diff --git a/Project.toml b/Project.toml
index ce99bfc..bf180f7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,4 +1,4 @@
-name = "MULTISPATI"
+name = "Multispati"
 uuid = "3ff64760-8a89-40e2-854d-b45336bb1975"
 authors = ["Niklas Müller-Bötticher <niklasmueboe@github.com>"]
 version = "0.1.0"
diff --git a/README.md b/README.md
index baa96bb..6558e39 100644
--- a/README.md
+++ b/README.md
@@ -1,10 +1,10 @@
-# MULTISPATI.jl
+# Multispati.jl
 
-[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://niklasmueboe.github.io/MULTISPATI.jl/stable)
-[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://niklasmueboe.github.io/MULTISPATI.jl/dev)
+[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://niklasmueboe.github.io/Multispati.jl/stable)
+[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://niklasmueboe.github.io/Multispati.jl/dev)
 [![Code Style: Blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)
 [![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)
-[![CI](https://github.com/niklasmueboe/MULTISPATI.jl/workflows/CI/badge.svg)](https://github.com/niklasmueboe/MULTISPATI.jl/actions?query=workflows:CI)
+[![CI](https://github.com/niklasmueboe/Multispati.jl/workflows/CI/badge.svg)](https://github.com/niklasmueboe/Multispati.jl/actions?query=workflows:CI)
 
 Julia implementation of [MULTISPATI](https://doi.org/10.3170/2007-8-18312)
 
@@ -14,16 +14,16 @@ The package can be installed with the Julia package manager.
 From the Julia REPL, type `]` to enter the `Pkg` REPL mode and run:
 
 ```
-pkg> add MULTISPATI
+pkg> add Multispati
 ```
 
 Or, alternatively, via the `Pkg` API:
 
 ```julia
 using Pkg
-Pkg.add("MULTISPATI")
+Pkg.add("Multispati")
 ```
 
 ## Documentation
 
-The documentation for MULTISPATI.jl is available [here](https://niklasmueboe.github.io/MULTISPATI.jl/stable).
+The documentation for Multispati.jl is available [here](https://niklasmueboe.github.io/Multispati.jl/).
diff --git a/docs/Project.toml b/docs/Project.toml
index 47d7cbc..a65f110 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,7 +1,7 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DocumenterInterLinks = "d12716ef-a0f6-4df4-a9f1-a5a34e75c656"
-MULTISPATI = "3ff64760-8a89-40e2-854d-b45336bb1975"
+Multispati = "3ff64760-8a89-40e2-854d-b45336bb1975"
 
 [compat]
 Documenter = "1.3"
diff --git a/docs/make.jl b/docs/make.jl
index f476f96..d24a309 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,16 +1,16 @@
 using Documenter
 using DocumenterInterLinks
-using MULTISPATI
+using Multispati
 
 links = InterLinks(
 # "CategoricalArrays" => "https://categoricalarrays.juliadata.org/stable/",
 )
 
 makedocs(;
-    sitename="MULTISPATI.jl",
+    sitename="Multispati.jl",
     pages=["Home" => "index.md", "Reference API" => "api.md"],
     authors="Niklas Müller-Bötticher",
     plugins=[links],
 )
 
-deploydocs(; repo="github.com/niklasmueboe/MULTISPATI.jl.git")
+deploydocs(; repo="github.com/niklasmueboe/Multispati.jl.git")
diff --git a/docs/src/api.md b/docs/src/api.md
index f8441d0..e0e075e 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -1,6 +1,6 @@
 # Reference API
 
-Documentation for `MULTISPATI.jl`'s public interface.
+Documentation for `Multispati.jl`'s public interface.
 
 ## Index
 
@@ -10,19 +10,19 @@ Pages = ["api.md"]
 
 ## API
 
-### MULTISPATI
+### Multispati
 ```@docs
 AbstractMultispati
-Multispati
-fit(::Type{Multispati},
+MULTISPATI
+fit(::Type{MULTISPATI},
     X::AbstractMatrix{T},
     W::AbstractMatrix{U},
     Q::AbstractMatrix{T}=I,
     D::AbstractMatrix{T}=I / size(X, 2);
     kwargs
 ) where {T<:Real,U<:Real}
-predict(::Multispati, x::AbstractVecOrMat{T}) where {T<:Real}
-reconstruct(::Multispati, y::AbstractVecOrMat{T}) where {T<:Real}
+predict(::MULTISPATI, x::AbstractVecOrMat{T}) where {T<:Real}
+reconstruct(::MULTISPATI, y::AbstractVecOrMat{T}) where {T<:Real}
 moransIbounds
 size(::AbstractMultispati)
 projection(::AbstractMultispati)
diff --git a/docs/src/index.md b/docs/src/index.md
index 0412351..1716c36 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,4 +1,4 @@
-# MULTISPATI.jl
+# Multispati.jl
 
 Julia implementation of [MULTISPATI](https://doi.org/10.3170/2007-8-18312)
 
@@ -8,14 +8,14 @@ The package can be installed with the Julia package manager.
 From the Julia REPL, type `]` to enter the `Pkg` REPL mode and run:
 
 ```
-pkg> add MULTISPATI
+pkg> add Multispati
 ```
 
 Or, alternatively, via the `Pkg` API:
 
 ```julia
 using Pkg
-Pkg.add("MULTISPATI")
+Pkg.add("Multispati")
 ```
 
 ## Index
diff --git a/src/multispati_.jl b/src/MULTISPATI_.jl
similarity index 86%
rename from src/multispati_.jl
rename to src/MULTISPATI_.jl
index afd3631..058bdd3 100644
--- a/src/multispati_.jl
+++ b/src/MULTISPATI_.jl
@@ -1,7 +1,3 @@
-# MULTISPATI
-
-# TODO: :auto solver
-# TODO: centering of Multispati?
 
 """
     AbstractMultispati
@@ -9,9 +5,9 @@
 abstract type AbstractMultispati <: LinearDimensionalityReduction end
 
 """
-    Multispati <: AbstractMultispati
+    MULTISPATI <: AbstractMultispati
 """
-struct Multispati{T<:Real} <: AbstractMultispati
+struct MULTISPATI{T<:Real} <: AbstractMultispati
     proj::AbstractMatrix{T}
     eigvals::AbstractVector{T}
     W::AbstractMatrix{T}
@@ -36,36 +32,36 @@ projection(M::AbstractMultispati) = M.proj
 """
     eigvecs(M::AbstractMultispati)
 
-Get the eigenvectors of the Multispati model `M`.
+Get the eigenvectors of the model `M`.
 """
 eigvecs(M::AbstractMultispati) = projection(M)
 
 """
     eigvals(M::AbstractMultispati)
 
-Get the eigenvalues of the Multispati model `M`.
+Get the eigenvalues of the model `M`.
 """
 eigvals(M::AbstractMultispati) = M.eigvals
 
 """
-    predict(M::Multispati, x::AbstractVecOrMat{<:Real})
+    predict(M::MULTISPATI, x::AbstractVecOrMat{<:Real})
 
-Transform the observations `x` with the Multispati model `M`.
+Transform the observations `x` with the model `M`.
 
 Here, `x` can be either a vector of length `d` or a matrix where each column is an observation.
 """
-predict(M::Multispati, x::AbstractVecOrMat{T}) where {T<:Real} =
+predict(M::MULTISPATI, x::AbstractVecOrMat{T}) where {T<:Real} =
     transpose(projection(M)) * x
 
 """
-    reconstruct(M::Multispati, y::AbstractVecOrMat{<:Real})
+    reconstruct(M::MULTISPATI, y::AbstractVecOrMat{<:Real})
 
-Approximately reconstruct the observations `y` to the original space using the Multispati model `M`.
+Approximately reconstruct the observations `y` to the original space using the model `M`.
 
 Here, `y` can be either a vector of length `p` or a matrix where each column
 gives the components for an observation.
 """
-reconstruct(M::Multispati, y::AbstractVecOrMat{T}) where {T<:Real} = projection(M) * y
+reconstruct(M::MULTISPATI, y::AbstractVecOrMat{T}) where {T<:Real} = projection(M) * y
 
 """
     moransIbounds(M::AbstractMultispati; sparse_approx::Bool=true)
@@ -91,24 +87,28 @@ function moransIbounds(M::AbstractMultispati; sparse_approx::Bool=true)
         doublecenter!(L)
     end
 
-    eigenvals = n / sum(L) * eigs(L; nev=2, which=:BE, ritzvec=false)
+    eigenvals, _ = eigs(L; nev=2, which=:BE, ritzvec=false)
+    eigenvals .*= n / sum(L)
 
     I0 = -1 / (n - 1)
-    Imin = min(eigenvals)
-    Imax = max(eigenvals)
+    Imin = minimum(eigenvals)
+    Imax = maximum(eigenvals)
 
     return Imin, Imax, I0
 end
 
-function show(io::IO, M::Multispati)
+function show(io::IO, M::MULTISPATI)
     idim, odim = size(M)
-    return print(io, "Multispati(indim = $idim, outdim = $odim)")
+    return print(io, "MULTISPATI(indim = $idim, outdim = $odim)")
 end
 
+# TODO: :auto solver
+# TODO: centering of MULTISPATI.fit?
+
 """
-    fit(Multispati, X, W, Q=I, D=I / size(X, 2); ...)
