Add badges and format

Author: ASKabalan

README.md

@@ -3,6 +3,9 @@
 [![PyPI version](https://badge.fury.io/py/furax-cs.svg)](https://badge.fury.io/py/furax-cs)
 [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
 [![pre-commit](https://img.shields.io/badge/pre--commit-enabled-brightgreen?logo=pre-commit&logoColor=white)](https://github.com/pre-commit/pre-commit)
+[![Documentation](https://img.shields.io/badge/docs-readthedocs-blue?logo=readthedocs)](https://furax-cs.readthedocs.io/en/latest/)
+[![Results Explorer](https://img.shields.io/badge/%F0%9F%A4%97%20Results-Explorer-yellow?)](https://askabalan-furax-cs-results.hf.space/)
+[![arXiv](https://img.shields.io/badge/arXiv-XXXX.XXXXX-b31b1b?logo=arxiv)](https://arxiv.org/abs/XXXX.XXXXX)
 
 **FURAX-CS** (FURAX Component Separation) is a Python package designed to benchmark and implement advanced component separation techniques for Cosmic Microwave Background (CMB) analysis. It leverages **JAX** for high-performance computing on GPUs and implements novel adaptive clustering methods.
 
@@ -30,6 +33,9 @@ This has an impact on the estimated r tensor-to-scalar ratio as shown in the fig
 
 ---
 
+
+> **Interactive Results:** Explore the results from our paper ([PLACEHOLDER](https://arxiv.org/abs/XXXX.XXXXX)) using the [Results Explorer](https://askabalan-furax-cs-results.hf.space/) Streamlit app.
+
 ## Installation
 
 ### 1. Prerequisites (JAX)
@@ -62,10 +68,12 @@ pip install -r https://raw.githubusercontent.com/CMBSciPol/furax-cs/main/require
 
 ## Documentation
 
-*   **[Quick Start (Python API)](docs/quick_start.md)**: Learn how to use the Python API for data loading and running component separation.
-*   **[CLI Reference & Workflow](docs/cli_reference.md)**: Comprehensive guide on using the command-line interface for the full analysis pipeline.
-*   **[Minimization Solvers](docs/minimization.md)**: Guide to available optimization algorithms (Active Set, L-BFGS, etc.) and programmatic usage.
-*   **[Analysis Tools (r_analysis)](docs/r_analysis.md)**: Detailed documentation for the result analysis and plotting suite.
+Full documentation is available at **[furax-cs.readthedocs.io](https://furax-cs.readthedocs.io/en/latest/)**.
+
+*   **[Quick Start (Python API)](https://furax-cs.readthedocs.io/en/latest/quick_start.html)**: Learn how to use the Python API for data loading and running component separation.
+*   **[CLI Reference & Workflow](https://furax-cs.readthedocs.io/en/latest/cli_reference.html)**: Comprehensive guide on using the command-line interface for the full analysis pipeline.
+*   **[Minimization Solvers](https://furax-cs.readthedocs.io/en/latest/minimization.html)**: Guide to available optimization algorithms (Active Set, L-BFGS, etc.) and programmatic usage.
+*   **[Analysis Tools (r_analysis)](https://furax-cs.readthedocs.io/en/latest/r_analysis/index.html)**: Detailed documentation for the result analysis and plotting suite.
 
 ---
 

notebooks/01_FGBuster_vs_FURAX_Comparison.ipynb

@@ -56,7 +56,6 @@
    "outputs": [],
    "source": [
     "# Core scientific computing\n",
-    "import operator\n",
     "from functools import partial\n",
     "\n",
     "import furax_cs as fcs\n",
@@ -76,7 +75,7 @@
     ")\n",
     "\n",
     "# FURAX - Modern JAX-based framework\n",
-    "from furax import HomothetyOperator , tree\n",
+    "from furax import HomothetyOperator, tree\n",
     "from furax.obs.landscapes import Stokes\n",
     "from furax.obs.operators import (\n",
     "    CMBOperator,\n",
@@ -299,7 +298,7 @@
     "    # L = (A^T N^-1 d)^T (A^T N^-1 A)^-1 (A^T N^-1 d)\n",
     "    x = (A.T @ invN)(d)  # A^T N^-1 d\n",
     "    s = (A.T @ invN @ A).I(x)\n",
-    "    L = tree.dot(x, s) \n",
+    "    L = tree.dot(x, s)\n",
     "\n",
     "    return -L  # Return negative for minimization"
    ]