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Knowledge Base

Returns the first derivative of the Chebyshev polynomials of the first kind.

 

Supported Product: FDTD, MODE

 

Syntax

Description

chebpol1(N,xi,xmin,xmax)

This command generates a matrix containing the Chebyshev polynomials of the first kind of orders zero to N-1 evaluated at the xi points.

 

Example

This example uses chebpol1 to calculate the first derivative of a function f sampled on a Chebishev grid.

clear;

closeall;

 

# Sample function on Chebyshev grid 

 

xmin = 0.0;

xmax = 1.0;

Nc = 11;

x = chpts(xmin,xmax,Nc);

f = cos(2.0*pi*x)+1i*sin(2.0*pi*x); # function and

fp = -2.0*pi*sin(2*pi*x)+1i*2.0*pi*cos(2.0*pi*x); # its derivative

Ni = 100;

xi = linspace(xmin,xmax,Ni);

 

 

# Function derivative from Chebyshev transform

dchtf = dcht(f);

Txp = chebpol1(length(f),xi,xmin,xmax);

fip = mult(Txp,dchtf);

 

plot(xi,fip,"x","f'(x)","Function Derivative");

holdon;

plot(x,fp,"x","f'(x)","Function Derivative","plot points");

holdoff;

legend("Re - Interpolated","Im - Interpolated","Re - Exact","Im - Exact");

setplot("y1 max",8);

setplot("y1 min",-8);

setplot("y2 max",8);

setplot("y2 min",-8);

 

 

See Also

dcht,chpts,icht,chebin,chebpol

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