SpectralToolbox.Spectral1DΒΆ

Functions

BarycentricWeights(x) BarycentricWeights(): Returns a 1-d array of weights for Lagrange Interpolation
FirstPolynomialDerivativeMatrix(x) PolynomialDerivativeMatrix(): Assemble the first Polynomial Derivative Matrix using matrix multiplication.
LagrangeInterpolate(x, f, xi) LagrangeInterpolate(): Interpolate function values f from points x to points xi using Lagrange weights
LagrangeInterpolationMatrix(x, w, xi) LagrangeInterpolationMatrix(): constructs the Lagrange Interpolation Matrix from points x to points xi
LinearInterpolationMatrix(x, xi) LinearInterpolationMatrix(): constructs the Linear Interpolation Matrix from points x to points xi
LinearShapeFunction(x, xm, xp, xi) Hat function used for linear interpolation
PolynomialDerivativeMatrix(x, k) PolynomialDerivativeMatrix(): Assemble the Polynomial k-th Derivative Matrix using the matrix recursion.
SparseLinearInterpolationMatrix(x, xi) LinearInterpolationMatrix(): constructs the Linear Interpolation Matrix from points x to points xi.
SparseLinearShapeFunction(x, xm, xp, xi) Hat function used for linear interpolation.
cc(N[, norm]) cc(): function for generating 1D Nested Clenshaw-Curtis [-1,1]
fej(N[, norm]) fej(): function for generating 1D Nested Fejer’s rule [-1,1]
generate(ptype, params) Generate orthogonal basis objects from Spectral1D.AVAIL_POLY.
gqn(N) GQN(): function for generating 1D Gaussian quadrature for integral with Gaussian weight (Gauss-Hermite)
gqu(N[, norm]) GQU(): function for generating 1D Gaussian quadrature rules for unweighted integral over [-1,1] (Gauss-Legendre)
kpn(N) KPN(): function for generating 1D Nested rule for integral with Gaussian weight
kpu(N[, norm]) KPU(): function for generating 1D Nested rule for unweighted integral over [-1,1]
nestedgauss(N[, norm]) nestedgauss(): function for generating 1D Nested rule for integral with Uniform weight with 2**l scaling
nestedlobatto(N[, norm]) nestedlobatto(): function for generating 1D Nested rule for integral with Uniform weight with 2**l scaling

Classes

Basis() This is an abstract class for 1-d basis
ConstantExtendedHermiteProbabilistsFunction([...]) Construction of the Hermite Probabilists’ functions extended with the constant basis
ConstantExtendedHermiteProbabilistsRadialBasisFunction(nbasis) Construction of the Hermite Probabilists’ Radial Basis Functions
Fourier()
GenericOrthogonalPolynomial(mu, endl, endr) Construction of polynomials orthogonal with respect to a generic measure
HermitePhysicistsFunction([normalized]) Construction of the Hermite Physiticists’ functions
HermitePhysicistsPolynomial([normalized]) Construction of the Hermite Physicists’ polynomials
HermiteProbabilistsFunction([normalized]) Construction of the Hermite Probabilists’ functions
HermiteProbabilistsPolynomial([normalized]) Construction of the Hermite Probabilists polynomials
HermiteProbabilistsRadialBasisFunction(order) Construction of the Hermite Probabilists’ Radial Basis Functions
JacobiPolynomial(alpha, beta[, span, normalized]) Construction of Jacobi polynomials
LaguerreFunction(alpha[, normalized]) Construction of the Laguerre functions
LaguerrePolynomial(alpha[, normalized]) Construction of Laguerre polynomials
LinearExtendedHermiteProbabilistsRadialBasisFunction(nbasis) Construction of the Hermite Probabilists’ Radial Basis Functions
OrthogonalBasis([normalized]) This is an abstract class for 1-d orthogonal basis
OrthogonalPolynomial([normalized]) This is an abstract class for 1-d polynomials
Poly1D(poly, params[, sdout]) Initialization of the Polynomial instance.