_R_R_D_T_U_T_O_R_I_A_L(1)                      rrdtool                     _R_R_D_T_U_T_O_R_I_A_L(1)

NNAAMMEE
       rrdtutorial - Alex van den Bogaerdt's RRDtool tutorial

DDEESSCCRRIIPPTTIIOONN
       RRDtool is written by Tobias Oetiker <tobi@oetiker.ch> with
       contributions from many people all around the world. This document is
       written by Alex van den Bogaerdt <alex@vandenbogaerdt.nl> to help you
       understand what RRDtool is and what it can do for you.

       The documentation provided with RRDtool can be too technical for some
       people. This tutorial is here to help you understand the basics of
       RRDtool. It should prepare you to read the documentation yourself.  It
       also explains the general things about statistics with a focus on
       networking.

TTUUTTOORRIIAALL
   IImmppoorrttaanntt
       Please don't skip ahead in this document!  The first part of this
       document explains the basics and may be boring.  But if you don't
       understand the basics, the examples will not be as meaningful to you.

       Sometimes things change.  This example used to provide numbers like
       "0.04" instead of "4.00000e-02".  Those are really the same numbers,
       just written down differently.  Don't be alarmed if a future version of
       rrdtool displays a slightly different form of output. The examples in
       this document are correct for version 1.2.0 of RRDtool.

       Also, sometimes bugs do occur. They may also influence the outcome of
       the examples. Example speed4.png was suffering from this (the handling
       of unknown data in an if-statement was wrong). Normal data will be just
       fine (a bug in rrdtool wouldn't last long) but special cases like NaN,
       INF and so on may last a bit longer.  Try another version if you can,
       or just live with it.

       I fixed the speed4.png example (and added a note). There may be other
       examples which suffer from the same or a similar bug.  Try to fix it
       yourself, which is a great exercise. But please do not submit your
       result as a fix to the source of this document. Discuss it on the
       user's list, or write to me.

   WWhhaatt iiss RRRRDDttooooll??
       RRDtool refers to Round Robin Database tool.  Round robin is a
       technique that works with a fixed amount of data, and a pointer to the
       current element. Think of a circle with some dots plotted on the edge.
       These dots are the places where data can be stored. Draw an arrow from
       the center of the circle to one of the dots; this is the pointer.  When
       the current data is read or written, the pointer moves to the next
       element. As we are on a circle there is neither a beginning nor an end,
       you can go on and on and on. After a while, all the available places
       will be used and the process automatically reuses old locations. This
       way, the dataset will not grow in size and therefore requires no
       maintenance.  RRDtool works with Round Robin Databases (RRDs). It
       stores and retrieves data from them.

   WWhhaatt ddaattaa ccaann bbee ppuutt iinnttoo aann RRRRDD??
       You name it, it will probably fit as long as it is some sort of time-
       series data. This means you have to be able to measure some value at
       several points in time and provide this information to RRDtool. If you
       can do this, RRDtool will be able to store it. The values must be
       numerical but don't have to be integers, as is the case with MRTG (the
       next section will give more details on this more specialized
       application).

       Many examples below talk about SNMP which is an acronym for Simple
       Network Management Protocol. "Simple" refers to the protocol. It does
       not mean it is simple to manage or monitor a network. After working
       your way through this document, you should know enough to be able to
       understand what people are talking about. For now, just realize that
       SNMP can be used to query devices for the values of counters they keep.
       It is the value from those counters that we want to store in the RRD.

   WWhhaatt ccaann II ddoo wwiitthh tthhiiss ttooooll??
       RRDtool originated from MRTG (Multi Router Traffic Grapher). MRTG
       started as a tiny little script for graphing the use of a university's
       connection to the Internet. MRTG was later (ab-)used as a tool for
       graphing other data sources including temperature, speed, voltage,
       number of printouts and the like.

       Most likely you will start to use RRDtool to store and process data
       collected via SNMP. The data will most likely be bytes (or bits)
       transferred from and to a network or a computer.  But it can also be
       used to display tidal waves, solar radiation, power consumption, number
       of visitors at an exhibition, noise levels near an airport, temperature
       on your favorite holiday location, temperature in the fridge and
       whatever your imagination can come up with.

       You only need a sensor to measure the data and be able to feed the
       numbers into RRDtool. RRDtool then lets you create a database, store
       data in it, retrieve that data and create graphs in PNG format for
       display on a web browser. Those PNG images are dependent on the data
       you collected and could be, for instance, an overview of the average
       network usage, or the peaks that occurred.

   WWhhaatt iiff II ssttiillll hhaavvee pprroobblleemmss aafftteerr rreeaaddiinngg tthhiiss ddooccuummeenntt??
       First of all: read it again! You may have missed something.  If you are
       unable to compile the sources and you have a fairly common OS, it will
       probably not be the fault of RRDtool. There may be pre-compiled
       versions around on the Internet. If they come from trusted sources, get
       one of those.

       If on the other hand the program works but does not give you the
       expected results, it will be a problem with configuring it. Review your
       configuration and compare it with the examples that follow.

       There is a mailing list and an archive of it. Read the list for a few
       weeks and search the archive. It is considered rude to just ask a
       question without searching the archives: your problem may already have
       been solved for somebody else!  This is true for most, if not all,
       mailing lists and not only for this particular one. Look in the
       documentation that came with RRDtool for the location and usage of the
       list.

       I suggest you take a moment to subscribe to the mailing list right now
       by sending an email to <rrd-users-request@lists.oetiker.ch> with a
       subject of "subscribe". If you ever want to leave this list, just write
       an email to the same address but now with a subject of "unsubscribe".

   HHooww wwiillll yyoouu hheellpp mmee??
       By giving you some detailed descriptions with detailed examples.  I
       assume that following the instructions in the order presented will give
       you enough knowledge of RRDtool to experiment for yourself.  If it
       doesn't work the first time, don't give up. Reread the stuff that you
       did understand, you may have missed something.

       By following the examples you get some hands-on experience and, even
       more important, some background information of how it works.

       You will need to know something about hexadecimal numbers. If you
       don't, start with reading bin_dec_hex before you continue here.

   YYoouurr ffiirrsstt RRoouunndd RRoobbiinn DDaattaabbaassee
       In my opinion the best way to learn something is to actually do it.
       Why not start right now?  We will create a database, put some values in
       it and extract this data again.  Your output should be the same as the
       output that is included in this document.

