AlgebraicCurveOrthogonalPolynomials.Arc
— TypeThe arc y ≥ h
AlgebraicCurveOrthogonalPolynomials.CubicCurve
— TypeCubicCurve represents y^2 = x * (1-x) * (t-x) for x in 0..1
AlgebraicCurveOrthogonalPolynomials.HermLaurent
— TypeRepresents Hermitian-valued Laurent series of the form
A[1] + A[2]/z + A[2]'z + A[3]/z^2 + A[3]'z^2 + …
where A[k] is real. Reduces to cosine series when A[k] is 1x1.
AlgebraicCurveOrthogonalPolynomials.ImHermLaurent
— TypeRepresents Hermitian-valued Laurent series of the form
im*(A[1]/z - A[1]'z) + im*(A[2]/z^2 - A[2]'z^2) + …
where A[k] is real. Reduces to sine series when A[k] is 1x1.
AlgebraicCurveOrthogonalPolynomials.LegendreCircle
— TypeOrtogonal polynomials w.r.t. uniform weight on circle. Equivalent to Fourier.
AlgebraicCurveOrthogonalPolynomials.TwoBandJacobi
— TypeTwoBandJacobi(ρ, a, b, c)
is a quasi-matrix orthogonal |x|^(2c) * (x^2 - ρ^2)^b * (1-x^2)^a
for ρ ≤ |x| ≤ 1
.
AlgebraicCurveOrthogonalPolynomials.TwoBandWeight
— TypeTwoBandWeight(ρ, a, b, c)
is a quasi-vector representing |x|^(2c) * (x^2-ρ^2)^b * (1-x^2)^a
for ρ ≤ |x| ≤ 1
AlgebraicCurveOrthogonalPolynomials.UltrasphericalArc
— TypeOrtogonal polynomials w.r.t. y^a for y^2 + x^2 = 1, y ≥ h
AlgebraicCurveOrthogonalPolynomials.UltrasphericalArcWeight
— Typey^a on arc
AlgebraicCurveOrthogonalPolynomials.UltrasphericalCircle
— TypeOrtogonal polynomials w.r.t. y^a
AlgebraicCurveOrthogonalPolynomials.UltrasphericalCircleWeight
— Typey^a on unit circle
AlgebraicCurveOrthogonalPolynomials._hermitian_isdiag
— Methodreturns a tuple which tells if an entry lies on the diag
AlgebraicCurveOrthogonalPolynomials.blocksymtricirculant
— Methodblocksymtricirculant(A,B, N)
Creates a Block N x N Symmetric-Tridiagonal-Circulant matrix with diagonal blocks A and off-diagonal block B.
AlgebraicCurveOrthogonalPolynomials.cmjac
— MethodJacobian of cm(A,X)
AlgebraicCurveOrthogonalPolynomials.comunroll
— Methodparameterise A and Bʸ
AlgebraicCurveOrthogonalPolynomials.diagjac
— MethodJacobian of Diagonal(λ)
AlgebraicCurveOrthogonalPolynomials.ljac
— MethodJacobian of A*X
AlgebraicCurveOrthogonalPolynomials.qr_nullspace
— Methodspecial implementation for autodiff
AlgebraicCurveOrthogonalPolynomials.randspeccurve
— MethodCreate random spectral curve
AlgebraicCurveOrthogonalPolynomials.rjac
— MethodJacobian of X*A
AlgebraicCurveOrthogonalPolynomials.spec2alg
— MethodGives coefficients in monomial basis of polynomial vanishing on curve
AlgebraicCurveOrthogonalPolynomials.speccurvemat
— MethodCreate a spectral curve from parameters
AlgebraicCurveOrthogonalPolynomials.specgrid
— Methodevaluate spectral curve at grid
AlgebraicCurveOrthogonalPolynomials.symjac
— MethodJacobian of symunroll(λ)
AlgebraicCurveOrthogonalPolynomials.trjac
— MethodJacobian of transpose(A)
AlgebraicCurveOrthogonalPolynomials.unroll
— Methodunroll variables into Symmetric Ax and non-symmetric Bx