RRDGRAPH_RPN(1)                     rrdtool                    RRDGRAPH_RPN(1)

       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 parentheses.

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

           Less than, Less or equal, Greater than, Greater or equal, Equal,
           Not equal all 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 true.

           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.

           MINNAN, MAXNAN

           NAN-safe version of MIN and MAX. If one of the input numbers is
           unknown then the result of the operation will be the other one. If
           both are unknown, then the result of the operation is unknown.


           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


           Raise value to the power of power.

           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 degrees.

           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

           Pop one element from the stack.  This is the count of items to be
           sorted.  The top count of the remaining elements are then sorted
           from the smallest to the largest, in place on the stack.

              4,3,22.1,1,4,SORT -> 1,3,4,22.1


           Reverse the number

           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"

           count,SMIN and count,SMAX

           Pop one element (count) from the stack. Now pop count elements and
           push the minimum/maximum back onto the stack.

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


           pop one element (count) from the stack. Now pop count elements and
           find the median, ignoring all UNKNOWN values in the process. If
           there are an even number of non-UNKNOWN values, the average of the
           middle two will be pushed on the stack.

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


           pop one element (count) from the stack. Now pop count elements and
           calculate the standard deviation over these values (ignoring any
           NAN values). Push the result back on to the stack.

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


           pop two elements (count,percent) from the stack. Now pop count
           element, order them by size (while the smalles elements are -INF,
           the largest are INF and NaN is larger than -INF but smaller than
           anything else. No pick the element from the ordered list where
           percent of the elements are equal then the one picked. Push the
           result back on to the stack.

           Example: "CDEF:x=a,b,c,d,95,4,PERCENT"

           count,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/percentil of another data
           series, that also shifts the data series by given amounts 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" "CDEF:perc=<shift n>,...,<shift

           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 multiplier>,-n,<window>,x,PREDICTSIGMA"

           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

                                                             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...

           The percentile can be between [-100:+100].  The positive
           percentiles interpolates between values while the negative will
           take the closest.

           Example: you run 7 shifts with a window of 1800seconds. Assuming
           that the rrd-file has a step size of 300 seconds this means we have
           to do the percentile calculation based on a max of 42 distinct
           values (less if you got NAN). that means that in the best case you
           get a step rate between values of 2.4 percent.  so if you ask for
           the 99th percentile, then you would need to look at the 41.59th
           value. As we only have integers, either the 41st or the 42nd value.

           With the positive percentile a linear interpolation between the 2
           values is done to get the effective value.

           The negative returns the closest value distance wise - so in the
           above case 42nd value, which is effectively returning the
           Percentile100 or the max of the previous 7 days in the window.

           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 \
               TICK:exceeds#aa000080:1 \
               CDEF:perc95=86400,-7,1800,95,value,PREDICTPERC \

           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.

           Also Note the explicit use of start= in the CDEF - this is
           necessary to load all the necessary data (even if it is not

           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 instructions.

           Time inside RRDtool is measured in seconds since the epoch. The
           epoch is defined to be "ThuJan100:00:00UTC1970".


           Pushes the current time on the stack.


           The with of the current step in seconds. You can use this to go
           back from rate based presentations to absolute numbers



           These three operators will return 1.0 whenever a step is the first
           of the given period. The periods are determined according to the
           local timezone AND the "LC_TIME" settings.



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


           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 this.

       Processing the stack directly
           DUP, POP, EXC

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


           pushes the current depth of the stack onto the stack

            a,b,DEPTH -> a,b,2


           push a copy of the top n elements onto the stack

            a,b,c,d,2,COPY => a,b,c,d,c,d


           push the nth element onto the stack.

            a,b,c,d,3,INDEX -> a,b,c,d,b


           rotate the top n elements of the stack by m

            a,b,c,d,3,1,ROLL => a,d,b,c
            a,b,c,d,3,-1,ROLL => a,c,d,b

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

           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

           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 <tobi@oetiker.ch>

       This manual page by Alex van den Bogaerdt <alex@vandenbogaerdt.nl> with
       corrections and/or additions by several people

1.7.0                             2018-02-07                   RRDGRAPH_RPN(1)

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