       We will start with some easy stuff and compare a car with a router, or
       compare kilometers (miles if you wish) with bits and bytes. It's all
       the same: some number over some time.

       Assume we have a device that transfers bytes to and from the Internet.
       This device keeps a counter that starts at zero when it is turned on,
       increasing with every byte that is transferred. This counter will
       probably have a maximum value. If this value is reached and an extra
       byte is counted, the counter starts over at zero. This is the same as
       many counters in the world such as the mileage counter in a car.

       Most discussions about networking talk about bits per second so let's
       get used to that right away. Assume a byte is eight bits and start to
       think in bits not bytes. The counter, however, still counts bytes!  In
       the SNMP world most of the counters are 32 bits. That means they are
       counting from 0 to 4294967295. We will use these values in the
       examples.  The device, when asked, returns the current value of the
       counter. We know the time that has passes since we last asked so we now
       know how many bytes have been transferred ***on average*** per second.
       This is not very hard to calculate. First in words, then in
       calculations:

       1. Take the current counter, subtract the previous value from it.

       2. Do  the  same  with  the  current  time  and  the  previous time (in
          seconds).

       3. Divide the outcome of (1) by the outcome of (2), the result  is  the
          amount  of  bytes per second. Multiply by eight to get the number of
          bits per second (bps).

         bps = (counter_now - counter_before) / (time_now - time_before) * 8

       For some people it may help to translate this to an automobile example.
       Do not try this example, and if you do, don't blame me for the results!

       People who are not used to think in kilometers per hour  can  translate
       most  into miles per hour by dividing km by 1.6 (close enough).  I will
       use the following abbreviations:

        m:    meter
        km:   kilometer (= 1000 meters).
        h:    hour
        s:    second
        km/h: kilometers per hour
        m/s:  meters per second

       You are driving a car. At 12:05 you read the counter in  the  dashboard
       and it tells you that the car has moved 12345 km until that moment.  At
       12:10  you  look again, it reads 12357 km. This means you have traveled
       12 km in five minutes. A scientist would translate that into meters per
       second and this makes a nice comparison toward the  problem  of  (bytes
       per five minutes) versus (bits per second).

       We  traveled  12  kilometers which is 12000 meters. We did that in five
       minutes or 300 seconds. Our speed is 12000m / 300s or 40 m/s.

       We could also calculate the speed in km/h: 12 times  5  minutes  is  an
       hour,  so  we  have  to  multiply 12 km by 12 to get 144 km/h.  For our
       native English speaking friends:  that's  90  mph  so  don't  try  this
       example at home or where I live :)

       Remember:  these  numbers are averages only.  There is no way to figure
       out from the numbers, if you drove at a constant speed.   There  is  an
       example later on in this tutorial that explains this.

       I hope you understand that there is no difference in calculating m/s or
       bps;  only  the  way  we collect the data is different. Even the k from
       kilo is the same as in networking terms k also means 1000.

       We will now create a database where we can keep all  these  interesting
       numbers.  The method used to start the program may differ slightly from
       OS to OS, but I assume you can figure it out if it works  different  on
       yours.  Make  sure  you  do  not overwrite any file on your system when
       executing the following command and type the whole  line  as  one  long
       line  (I  had  to  split  it  for  readability) and skip all of the '\'
       characters.

          rrdtool create test.rrd             \
                   --start 920804400          \
                   DS:speed:COUNTER:600:U:U   \
                   RRA:AVERAGE:0.5:1:24       \
                   RRA:AVERAGE:0.5:6:10

       (So enter: "rrdtool create test.rrd --start 920804400 DS ...")

   WWhhaatt hhaass bbeeeenn ccrreeaatteedd??
       We created the round robin database called test (test.rrd) which starts
       at noon the day I started writing this document,  7th  of  March,  1999
       (this  date  translates  to  920804400 seconds as explained below). Our
       database holds one data source (DS) named  "speed"  that  represents  a
       counter.  This  counter is read every five minutes (this is the default
       therefore you don't have to put "--step=300").  In  the  same  database
       two  round  robin archives (RRAs) are kept, one averages the data every
       time it is read (i.e., there's nothing to average) and keeps 24 samples
       (24 times 5 minutes is 2 hours). The  other  averages  6  values  (half
       hour) and contains 10 such averages (e.g. 5 hours).

       RRDtool  works  with  special  time  stamps coming from the UNIX world.
       This time stamp is the number of seconds that passed since January  1st
       1970  UTC.   The  time stamp value is translated into local time and it
       will therefore look different for different time zones.

       Chances are that you are not in the same part of the  world  as  I  am.
       This  means  your  time zone is different. In all examples where I talk
       about time, the hours may be wrong for you. This has little  effect  on
       the  results of the examples, just correct the hours while reading.  As
       an example: where I will see "12:05" the UK folks will see "11:05".

       We now have to fill our database with some numbers.  We'll  pretend  to
       have read the following numbers:

        12:05  12345 km
        12:10  12357 km
        12:15  12363 km
        12:20  12363 km
        12:25  12363 km
        12:30  12373 km
        12:35  12383 km
        12:40  12393 km
        12:45  12399 km
        12:50  12405 km
        12:55  12411 km
        13:00  12415 km
        13:05  12420 km
        13:10  12422 km
        13:15  12423 km

       We fill the database as follows:

        rrdtool update test.rrd 920804700:12345 920805000:12357 920805300:12363
        rrdtool update test.rrd 920805600:12363 920805900:12363 920806200:12373
        rrdtool update test.rrd 920806500:12383 920806800:12393 920807100:12399
        rrdtool update test.rrd 920807400:12405 920807700:12411 920808000:12415
        rrdtool update test.rrd 920808300:12420 920808600:12422 920808900:12423

       This reads: update our test database with the following numbers

        time 920804700, value 12345
        time 920805000, value 12357

       etcetera.

       As  you  can  see,  it is possible to feed more than one value into the
       database in one command. I had to stop at three for readability but the
       real maximum per line is OS dependent.

