diff --git a/README.md b/README.md index d9a64551..ea9b921c 100644 --- a/README.md +++ b/README.md @@ -52,7 +52,6 @@ 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`. @@ -60,7 +59,6 @@ corresponding to `(u,t)` pairs. - `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 diff --git a/docs/src/index.md b/docs/src/index.md index 7e31d620..47cc6723 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -21,7 +21,6 @@ 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`. @@ -29,7 +28,6 @@ corresponding to `(u,t)` pairs. - `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