test.for.zero<- function( xtest,xtrue,  tol= 1.0e-8, relative=TRUE, 
tag=NULL){

  if( !is.null(tag)){
     cat( "testing: ", tag, fill=TRUE)}

  denom<-   ifelse( relative, mean( abs(c(xtrue))),1.0)

   test.value<- sum( abs(c(xtest) - c( xtrue) ) ) /denom
  if(   test.value < tol ){
          cat("** PASSED test at tolerance ", tol, fill=TRUE)}
  else{ cat( "## FAILED test value = ", test.value, " at tolerance ", tol, 
              fill=TRUE)} 

}