RRDGRAPH_RPN(1) rrdtool RRDGRAPH_RPN(1) NNAAMMEE rrdgraph_rpn - About RPN Math in rrdtool graph SSYYNNOOPPSSIISS _R_P_N _e_x_p_r_e_s_s_i_o_n:=_v_n_a_m_e|_o_p_e_r_a_t_o_r|_v_a_l_u_e[,_R_P_N _e_x_p_r_e_s_s_i_o_n] DDEESSCCRRIIPPTTIIOONN If you have ever used a traditional HP calculator you already know RRPPNN (Reverse Polish Notation). The idea behind RRPPNN is that you have a stack and push your data onto this stack. Whenever you execute an operation, it takes as many elements from the stack as needed. Pushing is done implicitly, so whenever you specify a number or a variable, it gets pushed onto the stack automatically. 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 _v_n_a_m_e. For CCDDEEFF instructions, the stack is processed for each data point on the graph. VVDDEEFF instructions work on an entire data set in one run. Note, that currently VVDDEEFF 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 _m_y_d_a_t_a, 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 _m_y_d_a_t_a_b_i_t_s. As you may have guessed, this instruction means nothing more than _m_y_d_a_t_a_b_i_t_s _= _m_y_d_a_t_a _* _8. The real power of RRPPNN 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 RRPPNN, you would do "a = b, 3, +, 5, *" without the need for parentheses. OOPPEERRAATTOORRSS Boolean operators LLTT,, LLEE,, GGTT,, GGEE,, EEQQ,, NNEE Pop two elements from the stack, compare them for the selected condition and return 1 for true or 0 for false. Comparing an _u_n_k_n_o_w_n or an _i_n_f_i_n_i_t_e value will result in _u_n_k_n_o_w_n returned ... which will also be treated as false by the IIFF call. UUNN,, IISSIINNFF Pop one element from the stack, compare this to _u_n_k_n_o_w_n respectively to _p_o_s_i_t_i_v_e _o_r _n_e_g_a_t_i_v_e _i_n_f_i_n_i_t_y. Returns 1 for true or 0 for false. IIFF 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)" Comparing values MMIINN,, MMAAXX Pops two elements from the stack and returns the smaller or larger, respectively. Note that _i_n_f_i_n_i_t_e is larger than anything else. If one of the input numbers is _u_n_k_n_o_w_n then the result of the operation will be _u_n_k_n_o_w_n too. LLIIMMIITT 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 _u_n_k_n_o_w_n 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 _u_n_k_n_o_w_n or _i_n_f_i_n_i_t_e this function will always return an _u_n_k_n_o_w_n Example: "CDEF:a=alpha,0,100,LIMIT" will return _u_n_k_n_o_w_n if alpha is lower than 0 or if it is higher than 100. Arithmetics ++,, --,, **,, //,, %% Add, subtract, multiply, divide, modulo AADDDDNNAANN 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. SSIINN,, CCOOSS,, LLOOGG,, EEXXPP,, SSQQRRTT Sine and cosine (input in radians), log and exp (natural logarithm), square root. AATTAANN Arctangent (output in radians). AATTAANN22 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. FFLLOOOORR,, CCEEIILL Round down or up to the nearest integer. DDEEGG22RRAADD,, RRAADD22DDEEGG Convert angle in degrees to radians, or radians to degrees. AABBSS Take the absolute value. Set Operations SSOORRTT,, RREEVV Pop one element from the stack. This is the _c_o_u_n_t of items to be sorted (or reversed). The top _c_o_u_n_t of the remaining elements are then sorted (or reversed) in place on the stack. 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. AAVVGG Pop one element (_c_o_u_n_t) from the stack. Now pop _c_o_u_n_t elements and build the average, ignoring all UNKNOWN values in the process. Example: "CDEF:x=a,b,c,d,4,AVG" TTRREENNDD,, TTRREENNDDNNAANN 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. PPRREEDDIICCTT,, PPRREEDDIICCTTSSIIGGMMAA Create a "sliding window" average/sigma of another data series, that also shifts the data series by given amounts of of time as well Usage - explicit stating shifts: CDEF:predict=,...,,n,,x,PREDICT CDEF:sigma=,...,,n,,x,PREDICTSIGMA Usage - shifts defined as a base shift and a number of time this is applied CDEF:predict=,-n,,x,PREDICT CDEF:sigma=,-n,,x,PREDICTSIGMA 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 whit the optional start= parameter, so that the source data series has enough data to provide prediction also at the beginning of a graph... 