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() |
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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. |