####
# function prototype
####
# max.row.col(mat)
# min.row.col(mat)
# which.row.col(mat, value)
#
##############################################################


# obtain the row and column numbers of the maximum element of the matrix
# "mat"
max.row.col<-function(mat)
{ max.value<-max(mat) # the maximum value in the matrix "mat"
  # find the row and column numbers of the maximum value in "mat"
  res<-which.row.col(mat, value=max.value)
  # res contains 2 elements. The frist element is the row number of the
  # maximum value in "mat". The second element is the column number of the
  # maximum value in "mat".
  return(as.vector(res))
}

# obtain the row and column number of the minimum element of the matrix mat
min.row.col<-function(mat)
{ min.value<-min(mat) # the minimum value in the matrix "mat"
  # find the row and column numbers of the minimum value in "mat"
  res<-which.row.col(mat, value=min.value)
  # res contains 2 elements. The frist element is the row number of the
  # minimum value in "mat". The second element is the column number of the
  # minimum value in "mat".
  return(as.vector(res))
}

# find the row and column numbers of "value" in a matrix mat
# if there is a tie, then only one position is returned
# If "value" is not in "mat", then the vector (0,0) will be returned. And a
# warning message will be printed out.
which.row.col<-function(mat, value)
{ mat<-as.matrix(mat); p<-ncol(mat);
  row<-0; col<-0;
  for(i in 1:p)
  { coli<-mat[,i] # the i-th column of the matrix "mat"
    tmp<-abs(coli-value)
    # check if "value" is in the i-th column
    tmppos<-which(abs(mat[,i]-value)<1.0e-6)
    if(length(tmppos)>0)
    { row<-tmppos[1] # the row number of "value" in "mat"
      col<-i # the column number of "value" in "mat"
      break
    }
  }
  res<-c(row, col)
  if(sum(res)==0) 
  { cat("******** Warning!!! ********\n");
    cat("the value ", value, " is not in the matrix >>\n");
    print(mat);
  }
  return(as.vector(res))
}