add new page for tools and mps-analysis related functions

README.md

@@ -33,7 +33,7 @@ We provide [tutorials](https://jmoo2880.github.io/MPSTime.jl/dev/tutorial/) and
 - [LATEST DOCS](https://jmoo2880.github.io/MPSTime.jl/) -- the latest documentation.
 
 ## Citation
-If you use this software in your work, please read and cite the ([arXiv preprint](https://arxiv.org/abs/2412.15826)):
+If you use this software in your work, please read and cite the [arXiv preprint](https://arxiv.org/abs/2412.15826):
 ```
 @misc{MPSTime2024,
       title={Using matrix-product states for time-series machine learning}, 

docs/make.jl

@@ -18,6 +18,7 @@ makedocs(
     "Imputation" => "imputation.md",
     "Synthetic Data Generation" => "synthdatagen.md",
     "Encodings" => "encodings.md",
+    "Tools" => "Tools.md",
     "Docstrings" => "docstrings.md",
     "References" => "references.md",
     ]

docs/src/docstrings.md

@@ -25,11 +25,3 @@ MPSTime.symbolic_encoding
 MPSTime.model_loss_func
 MPSTime.model_bbopt
 ```
-
-## Analysis
-```@docs
-MPSTime.von_neumann_entropy
-MPSTime.rho_correct
-MPSTime.bipartite_spectrum
-MPSTime.single_site_spectrum
-```

docs/src/imputation.md

@@ -11,15 +11,6 @@ MPSTime supports univariate time-series imputation with three key patterns of mi
 MPSTime can also handle any combination of these patterns.
 For instance, you might need to impute a single contiguous block from $t = 10-30$, plus individual missing points at $t = 50$ and $t=80$.
 
-#### Imputation Methods
-We offer several options for imputing missing data points, based on how we estimate their values from the conditional probability distribution:
-| __Method__      | Description | Type|
-| ----------- | ----------- | ----------- | 
-| Mean      | `:mean`       |Deterministic | 
-| Median   | `:median`        |Deterministic|
-| Mode   | `:mode`        |Deterministic| 
-| Inverse Transform Sampling   | `:ITS`        |Stochastic|  
-
 ## Setup
 
 The first step is to train an MPS (see [Tutorial](@ref)). 

docs/src/tools.md

@@ -0,0 +1,15 @@
+# Tools
+
+
+## Entanglement Entropy
+What it is? What it tells us...
+### Bipartite Entanglement Entropy (BEE)
+
+
+### Single-Site Entanglement Entropy (SEE)
+
+```@docs
+MPSTime.von_neumann_entropy
+MPSTime.bipartite_spectrum
+MPSTime.single_site_spectrum
+```

src/Analysis/analyse.jl

@@ -46,13 +46,14 @@ end
 
 """
 ```Julia
+bipartite_spectrum(mps::TrainedMPS; logfn::Function=log) -> Vector{Vector{Float64}}
+```
 Compute the bipartite entanglement entropy (BEE) of a trained MPS across each bond.
 Given a single unlabeled MPS the BEE is defined as:
 
 ∑ α^2 log(α^2)
 where α are the eigenvalues obtained from the shmidt decomposition. 
     
-```
 Compute the bipartite entanglement entropy (BEE) of a trained MPS.
 """
 function bipartite_spectrum(mps::TrainedMPS; logfn::Function=log)
@@ -67,12 +68,6 @@ function bipartite_spectrum(mps::TrainedMPS; logfn::Function=log)
     return bees
 end
 
-"""
-Check whether the reduced density matrix (rho) is positive semidefinite by
-eigendecomposition.
-\nIf the eigenvalue decomp of ρ yields negative but small (< tol) eigenvalues, 
-clamp to them to range [threshold, ∞] and reconstruct ρ. 
-"""
 function rho_correct(rho::Matrix, eigentol::Float64=sqrt(eps()))
 
     eigvals, eigvecs = eigen(rho) # do an eigendecomp on the rdm
@@ -118,8 +113,9 @@ function single_site_entropy(mps::MPS)
 end
 
 """
-    single_site_spectrum(mps::TrainedMPS) -> Vector{Vector{Float64}}
-
+```Julia
+single_site_spectrum(mps::TrainedMPS) -> Vector{Vector{Float64}}
+```
 Compute the single-site entanglement entropy (SEE) spectrum of a trained MPS.
 
 The single-site entanglement entropy (SEE) quantifies the entanglement at each site of the MPS. It is computed as: