typos

Author: jarlebring

src/NEPTypes.jl

@@ -1335,7 +1335,7 @@ Returns true/false if the NEP is sparse (if compute_Mder() returns sparse)
     """
         struct DerSPMF{T<:AbstractMatrix,FDtype,TT<:Number} <: AbstractSPMF{T}
 
-    A DerSPMF is a shift-tuned representation of NEP defined by a Sum of Products of Matrices and Functions [`SPMF_NEP`](@ref). This format makes more efficient the execution of [`compute_Mlincomb`](@ref) for the selected shift σ.
+    A DerSPMF is a representation of a NEP defined by a Sum of Products of Matrices and Functions [`SPMF_NEP`](@ref). This format makes the execution of [`compute_Mlincomb`](@ref) for the specified `σ` more efficient.
     """
     struct DerSPMF{T<:AbstractMatrix,TT<:Number,FDtype} <: AbstractSPMF{T}
         spmf::AbstractSPMF{T}
@@ -1358,23 +1358,23 @@ Returns true/false if the NEP is sparse (if compute_Mder() returns sparse)
     end
 
     """
-         DerSPMF(spmf,σ,m)
+    newspmf=DerSPMF(spmf,σ,m)
 
-    Creates a `DerSPMF` representing the NEP `spmf` where the first `m` derivatives of the functions `f_i` in the number `σ` are precomputed. This format makes more efficient the execution of [`compute_Mlincomb`](@ref) for the selected shift σ.
+    Creates a `DerSPMF` representing the NEP `spmf` where the first `m` derivatives of the functions `f_i` in the number `σ` are precomputed. This will in general speed up the execution of [`compute_Mlincomb`](@ref) for the selected shift σ.
 
     # Parameters
 
-    * `spmf` is an `AbstractSPMF`.
+    * `spmf` is the original `AbstractSPMF`.
 
-    * `σ` is a `Number` represeing the shift where the derivatives will be precomputed.
+    * `σ::Number` specifies where the derivatives will be precomputed.
 
     # Example
     ```julia-repl
     julia> A0=[1 3; 4 5]; A1=[3 4; 5 6];
     julia> id_op=S -> one(S) # Note: We use one(S) to be valid both for matrices and scalars
     julia> exp_op=S -> exp(S)
     julia> nep=SPMF_NEP([A0,A1],[id_op,exp_op]);
-    julia> m=5
+    julia> m=5 # Precompute 5 derivatives
     julia> Dnep=DerSPMF(nep,σ,m)
     julia> V=rand(2,m)
     julia> z=compute_Mlincomb(Dnep,σ,V)