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