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]
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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.
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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 Special values
182 UNKN
183 Pushes an unknown value on the stack
185 INF, NEGINF
187 Pushes a positive or negative infinite value on the stack. When
189 such a value is graphed, it appears at the top or bottom of the
190 graph, no matter what the actual value on the y-axis is.
191 PREV
193 Pushes an unknown value if this is the first value of a data set or
195 otherwise the result of this CDEF at the previous time step. This
196 allows you to do calculations across the data. This function
197 cannot be used in VDEF instructions.
198 PREV(vname)
200 Pushes an unknown value if this is the first value of a data set or
202 otherwise the result of the vname variable at the previous time
203 step. This allows you to do calculations across the data. This
204 function cannot be used in VDEF instructions.
205 COUNT
207 Pushes the number 1 if this is the first value of the data set, the
209 number 2 if it is the second, and so on. This special value allows
210 you to make calculations based on the position of the value within
211 the data set. This function cannot be used in VDEF instructions.
212 Time
214 Time inside RRDtool is measured in seconds since the epoch. The
215 epoch is defined to be "Thu Jan 1 00:00:00 UTC 1970".
216 NOW
218 Pushes the current time on the stack.
220 TIME
222 Pushes the time the currently processed value was taken at onto the
224 stack.
225 LTIME
227 Takes the time as defined by TIME, applies the time zone offset
229 valid at that time including daylight saving time if your OS
230 supports it, and pushes the result on the stack. There is an
231 elaborate example in the examples section below on how to use this.
232 Processing the stack directly
234 DUP, POP, EXC
235 Duplicate the top element, remove the top element, exchange the two
237 top elements.
238
242 These operators work only on VDEF statements. Note that currently ONLY
243 these work for VDEF.
244 MAXIMUM, MINIMUM, AVERAGE
246 Return the corresponding value, MAXIMUM and MINIMUM also return the
247 first occurrence of that value in the time component.
248 Example: "VDEF:avg=mydata,AVERAGE"
250 STDEV
252 Returns the standard deviation of the values.
253 Example: "VDEF:stdev=mydata,STDEV"
255 LAST, FIRST
257 Return the last/first value including its time. The time for FIRST
258 is actually the start of the corresponding interval, whereas LAST
259 returns the end of the corresponding interval.
260 Example: "VDEF:first=mydata,FIRST"
262 TOTAL
264 Returns the rate from each defined time slot multiplied with the
265 step size. This can, for instance, return total bytes transfered
266 when you have logged bytes per second. The time component returns
267 the number of seconds.
268 Example: "VDEF:total=mydata,TOTAL"
270 PERCENT
272 This should follow a DEF or CDEF vname. The vname is popped,
273 another number is popped which is a certain percentage (0..100).
274 The data set is then sorted and the value returned is chosen such
275 that percentage percent of the values is lower or equal than the
276 result. Unknown values are considered lower than any finite number
277 for this purpose so if this operator returns an unknown you have
278 quite a lot of them in your data. Infinite numbers are lesser, or
279 more, than the finite numbers and are always more than the Unknown
280 numbers. (NaN < -INF < finite values < INF)
281 Example: "VDEF:perc95=mydata,95,PERCENT"
283 LSLSLOPE, LSLINT, LSLCORREL
285 Return the parameters for a Least Squares Line (y = mx +b) which
286 approximate the provided dataset. LSLSLOPE is the slope (m) of the
287 line related to the COUNT position of the data. LSLINT is the
288 y-intercept (b), which happens also to be the first data point on
289 the graph. LSLCORREL is the Correlation Coefficient (also know as
290 Pearson's Product Moment Correlation Coefficient). It will range
291 from 0 to +/-1 and represents the quality of fit for the
292 approximation.
293 Example: "VDEF:slope=mydata,LSLSLOPE"
295
297 rrdgraph gives an overview of how rrdtool graph works. rrdgraph_data
298 describes DEF,CDEF and VDEF in detail. rrdgraph_rpn describes the RPN
299 language used in the ?DEF statements. rrdgraph_graph page describes
300 all of the graph and print functions.
301 Make sure to read rrdgraph_examples for tips&tricks.
303
305 Program by Tobias Oetiker <tobi@oetiker.ch>
306 This manual page by Alex van den Bogaerdt <alex@vandenbogaerdt.nl> with
308 corrections and/or additions by several people
3091.3.8 2009-02-21 RRDGRAPH_RPN(1)