Provided by: rrdtool_1.4.7-2ubuntu5_amd64 bug


       rrdgraph_rpn - About RPN Math in rrdtool graph


       RPN expression:=vname|operator|value[,RPN expression]


       If you have ever used a traditional HP calculator you already know RPN (Reverse Polish
       Notation).  The idea behind RPN is that you have a stack and push your data onto this
       stack. Whenever you execute an operation, it takes as many elements from the stack as
       needed. Pushing is done implicitly, so whenever you specify a number or a variable, it
       gets pushed onto the stack automatically.

       At the end of the calculation there should be one and only one value left on the stack.
       This is the outcome of the function and this is what is put into the vname.  For CDEF
       instructions, the stack is processed for each data point on the graph. VDEF instructions
       work on an entire data set in one run. Note, that currently VDEF instructions only support
       a limited list of functions.

       Example: "VDEF:maximum=mydata,MAXIMUM"

       This will set variable "maximum" which you now can use in the rest of your RRD script.

       Example: "CDEF:mydatabits=mydata,8,*"

       This means:  push variable mydata, push the number 8, execute the operator *. The operator
       needs two elements and uses those to return one value.  This value is then stored in
       mydatabits.  As you may have guessed, this instruction means nothing more than mydatabits
       = mydata * 8.  The real power of RPN lies in the fact that it is always clear in which
       order to process the input.  For expressions like "a = b + 3 * 5" you need to multiply 3
       with 5 first before you add b to get a. However, with parentheses you could change this
       order: "a = (b + 3) * 5". In RPN, you would do "a = b, 3, +, 5, *" without the need for


       Boolean operators
           LT, LE, GT, GE, EQ, NE

           Pop two elements from the stack, compare them for the selected condition and return 1
           for true or 0 for false. Comparing an unknown or an infinite value will result in
           unknown returned ... which will also be treated as false by the IF call.

           UN, ISINF

           Pop one element from the stack, compare this to unknown respectively to positive or
           negative infinity. Returns 1 for true or 0 for false.


           Pops three elements from the stack.  If the element popped last is 0 (false), the
           value popped first is pushed back onto the stack, otherwise the value popped second is
           pushed back. This does, indeed, mean that any value other than 0 is considered to be

           Example: "A,B,C,IF" should be read as "if (A) then (B) else (C)"

       Comparing values
           MIN, MAX

           Pops two elements from the stack and returns the smaller or larger, respectively.
           Note that infinite is larger than anything else.  If one of the input numbers is
           unknown then the result of the operation will be unknown too.


           Pops two elements from the stack and uses them to define a range.  Then it pops
           another element and if it falls inside the range, it is pushed back. If not, an
           unknown is pushed.

           The range defined includes the two boundaries (so: a number equal to one of the
           boundaries will be pushed back). If any of the three numbers involved is either
           unknown or infinite this function will always return an unknown

           Example: "CDEF:a=alpha,0,100,LIMIT" will return unknown if alpha is lower than 0 or if
           it is higher than 100.

           +, -, *, /, %

           Add, subtract, multiply, divide, modulo


           NAN-safe addition. If one parameter is NAN/UNKNOWN it'll be treated as zero. If both
           parameters are NAN/UNKNOWN, NAN/UNKNOWN will be returned.

           SIN, COS, LOG, EXP, SQRT

           Sine and cosine (input in radians), log and exp (natural logarithm), square root.


           Arctangent (output in radians).


           Arctangent of y,x components (output in radians).  This pops one element from the
           stack, the x (cosine) component, and then a second, which is the y (sine) component.
           It then pushes the arctangent of their ratio, resolving the ambiguity between

           Example: "CDEF:angle=Y,X,ATAN2,RAD2DEG" will convert "X,Y" components into an angle in

           FLOOR, CEIL

           Round down or up to the nearest integer.

           DEG2RAD, RAD2DEG

           Convert angle in degrees to radians, or radians to degrees.


           Take the absolute value.

       Set Operations
           SORT, REV

           Pop one element from the stack.  This is the count of items to be sorted (or
           reversed).  The top count of the remaining elements are then sorted (or reversed) in
           place on the stack.

           Example: "CDEF:x=v1,v2,v3,v4,v5,v6,6,SORT,POP,5,REV,POP,+,+,+,4,/" will compute the
           average of the values v1 to v6 after removing the smallest and largest.


           Pop one element (count) from the stack. Now pop count elements and build the average,
           ignoring all UNKNOWN values in the process.

           Example: "CDEF:x=a,b,c,d,4,AVG"

           TREND, TRENDNAN

           Create a "sliding window" average of another data series.

           Usage: CDEF:smoothed=x,1800,TREND

           This will create a half-hour (1800 second) sliding window average of x.  The average
           is essentially computed as shown here:

                                  delay     t0
                                    delay       t1
                                         delay      t2

                Value at sample (t0) will be the average between (t0-delay) and (t0)
                Value at sample (t1) will be the average between (t1-delay) and (t1)
                Value at sample (t2) will be the average between (t2-delay) and (t2)

           TRENDNAN is - in contrast to TREND - NAN-safe. If you use TREND and one source value
           is NAN the complete sliding window is affected. The TRENDNAN operation ignores all
           NAN-values in a sliding window and computes the average of the remaining values.