       We can now retrieve the data from our database using "rrdtool fetch":

        rrdtool fetch test.rrd AVERAGE --start 920804400 --end 920809200

       It should return the following output:

                                 speed

        920804700: nan
        920805000: 4.0000000000e-02
        920805300: 2.0000000000e-02
        920805600: 0.0000000000e+00
        920805900: 0.0000000000e+00
        920806200: 3.3333333333e-02
        920806500: 3.3333333333e-02
        920806800: 3.3333333333e-02
        920807100: 2.0000000000e-02
        920807400: 2.0000000000e-02
        920807700: 2.0000000000e-02
        920808000: 1.3333333333e-02
        920808300: 1.6666666667e-02
        920808600: 6.6666666667e-03
        920808900: 3.3333333333e-03
        920809200: nan
        920809500: nan

       Note that you might get more rows than you expect. The reason for  this
       is  that  you  ask  for a time range that ends on 920809200. The number
       that is written behind 920809200: in the list  above  covers  the  time
       range  from 920808900 to 920809200, EXCLUDING 920809200. Hence to be on
       the sure side, you receive the entry from  920809200  to  920809500  as
       well  since  it  INCLUDES  920809200. You may also see "NaN" instead of
       "nan" this is OS dependent.  "NaN" stands for "Not A Number".  If  your
       OS writes "U" or "UNKN" or something similar that's okay.  If something
       else  is  wrong, it will probably be due to an error you made (assuming
       that my tutorial is correct of course :-). In  that  case:  delete  the
       database and try again.

       The meaning of the above output will become clear below.

   TTiimmee ttoo ccrreeaattee ssoommee ggrraapphhiiccss
       Try the following command:

        rrdtool graph speed.png                                 \
                --start 920804400 --end 920808000               \
                DEF:myspeed=test.rrd:speed:AVERAGE              \
                LINE2:myspeed#FF0000

       This  will  create  speed.png  which starts at 12:00 and ends at 13:00.
       There is a definition of a variable called myspeed, using the data from
       RRA "speed" out of database "test.rrd". The line drawn is 2 pixels high
       and represents the variable myspeed. The color is red (specified by its
       rgb-representation, see below).

       You'll notice that the start of the graph is not at 12:00 but at 12:05.
       This is because we have insufficient data to tell  the  average  before
       that  time. This will only happen when you miss some samples, this will
       not happen a lot, hopefully.

       If this has worked: congratulations! If not, check what went wrong.

       The colors are built up from red, green  and  blue.  For  each  of  the
       components,  you  specify how much to use in hexadecimal where 00 means
       not included and FF means fully  included.   The  "color"  white  is  a
       mixture  of red, green and blue: FFFFFF The "color" black is all colors
       off: 000000

          red     #FF0000
          green   #00FF00
          blue    #0000FF
          magenta #FF00FF     (mixed red with blue)
          gray    #555555     (one third of all components)

       Additionally you can (with a recent  RRDtool)   add  an  alpha  channel
       (transparency).  The default will be "FF" which means non-transparent.

       The  PNG  you  just  created can be displayed using your favorite image
       viewer.   Web   browsers   will   display   the   PNG   via   the   URL
       "file:///the/path/to/speed.png"

   GGrraapphhiiccss wwiitthh ssoommee mmaatthh
       When  looking  at  the  image,  you  notice that the horizontal axis is
       labeled 12:10, 12:20, 12:30, 12:40 and 12:50. Sometimes a label doesn't
       fit (12:00 and 13:00 would be likely candidates) so they are skipped.

       The vertical axis displays the range we entered. We provided kilometers
       and when divided by 300 seconds, we  get  very  small  numbers.  To  be
       exact,  the  first  value  was 12 (12357-12345) and divided by 300 this
       makes 0.04, which is displayed by RRDtool as "40 m" meaning  "40/1000".
       The  "m"  (milli) has nothing to do with meters (also m), kilometers or
       millimeters! RRDtool doesn't know about the physical units of our data,
       it just works with dimensionless numbers.

       If we had measured our  distances  in  meters,  this  would  have  been
       (12357000-12345000)/300 = 12000/300 = 40.

       As  most  people  have  a  better feel for numbers in this range, we'll
       correct that. We could recreate our  database  and  store  the  correct
       data, but there is a better way: we do some calculations while creating
       the png file!

          rrdtool graph speed2.png                           \
             --start 920804400 --end 920808000               \
             --vertical-label m/s                            \
             DEF:myspeed=test.rrd:speed:AVERAGE              \
             CDEF:realspeed=myspeed,1000,\*                  \
             LINE2:realspeed#FF0000

       Note:  I need to escape the multiplication operator * with a backslash.
       If I don't, the operating system may interpret it and use it  for  file
       name  expansion.  You  could also place the line within quotation marks
       like so:

             "CDEF:realspeed=myspeed,1000,*"                  \

       It boils down to: it is RRDtool which should see  *,  not  your  shell.
       And  it  is  your  shell  interpreting  \, not RRDtool. You may need to
       adjust examples accordingly if you happen to use an operating system or
       shell which behaves differently.

       After viewing this PNG, you notice the  "m"  (milli)  has  disappeared.
       This  is what the correct result would be. Also, a label has been added
       to the image.  Apart from the things mentioned above,  the  PNG  should
       look the same.

       The  calculations  are  specified  in  the  CDEF  part above and are in
       Reverse Polish Notation ("RPN"). What we requested RRDtool  to  do  is:
       "take  the  data  source  myspeed and the number 1000; multiply those".
       Don't bother with RPN yet, it  will  be  explained  later  on  in  more
       detail.  Also,  you  may  want  to  read my tutorial on CDEFs and Steve
       Rader's tutorial on RPN. But first finish this tutorial.

       Hang on! If we can  multiply  values  with  1000,  it  should  also  be
       possible to display kilometers per hour from the same data!

       To change a value that is measured in meters per second:

        Calculate meters per hour:     value * 3600
        Calculate kilometers per hour: value / 1000
        Together this makes:           value * (3600/1000) or value * 3.6

       In our example database we made a mistake and we need to compensate for
       this by multiplying with 1000. Applying that correction:

        value * 3.6  * 1000 == value * 3600

       Now let's create this PNG, and add some more magic ...

        rrdtool graph speed3.png                             \
             --start 920804400 --end 920808000               \
             --vertical-label km/h                           \
             DEF:myspeed=test.rrd:speed:AVERAGE              \
             "CDEF:kmh=myspeed,3600,*"                       \
             CDEF:fast=kmh,100,GT,kmh,0,IF                   \
             CDEF:good=kmh,100,GT,0,kmh,IF                   \
             HRULE:100#0000FF:"Maximum allowed"              \
             AREA:good#00FF00:"Good speed"                   \
             AREA:fast#FF0000:"Too fast"

       Note:  here  we use another means to escape the * operator by enclosing
       the whole string in double quotes.

