fitme

CLI curve fitting tool. Parameterise an equation from a CSV dataset.

fitme is primarily a CLI tool, and this README details the CLI use.

If one is wanting to use fitme as a library, please see the API docs.

```plaintext

fitme y "m * x + c" tests/file1.csv ────────────────────────────────────────────── Parameter Value Standard Error t-value ══════════════════════════════════════════════ c 3.209 0.013 230.3 ────────────────────────────────────────────── m 1.770 0.011 149.0 ────────────────────────────────────────────── Number of observations: 10.0 Root Mean Squared Residual error: 0.043 R-sq Adjusted: 0.999 ```

Features

• simple interface
• fast
• flexible equations
• helpful error messages

Installation

Currently, only installation from source is supported:

```plaintext

using crates.io

cargo install fitme

using github

cargo install --git https://github.com/kdr-aus/fitme ```

Usage

• fitme --help for detailed help.

fitme requires just two arguments, the target column to fit against, and the mathematical expression. The third optional argument specifies the file to read the CSV from. fitme uses a least-squares fitting approach.

Let's fit a linear regression to the following data:

| y | x | | --- | --- | | 1.9000429E-01 | -1.7237128E+00 | | 6.5807428E+00 | 1.8712276E+00 | | 1.4582725E+00 | -9.6608055E-01 | | 2.7270851E+00 | -2.8394297E-01 | | 5.5969253E+00 | 1.3416969E+00 | | 5.6249280E+00 | 1.3757038E+00 | | 0.787615 | -1.3703436E+00 | | 3.2599759E+00 | 4.2581975E-02 | | 2.9771762E+00 | -1.4970151E-01 | | 4.5936475E+00 | 8.2065094E-01 |

Equation: y = m * x + c

Here the: - target: y - variables: x - parameters: m, c

To run a fit, simply use fitme y "m * x + c" test-file.csv:

```plaintext

fitme y "m * x + c" test-file.csv ────────────────────────────────────────────── Parameter Value Standard Error t-value ══════════════════════════════════════════════ c 3.209 0.013 230.3 ────────────────────────────────────────────── m 1.770 0.011 149.0 ────────────────────────────────────────────── Number of observations: 10.0 Root Mean Squared Residual error: 0.043 R-sq Adjusted: 0.999 ```

Notice that fitme will automatically match column names in the equation, binding them as variables. Unmatched variables become parameters.

Multi Parameters

fitme is useful for fitting multiple least squares linear regressions:

```plaintext

fitme sepalLength "a * petalLength + b * sepalWidth + c * petalWidth + d" iris.csv ─────────────────────────────────────────────── Parameter Value Standard Error t-value ═══════════════════════════════════════════════ a 0.711 0.056 12.51 ─────────────────────────────────────────────── b 0.654 0.066 9.788 ─────────────────────────────────────────────── c -0.562 0.127 -4.410 ─────────────────────────────────────────────── d 1.845 0.251 7.342 ─────────────────────────────────────────────── Number of observations: 150.0 Root Mean Squared Residual error: 0.314 R-sq Adjusted: 0.855 ```

Flexible Output

Alter the output via the --out switch.

CSV

```plaintext

fitme y "m * x + c" file1.csv -o=csv -n Parameter,Value,Standard Error,t-value m,1.7709542029456211,0.011883297834310212,149.02884936809457 c,3.2099657167997013,0.013936863525869892,230.32195951702457 ```

Markdown

```plaintext

fitme y "m * x + c" file1.csv -o=md -n | Parameter | Value | Standard Error | t-value | |-----------|-------|----------------|---------| | c | 3.209 | 0.013 | 230.3 | | m | 1.770 | 0.011 | 149.0 | ```

JSON

```plaintext

fitme y "m * x + c" file1.csv -o=json -n {"parameternames":["m","c"],"parametervalues":[1.7709542029456211,3.2099657167997013],"n":10,"xerrs":[0.011883297834310212,0.013936863525869892],"rmsr":0.04392493014188053,"rsq":0.9995948974725735,"tvals":[149.02884936809457,230.32195951702457]} ```

+ more!

Mathematical Expressions

• +,-,*,/
• %: remainder
• ^: power
• pi, e
• sqrt(), abs()
• exp(), ln(), log()
• sin(), cos(), tan()
• sinh(), cosh(), tanh()
• floor(), ceil(), round()

🔬 If you need more math support, please raise an issue.

Example Equations

Linear

• Equation: y = Ax + B
• Columns: y, x
• Parameters: A, B

```bash

fitme y "Ax + B" ```

Multiple Linear Regression

• Equation: y = P0 * x0 + P1 * x1 + ... + Pn * xn + C
• Columns: y, x0, x1, ... , xn
• Parameters: P0, P1, ... , Pn, C

```bash

fitme y "P0 * x0 + P1 * x1 + ... + Pn * xn + C" ```

Normal Distribution

The goal is to fit to a CDF, so the input CSV will have P as the probability [0,1], and x as the variable.

$$P = {1\over2} \bigg\lbrack {1 + erf \Big( {{x-mu}\over{\sigma^2\sqrt2}} \Big)}\bigg\rbrack$$

We can approximate the erf function with:

$$erf(x) \approx \tanh \big( {\sqrt{\pi}\log(2)x} \big)$$

So:

math P = {1\over2} \bigg\lbrack {1 + \tanh \Big( {{(x-\mu)\sqrt\pi\log(2)}\over{\sigma^2\sqrt2}} \Big)} \bigg\rbrack

This transforms into the expression: ```plaintext 0.5 * (1 + tanh(((x - Mean) * sqrt(pi) * log(2)) / (Stdev^2 * sqrt(2))))

Parameters: Mean, Stdev Variables: x ```

And to fit:

```bash

fitme P "0.5 * (1 + tanh(((x - Mean) * sqrt(pi) * log(2)) / (Stdev^2 * sqrt(2))))" ```