1RRDGRAPH_RPN(1) rrdtool RRDGRAPH_RPN(1)
2
6 rrdgraph_rpn - About RPN Math in rrdtool graph
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9 RPN expression:=vname|operator|value[,RPN expression]
10
12 If you have ever used a traditional HP calculator you already know RPN
13 (Reverse Polish Notation). The idea behind RPN is that you have a
14 stack and push your data onto this stack. Whenever you execute an
15 operation, it takes as many elements from the stack as needed. Pushing
16 is done implicitly, so whenever you specify a number or a variable, it
17 gets pushed onto the stack automatically.
18 At the end of the calculation there should be one and only one value
20 left on the stack. This is the outcome of the function and this is
21 what is put into the vname. For CDEF instructions, the stack is
22 processed for each data point on the graph. VDEF instructions work on
23 an entire data set in one run. Note, that currently VDEF instructions
24 only support a limited list of functions.
25 Example: "VDEF:maximum=mydata,MAXIMUM"
27 This will set variable "maximum" which you now can use in the rest of
29 your RRD script.
30 Example: "CDEF:mydatabits=mydata,8,*"
32 This means: push variable mydata, push the number 8, execute the
34 operator *. The operator needs two elements and uses those to return
35 one value. This value is then stored in mydatabits. As you may have
36 guessed, this instruction means nothing more than mydatabits = mydata *
37 8. The real power of RPN lies in the fact that it is always clear in
38 which order to process the input. For expressions like "a = b + 3 * 5"
39 you need to multiply 3 with 5 first before you add b to get a. However,
40 with parentheses you could change this order: "a = (b + 3) * 5". In
41 RPN, you would do "a = b, 3, +, 5, *" without the need for parentheses.
42
44 Boolean operators
45 LT, LE, GT, GE, EQ, NE
46 Pop two elements from the stack, compare them for the selected
48 condition and return 1 for true or 0 for false. Comparing an
49 unknown or an infinite value will always result in 0 (false).
50 UN, ISINF
52 Pop one element from the stack, compare this to unknown
54 respectively to positive or negative infinity. Returns 1 for true
55 or 0 for false.
56 IF
58 Pops three elements from the stack. If the element popped last is
60 0 (false), the value popped first is pushed back onto the stack,
61 otherwise the value popped second is pushed back. This does,
62 indeed, mean that any value other than 0 is considered to be true.
63 Example: "A,B,C,IF" should be read as "if (A) then (B) else (C)"
65 Comparing values
69 MIN, MAX
70 Pops two elements from the stack and returns the smaller or larger,
72 respectively. Note that infinite is larger than anything else. If
73 one of the input numbers is unknown then the result of the
74 operation will be unknown too.
75 LIMIT
77 Pops two elements from the stack and uses them to define a range.
79 Then it pops another element and if it falls inside the range, it
80 is pushed back. If not, an unknown is pushed.
81 The range defined includes the two boundaries (so: a number equal
83 to one of the boundaries will be pushed back). If any of the three
84 numbers involved is either unknown or infinite this function will
85 always return an unknown
86 Example: "CDEF:a=alpha,0,100,LIMIT" will return unknown if alpha is
88 lower than 0 or if it is higher than 100.
89 Arithmetics
93 +, -, *, /, %
94 Add, subtract, multiply, divide, modulo
96 ADDNAN
98 NAN-safe addition. If one parameter is NAN/UNKNOWN it'll be treated
100 as zero. If both parameters are NAN/UNKNOWN, NAN/UNKNOWN will be
101 returned.
102 SIN, COS, LOG, EXP, SQRT
104 Sine and cosine (input in radians), log and exp (natural
106 logarithm), square root.
107 ATAN
109 Arctangent (output in radians).
111 ATAN2
113 Arctangent of y,x components (output in radians). This pops one
115 element from the stack, the x (cosine) component, and then a
116 second, which is the y (sine) component. It then pushes the
117 arctangent of their ratio, resolving the ambiguity between
118 quadrants.
119 Example: "CDEF:angle=Y,X,ATAN2,RAD2DEG" will convert "X,Y"
121 components into an angle in degrees.
122 FLOOR, CEIL
124 Round down or up to the nearest integer.
126 DEG2RAD, RAD2DEG
128 Convert angle in degrees to radians, or radians to degrees.
130 ABS
132 Take the absolute value.
134 Set Operations
136 SORT, REV
137 Pop one element from the stack. This is the count of items to be
139 sorted (or reversed). The top count of the remaining elements are
140 then sorted (or reversed) in place on the stack.
