Polynomials

MultiCheb(coeff; clean_zeros=true)

A polynomial in the Chebyshev basis, wrapping its coefficient array so it can be passed straight to solve instead of being approximated from a callable.

coeff[i, j, ...] is the coefficient of T_(i-1)(x) * T_(j-1)(y) * ..., where T_n is the Chebyshev polynomial of the first kind, so coeff[1, 1] is the constant term. The number of axes is the number of variables, available afterwards as the dim field.

clean_zeros=true trims trailing all-zero slices, so a padded array does not inflate the reported degree. Pass false to keep the array's shape as given.

Examples

julia> p = MultiCheb([0.0, 0.0, 1.0]);       # T2(x) = 2x^2 - 1

julia> eval_MultiCheb(p, [0.5])
-0.5

julia> q = MultiCheb([1.0 0.0; 0.0 2.0]);    # 1 + 2*T1(x)*T1(y)

julia> eval_MultiCheb(q, [0.5, 0.3])
1.3

MultiPower(coeff; clean_zeros=true)

A polynomial in the power basis, wrapping its coefficient array so it can be passed straight to solve instead of being approximated from a callable.

coeff[i, j, ...] is the coefficient of x^(i-1) * y^(j-1) * ..., so coeff[1, 1] is the constant term. The number of axes is the number of variables, available afterwards as the dim field.

clean_zeros=true trims trailing all-zero slices, so a padded array does not inflate the reported degree. Pass false to keep the array's shape as given.

Examples

julia> p = MultiPower([1.0 0.0; 2.0 3.0]);   # 1 + 2x + 3xy

julia> p.dim
2

julia> eval_MultiPower(p, [0.5, 0.3])
2.45

eval_MultiCheb(multiCheb, points)

Evaluate a MultiCheb at one point or at many.

points is either a single point as a length-dim vector, or a dim x npoints matrix whose columns are the points. A single point returns a scalar; several return a vector of values, one per column.

Examples

julia> p = MultiCheb([0.0, 0.0, 1.0]);       # T2(x) = 2x^2 - 1

julia> eval_MultiCheb(p, [0.5])
-0.5

julia> eval_MultiCheb(p, [0.5 0.1])
2-element Vector{Float64}:
 -0.5
 -0.98

eval_MultiPower(multiPower, points)

Evaluate a MultiPower at one point or at many.

points is either a single point as a length-dim vector, or a dim x npoints matrix whose columns are the points. A single point returns a scalar; several return one value per column.

Examples

julia> p = MultiPower([1.0 0.0; 2.0 3.0]);   # 1 + 2x + 3xy

julia> eval_MultiPower(p, [0.5, 0.3])
2.45