+    fit(MULTISPATI, X, W, Q=I, D=I / size(X, 2); ...)
 
-Perform Multispati over the data given a matrix `X`. Each column of `X` is an **observation**.
+Perform MULTISPATI over the data given a matrix `X`. Each column of `X` is an **observation**.
 `W` is a connectivity matrix where ``w_{ij}`` is the connection from j -> i.
 `Q` is a symmetric matrix of size `n` (or LinearAlgebra.UniformScaling(@ref)) 
 and `D` a symmetric matrix of size `d` (or LinearAlgebra.UniformScaling(@ref)) 
@@ -131,7 +131,7 @@ multivariate spatial correlation." *Journal of vegetation science* (2008)](https
 *The annals of applied statistics* (2011)](https://doi.org/10.1214/10-aoas408)
 """
 function fit(
-    ::Type{Multispati},
+    ::Type{MULTISPATI},
     X::AbstractMatrix{T},
     W::AbstractMatrix{U},
     Q=I,
@@ -171,7 +171,7 @@ function fit(
         Symmetric(H), maxoutdim; solver=solver, tol=tol, maxiter=maxiter
     )
 
-    return Multispati(eigenvecs, eigenvals, W)
+    return MULTISPATI(eigenvecs, eigenvals, W)
 end
 
 function validate_maxoutdim(d::Integer, n::Integer, maxoutdim)
diff --git a/src/MULTISPATI.jl b/src/Multispati.jl
similarity index 82%
rename from src/MULTISPATI.jl
rename to src/Multispati.jl
index b2a0e2b..287947f 100644
--- a/src/MULTISPATI.jl
+++ b/src/Multispati.jl
@@ -1,4 +1,4 @@
-module MULTISPATI
+module Multispati
 
 import Base: size, show
 import LinearAlgebra: eigvals, eigvecs, issymmetric
@@ -12,7 +12,7 @@ using LinearAlgebra: I, Symmetric, eigen, normalize!
 using SparseArrays: issparse
 
 export AbstractMultispati,
-    Multispati,
+    MULTISPATI,
     SpatialPCA,
     fit,
     predict,
@@ -24,7 +24,7 @@ export AbstractMultispati,
     moransIbounds,
     varianceMoransIdecomposition
 
-include("multispati_.jl")
-include("spatialPCA.jl")
+include("MULTISPATI_.jl")
+include("SpatialPCA.jl")
 
-end # module MULTISPATI
+end # module Multispati
diff --git a/src/spatialPCA.jl b/src/SpatialPCA.jl
similarity index 98%
rename from src/spatialPCA.jl
rename to src/SpatialPCA.jl
index 0b0c500..f1ffd5a 100644
--- a/src/spatialPCA.jl
+++ b/src/SpatialPCA.jl
@@ -64,7 +64,7 @@ function varianceMoransIdecomposition(M::SpatialPCA, X)
     laggedX = transformedX * M.W
     w = 1 / size(M.W, 1) # sum of row_weights but because its normed the sum is n
     variance = sum(transformedX .* transformedX .* w; dims=2)
-    moransI = sum(transformedX .* laggedX .* w; dims=2) ./ variance # TODO ? 
+    moransI = sum(transformedX .* laggedX .* w; dims=2) ./ variance
     return variance, moransI
 end
 
@@ -76,7 +76,7 @@ end
 """
     fit(SpatialPCA, X, W; ...)
 
-Perform spatialPCA over the data given a matrix `X` and `W`. Each column of `X` is an **observation**. 
+Perform SpatialPCA over the data given a matrix `X` and `W`. Each column of `X` is an **observation**. 
 `W` is a connectivity matrix where ``w_{ij}`` is the connection from j -> i.
 
 **Keyword arguments**
diff --git a/test/Aqua.jl b/test/Aqua.jl
index b678d18..3d608a0 100644
--- a/test/Aqua.jl
+++ b/test/Aqua.jl
@@ -1,3 +1,3 @@
 using Aqua
 
-Aqua.test_all(MULTISPATI; ambiguities=(recursive = false))
+Aqua.test_all(Multispati; ambiguities=(recursive = false))
diff --git a/test/runtests.jl b/test/runtests.jl
index 72de22b..c044c83 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,4 +1,4 @@
 using Test
-using MULTISPATI
+using Multispati
 
 include("Aqua.jl")