mech-math 0.3.4

Math library for the Mech language
Documentation 
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math/abs
===============================================================================

%% Floating-point absolute value

1. Usage
-------------------------------------------------------------------------------

```mech:disabled
Y := math/abs(X)
```

2. Description
-------------------------------------------------------------------------------

Computes the absolute value of each element of `X`. The input `X` may be a scalar, vector, or matrix of floating-point values. The result `Y` has the same shape as the input `X`.

3. Input
-------------------------------------------------------------------------------

| Argument | Kind                     | Description                           |
|----------|--------------------------|---------------------------------------|
| `X`      | `float`, `[float]`       | Input floating-point value(s). Can be single or double precision. |

4. Output
-------------------------------------------------------------------------------

| Argument | Kind                     | Description                           |
|----------|--------------------------|---------------------------------------|
| `Y`      | matches input            | Absolute value of the input. The shape of `Y` matches the shape of `X`. |

5. Examples  
-------------------------------------------------------------------------------

(a) Find the absolute value of a number 

```mech:ex1
y := math/abs(-3.14)
```

(b) Find the absolute value for a vector of numbers

```mech:ex2
x := [-1.0, 0.0, 2.5]
y := math/abs(x)
```

(c) Find the absolute value for a matrix of numbers

```mech:ex3
x := [-1.0, 2.0; -3.0, 4.0]
y := math/abs(x)
```

6. Details
-------------------------------------------------------------------------------

The absolute value of a real number is defined as its distance from zero on the number line:

$$ |x| = \begin{cases} x & x \geq 0 \\ -x & x < 0 \end{cases}

This function applies element-wise to arrays and matrices of floating-point values.  
For floating-point numbers, the result is always non-negative.

For complex numbers, the absolute value defined as the distance from the origin in the complex plane:

$$ |a + bi| = \sqrt{a^2 + b^2} $$

where `a` is the real part and `b` is the imaginary part of the complex number.