Tiny, tiny documentation fix -- Peter Valdemar Mørch

[rrdtool.git] / doc / rrdgraph_rpn.pod

diff --git a/doc/rrdgraph_rpn.pod b/doc/rrdgraph_rpn.pod
index f54bd38..16f7610 100644 (file)
--- a/doc/rrdgraph_rpn.pod
+++ b/doc/rrdgraph_rpn.pod
@@ -1,41 +1,37 @@
 =head1 NAME
 
 =head1 NAME
 

-rrdtool graph - Round Robin Database tool grapher functions
+rrdgraph_rpn - About RPN Math in rrdtool graph

 
 

-WARNING: This is for version 1.1.x which is B<I<BETA>> software.
-The software may contain serious bugs. Some of the items
-described in here may not yet exist (although this should
-be mentioned) or still be in the alpha stage.  As with every
-other RRDtool release: use at your own risk.  In contrast with
-the stable version of RRDtool, this release may contain bugs
-known to the authors.  It is highly recommended that you subscribe
-to the mailing list.
+=head1 SYNOPSIS

 
 

-=head1 SYNOPSYS
-
-I<E<lt>RPN expressionE<gt>> := 
-I<E<lt>vnameE<gt>>|I<E<lt>operatorE<gt>>|I<E<lt>valueE<gt>>
-[ , I<E<lt>RPN expressionE<gt>>]
+I<RPN expression>:=I<vname>|I<operator>|I<value>[,I<RPN expression>]

 
 =head1 DESCRIPTION
 
 If you have ever used a traditional HP calculator you already know
 
 =head1 DESCRIPTION
 
 If you have ever used a traditional HP calculator you already know

-B<RPN>. The idea behind B<RPN> is that you have a stack and push
+B<RPN> (Reverse Polish Notation).
+The idea behind B<RPN> 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
 your data onto this stack. Whenever you execute an operation, it
 takes as many elements from the stack as needed. Pushing is done

-implicit so whenever you specify a number or a variable, it gets
-pushed automatically.
+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 I<vname>.  For B<CDEF> instructions, the stack is processed for each
+data point on the graph. B<VDEF> instructions work on an entire data set in
+one run. Note, that currently B<VDEF> instructions only support a limited
+list of functions.
+
+Example: C<VDEF:maximum=mydata,MAXIMUM>

 
 

-At the end of the calculation there should be one and exactly one
-value left on the stack.  This is the outcome of the function and
-this is what is put into the I<vname>.  For B<CDEF> instructions,
-the stack is processed for each data point on the graph. B<VDEF>
-instructions work on an entire data set in one run.
+This will set variable "maximum" which you now can use in the rest
+of your RRD script.

 
 Example: C<CDEF:mydatabits=mydata,8,*>
 
 This means:  push variable I<mydata>, push the number 8, execute
 
 Example: C<CDEF:mydatabits=mydata,8,*>
 
 This means:  push variable I<mydata>, push the number 8, execute

-the operator I<+>. The operator needs two elements and uses those
+the operator I<*>. The operator needs two elements and uses those

 to return one value.  This value is then stored in I<mydatabits>.
 As you may have guessed, this instruction means nothing more than
 I<mydatabits = mydata * 8>.  The real power of B<RPN> lies in the
 to return one value.  This value is then stored in I<mydatabits>.
 As you may have guessed, this instruction means nothing more than
 I<mydatabits = mydata * 8>.  The real power of B<RPN> lies in the


@@ -43,7 +39,7 @@ fact that it is always clear in which order to process the input.
 For expressions like C<a = b + 3 * 5> you need to multiply 3 with
 5 first before you add I<b> to get I<a>. However, with parentheses
 you could change this order: C<a = (b + 3) * 5>. In B<RPN>, you
 For expressions like C<a = b + 3 * 5> you need to multiply 3 with
 5 first before you add I<b> to get I<a>. However, with parentheses
 you could change this order: C<a = (b + 3) * 5>. In B<RPN>, you

-would do C<a = b, 3, +, 5, *> and need no parentheses.
+would do C<a = b, 3, +, 5, *> without the need for parentheses.

