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# man pages section 1: User Commands

Updated: Wednesday, February 10, 2021

## rrdgraph_rpn (1)

### Name

rrdgraph_rpn - About RPN Math in rrdtool graph

### Synopsis

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

### Description

```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 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"

ATTRIBUTES
See attributes(7) for descriptions of the following attributes:

+---------------+------------------+
|ATTRIBUTE TYPE | ATTRIBUTE VALUE  |
+---------------+------------------+
|Availability   | image/rrdtool    |
+---------------+------------------+
|Stability      | Uncommitted      |
+---------------+------------------+
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

NOTES
This software was built from source available at
https://github.com/oracle/solaris-userland.  The original community
source was downloaded from
http://oss.oetiker.ch/rrdtool/pub/rrdtool-1.6.0.tar.gz

Further information about this software can be found on the open source
community website at http://oss.oetiker.ch/rrdtool/.

1.6.0                             2016-04-19                   RRDGRAPH_RPN(1)
```