141 Example: "CDEF:x=v1,v2,v3,v4,v5,v6,6,SORT,POP,5,REV,POP,+,+,+,4,/"
143 will compute the average of the values v1 to v6 after removing the
144 smallest and largest.
145 AVG
147 Pop one element (count) from the stack. Now pop count elements and
149 build the average, ignoring all UNKNOWN values in the process.
150 Example: "CDEF:x=a,b,c,d,4,AVG"
152 TREND, TRENDNAN
154 Create a "sliding window" average of another data series.
156 Usage: CDEF:smoothed=x,1800,TREND
158 This will create a half-hour (1800 second) sliding window average
160 of x. The average is essentially computed as shown here:
161 +---!---!---!---!---!---!---!---!--->
163 now
164 delay t0
165 <--------------->
166 delay t1
167 <--------------->
168 delay t2
169 <--------------->
170 Value at sample (t0) will be the average between (t0-delay) and (t0)
173 Value at sample (t1) will be the average between (t1-delay) and (t1)
174 Value at sample (t2) will be the average between (t2-delay) and (t2)
175 TRENDNAN is - in contrast to TREND - NAN-safe. If you use TREND and
177 one source value is NAN the complete sliding window is affected.
178 The TRENDNAN operation ignores all NAN-values in a sliding window
179 and computes the average of the remaining values.
180 PREDICT, PREDICTSIGMA
182 Create a "sliding window" average/sigma of another data series,
184 that also shifts the data series by given amounts of of time as
185 well
186 Usage - explicit stating shifts: CDEF:predict=<shift n>,...,<shift
188 1>,n,<window>,x,PREDICT CDEF:sigma=<shift n>,...,<shift
189 1>,n,<window>,x,PREDICTSIGMA
190 Usage - shifts defined as a base shift and a number of time this is
192 applied CDEF:predict=<shift multiplier>,-n,<window>,x,PREDICT
193 CDEF:sigma=<shift multiplier>,-n,<window>,x,PREDICTSIGMA
194 Example: CDEF:predict=172800,86400,2,1800,x,PREDICT
196 This will create a half-hour (1800 second) sliding window
198 average/sigma of x, that average is essentially computed as shown
199 here:
200 +---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!--->
202 now
203 shift 1 t0
204 <----------------------->
205 window
206 <--------------->
207 shift 2
208 <----------------------------------------------->
209 window
210 <--------------->
211 shift 1 t1
212 <----------------------->
213 window
214 <--------------->
215 shift 2
216 <----------------------------------------------->
217 window
218 <--------------->
219 Value at sample (t0) will be the average between (t0-shift1-window) and (t0-shift1)
221 and between (t0-shift2-window) and (t0-shift2)
222 Value at sample (t1) will be the average between (t1-shift1-window) and (t1-shift1)
223 and between (t1-shift2-window) and (t1-shift2)
224 The function is by design NAN-safe. This also allows for
226 extrapolation into the future (say a few days) - you may need to
227 define the data series whit the optional start= parameter, so that
228 the source data series has enough data to provide prediction also
229 at the beginning of a graph...
230 Here an example, that will create a 10 day graph that also shows
232 the prediction 3 days into the future with its uncertainty value
233 (as defined by avg+-4*sigma) This also shows if the prediction is
234 exceeded at a certain point.
235 rrdtool graph image.png --imgformat=PNG \
237 --start=-7days --end=+3days --width=1000 --height=200
238 --alt-autoscale-max \
239 DEF:value=value.rrd:value:AVERAGE:start=-14days \
240 LINE1:value#ff0000:value \
241 CDEF:predict=86400,-7,1800,value,PREDICT \
242 CDEF:sigma=86400,-7,1800,value,PREDICTSIGMA \
243 CDEF:upper=predict,sigma,3,*,+ \
244 CDEF:lower=predict,sigma,3,*,- \
245 LINE1:predict#00ff00:prediction \
246 LINE1:upper#0000ff:upper\ certainty\ limit \
247 LINE1:lower#0000ff:lower\ certainty\ limit \
248 CDEF:exceeds=value,UN,0,value,lower,upper,LIMIT,UN,IF \
249 TICK:exceeds#aa000080:1
250 Note: Experience has shown that a factor between 3 and 5 to scale
252 sigma is a good discriminator to detect abnormal behavior. This
253 obviously depends also on the type of data and how "noisy" the data
254 series is.