 
 =head1 OPERATORS
 
 
 =head1 OPERATORS
 


@@ -53,27 +49,21 @@ would do C<a = b, 3, +, 5, *> and need no parentheses.
 
 B<LT, LE, GT, GE, EQ, NE>
 
 
 B<LT, LE, GT, GE, EQ, NE>
 

-I<Note: NE is not yet implemented>
-

 Pop two elements from the stack, compare them for the selected condition
 and return 1 for true or 0 for false. Comparing an I<unknown> or an
 I<infinite> value will always result in 0 (false).
 
 B<UN, ISINF>
 
 Pop two elements from the stack, compare them for the selected condition
 and return 1 for true or 0 for false. Comparing an I<unknown> or an
 I<infinite> value will always result in 0 (false).
 
 B<UN, ISINF>
 

-I<Note: ISINF is not yet implemented>
-

 Pop one element from the stack, compare this to I<unknown> respectively
 to I<positive or negative infinity>. Returns 1 for true or 0 for false.
 
 B<IF>
 
 Pop one element from the stack, compare this to I<unknown> respectively
 to I<positive or negative infinity>. Returns 1 for true or 0 for false.
 
 B<IF>
 

-Pops three elements from the stack.  If the last element is 0 (false),
-the first value is pushed back onto the stack, otherwise the second
-popped value is pushed back. This does, indeed, mean that any value
-other than 0 is considered true.
-I<Note: Should this change? It should IMHO as all the other functions
-would return unknown if A,B or C were unknown>
+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: C<A,B,C,IF> should be read as C<if (A) then (B) else (C)>
 
 
 Example: C<A,B,C,IF> should be read as C<if (A) then (B) else (C)>
 


@@ -81,11 +71,12 @@ Z<>
 
 =item Comparing values
 
 
 =item Comparing values
 

-B<MIN, MAX> 
+B<MIN, MAX>

 
 

-Pops two elements from the stack and returns the lesser or larger.
-The two numbers shouldn't be I<infinite> or I<unknown>, if they are
-that value is pushed back onto the stack as the result.
+Pops two elements from the stack and returns the smaller or larger,
+respectively.  Note that I<infinite> is larger than anything else.
+If one of the input numbers is I<unknown> then the result of the operation will be
+I<unknown> too.

 
 B<LIMIT>
 
 
 B<LIMIT>
 


@@ -109,15 +100,163 @@ B<+, -, *, /, %>
 
 Add, subtract, multiply, divide, modulo
 
 
 Add, subtract, multiply, divide, modulo
 

-B<SIN, COS, LOG, EXP>
+B<ADDNAN>
+
+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.
+
+B<SIN, COS, LOG, EXP, SQRT>
+
+Sine and cosine (input in radians), log and exp (natural logarithm),
+square root.
+
+B<ATAN>
+
+Arctangent (output in radians).

 
 

-Sine, cosine (input in radians), log, exp (natural logarithm)
+B<ATAN2>
+
+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: C<CDEF:angle=Y,X,ATAN2,RAD2DEG> will convert C<X,Y>
+components into an angle in degrees.

 
 B<FLOOR, CEIL>
 
 
 B<FLOOR, CEIL>
 

-Round down,up to the nearest integer
+Round down or up to the nearest integer.

 
 

