142 lines
4.9 KiB
Markdown
142 lines
4.9 KiB
Markdown
# Classes
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---
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## eos.class.php
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### Equation Operating System
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This class makes it incredibly easy to use and parse/solve equations in
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your own applications. It includes a graph generator to turn an equation
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with a variable in to a `y=x` graph, with the capability to calculate
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the upper and lower `y-bounds`. __NOTE__ NONE of the functions within
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these two classes are static, any example that looks like a static function
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call is representational of the class being used, but should be initialized
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and assigned to a variable first. It is also important to note that these
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classes throw exceptions if running in to errors, please read the beginning
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of the `eos.class.php` file for the defines of the exceptions thrown. Exceptions
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includes a descriptive message of the error encountered and within `eqEOS` will
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also typically include the full equation used.
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#### eqEOS
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This class has one important function, `eqEOS::solveIF()` which does all the legwork,
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so we'll start there and end with examples.
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To initialize this class, use:
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$eos = new eqEOS();
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##### solveIF($infix, $variables)
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To use this function:
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$value = $eos->solveIF($eq, $vars);
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###### _$infix_
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Is simply a standard equation with variable support. Variables
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have two forms, one is native to PHP programmers already, prefixed with '$'.
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The other way to declare a variable is with '&' and is included for
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backward compatibility for with the initial version from 2005.
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Example Equations:
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2(4$x)
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2(4&x)
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5+ ((1+2)*4) +3
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5+4(1+2)+3
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10*sin($x)
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10*cos($x)
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The first two pairs shown are exactly the same. The parser has good implied
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multiplication, for everything but allowed functions. Allowed functions require
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an implicit operator on either/both sides to work properly, I hope to change
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that in the next revision; but for now, note that it will not work as you would
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expect.
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For example:
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5sin(1.5707963267) = 51
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5*sin(1.5707963267) = 5
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sin(1.5707963267)5 = 15
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The reason is because there is no implied multiplication being applied, the result
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of `sin(1.5707963267) = 1` is being concatenated with the number 5, giving
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incredibly odd results if you are not expecting it.
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###### _$variables_
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The variables are fairly simple to understand. If it contains a scalar (ie
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a non-array value) _every_ variable within the equation will be replaced with
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that number. If it contains an array, there will be a by-variable replacement -
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note that the array MUST be in the format of `'variable' => value`
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Such as:
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array(
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'x' => 2,
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'y' => 3
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)
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Given the equation:
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5$x^$y
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If this is called by:
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eqEOS::solveIF('5$x^$y', 2)
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It will equal '20', as every variable is replaced by 2. However, if called like:
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eqEOS::solveIF('5$x^$y', array(
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'x' => 2,
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'y' => 3);
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You will get the result of '40' as it would equate to '5*2^3', as expected.
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#### eqGraph
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This is the fun class that can create graphs. It extends `eqEOS`.
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To initialize use:
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$graph = new eqGraph($width, $height);
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The `$width` and `$height` are the values used for the image size, defaulting to
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a `640x480` image size if initialized with `$graph = new eqGraph();`
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##### graph($eq, $xLow, $xHigh, $xStep, [$xyGrid, $yGuess, ...])
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This method will generate the graph for the equation (`$eq`) with a min and max
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`x` range that it will parse through. All Variables explained:
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* `$eq`
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The Standard Equation to use. _Must_ have a variable in it. (ie `$x`)
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* `$xLow`
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The starting point for the calculations - the left side of the graph.
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* `$xHigh`
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The last point calculated for the variable - the right side of the graph.
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* `$xStep`
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Stepping point for the variable. Suggested not to use a value less than
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`.01`. This is the precision of the graph.
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* `$xyGrid = false`
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Show `x/y` gridlines on the graph. Defaults to false. Each grid line
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is set at every integer (ie `1,2,3,...100`). If working with small ranges,
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it is suggested to turn this on.
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* `$yGuess = true`
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Guess the Lower and Upper `y-bounds` (The bottom and top of the image
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respectively.) This will set the the bounds to the lowest `y` value
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encountered for the `$yLow`, and the largest `y` value for `$yHight`.
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* `$yLow = false`
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Lower bound for `y`, will be reset if a lower value for `y` is found.
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* `$yHigh = false`
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Upper bound for `y`, will be reset if a larger `y` value is found.
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TODO:
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* Add `x` and `y` labels
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* Smart `grid spacing` calculations so can be effective with large ranges.
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* Smart (default) `$xStep` calcuations based on image size and ranges.
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To set up a graph with a `21x21` window (ie `-10 to 10`) for the equation
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`sin($x)` and output as PNG, would use as:
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$graph->graph('sin($x)', -10, 10, 0.01, true, false, -10, 10);
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$graph->outPNG();
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It would look like:
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--- |