       This graph looks much better. Speed is shown in km/h and there is  even
       an extra line with the maximum allowed speed (on the road I travel on).
       I  also  changed the colors used to display speed and changed it from a
       line into an area.

       The calculations are more complex now. For  speed  measurements  within
       the speed limit they are:

          Check if kmh is greater than 100    ( kmh,100 ) GT
          If so, return 0, else kmh           ((( kmh,100 ) GT ), 0, kmh) IF

       For values above the speed limit:

          Check if kmh is greater than 100    ( kmh,100 ) GT
          If so, return kmh, else return 0    ((( kmh,100) GT ), kmh, 0) IF

   GGrraapphhiiccss MMaaggiicc
       I  like  to  believe there are virtually no limits to how RRDtool graph
       can manipulate data. I will not explain how it works, but look  at  the
       following PNG:

          rrdtool graph speed4.png                           \
             --start 920804400 --end 920808000               \
             --vertical-label km/h                           \
             DEF:myspeed=test.rrd:speed:AVERAGE              \
             CDEF:nonans=myspeed,UN,0,myspeed,IF             \
             CDEF:kmh=nonans,3600,*                          \
             CDEF:fast=kmh,100,GT,100,0,IF                   \
             CDEF:over=kmh,100,GT,kmh,100,-,0,IF             \
             CDEF:good=kmh,100,GT,0,kmh,IF                   \
             HRULE:100#0000FF:"Maximum allowed"              \
             AREA:good#00FF00:"Good speed"                   \
             AREA:fast#550000:"Too fast"                     \
             STACK:over#FF0000:"Over speed"

       Remember  the note in the beginning?  I had to remove unknown data from
       this example. The 'nonans' CDEF is new, and the 6th line (which used to
       be the 5th line) used to read 'CDEF:kmh=myspeed,3600,*'

       Let's create a quick and dirty HTML page to view the three PNGs:

          <HTML><HEAD><TITLE>Speed</TITLE></HEAD><BODY>
          <IMG src="speed2.png" alt="Speed in meters per second">
          <BR>
          <IMG src="speed3.png" alt="Speed in kilometers per hour">
          <BR>
          <IMG src="speed4.png" alt="Traveled too fast?">
          </BODY></HTML>

       Name the file "speed.html" or similar, and  look  at  it  in  your  web
       browser.

       Now,  all you have to do is measure the values regularly and update the
       database.  When you want to view the data, recreate the PNGs  and  make
       sure  to  refresh them in your browser. (Note: just clicking reload may
       not be enough, especially when proxies are involved.  Try  shift-reload
       or ctrl-F5).

   UUppddaatteess iinn RReeaalliittyy
       We've already used the "update" command: it took one or more parameters
       in  the  form  of "<time>:<value>". You'll be glad to know that you can
       specify the current time by filling in a "N" as the time.  Or you could
       use  the  "time"  function  in  Perl  (the  shortest  example  in  this
       tutorial):

          perl -e 'print time, "\n" '

       How  to  run a program on regular intervals is OS specific. But here is
       an example in pseudo code:

          - Get the value and put it in variable "$speed"
          - rrdtool update speed.rrd N:$speed

       (do not try this with our  test  database,  we'll  use  it  in  further
       examples)

       This  is all. Run the above script every five minutes. When you need to
       know what the graphs look like, run the examples above. You  could  put
       them  in  a  script  as  well. After running that script, view the page
       speed.html we created above.

   SSoommee wwoorrddss oonn SSNNMMPP
       I can imagine very few people that will be able to get real  data  from
       their  car every five minutes. All other people will have to settle for
       some other kind of counter. You  could  measure  the  number  of  pages
       printed  by  a  printer,  for  example,  the cups of coffee made by the
       coffee machine, a device that counts the  electricity  used,  whatever.
       Any  incrementing  counter can be monitored and graphed using the stuff
       you learned so far. Later on we will also  be  able  to  monitor  other
       types of values like temperature.

       Many people interested in RRDtool will use the counter that keeps track
       of  octets  (bytes)  transferred  by a network device. So let's do just
       that next. We will start with a description of how to collect data.

       Some people will make a remark that there are tools which can  do  this
       data  collection  for  you.  They  are  right!  However,  I  feel it is
       important that you understand they are not necessary. When you have  to
       determine why things went wrong you need to know how they work.

       One  tool used in the example has been talked about very briefly in the
       beginning of this document, it is called SNMP. It is a way  of  talking
       to  networked  equipment.  The tool I use below is called "snmpget" and
       this is how it works:

          snmpget device password OID

       or

          snmpget -v[version] -c[password] device OID

       For device you substitute the name, or the IP address, of your  device.
       For password you use the "community read string" as it is called in the
       SNMP  world.   For  some  devices  the  default of "public" might work,
       however this can be disabled, altered  or  protected  for  privacy  and
       security  reasons.   Read the documentation that comes with your device
       or program.

       Then  there  is  this  parameter,  called  OID,  which  means   "object
       identifier".

       When  you  start  to learn about SNMP it looks very confusing. It isn't
       all that difficult when you look at  the  Management  Information  Base
       ("MIB").   It is an upside-down tree that describes data, with a single
       node as the root and from there a number of branches.   These  branches
       end  up in another node, they branch out, etc.  All the branches have a
       name and they form the path that we  follow  all  the  way  down.   The
       branches  that  we  follow are named: iso, org, dod, internet, mgmt and
       mib-2.  These names can also be written down as numbers and are 1 3 6 1
       2 1.

          iso.org.dod.internet.mgmt.mib-2 (1.3.6.1.2.1)

       There is a lot of confusion about the leading dot  that  some  programs
       use.   There is *no* leading dot in an OID.  However, some programs can
       use the above part of OIDs as a default.  To  indicate  the  difference
       between abbreviated OIDs and full OIDs they need a leading dot when you
       specify  the  complete  OID.   Often  those programs will leave out the
       default portion when returning the data to you.  To make things  worse,
       they have several default prefixes ...

       Ok,  lets  continue  to  the  start of our OID: we had 1.3.6.1.2.1 From
       there, we are especially interested in the  branch  "interfaces"  which
       has number 2 (e.g., 1.3.6.1.2.1.2 or 1.3.6.1.2.1.interfaces).

