man > rrdgraph_rpn(1)

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RRDGRAPH_RPN(1) rrdtool RRDGRAPH_RPN(1)

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 with 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 1800 seconds. 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.

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 width 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 AT oetiker.ch>

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

1.7.2 2024-03-31 RRDGRAPH_RPN(1)

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