ChebyshevTools: y=cheb2phys(F); - File Exchange

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Highlights from
ChebyshevTools

A=expD(M,ord,mod);
A_res=restrictA(A,m) this function extracts the submatrix A(1+m:end,1:end-m)
B=inv_deriv1(M); This function returns one matrix, for solving
B=inv_derivP(M,P) this function returns the Pth quasi inverse for Chebycheb differentiation
B=pseudo_eye(M,P) this function returns the pseudo-identity matrix I^(P), where there are
D=deriv(M); returns the first order chebyshev spectral differentiation matrix
D=deriv2(M);
P=cheb2poly(U) this function converts the spectral representation of a function in Chebyshev polynomials
S=stencil_mat(M,typ) this function returns the stencil matrix associated with the related
Y=cheb2phys2(X);
Y=cheb2phys3(X); 3d transform chebyshev to physical space
Y=phys2cheb2(X);
Y=phys2cheb3(X); 3d transform physical space to chebyshev
[BIG_OP,BIG_rhs]=bc_2d_new(P,... Generate the tau line boundary conditions and the appropriate rhs vector
[BIG_OP,BIG_rhs]=bc_2d_new_to... Generate the tau line boundary conditions and the appropriate rhs vector
[OP,rhs]=bc_1d(M,bc_type,bc_v...
f=galerkin2cheb(g,typ) this function transforms from the galerkin basis to the chebyshev basis
f=galerkin2cheb2(g,typ) this function transforms from the galerkin basis to the chebyshev basis in
f=galerkin2cheb3(g,typ) this function transforms from the galerkin basis to the chebyshev basis in
g=cheb2galerkin(f,typ) this function transforms from the chebyshev basis to the galerkin basis
g=cheb2galerkin2(f,typ) this function transforms from the galerkin basis to the chebyshev basis in
g=cheb2galerkin3(f,typ) this function transforms from the galerkin basis to the chebyshev basis in
test_problem(M,N,tc) This function is run from the command line taking argumetns
v=getdiag(A,n); extract the nth diag from matrix A
x=cheb_grid(N); this function returns a chebyshev grid on the interval [-1,1]
y=cheb2phys(F); Written by Mike Watson, November 29
y=definite_integral_cart(F,X1... Calculate the definite integral of a function defined by spectral
y=myC(p)
y=phys2cheb(f); Written by Mike Watson, November 29
deriv3.m
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from ChebyshevTools by Michael Watson
Tool box for solving ODE/PDEs using spectral Chebyshev differentiation matrices.

y=cheb2phys(F);

function y=cheb2phys(F);

% Written by Mike Watson, November 29
% takes a real vector of normalized Chebyshev spectral coeffients F and outputs
% the physical coefficients f on the interval [-1,1]


N=length(F);

if (N==1)
    y=F;
else
    F_even=(N-1).*[F;flipud(F(2:N-1))];  % create an even extension of F, including Nyquist;
    % and renormalize
    F_even(1)=F_even(1)*2;
    F_even(N)=F_even(N)*2;

    f=real(ifft(F_even));  %perform a discrete cosine transform (DCT);

    y=f(1:N);

end

Highlights from ChebyshevTools

Highlights from
ChebyshevTools