update docs

Author: s3alfisc

pyfixest/estimation/demean_.py

@@ -327,16 +327,13 @@ def _set_demeaner_backend(
     """Set the demeaning backend.
 
     Currently, we allow for a numba backend, rust backend, jax backend, and cupy backend.
-    JAX and CuPy are expected to be faster on GPU.
+    JAX and CuPy are expected to be faster on GPU for larger problems, but not necessarily 
+    faster than the numba and rust algos.
 
     Parameters
     ----------
     demeaner_backend : Literal["numba", "jax", "rust", "cupy", "cupy32", "cupy64"]
         The demeaning backend to use.
-        - "cupy": CuPy backend with float64
-        - "cupy32": CuPy backend with float32
-        - "cupy64": CuPy backend with float64
-
     Returns
     -------
     Callable

pyfixest/estimation/estimation.py

@@ -138,12 +138,15 @@ def feols(
 
     demeaner_backend: DemeanerBackendOptions, optional
         The backend to use for demeaning. Options include:
-        - "numba" (default): Fast CPU-based demeaning using Numba JIT
-        - "jax": GPU-accelerated using JAX (requires jax/jaxlib)
-        - "rust": Rust-based implementation
-        - "cupy" or "cupy64": GPU-accelerated using CuPy with float64 precision (requires cupy & GPU, defaults to scipy/CPU if no GPU available)
-        - "cupy32": GPU-accelerated using CuPy with float32 precision (requires cupy & GPU, defaults to scipy/CPU and float64 if no GPU available)
-        - "scipy": Forces to use a scipy-sparse backend even when cupy is installed and GPU is available.
+        - "numba" (default): CPU-based demeaning using Numba JIT via the Alternating Projections Algorithm.
+        - "rust": CPU-based demeaning implemented in Rust via the Alternating Projections Algorithm.
+        - "jax": CPU or GPU-accelerated using JAX (requires jax/jaxlib) via the Alternating Projections Algorithm.
+        - "cupy" or "cupy64": GPU-accelerated using CuPy with float64 precision via direct application of the Frisch-Waugh-Lovell Theorem on sparse 
+          matrices (requires cupy & GPU, defaults to scipy/CPU if no GPU available)
+        - "cupy32": GPU-accelerated using CuPy with float32 precision via direct application of the Frisch-Waugh-Lovell Theorem on sparse 
+          matrices (requires cupy & GPU, defaults to scipy/CPU and float64 if no GPU available)
+        - "scipy": Direct application of the Frisch-Waugh-Lovell Theorem on sparse matrice.
+          Forces to use a scipy-sparse backend even when cupy is installed and GPU is available. 
         Defaults to "numba".
 
     use_compression: bool
@@ -616,12 +619,15 @@ def fepois(
 
     demeaner_backend: DemeanerBackendOptions, optional
         The backend to use for demeaning. Options include:
-        - "numba" (default): Fast CPU-based demeaning using Numba JIT
-        - "jax": GPU-accelerated using JAX (requires jax/jaxlib)
-        - "rust": Rust-based implementation
-        - "cupy" or "cupy64": GPU-accelerated using CuPy with float64 precision (requires cupy & GPU, defaults to scipy/CPU if no GPU available)
-        - "cupy32": GPU-accelerated using CuPy with float32 precision (requires cupy & GPU, defaults to scipy/CPU and float64 if no GPU available)
-        - "scipy": Forces to use a scipy-sparse backend even when cupy is installed and GPU is available.
+        - "numba" (default): CPU-based demeaning using Numba JIT via the Alternating Projections Algorithm.
+        - "rust": CPU-based demeaning implemented in Rust via the Alternating Projections Algorithm.
+        - "jax": CPU or GPU-accelerated using JAX (requires jax/jaxlib) via the Alternating Projections Algorithm.
+        - "cupy" or "cupy64": GPU-accelerated using CuPy with float64 precision via direct application of the Frisch-Waugh-Lovell Theorem on sparse 
+          matrices (requires cupy & GPU, defaults to scipy/CPU if no GPU available)
+        - "cupy32": GPU-accelerated using CuPy with float32 precision via direct application of the Frisch-Waugh-Lovell Theorem on sparse 
+          matrices (requires cupy & GPU, defaults to scipy/CPU and float64 if no GPU available)
+        - "scipy": Direct application of the Frisch-Waugh-Lovell Theorem on sparse matrice.
+          Forces to use a scipy-sparse backend even when cupy is installed and GPU is available. 
         Defaults to "numba".
 
     drop_intercept : bool, optional