-Z<>
+B<DEG2RAD, RAD2DEG>
+
+Convert angle in degrees to radians, or radians to degrees.
+
+B<ABS>
+
+Take the absolute value.
+
+=item Set Operations
+
+B<SORT, REV>
+
+Pop one element from the stack.  This is the I<count> of items to be sorted
+(or reversed).  The top I<count> of the remaining elements are then sorted
+(or reversed) in place on the stack.
+
+Example: C<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.
+
+B<AVG>
+
+Pop one element (I<count>) from the stack. Now pop I<count> elements and build the
+average, ignoring all UNKNOWN values in the process.
+
+Example: C<CDEF:x=a,b,c,d,4,AVG>
+
+B<TREND, TRENDNAN>
+
+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.
+
+B<PREDICT, PREDICTSIGMA>
+
+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=<shift n>,...,<shift 1>,n,<window>,x,PREDICT
+CDEF:sigma=<shift n>,...,<shift 1>,n,<window>,x,PREDICTSIGMA
+
+Usage - shifts defined as a base shift and a number of time this is applied
+CDEF:predict=<shift multiplier>,-n,<window>,x,PREDICT
+CDEF:sigma=<shift multiplier>,-n,<window>,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-

 
 =item Special values
 
 
 =item Special values
 


@@ -138,47 +277,39 @@ set or otherwise the result of this B<CDEF> at the previous time
 step. This allows you to do calculations across the data.  This
 function cannot be used in B<VDEF> instructions.
 
 step. This allows you to do calculations across the data.  This
 function cannot be used in B<VDEF> instructions.
 

-Z<>
-
-=item Time
+B<PREV(vname)>

 
 

-Time inside RRDtool is measured in seconds since the epoch. This
-epoch is defined to be S<C<Thu Jan  1 00:00:00 UTC 1970>>.
+Pushes an I<unknown> 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 B<VDEF> instructions.

 
 

-Z<>
+B<COUNT>

 
 

-=over 4
+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 B<VDEF> instructions.

 
 

-=item NOW
+=item Time

 
 

-Pushes the current time on the stack.
+Time inside RRDtool is measured in seconds since the epoch. The
+epoch is defined to be S<C<Thu Jan  1 00:00:00 UTC 1970>>.

 
 

-Z<>
+B<NOW>

 
 

-=item TIME
+Pushes the current time on the stack.

 
 

-Pushes the time the currently processed value was taken onto the stack.
+B<TIME>

 
 

-Z<>
+Pushes the time the currently processed value was taken at onto the stack.

 
 

-=item LTIME
+B<LTIME>

 
 Takes the time as defined by B<TIME>, 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
 
 Takes the time as defined by B<TIME>, 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 on how to use this.
-
-=back
-
-For B<VDEF> operations, B<TIME> and B<LTIME> have a different meaning
-I<not yet implemented>.  As the B<VDEF> statement does not work per
-value but rather on a complete time series, there is no such thing as
-the currently processed value.  However, if you have used an operator
-that returned a time component and would like to have this available
-in the value component in stead (so you can use it as a number), you
-can use B<TIME> or B<LTIME> for that.
-
-Z<>
+in the examples section below on how to use this.

 
 =item Processing the stack directly
 
 
 =item Processing the stack directly
 


@@ -189,74 +320,86 @@ top elements.
 
 Z<>
 
 
 Z<>
 

-=item Selecting characteristics
+=back

 
 

-These operators work only on B<VDEF> statements.
-I<We can make most of them work at DEF and CDEF statements. If we do
-so, we have a moving (not rolling!) average, max,min etcetera>
+=head1 VARIABLES

 
 

-Z<>
+These operators work only on B<VDEF> statements. Note that currently ONLY these work for B<VDEF>.

 
 =over 4
 
 =item MAXIMUM, MINIMUM, AVERAGE
 
 Return the corresponding value, MAXIMUM and MINIMUM also return
 
 =over 4
 
 =item MAXIMUM, MINIMUM, AVERAGE
 
 Return the corresponding value, MAXIMUM and MINIMUM also return

-the first occurance of that value in the time component.
+the first occurrence of that value in the time component.

 
 Example: C<VDEF:avg=mydata,AVERAGE>
 
 
 Example: C<VDEF:avg=mydata,AVERAGE>
 

-Z<>
+=item STDEV
+
+Returns the standard deviation of the values.
+
+Example: C<VDEF:stdev=mydata,STDEV>

 
 =item LAST, FIRST
 
 
 =item LAST, FIRST
 

-Return the last,first value including its time.  The time for
-FIRST is actually the start of the corresponding interval, where
-LASTs time component returns the end of the corresponding interval.
+Return the last/first value including its time.  The time for
+FIRST is actually the start of the corresponding interval, whereas
+LAST returns the end of the corresponding interval.

