3 rrdgraph_rpn - About RPN Math in rrdtool graph
7 I<RPN expression>:=I<vname>|I<operator>|I<value>[,I<RPN expression>]
11 If you have ever used a traditional HP calculator you already know
12 B<RPN>. The idea behind B<RPN> is that you have a stack and push
13 your data onto this stack. Whenever you execute an operation, it
14 takes as many elements from the stack as needed. Pushing is done
15 implicitly, so whenever you specify a number or a variable, it gets
16 pushed onto the stack automatically.
18 At the end of the calculation there should be one and only one value left on
19 the stack. This is the outcome of the function and this is what is put into
20 the I<vname>. For B<CDEF> instructions, the stack is processed for each
21 data point on the graph. B<VDEF> instructions work on an entire data set in
22 one run. Note, that currently B<VDEF> instructions only support a limited
25 Example: C<VDEF:maximum=mydata,MAXIMUM>
27 This will set variable "maximum" which you now can use in the rest
30 Example: C<CDEF:mydatabits=mydata,8,*>
32 This means: push variable I<mydata>, push the number 8, execute
33 the operator I<*>. The operator needs two elements and uses those
34 to return one value. This value is then stored in I<mydatabits>.
35 As you may have guessed, this instruction means nothing more than
36 I<mydatabits = mydata * 8>. The real power of B<RPN> lies in the
37 fact that it is always clear in which order to process the input.
38 For expressions like C<a = b + 3 * 5> you need to multiply 3 with
39 5 first before you add I<b> to get I<a>. However, with parentheses
40 you could change this order: C<a = (b + 3) * 5>. In B<RPN>, you
41 would do C<a = b, 3, +, 5, *> without the need for parentheses.
47 =item Boolean operators
49 B<LT, LE, GT, GE, EQ, NE>
51 Pop two elements from the stack, compare them for the selected condition
52 and return 1 for true or 0 for false. Comparing an I<unknown> or an
53 I<infinite> value will always result in 0 (false).
57 Pop one element from the stack, compare this to I<unknown> respectively
58 to I<positive or negative infinity>. Returns 1 for true or 0 for false.
62 Pops three elements from the stack. If the element popped last is 0
63 (false), the value popped first is pushed back onto the stack,
64 otherwise the value popped second is pushed back. This does, indeed,
65 mean that any value other than 0 is considered to be true.
67 Example: C<A,B,C,IF> should be read as C<if (A) then (B) else (C)>
71 =item Comparing values
75 Pops two elements from the stack and returns the smaller or larger,
76 respectively. Note that I<infinite> is larger than anything else.
77 If one of the input numbers is I<unknown> then the result of the operation will be
82 Pops two elements from the stack and uses them to define a range.
83 Then it pops another element and if it falls inside the range, it
84 is pushed back. If not, an I<unknown> is pushed.
86 The range defined includes the two boundaries (so: a number equal
87 to one of the boundaries will be pushed back). If any of the three
88 numbers involved is either I<unknown> or I<infinite> this function
89 will always return an I<unknown>
91 Example: C<CDEF:a=alpha,0,100,LIMIT> will return I<unknown> if
92 alpha is lower than 0 or if it is higher than 100.
100 Add, subtract, multiply, divide, modulo
104 NAN-safe addition. If one parameter is NAN/UNKNOWN it'll be treated as
105 zero. If both parameters are NAN/UNKNOWN, NAN/UNKNOWN will be returned.
107 B<SIN, COS, LOG, EXP, SQRT>
109 Sine and cosine (input in radians), log and exp (natural logarithm),
114 Arctangent (output in radians).
118 Arctangent of y,x components (output in radians).
119 This pops one element from the stack, the x (cosine) component, and then
120 a second, which is the y (sine) component.
121 It then pushes the arctangent of their ratio, resolving the ambiguity between
124 Example: C<CDEF:angle=Y,X,ATAN2,RAD2DEG> will convert C<X,Y>
125 components into an angle in degrees.
129 Round down or up to the nearest integer.
133 Convert angle in degrees to radians, or radians to degrees.
137 Take the absolute value.
143 Pop one element from the stack. This is the I<count> of items to be sorted
144 (or reversed). The top I<count> of the remaining elements are then sorted
145 (or reversed) in place on the stack.
