Provided by: rrdtool_1.7.0-1build2_amd64 bug

NAME

       rrdgraph_rpn - About RPN Math in rrdtool graph

SYNOPSIS

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

DESCRIPTION

       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.

OPERATORS

       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.

           then,else,condition,IF

           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.

           lower-limit,upper-limit,LIMIT

           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.

       Arithmetics
           +, -, *, /, %

           Add, subtract, multiply, divide, modulo

           ADDNAN

           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.

           value,power,POW

           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.

           ATAN

           Arctangent (output in radians).

           ATAN2

           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
           quadrants.

           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.

           ABS

           Take the absolute value.

       Set Operations
           count,SORT

           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

           count,REV

           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.

           count,AVG

           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"

           count,MEDIAN

           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"

           count,STDEV

           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"

           percent,count,PERCENT

           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:

                            +---!---!---!---!---!---!---!---!--->
                                                                now
                                  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.

           PREDICT, PREDICTSIGMA, PREDICTPERC

           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
           1>,n,<window>,<percentil>,x,PREDICTPERC"

           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" "CDEF:sigma=<shift
           multiplier>,-n,<window>,<percentil>,x,PREDICTPERC"

           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:

            +---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!--->
                                                                                now
                                                             shift 1        t0
                                                    <----------------------->
                                          window
                                    <--------------->
                                                  shift 2
                            <----------------------------------------------->
                  window
            <--------------->
                                                                 shift 1        t1
                                                        <----------------------->
                                              window
                                        <--------------->
                                                       shift 2
                                <----------------------------------------------->
                      window
                <--------------->

            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 \
               LINE1:perc95#ffff00:95th_percentile

           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 displayed)

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

       Special values
           UNKN

           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.

           PREV

           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.

           PREV(vname)

           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.

           COUNT

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

           NOW

           Pushes the current time on the stack.

           STEPWIDTH

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

             CDEF:abs=rate,STEPWIDTH,*,PREV,ADDNAN

           NEWDAY,NEWWEEK,NEWMONTH,NEWYEAR

           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.

             CDEF:mtotal=rate,STEPWIDTH,*,NEWMONTH,0,PREV,IF,ADDNAN

           TIME

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

           LTIME

           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.

           DEPTH

           pushes the current depth of the stack onto the stack

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

           n,COPY

           push a copy of the top n elements onto the stack

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

           n,INDEX

           push the nth element onto the stack.

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

           n,m,ROLL

           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

VARIABLES

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

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

           Example: "VDEF:avg=mydata,AVERAGE"

       STDEV
           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"

       TOTAL
           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"

       PERCENT, PERCENTNAN
           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"
                    "VDEF:percnan95=mydata,95,PERCENTNAN"

       LSLSLOPE, LSLINT, LSLCORREL
           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"

SEE ALSO

       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.

AUTHOR

       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