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
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.
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
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.
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
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.
AVG
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
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 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 here:
+---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!--->
now
shift 1 t0
<----------------------->
window
<--------------->
shift 2
<----------------------------------------------->
window
<--------------->
shift 1 t1
<----------------------->
window
<--------------->
shift 2
<----------------------------------------------->
window
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
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
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".
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.
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.
This manual page by Alex van den Bogaerdt <[email protected]> with corrections and/or additions by
several people
1.4.8 2013-05-23 RRDGRAPH_RPN(1)
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