       First,  we have to get some SNMP program. First look if there is a pre-
       compiled package available for your OS. This is the preferred way.   If
       not,  you will have to get the sources yourself and compile those.  The
       Internet is full of sources, programs etc.  Find  information  using  a
       search engine or whatever you prefer.

       Assume  you  got  the  program.  First try to collect some data that is
       available on most systems. Remember: there is a short name for the part
       of the tree that interests us most in the world we live in!

       I will give an example which can be used  on  Fedora  Core  3.   If  it
       doesn't  work  for  you,  work  your way through the manual of snmp and
       adapt the example to make it work.

          snmpget -v2c -c public myrouter system.sysDescr.0

       The device should answer with a description of itself, perhaps an empty
       one. Until you got a valid  answer  from  a  device,  perhaps  using  a
       different  "password",  or  a  different  device,  there is no point in
       continuing.

          snmpget -v2c -c public myrouter interfaces.ifNumber.0

       Hopefully you get a number as a result, the number of  interfaces.   If
       so, you can carry on and try a different program called "snmpwalk".

          snmpwalk -v2c -c public myrouter interfaces.ifTable.ifEntry.ifDescr

       If  it  returns with a list of interfaces, you're almost there.  Here's
       an example:
          [user@host /home/alex]$ snmpwalk -v2c -c public cisco 2.2.1.2

          interfaces.ifTable.ifEntry.ifDescr.1 = "BRI0: B-Channel 1"
          interfaces.ifTable.ifEntry.ifDescr.2 = "BRI0: B-Channel 2"
          interfaces.ifTable.ifEntry.ifDescr.3 = "BRI0" Hex: 42 52 49 30
          interfaces.ifTable.ifEntry.ifDescr.4 = "Ethernet0"
          interfaces.ifTable.ifEntry.ifDescr.5 = "Loopback0"

       On this cisco equipment,  I  would  like  to  monitor  the  "Ethernet0"
       interface  and  from  the  above output I see that it is number four. I
       try:

          [user@host /home/alex]$ snmpget -v2c -c public cisco 2.2.1.10.4 2.2.1.16.4

          interfaces.ifTable.ifEntry.ifInOctets.4 = 2290729126
          interfaces.ifTable.ifEntry.ifOutOctets.4 = 1256486519

       So now I have two OIDs to monitor and they are (in full, this time):

          1.3.6.1.2.1.2.2.1.10

       and

          1.3.6.1.2.1.2.2.1.16

       both with an interface number of 4.

       Don't get fooled, this wasn't my first try. It took some  time  for  me
       too  to understand what all these numbers mean. It does help a lot when
       they get translated into descriptive text... At least, when people  are
       talking  about  MIBs  and  OIDs  you  know what it's all about.  Do not
       forget the interface number (0 if it is not  interface  dependent)  and
       try snmpwalk if you don't get an answer from snmpget.

       If  you  understand the above section and get numbers from your device,
       continue on with this tutorial. If not, then go back and  re-read  this
       part.

   AA RReeaall WWoorrlldd EExxaammppllee
       Let  the fun begin. First, create a new database. It contains data from
       two counters, called input and output. The data is  put  into  archives
       that  average  it.  They  take 1, 6, 24 or 288 samples at a time.  They
       also go into archives that keep  the  maximum  numbers.  This  will  be
       explained  later on. The time in-between samples is 300 seconds, a good
       starting point, which is the same as five minutes.

        1 sample "averaged" stays 1 period of 5 minutes
        6 samples averaged become one average on 30 minutes
        24 samples averaged become one average on 2 hours
        288 samples averaged become one average on 1 day

       Lets try to be compatible with MRTG which stores  about  the  following
       amount of data:

        600 5-minute samples:    2   days and 2 hours
        600 30-minute samples:  12.5 days
        600 2-hour samples:     50   days
        732 1-day samples:     732   days

       These  ranges  are  appended, so the total amount of data stored in the
       database  is  approximately  797  days.   RRDtool   stores   the   data
       differently,  it  doesn't  start the "weekly" archive where the "daily"
       archive stopped. For both archives the most recent data  will  be  near
       "now" and therefore we will need to keep more data than MRTG does!

       We will need:

        600 samples of 5 minutes  (2 days and 2 hours)
        700 samples of 30 minutes (2 days and 2 hours, plus 12.5 days)
        775 samples of 2 hours    (above + 50 days)
        797 samples of 1 day      (above + 732 days, rounded up to 797)

          rrdtool create myrouter.rrd         \
                   DS:input:COUNTER:600:U:U   \
                   DS:output:COUNTER:600:U:U  \
                   RRA:AVERAGE:0.5:1:600      \
                   RRA:AVERAGE:0.5:6:700      \
                   RRA:AVERAGE:0.5:24:775     \
                   RRA:AVERAGE:0.5:288:797    \
                   RRA:MAX:0.5:1:600          \
                   RRA:MAX:0.5:6:700          \
                   RRA:MAX:0.5:24:775         \
                   RRA:MAX:0.5:288:797

       Next  thing  to do is to collect data and store it. Here is an example.
       It is written partially in pseudo code,  you will have to find out what
       to do exactly on your OS to make it work.

          while not the end of the universe
          do
             get result of
                snmpget router community 2.2.1.10.4
             into variable $in
             get result of
                snmpget router community 2.2.1.16.4
             into variable $out

             rrdtool update myrouter.rrd N:$in:$out

             wait for 5 minutes
          done

       Then, after collecting data for a day, try to create an image using:

          rrdtool graph myrouter-day.png --start -86400 \
                   DEF:inoctets=myrouter.rrd:input:AVERAGE \
                   DEF:outoctets=myrouter.rrd:output:AVERAGE \
                   AREA:inoctets#00FF00:"In traffic" \
                   LINE1:outoctets#0000FF:"Out traffic"

       This should produce a picture with one day worth of traffic.   One  day
       is  24  hours  of 60 minutes of 60 seconds: 24*60*60=86400, we start at
       now minus 86400 seconds. We define (with DEFs) inoctets  and  outoctets
       as  the  average values from the database myrouter.rrd and draw an area
       for the "in" traffic and a line for the "out" traffic.

       View the image and keep logging data for a few more days.  If you like,
       you could try the examples from the test database and see  if  you  can
       get various options and calculations to work.

       Suggestion:  Display  in  bytes per second and in bits per second. Make
       the Ethernet graphics go red if they are over four megabits per second.

