vec = function(...){vals = c(...);
  if (length(vals) == 0){
	return(c());
  }
  matrix(c(vals),length(vals),1)
}

mat = function(...){
	d = list(...);
	if (length(d)==0) return(c());
	if (length(d)==1) return(vec(d[[1]]));
        if (length(d[[1]]) == 0) return(c());
	contents = c(d[[1]]);
        rows = length(d[[1]]);
	for (k in 2:length(d)) {
		if ( length(d[[k]]) != rows ) {
			stop('Unequal length vectors given as arguments.');
		}
		contents = c(contents, d[[k]]);
	}
	matrix(contents, rows, length(d));
}

project = function(A,b) {
  foo = dim(A);
  goo = dim(b);
  if (goo[1] !=1 & goo[2] != 1){
	stop('b must be a vector');
  }
  if (foo[1] != length(b)) {
	stop('A must contain vectors of the same dimension as b');
  }
  if (foo[2] <= foo[1]) {
	return(  vec(lsfit(A,b,intercept=F)$coef ) );
  }
  n = svd(A);
  zeros = n$d < .0000001;
  recip = n$d;
  recip[!zeros] = 1/recip[!zeros];
  n$v%*%diag(recip)%*%t(n$u)%*%b
}


dot = function(u,v){
	if (length(u) != length(v)) {
		stop('Vectors not of equal length.');
        }
	return( sum(u*v) )
}

singvals = function(A){ 
        # formulated to give one singular value for each column in A
	foo = La.svd(A, nv=ncol(A), nu=ncol(A))$d;
        c( foo, rep(0,ncol(A) - length(foo)));
}