SpectralToolbox.Spectral1D

Functions

AlmostEqual(a, b)	b = AlmostEqual(a,b)
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.
SPcomb(N, k[, exact, repetition])	The number of combinations of N things taken k at a time.
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.
TestOrthogonality(V, w)
cc(N[, norm])	cc(): function for generating 1D Nested Clenshaw-Curtis [-1,1]
factorial(n[, exact])	The factorial function, n! = special.gamma(n+1).
fej(N[, norm])	fej(): function for generating 1D Nested Fejer’s rule [-1,1]
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

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