255 This prediction can only be used for short term extrapolations -
257 say a few days into the future-
258 Special values
260 UNKN
261 Pushes an unknown value on the stack
263 INF, NEGINF
265 Pushes a positive or negative infinite value on the stack. When
267 such a value is graphed, it appears at the top or bottom of the
268 graph, no matter what the actual value on the y-axis is.
269 PREV
271 Pushes an unknown value if this is the first value of a data set or
273 otherwise the result of this CDEF at the previous time step. This
274 allows you to do calculations across the data. This function
275 cannot be used in VDEF instructions.
276 PREV(vname)
278 Pushes an unknown value if this is the first value of a data set or
280 otherwise the result of the vname variable at the previous time
281 step. This allows you to do calculations across the data. This
282 function cannot be used in VDEF instructions.
283 COUNT
285 Pushes the number 1 if this is the first value of the data set, the
287 number 2 if it is the second, and so on. This special value allows
288 you to make calculations based on the position of the value within
289 the data set. This function cannot be used in VDEF instructions.
290 Time
292 Time inside RRDtool is measured in seconds since the epoch. The
293 epoch is defined to be "Thu Jan 1 00:00:00 UTC 1970".
294 NOW
296 Pushes the current time on the stack.
298 TIME
300 Pushes the time the currently processed value was taken at onto the
302 stack.
303 LTIME
305 Takes the time as defined by TIME, applies the time zone offset
307 valid at that time including daylight saving time if your OS
308 supports it, and pushes the result on the stack. There is an
309 elaborate example in the examples section below on how to use this.
310 Processing the stack directly
312 DUP, POP, EXC
313 Duplicate the top element, remove the top element, exchange the two
315 top elements.
316
320 These operators work only on VDEF statements. Note that currently ONLY
321 these work for VDEF.
322 MAXIMUM, MINIMUM, AVERAGE
324 Return the corresponding value, MAXIMUM and MINIMUM also return the
325 first occurrence of that value in the time component.
326 Example: "VDEF:avg=mydata,AVERAGE"
328 STDEV
330 Returns the standard deviation of the values.
331 Example: "VDEF:stdev=mydata,STDEV"
333 LAST, FIRST
335 Return the last/first value including its time. The time for FIRST
336 is actually the start of the corresponding interval, whereas LAST
337 returns the end of the corresponding interval.
338 Example: "VDEF:first=mydata,FIRST"
340 TOTAL
342 Returns the rate from each defined time slot multiplied with the
343 step size. This can, for instance, return total bytes transferred
344 when you have logged bytes per second. The time component returns
345 the number of seconds.
346 Example: "VDEF:total=mydata,TOTAL"
348 PERCENT, PERCENTNAN
350 This should follow a DEF or CDEF vname. The vname is popped,
351 another number is popped which is a certain percentage (0..100).
352 The data set is then sorted and the value returned is chosen such
353 that percentage percent of the values is lower or equal than the
354 result. For PERCENTNAN Unknown values are ignored, but for PERCENT
355 Unknown values are considered lower than any finite number for this
356 purpose so if this operator returns an unknown you have quite a lot
357 of them in your data. Infinite numbers are lesser, or more, than
358 the finite numbers and are always more than the Unknown numbers.
359 (NaN < -INF < finite values < INF)
360 Example: "VDEF:perc95=mydata,95,PERCENT"
362 "VDEF:percnan95=mydata,95,PERCENTNAN"
363 LSLSLOPE, LSLINT, LSLCORREL
365 Return the parameters for a Least Squares Line (y = mx +b) which
366 approximate the provided dataset. LSLSLOPE is the slope (m) of the
367 line related to the COUNT position of the data. LSLINT is the
368 y-intercept (b), which happens also to be the first data point on
369 the graph. LSLCORREL is the Correlation Coefficient (also know as
370 Pearson's Product Moment Correlation Coefficient). It will range
371 from 0 to +/-1 and represents the quality of fit for the
372 approximation.
373 Example: "VDEF:slope=mydata,LSLSLOPE"
375
377 rrdgraph gives an overview of how rrdtool graph works. rrdgraph_data
378 describes DEF,CDEF and VDEF in detail. rrdgraph_rpn describes the RPN
379 language used in the ?DEF statements. rrdgraph_graph page describes
380 all of the graph and print functions.
381 Make sure to read rrdgraph_examples for tips&tricks.
383
385 Program by Tobias Oetiker <tobi@oetiker.ch>
386 This manual page by Alex van den Bogaerdt <alex@vandenbogaerdt.nl> with
388 corrections and/or additions by several people
3891.4.4 2009-10-14 RRDGRAPH_RPN(1)