Routine User Tutorials

Welcome to NLSQ! This tutorial series will guide you through curve fitting using NLSQ’s 3-Workflow System - a simple but powerful approach that handles everything from small datasets to 100M+ points automatically.

Note

Coming from SciPy? NLSQ is a drop-in replacement. Your existing code will work with minimal changes. See Migration Guide.

The 3-Workflow System

NLSQ provides three workflows that cover all curve fitting use cases:

Workflow	When to Use	Bounds	Speed
auto	Standard fitting (default)	Optional	Fastest
auto_global	Multiple local minima, unknown initial guess	Required	Moderate
hpc	HPC clusters, long-running jobs	Required	Varies

Quick Start

Here’s all you need to fit data with NLSQ:

from nlsq import fit
import jax.numpy as jnp


# Define your model
def exponential(x, a, b, c):
    return a * jnp.exp(-b * x) + c


# Fit with default workflow (auto)
popt, pcov = fit(exponential, xdata, ydata, p0=[1.0, 0.5, 0.0])

# For global optimization (requires bounds)
popt, pcov = fit(
    exponential,
    xdata,
    ydata,
    p0=[1.0, 0.5, 0.0],
    workflow="auto_global",
    bounds=([0, 0, -1], [10, 5, 1]),
)

That’s it! NLSQ automatically handles memory management, GPU acceleration, and optimization strategy selection.

Tutorial Series

• 1. Getting Started
  • 1.1. Installation
  • 1.2. Your First Curve Fit
  • 1.3. Understanding Results
  • 1.4. Chapter Overview
  • 1.5. Quick Example
• 2. The 3-Workflow System
  • 2.1. workflow=”auto” - Local Optimization
  • 2.2. workflow=”auto_global” - Global Optimization
  • 2.3. workflow=”hpc” - HPC Cluster Optimization
  • 2.4. Overview
  • 2.5. Choosing the Right Workflow
  • 2.6. Quick Reference
  • 2.7. How Memory Selection Works
  • 2.8. Decision Flowchart
  • 2.9. Next Steps
• 3. Model Selection
  • 3.1. Built-in Models
  • 3.2. Custom Models
  • 3.3. Model Validation
  • 3.4. Chapter Overview
  • 3.5. Quick Reference
  • 3.6. Key Rule
• 4. Data Handling
  • 4.1. Basic Data
  • 4.2. Uncertainties (Sigma)
  • 4.3. Parameter Bounds
  • 4.4. Large Datasets
  • 4.5. Chapter Overview
  • 4.6. Quick Reference
• 5. GPU Acceleration
  • 5.1. GPU Setup
  • 5.2. GPU Usage
  • 5.3. Multi-GPU
  • 5.4. Chapter Overview
  • 5.5. Quick Start
  • 5.6. Performance Benefits
• 6. Desktop GUI Application
  • 6.1. Launching the GUI
  • 6.2. Workflow Pages
  • 6.3. Fitting Presets
  • 6.4. Chapter Overview
  • 6.5. Quick Start
  • 6.6. Features
  • 6.7. Screenshot Overview
  • 6.8. Keyboard Shortcuts
• 7. Troubleshooting
  • 7.1. Common Issues
  • 7.2. Getting Help
  • 7.3. Quick Fixes
  • 7.4. Error Messages

Learning Path

#	Chapter	What You’ll Learn	Time
1	Getting Started	Install NLSQ, fit your first curve, interpret results	20 min
2	The 3-Workflow System	Master the 3-workflow system: auto, auto_global, hpc	30 min
3	Model Selection	Built-in models, custom models, model validation	25 min
4	Data Handling	Data input, uncertainties, bounds, large datasets	25 min
5	GPU Acceleration	GPU setup, usage, multi-GPU	20 min
6	Desktop GUI Application	Desktop GUI application for interactive fitting	15 min
7	Troubleshooting	Common issues and solutions	15 min

Prerequisites

• Python 3.12 or higher

• Basic Python knowledge (variables, functions, imports)

• Basic understanding of scientific data (x, y coordinates)

No prior curve fitting experience is required.

Next Steps After Tutorials

• How-To Guides - Solve specific problems

• Reference - API reference documentation

• Advanced User Tutorials - Advanced API tutorials for custom workflows