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.

---

> 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:

# using crates.io
cargo install fitme

# using github
cargo install --git https://github.com/kurtlawrence/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:

> 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:

> 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

> 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

> 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

> fitme y "m * x + c" file1.csv -o=json -n
{"parameter_names":["m","c"],"parameter_values":[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

> 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

> 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:

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

This transforms into the expression:

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

Parameters: Mean, Stdev
Variables: x

And to fit:

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