   CCoonnssoolliiddaattiioonn FFuunnccttiioonnss
       A few paragraphs back  I  mentioned  the  possibility  of  keeping  the
       maximum  values instead of the average values. Let's go into this a bit
       more.

       Recall all the stuff about the speed of the car. Suppose  we  drove  at
       144  km/h  during  5 minutes and then were stopped by the police for 25
       minutes.  At the end of the lecture we would take our laptop and create
       and view the image taken from the database. If we look  at  the  second
       RRA  we  did  create,  we  would  have  the average from 6 samples. The
       samples measured would be 144+0+0+0+0+0=144,  divided  by  30  minutes,
       corrected for the error by 1000, translated into km/h, with a result of
       24 km/h.  I would still get a ticket but not for speeding anymore :)

       Obviously,  in  this  case  we  shouldn't look at the averages. In some
       cases they are handy. If you want to know how many km you had traveled,
       the averaged picture would be the right one to look at.  On  the  other
       hand,  for  the  speed that we traveled at, the maximum numbers seen is
       much more interesting. Later we will see more types.

       It is the same for data. If you want to know the amount,  look  at  the
       averages.  If  you  want  to  know the rate, look at the maximum.  Over
       time, they will grow apart more and more. In the last database we  have
       created,  there  are  two  archives that keep data per day. The archive
       that keeps averages will show  low  numbers,  the  archive  that  shows
       maxima will have higher numbers.

       For my car this would translate in averages per day of 96/24=4 km/h (as
       I  travel about 94 kilometers on a day) during working days, and maxima
       of 120 km/h (my top speed that I reach every day).

       Big difference. Do not  look  at  the  second  graph  to  estimate  the
       distances  that I travel and do not look at the first graph to estimate
       my speed. This will work if the samples are close together, as they are
       in five minutes, but not if you average.

       On some days, I go for a long ride. If I go across  Europe  and  travel
       for  12  hours,  the first graph will rise to about 60 km/h. The second
       one will show 180 km/h. This means that I traveled  a  distance  of  60
       km/h times 24 h = 1440 km. I did this with a higher speed and a maximum
       around  180 km/h. However, it probably doesn't mean that I traveled for
       8 hours at a constant speed of 180 km/h!

       This is a real example: go with the flow through  Germany  (fast!)  and
       stop  a  few times for gas and coffee. Drive slowly through Austria and
       the Netherlands. Be careful in the mountains and villages. If you would
       look at the graphs created from the five-minute averages you would  get
       a  totally  different  picture.  You  would  see the same values on the
       average and maximum graphs (provided I  measured  every  300  seconds).
       You would be able to see when I stopped, when I was in top gear, when I
       drove  over  fast  highways  etc.  The  granularity of the data is much
       higher, so you can see more. However, this takes 12 samples  per  hour,
       or  288  values  per  day,  so  it would be a lot of data over a longer
       period of time. Therefore we average it, eventually to  one  value  per
       day. From this one value, we cannot see much detail, of course.

       Make  sure you understand the last few paragraphs. There is no value in
       only a line and a few axis,  you  need  to  know  what  they  mean  and
       interpret the data in an appropriate way. This is true for all data.

       The  biggest  mistake  you  can  make  is to use the collected data for
       something that it is not suitable for. You would be better off  if  you
       didn't have the graph at all.

   LLeett''ss rreevviieeww wwhhaatt yyoouu nnooww sshhoouulldd kknnooww
       You  know  how to create a database and can put data in it. You can get
       the numbers out again by creating an image, do math on  the  data  from
       the  database  and  view  the result instead of the raw data.  You know
       about the difference between averages and  maximum,  and  when  to  use
       which (or at least you should have an idea).

       RRDtool  can  do  more  than what we have learned up to now. Before you
       continue with the rest of this doc, I recommend that  you  reread  from
       the  start  and  try  some modifications on the examples. Make sure you
       fully understand everything. It will be worth the effort and helps  you
       not  only  with  the rest of this tutorial, but also in your day to day
       monitoring long after you read this introduction.

   DDaattaa SSoouurrccee TTyyppeess
       All right, you feel like continuing. Welcome back and get ready for  an
       increased speed in the examples and explanations.

       You  know  that  in order to view a counter over time, you have to take
       two numbers and divide the difference of them by the time lapsed.  This
       makes  sense  for  the  examples  I  gave  you  but  there  are   other
       possibilities.  For instance, I'm able to retrieve the temperature from
       my  router in three places namely the inlet, the so called hot-spot and
       the exhaust.  These values are not counters.  If I take the  difference
       of the two samples and divide that by 300 seconds I would be asking for
       the temperature change per second.  Hopefully this is zero! If not, the
       computer room is probably on fire :)

       So, what can we do?  We can tell RRDtool to store the values we measure
       directly  as they are (this is not entirely true but close enough). The
       graphs we make will look much better, they will show a rather  constant
       value.  I  know  when  the  router  is  busy  (it works -> it uses more
       electricity -> it generates more heat -> the temperature rises). I know
       when the doors are left open (the room is air conditioned) -> the  warm
       air  from  the rest of the building flows into the computer room -> the
       inlet temperature rises). Etc. The data type we use when  creating  the
       database before was counter, we now have a different data type and thus
       a  different  name for it. It is called GAUGE. There are more such data
       types:

        - COUNTER   we already know this one
        - GAUGE     we just learned this one
        - DERIVE
        - ABSOLUTE

       The two additional types are DERIVE and ABSOLUTE. Absolute can be  used
       like  counter with one difference: RRDtool assumes the counter is reset
       when it's read. That is: its delta  is  known  without  calculation  by
       RRDtool  whereas  RRDtool  needs  to calculate it for the counter type.
       Example: our first example (12345, 12357,  12363,  12363)  would  read:
       unknown,  12,  6,  0.  The rest of the calculations stay the same.  The
       other one, derive,  is  like  counter.  Unlike  counter,  it  can  also
       decrease  so  it  can  have  a  negative  delta. Again, the rest of the
       calculations stay the same.

