1RRDGRAPH_RPN(1) rrdtool RRDGRAPH_RPN(1)
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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 result in unknown returned ...
50 which will also be treated as false by the IF call.
51 UN, ISINF
53 Pop one element from the stack, compare this to unknown
55 respectively to positive or negative infinity. Returns 1 for true
56 or 0 for false.
57 IF
59 Pops three elements from the stack. If the element popped last is
61 0 (false), the value popped first is pushed back onto the stack,
62 otherwise the value popped second is pushed back. This does,
63 indeed, mean that any value other than 0 is considered to be true.
64 Example: "A,B,C,IF" should be read as "if (A) then (B) else (C)"
66 Comparing values
70 MIN, MAX
71 Pops two elements from the stack and returns the smaller or larger,
73 respectively. Note that infinite is larger than anything else. If
74 one of the input numbers is unknown then the result of the
75 operation will be unknown too.
76 LIMIT
78 Pops two elements from the stack and uses them to define a range.
80 Then it pops another element and if it falls inside the range, it
81 is pushed back. If not, an unknown is pushed.
82 The range defined includes the two boundaries (so: a number equal
84 to one of the boundaries will be pushed back). If any of the three
85 numbers involved is either unknown or infinite this function will
86 always return an unknown
87 Example: "CDEF:a=alpha,0,100,LIMIT" will return unknown if alpha is
89 lower than 0 or if it is higher than 100.
90 Arithmetics
94 +, -, *, /, %
95 Add, subtract, multiply, divide, modulo
97 ADDNAN
99 NAN-safe addition. If one parameter is NAN/UNKNOWN it'll be treated
101 as zero. If both parameters are NAN/UNKNOWN, NAN/UNKNOWN will be
102 returned.
103 SIN, COS, LOG, EXP, SQRT
105 Sine and cosine (input in radians), log and exp (natural
107 logarithm), square root.
108 ATAN
110 Arctangent (output in radians).
112 ATAN2
114 Arctangent of y,x components (output in radians). This pops one
116 element from the stack, the x (cosine) component, and then a
117 second, which is the y (sine) component. It then pushes the
118 arctangent of their ratio, resolving the ambiguity between
119 quadrants.
120 Example: "CDEF:angle=Y,X,ATAN2,RAD2DEG" will convert "X,Y"
122 components into an angle in degrees.
123 FLOOR, CEIL
125 Round down or up to the nearest integer.
127 DEG2RAD, RAD2DEG
129 Convert angle in degrees to radians, or radians to degrees.
131 ABS
133 Take the absolute value.
135 Set Operations
137 SORT, REV
138 Pop one element from the stack. This is the count of items to be
140 sorted (or reversed). The top count of the remaining elements are
141 then sorted (or reversed) in place on the stack.
142 Example: "CDEF:x=v1,v2,v3,v4,v5,v6,6,SORT,POP,5,REV,POP,+,+,+,4,/"
144 will compute the average of the values v1 to v6 after removing the
145 smallest and largest.
146 AVG
148 Pop one element (count) from the stack. Now pop count elements and
150 build the average, ignoring all UNKNOWN values in the process.
151 Example: "CDEF:x=a,b,c,d,4,AVG"
153 TREND, TRENDNAN
155 Create a "sliding window" average of another data series.
157 Usage: CDEF:smoothed=x,1800,TREND
159 This will create a half-hour (1800 second) sliding window average
161 of x. The average is essentially computed as shown here:
162 +---!---!---!---!---!---!---!---!--->
164 now
165 delay t0
166 <--------------->
167 delay t1
168 <--------------->
169 delay t2
170 <--------------->
171 Value at sample (t0) will be the average between (t0-delay) and (t0)
174 Value at sample (t1) will be the average between (t1-delay) and (t1)
175 Value at sample (t2) will be the average between (t2-delay) and (t2)
176 TRENDNAN is - in contrast to TREND - NAN-safe. If you use TREND and
178 one source value is NAN the complete sliding window is affected.
179 The TRENDNAN operation ignores all NAN-values in a sliding window
180 and computes the average of the remaining values.