147 Example: C<CDEF:x=v1,v2,v3,v4,v5,v6,6,SORT,POP,5,REV,POP,+,+,+,4,/> will
148 compute the average of the values v1 to v6 after removing the smallest and
153 Pop one element (I<count>) from the stack. Now pop I<count> elements and build the
154 average, ignoring all UNKNOWN values in the process.
156 Example: C<CDEF:x=a,b,c,d,4,AVG>
160 Create a "sliding window" average of another data series.
163 CDEF:smoothed=x,1800,TREND
165 This will create a half-hour (1800 second) sliding window average of x. The
166 average is essentially computed as shown here:
168 +---!---!---!---!---!---!---!---!--->
178 Value at sample (t0) will be the average between (t0-delay) and (t0)
179 Value at sample (t1) will be the average between (t1-delay) and (t1)
180 Value at sample (t2) will be the average between (t2-delay) and (t2)
182 TRENDNAN is - in contrast to TREND - NAN-safe. If you use TREND and one
183 source value is NAN the complete sliding window is affected. The TRENDNAN
184 operation ignores all NAN-values in a sliding window and computes the
185 average of the remaining values.
187 B<PREDICT, PREDICTSIGMA>
189 Create a "sliding window" average/sigma of another data series, that also
190 shifts the data series by given amounts of of time as well
192 Usage - explicit stating shifts:
193 CDEF:predict=<shift n>,...,<shift 1>,n,<window>,x,PREDICT
194 CDEF:sigma=<shift n>,...,<shift 1>,n,<window>,x,PREDICTSIGMA
196 Usage - shifts defined as a base shift and a number of time this is applied
197 CDEF:predict=<shift multiplier>,-n,<window>,x,PREDICT
198 CDEF:sigma=<shift multiplier>,-n,<window>,x,PREDICTSIGMA
201 CDEF:predict=172800,86400,2,1800,x,PREDICT
203 This will create a half-hour (1800 second) sliding window average/sigma of x, that
204 average is essentially computed as shown here:
206 +---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!---!--->
209 <----------------------->
213 <----------------------------------------------->
217 <----------------------->
221 <----------------------------------------------->
225 Value at sample (t0) will be the average between (t0-shift1-window) and (t0-shift1)
226 and between (t0-shift2-window) and (t0-shift2)
227 Value at sample (t1) will be the average between (t1-shift1-window) and (t1-shift1)
228 and between (t1-shift2-window) and (t1-shift2)
231 The function is by design NAN-safe.
232 This also allows for extrapolation into the future (say a few days)
233 - you may need to define the data series whit the optional start= parameter, so that
234 the source data series has enough data to provide prediction also at the beginning of a graph...
236 Here an example, that will create a 10 day graph that also shows the
237 prediction 3 days into the future with its uncertainty value (as defined by avg+-4*sigma)
238 This also shows if the prediction is exceeded at a certain point.
240 rrdtool graph image.png --imgformat=PNG \
241 --start=-7days --end=+3days --width=1000 --height=200 --alt-autoscale-max \
242 DEF:value=value.rrd:value:AVERAGE:start=-14days \
243 LINE1:value#ff0000:value \
244 CDEF:predict=86400,-7,1800,value,PREDICT \
245 CDEF:sigma=86400,-7,1800,value,PREDICTSIGMA \
246 CDEF:upper=predict,sigma,3,*,+ \
247 CDEF:lower=predict,sigma,3,*,- \
248 LINE1:predict#00ff00:prediction \
249 LINE1:upper#0000ff:upper\ certainty\ limit \
250 LINE1:lower#0000ff:lower\ certainty\ limit \
251 CDEF:exceeds=value,UN,0,value,lower,upper,LIMIT,UN,IF \
252 TICK:exceeds#aa000080:1
254 Note: Experience has shown that a factor between 3 and 5 to scale sigma is a good
255 discriminator to detect abnormal behaviour. This obviously depends also on the type
256 of data and how "noisy" the data series is.
258 This prediction can only be used for short term extrapolations - say a few days into the future-
264 Pushes an unknown value on the stack
268 Pushes a positive or negative infinite value on the stack. When
269 such a value is graphed, it appears at the top or bottom of the
270 graph, no matter what the actual value on the y-axis is.
