way.

 >> whos
  Name        Size            Bytes  Class     Attributes

A         155x3              3720  double              
B         465x3             11160  double              
C         155x3              3720  double              
a         465x1              3720  double

Answer 3

[Kevin van Berkel]

Relocated to Comment by Matt J

Answer 4

[Kevin van Berkel]

Hello Matt, thanks for your effort but Andrei's solution is more suitable to me.

Andrei, thanks again, got it running perfectly now.

Answer 5

[Matt J]

Another loopless way. Note that it would all be much simpler/faster (i.e., no transposes) if the data were organized in columns instead of rows

      Ar=reshape(A.',1,3,[]);
      Br=reshape(B.',3,3,[]);

      Cr=sum(bsxfun(@times,Ar,Br),2);

      C=squeeze(Cr);

One could also use FEX: mtimes for part of the above

   Cr=mtimesx(Ar,Br,'t');