docs: add description for RegularizationSmooth

README.md

@@ -52,15 +52,13 @@ In all cases, `u` an `AbstractVector` of values and `t` is an `AbstractVector` o
 corresponding to `(u,t)` pairs.
 
   - `ConstantInterpolation(u,t)` - A piecewise constant interpolation.
-
   - `LinearInterpolation(u,t)` - A linear interpolation.
   - `QuadraticInterpolation(u,t)` - A quadratic interpolation.
   - `LagrangeInterpolation(u,t,n)` - A Lagrange interpolation of order `n`.
   - `QuadraticSpline(u,t)` - A quadratic spline interpolation.
   - `CubicSpline(u,t)` - A cubic spline interpolation.
   - `AkimaInterpolation(u, t)` - Akima spline interpolation provides a smoothing effect and is computationally efficient.
   - `BSplineInterpolation(u,t,d,pVec,knotVec)` - An interpolation B-spline. This is a B-spline which hits each of the data points. The argument choices are:
-
       + `d` - degree of B-spline
       + `pVec` - Symbol to Parameters Vector, `pVec = :Uniform` for uniform spaced parameters and `pVec = :ArcLen` for parameters generated by chord length method.
       + `knotVec` - Symbol to Knot Vector, `knotVec = :Uniform` for uniform knot vector, `knotVec = :Average` for average spaced knot vector.
@@ -70,7 +68,9 @@ corresponding to `(u,t)` pairs.
 
 The follow 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 RegularizationTools`
+  - `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.
+  Requires `using RegularizationTools`.
 
 ## Plotting
 

docs/src/index.md

@@ -21,15 +21,13 @@ In all cases, `u` an `AbstractVector` of values and `t` is an `AbstractVector` o
 corresponding to `(u,t)` pairs.
 
   - `ConstantInterpolation(u,t)` - A piecewise constant interpolation.
-
   - `LinearInterpolation(u,t)` - A linear interpolation.
   - `QuadraticInterpolation(u,t)` - A quadratic interpolation.
   - `LagrangeInterpolation(u,t,n)` - A Lagrange interpolation of order `n`.
   - `QuadraticSpline(u,t)` - A quadratic spline interpolation.
   - `CubicSpline(u,t)` - A cubic spline interpolation.
   - `AkimaInterpolation(u, t)` - Akima spline interpolation provides a smoothing effect and is computationally efficient.
   - `BSplineInterpolation(u,t,d,pVec,knotVec)` - An interpolation B-spline. This is a B-spline which hits each of the data points. The argument choices are:
-
       + `d` - degree of B-spline
       + `pVec` - Symbol to Parameters Vector, `pVec = :Uniform` for uniform spaced parameters and `pVec = :ArcLen` for parameters generated by chord length method.
       + `knotVec` - Symbol to Knot Vector, `knotVec = :Uniform` for uniform knot vector, `knotVec = :Average` for average spaced knot vector.
@@ -39,7 +37,9 @@ corresponding to `(u,t)` pairs.
 
 The follow 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 RegularizationTools`
+  - `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.
+  Requires `using RegularizationTools`.
 
 ## Plotting