Maximum and Local Maximum

#!/usr/bin/awk -f
BEGIN {
  format1 = "local-maximum: %.1f %.9f\n"
  format2 = "maximum: %.1f %.9f\n"
  out1 = "local-maximum.dat"
  out2 = "maximum.dat"
  printf "" >out1
  printf "" >out2
}
NF {
  if (!max_y) {
    max_x = $1; max_y = $2
  }
  if (max_y < $2) {
    max_x = $1; max_y = $2
  }
  if (py && y && py < y && y > $2) {
    printf format1, x, y >out1
  }
  px = x; py = y; x = $1; y = $2
}
!NF {
  printf format2, max_x, max_y >out2
  max_x = max_y = "";
  px = py = x = y = "";
}
END {
  if (max_y) {
    printf format2, max_x, max_y >out2
  }
}