           Create a "sliding window" average/sigma of another data series, that also shifts the
           data series by given amounts of of time as well

           Usage - explicit stating shifts: CDEF:predict=<shift n>,...,<shift
           1>,n,<window>,x,PREDICT CDEF:sigma=<shift n>,...,<shift 1>,n,<window>,x,PREDICTSIGMA

           Usage - shifts defined as a base shift and a number of time this is applied
           CDEF:predict=<shift multiplier>,-n,<window>,x,PREDICT CDEF:sigma=<shift

           Example: CDEF:predict=172800,86400,2,1800,x,PREDICT

           This will create a half-hour (1800 second) sliding window average/sigma of x, that
           average is essentially computed as shown here:

                                                             shift 1        t0
                                                  shift 2
                                                                 shift 1        t1
                                                       shift 2

            Value at sample (t0) will be the average between (t0-shift1-window) and (t0-shift1)
                                                 and between (t0-shift2-window) and (t0-shift2)
            Value at sample (t1) will be the average between (t1-shift1-window) and (t1-shift1)
                                                 and between (t1-shift2-window) and (t1-shift2)

           The function is by design NAN-safe.  This also allows for extrapolation into the
           future (say a few days) - you may need to define the data series whit the optional
           start= parameter, so that the source data series has enough data to provide prediction
           also at the beginning of a graph...

           Here an example, that will create a 10 day graph that also shows the prediction 3 days
           into the future with its uncertainty value (as defined by avg+-4*sigma) This also
           shows if the prediction is exceeded at a certain point.

           rrdtool graph image.png --imgformat=PNG \
            --start=-7days --end=+3days --width=1000 --height=200 --alt-autoscale-max \
            DEF:value=value.rrd:value:AVERAGE:start=-14days \
            LINE1:value#ff0000:value \
            CDEF:predict=86400,-7,1800,value,PREDICT \
            CDEF:sigma=86400,-7,1800,value,PREDICTSIGMA \
            CDEF:upper=predict,sigma,3,*,+ \
            CDEF:lower=predict,sigma,3,*,- \
            LINE1:predict#00ff00:prediction \
            LINE1:upper#0000ff:upper\ certainty\ limit \
            LINE1:lower#0000ff:lower\ certainty\ limit \
            CDEF:exceeds=value,UN,0,value,lower,upper,LIMIT,UN,IF \

           Note: Experience has shown that a factor between 3 and 5 to scale sigma is a good
           discriminator to detect abnormal behavior. This obviously depends also on the type of
           data and how "noisy" the data series is.

           This prediction can only be used for short term extrapolations - say a few days into

           the future-
       Special values

           Pushes an unknown value on the stack

           INF, NEGINF

           Pushes a positive or negative infinite value on the stack. When such a value is
           graphed, it appears at the top or bottom of the graph, no matter what the actual value
           on the y-axis is.


           Pushes an unknown value if this is the first value of a data set or otherwise the
           result of this CDEF at the previous time step. This allows you to do calculations
           across the data.  This function cannot be used in VDEF instructions.


           Pushes an unknown value if this is the first value of a data set or otherwise the
           result of the vname variable at the previous time step. This allows you to do
           calculations across the data. This function cannot be used in VDEF instructions.


           Pushes the number 1 if this is the first value of the data set, the number 2 if it is
           the second, and so on. This special value allows you to make calculations based on the
           position of the value within the data set. This function cannot be used in VDEF

           Time inside RRDtool is measured in seconds since the epoch. The epoch is defined to be
           "Thu Jan  1 00:00:00 UTC 1970".


           Pushes the current time on the stack.


           Pushes the time the currently processed value was taken at onto the stack.


           Takes the time as defined by TIME, applies the time zone offset valid at that time
           including daylight saving time if your OS supports it, and pushes the result on the
           stack.  There is an elaborate example in the examples section below on how to use

       Processing the stack directly
           DUP, POP, EXC

           Duplicate the top element, remove the top element, exchange the two top elements.


       These operators work only on VDEF statements. Note that currently ONLY these work for

           Return the corresponding value, MAXIMUM and MINIMUM also return the first occurrence
           of that value in the time component.

           Example: "VDEF:avg=mydata,AVERAGE"

           Returns the standard deviation of the values.

           Example: "VDEF:stdev=mydata,STDEV"

       LAST, FIRST
           Return the last/first non-nan or infinite value for the selected data stream,
           including its timestamp.

           Example: "VDEF:first=mydata,FIRST"

           Returns the rate from each defined time slot multiplied with the step size.  This can,
           for instance, return total bytes transferred when you have logged bytes per second.
           The time component returns the number of seconds.

           Example: "VDEF:total=mydata,TOTAL"

           This should follow a DEF or CDEF vname. The vname is popped, another number is popped
           which is a certain percentage (0..100). The data set is then sorted and the value
           returned is chosen such that percentage percent of the values is lower or equal than
           the result.  For PERCENTNAN Unknown values are ignored, but for PERCENT Unknown values
           are considered lower than any finite number for this purpose so if this operator
           returns an unknown you have quite a lot of them in your data.  Infinite numbers are
           lesser, or more, than the finite numbers and are always more than the Unknown numbers.
           (NaN < -INF < finite values < INF)

           Example: "VDEF:perc95=mydata,95,PERCENT"

           Return the parameters for a Least Squares Line (y = mx +b) which approximate the
           provided dataset.  LSLSLOPE is the slope (m) of the line related to the COUNT position
           of the data.  LSLINT is the y-intercept (b), which happens also to be the first data
           point on the graph. LSLCORREL is the Correlation Coefficient (also know as Pearson's
           Product Moment Correlation Coefficient).  It will range from 0 to +/-1 and represents
           the quality of fit for the approximation.

           Example: "VDEF:slope=mydata,LSLSLOPE"


       rrdgraph gives an overview of how rrdtool graph works.  rrdgraph_data describes DEF,CDEF
       and VDEF in detail.  rrdgraph_rpn describes the RPN language used in the ?DEF statements.
       rrdgraph_graph page describes all of the graph and print functions.

       Make sure to read rrdgraph_examples for tips&tricks.


       Program by Tobias Oetiker <>

       This manual page by Alex van den Bogaerdt <> with corrections and/or
       additions by several people