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 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. This prediction can only be used for short term extrapolations - say a few days into the future- Special values UUNNKKNN Pushes an unknown value on the stack IINNFF,, NNEEGGIINNFF 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. PPRREEVV Pushes an _u_n_k_n_o_w_n value if this is the first value of a data set or otherwise the result of this CCDDEEFF at the previous time step. This allows you to do calculations across the data. This function cannot be used in VVDDEEFF instructions. PPRREEVV((vvnnaammee)) Pushes an _u_n_k_n_o_w_n 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 VVDDEEFF instructions. CCOOUUNNTT 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 VVDDEEFF instructions. Time Time inside RRDtool is measured in seconds since the epoch. The epoch is defined to be "Thu Jan 1 00:00:00 UTC 1970". NNOOWW Pushes the current time on the stack. TTIIMMEE Pushes the time the currently processed value was taken at onto the stack. LLTTIIMMEE Takes the time as defined by TTIIMMEE, 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. Processing the stack directly DDUUPP,, PPOOPP,, EEXXCC Duplicate the top element, remove the top element, exchange the two top elements. VVAARRIIAABBLLEESS These operators work only on VVDDEEFF statements. Note that currently ONLY these work for VVDDEEFF. MAXIMUM, MINIMUM, AVERAGE Return the corresponding value, MAXIMUM and MINIMUM also return the first occurrence of that value in the time component. Example: "VDEF:avg=mydata,AVERAGE" STDEV Returns the standard deviation of the values. Example: "VDEF:stdev=mydata,STDEV" LAST, FIRST Return the last/first non-nan or infinite value for the selected data stream, including its timestamp. Example: "VDEF:first=mydata,FIRST" TOTAL Returns the rate from each defined time slot multiplied with the step size. This can, for instance, return total bytes transferred when you have logged bytes per second. The time component returns the number of seconds. Example: "VDEF:total=mydata,TOTAL" PERCENT, PERCENTNAN This should follow a DDEEFF or CCDDEEFF _v_n_a_m_e. The _v_n_a_m_e is popped, another number is popped which is a certain percentage (0..100). The data set is then sorted and the value returned is chosen such that _p_e_r_c_e_n_t_a_g_e percent of the values is lower or equal than the result. For PERCENTNAN _U_n_k_n_o_w_n values are ignored, but for PERCENT _U_n_k_n_o_w_n values are considered lower than any finite number for this purpose so if this operator returns an _u_n_k_n_o_w_n you have quite a lot of them in your data. IInnffinite numbers are lesser, or more, than the finite numbers and are always more than the _U_n_k_n_o_w_n numbers. (NaN < -INF < finite values < INF) Example: "VDEF:perc95=mydata,95,PERCENT" "VDEF:percnan95=mydata,95,PERCENTNAN" LSLSLOPE, LSLINT, LSLCORREL Return the parameters for a LLeast SSquares LLine _(_y _= _m_x _+_b_) which approximate the provided dataset. LSLSLOPE is the slope _(_m_) of the line related to the COUNT position of the data. LSLINT is the y-intercept _(_b_), which happens also to be the first data point on the graph. LSLCORREL is the Correlation Coefficient (also know as Pearson's Product Moment Correlation Coefficient). It will range from 0 to +/-1 and represents the quality of fit for the approximation. Example: "VDEF:slope=mydata,LSLSLOPE" SSEEEE AALLSSOO rrdgraph gives an overview of how rrrrddttooooll ggrraapphh works. rrdgraph_data describes DDEEFF,CCDDEEFF and VVDDEEFF in detail. rrdgraph_rpn describes the RRPPNN language used in the ??DDEEFF statements. rrdgraph_graph page describes all of the graph and print functions. Make sure to read rrdgraph_examples for tips&tricks. AAUUTTHHOORR Program by Tobias Oetiker This manual page by Alex van den Bogaerdt with corrections and/or additions by several people 1.4.8 2013-05-23 RRDGRAPH_RPN(1)