Jean-Paul
If I understand your questions, imposing your restrictions on  the 
predicted values
and on sums (or even using weighted sums where each  observation in the 
"sum" 
does not receive equal weight) of linear  combination of subsets of the 
columns of 
X is not difficult. Sets of the  resulting linear restrictions can be 
easily imposed and 
tested using the  "car" package.  Unless things have changed in the past 
year, 
I believe  the only package that currently allows you to explicitly recover 
your  
parameter estimates is the 'systemfit' package that can also be used  to
estimate a single equation.  I believe the author of "systemfit"  utilizes 
the 
augmented Lagrangian matrix in obtaining the parameter  estimates.   
 
Alternatively, I can send you an R function that uses generalized inverse  
projections
to obtain solutions and test statistics while imposing linear  equality 
restrictions 
on a linear regression.  I have other code  that uses the projection 
approach to impose linear 
equality parameter  restrictions when estimating and testing nonlinear 
(i.e. logit-probit  type)
models.   
 
To demonstate: 
Let w' be a weighted "summing" row vector. Note that if  each element in w 
is 1, you have the 
normal summing operator. Let X denote  the data matrix and let bhat denote 
the parameter vector.
Your restriction on  the predicted values can then be written as:
 
w' %*% (X %*% bhat) = c    or  (w' %*% X) bhat =  c  or  r' %*% bhat = c
 
where r' = w' %*% X is your restriction's  row vector.  Again all  elements 
in w' can be 1 giving your summing restriction.
 

What you wanted in the second part of your question was not as clear to  
me.  If you 
are wanting to impose restrictions on reachable subspaces  of the column 
space of X,
this can also be easily accomplished.
 
For example:  
 
Let w(j) denote a vector of weights that apply to the j'th column in X.  
Again summing is a special
case where w(j) (or all w(j)'s) can be set to a  vector of ones. Let x(j) 
denote 
the j'th column in X and bhat(j) the  corresponding parameter estimate.  
Assume that you 
want to impose the  following restriction:
 
w(1)' %*% [x(1)  bhat(1)]   +   w(2)' %*%  [x(2)  bhat(2)]  = c  
 
or
 
[w(1)' %*% x(1)] bhat(1)   +   [w(2)' %*% x(2)]   bhat(2)  = c  
 

which can be written as an additional restriction
 
(r(1) bhat(1) + r(2) bhat(2)) = c
 
or
 
r' %*% bhat = c
 
This can be easily extended to various type of restrictions or to  
incorporate additional simultaneous restrictions assuming they  are consistent and 
you have a sufficient number of variables in  your design matrix. If you have 
multiple simultaneous restrictions, both the  'car' and 'systemfit' 
packages allow multiple restrictions.  
 
If this is not clear please let me know.
 
Hope this helps.
 
Joe
 
#################################################################
In reply to:
>Hi All,

>I have two questions:
>
>I am computing  a linear regression model with 0 as Intercept.
>
>Well, I would like  the sum of my predicted values be equal to a constant
>and therefore  analyze if my coefficients are significatively different
>using or not  this constraint.
>
>Does anyone know how I can constrain my model in  a such way?
>
>Here is the code:
>
>data<-read.table  ("input.txt", header=T, dec=".", sep="\t"); attach(data)
>lm <-lm(pop ~  ag + sav + mf -1, data=data)
>pred <-  predict(lm)
>sum(pred)

>So I want to constrain my sum (pred) to  be equal to C, with C=sum(pop)


>
>My second question is: is  it possible to make the same constraint BUT with
>C as a vector of  values?

>If I have 5 observations in 'data' (for simplification  reasons), with
>'pop' as the first column. I want to compute the same  model as above with
>a 'vector' of constraints. In that case, C=xi (with i  from 1 to 3)

>x1 = sum (data[c(2:4), 1])
>x2 = sum(data [c(1,3),  1])
>x3 = data[5,1]


>Thanks in advance -- Any help is  welcome!
>
>
>Jean-Paul  Kibambe
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