 
 Example: C<VDEF:first=mydata,FIRST>
 
 
 Example: C<VDEF:first=mydata,FIRST>
 

-Z<>
-

 =item TOTAL
 
 =item TOTAL
 

-Returns the rate from each defined timeslot multiplied with the
-step size.  This can for instance return total bytes transfered
+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
 when you have logged bytes per second. The time component returns

-the amount of seconds 
+the number of seconds.

 
 Example: C<VDEF:total=mydata,TOTAL>
 
 
 Example: C<VDEF:total=mydata,TOTAL>
 

-Z<>
+=item PERCENT, PERCENTNAN

 
 

-=item PERCENT
-
-Should follow a B<DEF> or B<CDEF> I<vname>. This I<vname> is popped,
+This should follow a B<DEF> or B<CDEF> I<vname>. The I<vname> 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
 I<percentage> percent of the values is lower or equal than the result.
 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
 I<percentage> percent of the values is lower or equal than the result.

+For PERCENTNAN I<Unknown> values are ignored, but for PERCENT

 I<Unknown> values are considered lower than any finite number for this
 purpose so if this operator returns an I<unknown> you have quite a lot
 of them in your data.  B<Inf>inite numbers are lesser, or more, than the
 finite numbers and are always more than the I<Unknown> numbers.
 I<Unknown> values are considered lower than any finite number for this
 purpose so if this operator returns an I<unknown> you have quite a lot
 of them in your data.  B<Inf>inite numbers are lesser, or more, than the
 finite numbers and are always more than the I<Unknown> numbers.

+(NaN E<lt> -INF E<lt> finite values E<lt> INF)

 
 Example: C<VDEF:perc95=mydata,95,PERCENT>
 
 Example: C<VDEF:perc95=mydata,95,PERCENT>

+         C<VDEF:percnan95=mydata,95,PERCENTNAN>

 
 

-=back
+=item LSLSLOPE, LSLINT, LSLCORREL
+
+Return the parameters for a B<L>east B<S>quares B<L>ine I<(y = mx +b)> 
+which approximate the provided dataset.  LSLSLOPE is the slope I<(m)> of
+the line related to the COUNT position of the data.  LSLINT is the 
+y-intercept I<(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: C<VDEF:slope=mydata,LSLSLOPE>

 
 =back
 
 =head1 SEE ALSO
 
 L<rrdgraph> gives an overview of how B<rrdtool graph> works.
 
 =back
 
 =head1 SEE ALSO
 
 L<rrdgraph> gives an overview of how B<rrdtool graph> works.

-L<rrdgraph_data> describes B<DEF>,B<CDEF> and B<VDEF> in detail,
-L<rrdgraph_rpn> describes the B<RPN> language used in the B<?DEF> statements,
+L<rrdgraph_data> describes B<DEF>,B<CDEF> and B<VDEF> in detail.
+L<rrdgraph_rpn> describes the B<RPN> language used in the B<?DEF> statements.

 L<rrdgraph_graph> page describes all of the graph and print functions.
 
 Make sure to read L<rrdgraph_examples> for tipsE<amp>tricks.
 
 =head1 AUTHOR
 
 L<rrdgraph_graph> page describes all of the graph and print functions.
 
 Make sure to read L<rrdgraph_examples> for tipsE<amp>tricks.
 
 =head1 AUTHOR
 

-Program by Tobias Oetiker E<lt>oetiker@ee.ethz.chE<gt>
+Program by Tobias Oetiker E<lt>tobi@oetiker.chE<gt>

 
 

-This manual page by Alex van den Bogaerdt E<lt>alex@ergens.op.het.netE<gt>
+This manual page by Alex van den Bogaerdt E<lt>alex@vandenbogaerdt.nlE<gt>
+with corrections and/or additions by several people