ChebValues: ChebValues

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

ChebValues

Description

ChebValues(coeffs) converts the n-dimensional Chebyshev coefficients to

Usage

ChebValues(coeffs)

Arguments

coeffs

Chebyshev coefficients

Value

V = ChebValues(C) returns the n-dimensional vector of (polynomial) values evaluated at the Chebyshev points x such that V(i) = f(x(i))= C(1)*T_{0}(x(i)) + C(2)*T_{1}(x(i)) + ... + C(N)*T_{N-1}(x(i)) (where T_k(x) denotes the k-th 1st-kind Chebyshev polynomial, and x(i) are the 2nd-kind Chebyshev nodes.

If the input C is an (n x m)-matrix then V = ChebValues(C) returns (n x m)-matrix of values V such that V(i,j) = P_j(x_i) = C(1,j)*T_{0}(x(i)) + C(2,j)*T_{1}(x(i)) + ... + C(N,j)*T_{N-1}(x(i)).

Note

Ver.: 15-Nov-2021 17:55:08 (consistent with Matlab CharFunTool v1.3.0, 28-May-2021 14:28:24).

See Also

Other Utility Function: ChebCoefficients(), ChebPoints(), ChebPolyValues(), ChebPoly(), GammaLog(), GammaMultiLog(), GammaMulti(), GammaZX(), Hypergeom1F1MatApprox(), Hypergeom1F1Mat(), Hypergeom2F1Mat(), Hypergeom2F1(), HypergeompFqMat(), InterpChebValues(), hypergeom1F1(), interpBarycentric()

Examples

## EXAMPLE1 (Values of Sine function evaluated Chebyshev points on (-pi,pi))
   n      <- 2^5+1
   domain <- c(-pi,pi)
   x      <- ChebPoints(n,domain)
   f      <-list( sin(x[[1]]))
   coeffs <- ChebCoefficients(f)
   V      <- ChebValues(coeffs)
   print(list(x[[1]], coeffs, f, V))

## EXAMPLE2 (Chebyshev values of the Sine and the Cosine on (-pi,pi))
   n      <- 2^5+1
   domain <- c(-pi,pi)
   x      <- ChebPoints(n,domain)
   f      <-list( sin(x[[1]]), cos(x[[1]]))
   coeffs <- ChebCoefficients(f)
   V      <- ChebValues(coeffs)
   print(list(x[[1]], coeffs, f, V))

gajdosandrej/CharFunToolR documentation built on June 3, 2024, 7:46 p.m.