181 PREDICT, PREDICTSIGMA
183 Create a "sliding window" average/sigma of another data series,
185 that also shifts the data series by given amounts of of time as
186 well
187 Usage - explicit stating shifts: CDEF:predict=<shift n>,...,<shift
189 1>,n,<window>,x,PREDICT CDEF:sigma=<shift n>,...,<shift
190 1>,n,<window>,x,PREDICTSIGMA
191 Usage - shifts defined as a base shift and a number of time this is
193 applied CDEF:predict=<shift multiplier>,-n,<window>,x,PREDICT
194 CDEF:sigma=<shift multiplier>,-n,<window>,x,PREDICTSIGMA
195 Example: CDEF:predict=172800,86400,2,1800,x,PREDICT
197 This will create a half-hour (1800 second) sliding window
199 average/sigma of x, that average is essentially computed as shown
200 here:
201 +---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!--->
203 now
204 shift 1 t0
205 <----------------------->
206 window
207 <--------------->
208 shift 2
209 <----------------------------------------------->
210 window
211 <--------------->
212 shift 1 t1
213 <----------------------->
214 window
215 <--------------->
216 shift 2
217 <----------------------------------------------->
218 window
219 <--------------->
220 Value at sample (t0) will be the average between (t0-shift1-window) and (t0-shift1)
222 and between (t0-shift2-window) and (t0-shift2)
223 Value at sample (t1) will be the average between (t1-shift1-window) and (t1-shift1)
224 and between (t1-shift2-window) and (t1-shift2)
225 The function is by design NAN-safe. This also allows for
227 extrapolation into the future (say a few days) - you may need to
228 define the data series whit the optional start= parameter, so that
229 the source data series has enough data to provide prediction also
230 at the beginning of a graph...
231 Here an example, that will create a 10 day graph that also shows
233 the prediction 3 days into the future with its uncertainty value
234 (as defined by avg+-4*sigma) This also shows if the prediction is
235 exceeded at a certain point.
236 rrdtool graph image.png --imgformat=PNG \
238 --start=-7days --end=+3days --width=1000 --height=200
239 --alt-autoscale-max \
240 DEF:value=value.rrd:value:AVERAGE:start=-14days \
241 LINE1:value#ff0000:value \
242 CDEF:predict=86400,-7,1800,value,PREDICT \
243 CDEF:sigma=86400,-7,1800,value,PREDICTSIGMA \
244 CDEF:upper=predict,sigma,3,*,+ \
245 CDEF:lower=predict,sigma,3,*,- \
246 LINE1:predict#00ff00:prediction \
247 LINE1:upper#0000ff:upper\ certainty\ limit \
248 LINE1:lower#0000ff:lower\ certainty\ limit \
249 CDEF:exceeds=value,UN,0,value,lower,upper,LIMIT,UN,IF \
250 TICK:exceeds#aa000080:1
251 Note: Experience has shown that a factor between 3 and 5 to scale
253 sigma is a good discriminator to detect abnormal behavior. This
254 obviously depends also on the type of data and how "noisy" the data
255 series is.
256 This prediction can only be used for short term extrapolations -
258 say a few days into the future-
259 Special values
261 UNKN
262 Pushes an unknown value on the stack
264 INF, NEGINF
266 Pushes a positive or negative infinite value on the stack. When
268 such a value is graphed, it appears at the top or bottom of the
269 graph, no matter what the actual value on the y-axis is.
270 PREV
272 Pushes an unknown value if this is the first value of a data set or
274 otherwise the result of this CDEF at the previous time step. This
275 allows you to do calculations across the data. This function
276 cannot be used in VDEF instructions.
277 PREV(vname)
279 Pushes an unknown value if this is the first value of a data set or
281 otherwise the result of the vname variable at the previous time
282 step. This allows you to do calculations across the data. This
283 function cannot be used in VDEF instructions.
284 COUNT
286 Pushes the number 1 if this is the first value of the data set, the
288 number 2 if it is the second, and so on. This special value allows
289 you to make calculations based on the position of the value within
290 the data set. This function cannot be used in VDEF instructions.
291 Time
293 Time inside RRDtool is measured in seconds since the epoch. The
294 epoch is defined to be "Thu Jan 1 00:00:00 UTC 1970".
295 NOW
297 Pushes the current time on the stack.
299 TIME
301 Pushes the time the currently processed value was taken at onto the
303 stack.
304 LTIME
306 Takes the time as defined by TIME, applies the time zone offset
308 valid at that time including daylight saving time if your OS
309 supports it, and pushes the result on the stack. There is an
310 elaborate example in the examples section below on how to use this.
311 Processing the stack directly
313 DUP, POP, EXC
314 Duplicate the top element, remove the top element, exchange the two
316 top elements.
317
321 These operators work only on VDEF statements. Note that currently ONLY
322 these work for VDEF.
323 MAXIMUM, MINIMUM, AVERAGE
325 Return the corresponding value, MAXIMUM and MINIMUM also return the
326 first occurrence of that value in the time component.
327 Example: "VDEF:avg=mydata,AVERAGE"
329 STDEV
331 Returns the standard deviation of the values.
332 Example: "VDEF:stdev=mydata,STDEV"
334 LAST, FIRST
336 Return the last/first non-nan or infinite value for the selected
337 data stream, including its timestamp.
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
3891.4.8 2013-05-23 RRDGRAPH_RPN(1)