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.
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)"
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.
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.
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.
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.
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.
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
Example: "VDEF:avg=mydata,AVERAGE"
Example: "VDEF:stdev=mydata,STDEV"
Example: "VDEF:first=mydata,FIRST"
Example: "VDEF:total=mydata,TOTAL"
Example: "VDEF:perc95=mydata,95,PERCENT"
"VDEF:percnan95=mydata,95,PERCENTNAN"
Example: "VDEF:slope=mydata,LSLSLOPE"
Make sure to read rrdgraph_examples for tips&tricks.
This manual page by Alex van den Bogaerdt <alex@vandenbogaerdt.nl> with corrections and/or additions by several people