Merge pull request #492 from ChrisRackauckas-Claude/docs-improvements-20251230-070836

Documentation improvements: Fix grammar and typos

Author: ChrisRackauckas

README.md

@@ -43,7 +43,7 @@ interp(u′, t′)
 
 ## Available Interpolations
 
-In all cases, `u` an `AbstractVector` of values and `t` is an `AbstractVector` of timepoints
+In all cases, `u` is an `AbstractVector` of values and `t` is an `AbstractVector` of timepoints
 corresponding to `(u,t)` pairs.
 
   - `ConstantInterpolation(u,t)` - A piecewise constant interpolation.
@@ -67,7 +67,7 @@ corresponding to `(u,t)` pairs.
 
 ## Extension Methods
 
-The follow methods require extra dependencies and will be loaded as package extensions.
+The following methods require extra dependencies and will be loaded as package extensions.
 
   - `Curvefit(u,t,m,p,alg)` - An interpolation which is done by fitting a user-given functional form `m(t,p)` where `p` is the vector of parameters. The user's input `p` is a an initial value for a least-square fitting, `alg` is the algorithm choice to use for optimize the cost function (sum of squared deviations) via `Optim.jl` and optimal `p`s are used in the interpolation. Requires `using Optim`.
   - `RegularizationSmooth(u,t,d;λ,alg)` - A regularization algorithm (ridge regression) which is done by minimizing an objective function (l2 loss + derivatives of order `d`) integrated in the time span. It is a global method and creates a smooth curve.

docs/src/extrapolation_methods.md

@@ -48,33 +48,33 @@ This extrapolation type extends the interpolation with a continuation of the exp
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
 plot(A)
-plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
-plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## `ExtrapolationType.Periodic`
 
-this extrapolation type extends the interpolation such that `A(t + T) == A(t)` for all `t`, where the period is given by `T = last(A.t) - first(A.t)`.
+This extrapolation type extends the interpolation such that `A(t + T) == A(t)` for all `t`, where the period is given by `T = last(A.t) - first(A.t)`.
 
 ```@example tutorial
 T = last(A.t) - first(A.t)
 t_eval_left = range(first(t) - 2T, first(t), length = 100)
 t_eval_right = range(last(t), last(t) + 2T, length = 100)
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Periodic)
 plot(A)
-plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
-plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## `ExtrapolationType.Reflective`
 
-this extrapolation type extends the interpolation such that `A(t_ + t) == A(t_ - t)` for all `t_, t` such that `(t_ - first(A.t)) % T == 0` and `0 < t < T`, where `T = last(A.t) - first(A.t)`.
+This extrapolation type extends the interpolation such that `A(t_ + t) == A(t_ - t)` for all `t_, t` such that `(t_ - first(A.t)) % T == 0` and `0 < t < T`, where `T = last(A.t) - first(A.t)`.
 
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Reflective)
 plot(A)
-plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
-plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## Mixed extrapolation

docs/src/index.md

@@ -13,7 +13,7 @@ Pkg.add("DataInterpolations")
 
 ## Available Interpolations
 
-In all cases, `u` an `AbstractVector` of values and `t` is an `AbstractVector` of timepoints
+In all cases, `u` is an `AbstractVector` of values and `t` is an `AbstractVector` of timepoints
 corresponding to `(u,t)` pairs.
 
   - `ConstantInterpolation(u,t)` - A piecewise constant interpolation.

docs/src/interface.md

@@ -92,7 +92,7 @@ out_matrix
 
 ## Derivatives
 
-Derivatives of the interpolated curves can also be computed at any point for all the methods. Derivatives upto second order is supported where first order derivative is computed analytically and second order using `ForwardDiff.jl`. Order is passed as the third argument. It is 1 by default.
+Derivatives of the interpolated curves can also be computed at any point for all the methods. Derivatives up to second order are supported where first order derivative is computed analytically and second order using `ForwardDiff.jl`. Order is passed as the third argument. It is 1 by default.
 
 We will continue with the above example, but the API is the same for all the methods. If the interpolation is defined with `extrapolate=true`, derivatives can also be extrapolated.
 
@@ -135,5 +135,5 @@ DataInterpolations.integral(A2, 200.0, 300.0)
 ```
 
 !!! note
-    
-    If the times provided in the integral go beyond the range of the time points provided during interpolation, it uses extrapolation methods to compute the values, and hence the integral can be misrepsentative and might not reflect the true nature of the data.
+
+    If the times provided in the integral go beyond the range of the time points provided during interpolation, it uses extrapolation methods to compute the values, and hence the integral can be misrepresentative and might not reflect the true nature of the data.