6.0 KiB
Histogram
Arduino library for creating histograms math.
Description
One of the main applications for the Arduino board is reading and logging of sensor data. We often want to make a histogram of this data to get insight of the distribution of the measurements. This is where this Histogram library comes in.
The Histogram distributes the values added to it into buckets and keeps count.
If you need more quantitative analysis, you might need the statistics library,
Working
When the class is initialized an array of the boundaries to define the borders of the buckets is passed to the constructor. This array should be declared global as the Histogram class does not copy the values to keep memory usage low. This allows to change the boundaries runtime, so after a clear(), a new Histogram can be created.
The values in the boundary array do not need to be equidistant (equal in size) but they need to be in ascending order.
Internally the library does not record the individual values, only the count per bucket. If a new value is added - add() or sub() - the class checks in which bucket it belongs and the buckets counter is increased.
The sub() function is used to decrease the count of a bucket and it can cause the count to become below zero. Although seldom used but still depending on the application it can be useful. E.g. when you want to compare two value generating streams, you let one stream add() and the other sub(). If the histogram of both streams is similar they should cancel each other out (more or less), and the value of all buckets should be around 0. [not tried].
The frequency() function may be removed to reduce footprint as it can be calculated with the formula (1.0 * bucket(i))/count().
Experimental: Histogram8 Histogram16
Histogram8 and Histogram16 are classes with same interface but smaller buckets. Histogram can count to ±2^31 while often ±2^15 or even ±2^7 is sufficient. Saves memory.
| class name | length | count/bucket | max memory |
|---|---|---|---|
| Histogram | 65534 | ±2147483647 | 260 KB |
| Histogram8 | 65534 | ±127 | 65 KB |
| Histogram16 | 65534 | ±32767 | 130 KB |
The difference is the _data array, to reduce the memory footprint.
Note: max memory is without the boundary array.
Performance optimizations are possible too however not essential for the experimental version.
Interface
Constructor
- Histogram(uint16_t length, float *bounds) constructor, get an array of boundary values and array length. Length should be less than 65534.
- ~Histogram() destructor.
Base
- void clear(float value = 0) reset all bucket counters to value (default 0).
- void add(float value) add a value, increase count of bucket.
- void sub(float value) 'add' a value, but decrease count (subtract).
- uint16_t size() returns number of buckets.
- uint32_t count() returns total number of values added (or subtracted).
- int32_t bucket(uint16_t index) returns the count of single bucket, can be negative due to sub()
- float frequency(uint16_t index) returns the relative frequency of a bucket, always between 0.0 and 1.0.
Helper functions
- uint16_t find(float value) returns the index of the bucket for value.
- uint16_t findMin() returns the (first) index of the bucket with the minimum value.
- uint16_t findMax() returns the (first) index of the bucket with the maximum value.
- uint16_t countLevel(int32_t level) returns the number of buckets with exact that level (count).
- uint16_t countAbove(int32_t level) returns the number of buckets above level.
- uint16_t countBelow(int32_t level) returns the number of buckets below level.
Probability Distribution Functions
There are three functions:
- float PMF(float value) Probability Mass Function. Quite similar to frequency(), but uses a value as parameter.
- float CDF(float value) Cumulative Distribution Function. Returns the sum of frequencies <= value. Always between 0.0 and 1.0.
- float VAL(float prob) Value Function, is CDF() inverted. Returns the value of the original array for which the CDF is at least probability.
As the Arduino typical uses a small number of buckets these functions are quite coarse and/or inaccurate (linear interpolation within bucket is still to be investigated)
Note PDF() is a continuous function and therefore not applicable in discrete histogram.
Operation
See examples
Future
- performance - find() the right bucket.
- Binary search is faster
- need testing.
- improve accuracy - linear interpolation for PMF(), CDF() and VAL()
- performance - merge loops in PMF()
- performance - reverse loops - compare to zero.
- improve documentation
- explain PMF(), CDF() and VAL() functions.
- bucket full / overflow warning. The add() sub() should return a bool to indicate that a bucket is (almost) full.
- 2D histograms ? e.g. positions on a grid.
expensive ideas
Expensive ideas in terms of memory or performance
- Additional values per bucket.
- Sum, Min, Max, (average can be derived)
- separate bucket-array for sub()
- Copy the boundaries array?