       Let's try them all:

          rrdtool create all.rrd --start 978300900 \
                   DS:a:COUNTER:600:U:U \
                   DS:b:GAUGE:600:U:U \
                   DS:c:DERIVE:600:U:U \
                   DS:d:ABSOLUTE:600:U:U \
                   RRA:AVERAGE:0.5:1:10
          rrdtool update all.rrd \
                   978301200:300:1:600:300    \
                   978301500:600:3:1200:600   \
                   978301800:900:5:1800:900   \
                   978302100:1200:3:2400:1200 \
                   978302400:1500:1:2400:1500 \
                   978302700:1800:2:1800:1800 \
                   978303000:2100:4:0:2100    \
                   978303300:2400:6:600:2400  \
                   978303600:2700:4:600:2700  \
                   978303900:3000:2:1200:3000
          rrdtool graph all1.png -s 978300600 -e 978304200 -h 400 \
                   DEF:linea=all.rrd:a:AVERAGE LINE3:linea#FF0000:"Line A" \
                   DEF:lineb=all.rrd:b:AVERAGE LINE3:lineb#00FF00:"Line B" \
                   DEF:linec=all.rrd:c:AVERAGE LINE3:linec#0000FF:"Line C" \
                   DEF:lined=all.rrd:d:AVERAGE LINE3:lined#000000:"Line D"

   RRRRDDttooooll uunnddeerr tthhee MMiiccrroossccooppee
       • Line A is a COUNTER type, so it  should  continuously  increment  and
         RRDtool must calculate the differences. Also, RRDtool needs to divide
         the  difference by the amount of time lapsed. This should end up as a
         straight line at 1 (the deltas are 300, the time is 300).

       • Line B is of type GAUGE. These are "real" values so they should match
         what we put in: a sort of a wave.

       • Line C is of type DERIVE. It should be a counter that  can  decrease.
         It does so between 2400 and 0, with 1800 in-between.

       • Line  D  is  of  type  ABSOLUTE. This is like counter but it works on
         values without calculating the difference. The numbers are  the  same
         and as you can see (hopefully) this has a different result.

       This  translates  in the following values, starting at 23:10 and ending
       at 00:10 the next day (where "u" means unknown/unplotted):

        - Line A:  u  u  1  1  1  1  1  1  1  1  1  u
        - Line B:  u  1  3  5  3  1  2  4  6  4  2  u
        - Line C:  u  u  2  2  2  0 -2 -6  2  0  2  u
        - Line D:  u  1  2  3  4  5  6  7  8  9 10  u

       If your PNG shows  all  this,  you  know  you  have  entered  the  data
       correctly,  the  RRDtool  executable  is  working properly, your viewer
       doesn't fool you, and you successfully entered the year 2000 :)

       You could try the same example four times, each time with only  one  of
       the lines.

       Let's go over the data again:

       • Line  A:  300,600,900  and so on. The counter delta is a constant 300
         and so is the time delta. A number divided  by  itself  is  always  1
         (except when dividing by zero which is undefined/illegal).

         Why  is  it  that  the first point is unknown? We do know what we put
         into the database, right?  True,  But  we  didn't  have  a  value  to
         calculate the delta from, so we don't know where we started. It would
         be wrong to assume we started at zero so we don't!

       • Line B: There is nothing to calculate. The numbers are as they are.

       • Line C: Again, the start-out value is unknown. This is the same story
         as  for  line  A. In this case the deltas are not constant, therefore
         the line is not either. If we would  put  the  same  numbers  in  the
         database  as  we  did for line A, we would have gotten the same line.
         Unlike type counter, this type can decrease and I hope  to  show  you
         later on why this makes a difference.

       • Line  D:  Here the device calculates the deltas. Therefore we DO know
         the first delta and it is plotted. We had the same input as with line
         A, but the meaning of this input is different and thus  the  line  is
         different.   In this case the deltas increase each time with 300. The
         time delta stays at a constant 300 and therefore the division of  the
         two gives increasing values.

   CCoouunntteerr WWrraappss
       There  are  a few more basics to show. Some important options are still
       to be covered and we haven't look  at  counter  wraps  yet.  First  the
       counter  wrap:  In  our car we notice that the counter shows 999987. We
       travel 20 km and the counter should go to 1000007. Unfortunately, there
       are only six digits on our counter so it really  shows  000007.  If  we
       would  plot  that  on a type DERIVE, it would mean that the counter was
       set back 999980 km. It wasn't, and there has to be some protection  for
       this.  This  protection is only available for type COUNTER which should
       be used for this kind of  counter  anyways.  How  does  it  work?  Type
       counter  should  never  decrease  and  therefore RRDtool must assume it
       wrapped if it does decrease!  If the delta is  negative,  this  can  be
       compensated for by adding the maximum value of the counter + 1. For our
       car this would be:

        Delta = 7 - 999987 = -999980    (instead of 1000007-999987=20)

        Real delta = -999980 + 999999 + 1 = 20

       At  the  time  of writing this document, RRDtool knows of counters that
       are either 32 bits or 64 bits of size. These counters  can  handle  the
       following different values:

        - 32 bits: 0 ..           4294967295
        - 64 bits: 0 .. 18446744073709551615

       If  these  numbers  look  strange  to  you,  you can view them in their
       hexadecimal form:

        - 32 bits: 0 ..         FFFFFFFF
        - 64 bits: 0 .. FFFFFFFFFFFFFFFF

       RRDtool handles both counters the same. If an overflow occurs  and  the
       delta  would  be  negative,  RRDtool  first adds the maximum of a small
       counter + 1 to the delta. If the delta is still negative, it had to  be
       the  large  counter that wrapped. Add the maximum possible value of the
       large counter + 1 and subtract the erroneously added small value.

       There is a risk in this: suppose the large counter wrapped while adding
       a huge delta, it could happen, theoretically, that adding  the  smaller
       value  would make the delta positive. In this unlikely case the results
       would not be correct. The increase should be  nearly  as  high  as  the
       maximum counter value for that to happen, so chances are you would have
       several  other  problems  as well and this particular problem would not
       even be worth thinking about. Even though, I did include an example, so
       you can judge for yourself.