274 Pushes an I<unknown> value if this is the first value of a data
275 set or otherwise the result of this B<CDEF> at the previous time
276 step. This allows you to do calculations across the data. This
277 function cannot be used in B<VDEF> instructions.
281 Pushes an I<unknown> value if this is the first value of a data
282 set or otherwise the result of the vname variable at the previous time
283 step. This allows you to do calculations across the data. This
284 function cannot be used in B<VDEF> instructions.
288 Pushes the number 1 if this is the first value of the data set, the
289 number 2 if it is the second, and so on. This special value allows
290 you to make calculations based on the position of the value within
291 the data set. This function cannot be used in B<VDEF> instructions.
295 Time inside RRDtool is measured in seconds since the epoch. The
296 epoch is defined to be S<C<Thu Jan 1 00:00:00 UTC 1970>>.
300 Pushes the current time on the stack.
304 Pushes the time the currently processed value was taken at onto the stack.
308 Takes the time as defined by B<TIME>, applies the time zone offset
309 valid at that time including daylight saving time if your OS supports
310 it, and pushes the result on the stack. There is an elaborate example
311 in the examples section below on how to use this.
313 =item Processing the stack directly
317 Duplicate the top element, remove the top element, exchange the two
326 These operators work only on B<VDEF> statements. Note that currently ONLY these work for B<VDEF>.
330 =item MAXIMUM, MINIMUM, AVERAGE
332 Return the corresponding value, MAXIMUM and MINIMUM also return
333 the first occurrence of that value in the time component.
335 Example: C<VDEF:avg=mydata,AVERAGE>
339 Returns the standard deviation of the values.
341 Example: C<VDEF:stdev=mydata,STDEV>
345 Return the last/first value including its time. The time for
346 FIRST is actually the start of the corresponding interval, whereas
347 LAST returns the end of the corresponding interval.
349 Example: C<VDEF:first=mydata,FIRST>
353 Returns the rate from each defined time slot multiplied with the
354 step size. This can, for instance, return total bytes transfered
355 when you have logged bytes per second. The time component returns
356 the number of seconds.
358 Example: C<VDEF:total=mydata,TOTAL>
362 This should follow a B<DEF> or B<CDEF> I<vname>. The I<vname> is popped,
363 another number is popped which is a certain percentage (0..100). The
364 data set is then sorted and the value returned is chosen such that
365 I<percentage> percent of the values is lower or equal than the result.
366 I<Unknown> values are considered lower than any finite number for this
367 purpose so if this operator returns an I<unknown> you have quite a lot
368 of them in your data. B<Inf>inite numbers are lesser, or more, than the
369 finite numbers and are always more than the I<Unknown> numbers.
370 (NaN E<lt> -INF E<lt> finite values E<lt> INF)
372 Example: C<VDEF:perc95=mydata,95,PERCENT>
374 =item LSLSLOPE, LSLINT, LSLCORREL
376 Return the parameters for a B<L>east B<S>quares B<L>ine I<(y = mx +b)>
377 which approximate the provided dataset. LSLSLOPE is the slope I<(m)> of
378 the line related to the COUNT position of the data. LSLINT is the
379 y-intercept I<(b)>, which happens also to be the first data point on the
380 graph. LSLCORREL is the Correlation Coefficient (also know as Pearson's
381 Product Moment Correlation Coefficient). It will range from 0 to +/-1
382 and represents the quality of fit for the approximation.
384 Example: C<VDEF:slope=mydata,LSLSLOPE>
390 L<rrdgraph> gives an overview of how B<rrdtool graph> works.
391 L<rrdgraph_data> describes B<DEF>,B<CDEF> and B<VDEF> in detail.
392 L<rrdgraph_rpn> describes the B<RPN> language used in the B<?DEF> statements.
393 L<rrdgraph_graph> page describes all of the graph and print functions.
395 Make sure to read L<rrdgraph_examples> for tipsE<amp>tricks.
399 Program by Tobias Oetiker E<lt>tobi@oetiker.chE<gt>
401 This manual page by Alex van den Bogaerdt E<lt>alex@ergens.op.het.netE<gt>