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Description:

function tree

Function Tree #
Welcome to function_tree, a simple library for parsing strings into
callable function-trees.
Parsing strings as mathematical expressions #
At the simplest (and least efficient) level, we can interpret strings as
mathematical expressions:
final expressions = [
"2 + 2",
"(3 + 2)^3",
"3 * pi / 4",
"3 * sin(5 * pi / 6)",
"e^(-1)"
];
for (final expression in expressions) {
print("'$expression' -> ${expression.interpret()}");
}

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'2 + 2' -> 4.0
'(3 + 2)^3' -> 125.0
'3 * pi / 4' -> 2.356194490192345
'3 * sin(5 * pi / 6)' -> 1.5000000000000009
'e^(-1)' -> 0.36787944117144233
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Function Trees #
The library supports two types of callable, function-trees, namely
SingleVariableFunction and MultiVariableFunction.
Single variable functions #
We can create a single variable function from a string either by constructing
a SingleVariableFunction instance or by calling the toSingleVariableFunction
string extension directly on a string, as in the following example.
final f = "20 * (sin(x) + 1)".toSingleVariableFunction(),
pi = "pi".interpret();
for (var x = 0.0; x < 2 * pi; x += pi / 20) {
print("|" + " " * f(x).round() + "*");
}

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| *
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| *
| *
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|*
|*
|*
| *
| *
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| *
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| *
| *
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Multi-variable functions #
Similarly, we can construct a MultiVariableFunction instance or call the
toMultiVariableFunction string extension to create a multi-variable function
tree, as in the following example.
final times = "a * b".toMultiVariableFunction(["a", "b"]),
values = [1, 2, 3, 4, 5];
for (final a in values) {
final sb = StringBuffer();
for (final b in values) {
sb
..write(times({"a": a, "b": b}).floor())
..write("\t");
}
print(sb);
}

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1 2 3 4 5
2 4 6 8 10
3 6 9 12 15
4 8 12 16 20
5 10 15 20 25
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TeX expressions #
Function tree instances have a tex property for TeX expressions:
final f = "x * cos(y) + y * sin(x)".toMultiVariableFunction(["x", "y"]);
print(f.tex);

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x cdot \cos\left( y \right) + y cdot \sin\left( x \right)
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Derivatives #
Derivative trees can be constructed through the SingleVariableFunction.derivative and MultiVariableFunction.partial methods.
final f = "(2 * x) ^ (1 / (x ^ 2))".toSingleVariableFunction(),
fDash = f.derivative("x");
print("x y y'");
for (var x = 0.5; x < 3.0; x += 0.25) {
print(
"${x.toStringAsFixed(4)} "
"${f(x).toStringAsFixed(4)} "
"${fDash(x).toStringAsFixed(4)}");
}
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x y y'
0.5000 1.0000 8.0000
0.7500 2.0561 0.9215
1.0000 2.0000 -0.7726
1.2500 1.7976 -0.7663
1.5000 1.6295 -0.5780
1.7500 1.5054 -0.4229
2.0000 1.4142 -0.3134
2.2500 1.3460 -0.2373
2.5000 1.2937 -0.1837
2.7500 1.2529 -0.1452
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final f = "sin(u ^ 2 + 2 * v)".toMultiVariableFunction(["u", "v"]),
fu = f.partial("u"),
fv = f.partial("v"),
pi = "pi".interpret(),
u = pi / 3,
v = pi / 4;
for (final fun in [f, fu, fv]) {
print("${fun({"u": u, "v": v})}");
}
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0.4566033934365143
-1.8633212348878314
-1.779340710602958
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Interpreter #
The interpreter has support for the following:
Functions #
One-parameter functions
abs acos asin atan ceil
cos cosh cot coth csc
csch exp fact floor ln
log round sec sech sin
sinh sqrt tan tanh
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Two-parameter functions
log nrt pow
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Constants #
e pi ln2 ln10 log2e
log10e sqrt1_2 sqrt2
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Operations #
+ - * / % ^
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Thanks #
Thanks for your interest in this library. Please file any bugs or
requests here.