       The next section gives you some numerical examples  for  counter-wraps.
       Try  to  do  the  calculations  yourself  or  just  believe  me if your
       calculator can't handle the numbers :)

       Correction numbers:

        - 32 bits: (4294967295 + 1) =                                4294967296
        - 64 bits: (18446744073709551615 + 1)
                                           - correction1 = 18446744069414584320

        Before:        4294967200
        Increase:                100
        Should become: 4294967300
        But really is:             4
        Delta:        -4294967196
        Correction1:  -4294967196 + 4294967296 = 100

        Before:        18446744073709551000
        Increase:                             800
        Should become: 18446744073709551800
        But really is:                        184
        Delta:        -18446744073709550816
        Correction1:  -18446744073709550816
                                       + 4294967296 = -18446744069414583520
        Correction2:  -18446744069414583520
                          + 18446744069414584320 = 800

        Before:        18446744073709551615 ( maximum value )
        Increase:      18446744069414584320 ( absurd increase, minimum for
        Should become: 36893488143124135935             this example to work )
        But really is: 18446744069414584319
        Delta:                     -4294967296
        Correction1:  -4294967296 + 4294967296 = 0
        (not negative -> no correction2)

        Before:        18446744073709551615 ( maximum value )
        Increase:      18446744069414584319 ( one less increase )
        Should become: 36893488143124135934
        But really is: 18446744069414584318
        Delta:                     -4294967297
        Correction1:  -4294967297 + 4294967296 = -1
        Correction2:  -1 + 18446744069414584320 = 18446744069414584319

       As you can see from the last two examples, you need strange numbers for
       RRDtool to fail (provided it's bug free of course), so this should  not
       happen.  However,  SNMP  or  whatever  method you choose to collect the
       data, might also report wrong numbers occasionally.  We  can't  prevent
       all  errors,  but there are some things we can do. The RRDtool "create"
       command takes two special parameters for this. They define the  minimum
       and  maximum allowed values. Until now, we used "U", meaning "unknown".
       If you provide values for one or both of them and if  RRDtool  receives
       data points that are outside these limits, it will ignore those values.
       For  a  thermometer  in  degrees  Celsius, the absolute minimum is just
       under -273. For my router, I can assume this minimum is much higher  so
       I  would  set it to 10, where as the maximum temperature I would set to
       80. Any higher and the device would be out of order.

       For the speed of my car, I would never expect negative numbers and also
       I would not expect a speed  higher than 230. Anything else,  and  there
       must  have  been  an  error. Remember: the opposite is not true, if the
       numbers pass this check, it doesn't mean that they are correct.  Always
       judge  the  graph with a healthy dose of suspicion if it seems weird to
       you.

   DDaattaa RReessaammpplliinngg
       One important feature of RRDtool has not  been  explained  yet:  it  is
       virtually  impossible to collect data and feed it into RRDtool on exact
       intervals. RRDtool therefore interpolates the data, so they are  stored
       on exact intervals. If you do not know what this means or how it works,
       then here's the help you seek:

       Suppose  a  counter increases by exactly one for every second. You want
       to measure it in 300 seconds intervals. You should retrieve values that
       are exactly 300 apart. However, due to various circumstances you are  a
       few seconds late and the interval is 303. The delta will also be 303 in
       that  case.  Obviously,  RRDtool should not put 303 in the database and
       make you believe that the counter increased  by  303  in  300  seconds.
       This  is  where  RRDtool interpolates: it alters the 303 value as if it
       would have been stored earlier and it will be 300 in 300 seconds.  Next
       time you are at exactly the right time. This  means  that  the  current
       interval  is  297 seconds and also the counter increased by 297. Again,
       RRDtool interpolates and stores 300 as it should be.

             in the RRD                 in reality

        time+000:   0 delta="U"   time+000:    0 delta="U"
        time+300: 300 delta=300   time+300:  300 delta=300
        time+600: 600 delta=300   time+603:  603 delta=303
        time+900: 900 delta=300   time+900:  900 delta=297

       Let's create two  identical  databases.  I've  chosen  the  time  range
       920805000 to 920805900 as this goes very well with the example numbers.

          rrdtool create seconds1.rrd   \
             --start 920804700          \
             DS:seconds:COUNTER:600:U:U \
             RRA:AVERAGE:0.5:1:24

       Make a copy

          for Unix: cp seconds1.rrd seconds2.rrd
          for Dos:  copy seconds1.rrd seconds2.rrd
          for vms:  how would I know :)

       Put in some data

          rrdtool update seconds1.rrd \
             920805000:000 920805300:300 920805600:600 920805900:900
          rrdtool update seconds2.rrd \
             920805000:000 920805300:300 920805603:603 920805900:900

       Create output

          rrdtool graph seconds1.png                       \
             --start 920804700 --end 920806200             \
             --height 200                                  \
             --upper-limit 1.05 --lower-limit 0.95 --rigid \
             DEF:seconds=seconds1.rrd:seconds:AVERAGE      \
             CDEF:unknown=seconds,UN                       \
             LINE2:seconds#0000FF                          \
             AREA:unknown#FF0000
          rrdtool graph seconds2.png                       \
             --start 920804700 --end 920806200             \
             --height 200                                  \
             --upper-limit 1.05 --lower-limit 0.95 --rigid \
             DEF:seconds=seconds2.rrd:seconds:AVERAGE      \
             CDEF:unknown=seconds,UN                       \
             LINE2:seconds#0000FF                          \
             AREA:unknown#FF0000

       View  both  images  together  (add  them  to  your index.html file) and
       compare. Both graphs should show the  same,  despite  the  input  being
       different.

WWRRAAPPUUPP
       It's  time  now to wrap up this tutorial. We covered all the basics for
       you to be able  to  work  with  RRDtool  and  to  read  the  additional
       documentation available. There is plenty more to discover about RRDtool
       and  you  will find more and more uses for this package. You can easily
       create graphs using just the examples provided and using only  RRDtool.
       You can also use one of the front ends to RRDtool that are available.

MMAAIILLIINNGGLLIISSTT
       Remember  to subscribe to the RRDtool mailing list. Even if you are not
       answering to mails that come by, it helps both you and the rest of  the
       users.  A  lot of the stuff that I know about MRTG (and therefore about
       RRDtool) I've learned while just reading the list  without  posting  to
       it.  I  did not need to ask the basic questions as they are answered in
       the FAQ (read it!) and in various mails by other users. With  thousands
       of  users  all  over  the  world,  there  will always be people who ask
       questions  that  you  can  answer  because  you  read  this  and  other
       documentation and they didn't.

SSEEEE AALLSSOO
       The RRDtool manpages

AAUUTTHHOORR
       I hope you enjoyed the examples and their descriptions. If you do, help
       other  people  by  pointing  them to this document when they are asking
       basic questions. They will not only get their answers, but at the  same
       time learn a whole lot more.

       Alex van den Bogaerdt <alex@vandenbogaerdt.nl>

1.10.3                            2026-05-25                    _R_R_D_T_U_T_O_R_I_A_L(1)
