R Under development (unstable) (2023-11-08 r85496 ucrt) -- "Unsuffered Consequences"
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> ##
> ##  c h e b P o l y . R  Test suite
> ##
> 
> 
> chebPoly <- pracma::chebPoly
> chebCoeff <- pracma::chebCoeff
> chebApprox <- pracma::chebApprox
> 
> identical(chebPoly(6),
+           matrix( c(0,   0,   0,   0,   0,   0,   1,
+                     0,   0,   0,   0,   0,   1,   0,
+                     0,   0,   0,   0,   2,   0,  -1,
+                     0,   0,   0,   4,   0,  -3,   0,
+                     0,   0,   8,   0,  -8,   0,   1,
+                     0,  16,   0, -20,   0,   5,   0,
+                    32,   0, -48,   0,  18,   0,  -1),
+                  nrow = 7, ncol = 7, byrow=TRUE))
[1] TRUE
> 
> f <- function(x) 1 + x/1 + x^2/2 + x^3/6 + x^4/24 + x^5/120 + x^6/720
> cC <- chebCoeff(f, -1, 1, 6)
> cC[1] <- cC[1]/2
> all.equal(cC,
+           c(1.26606, 1.13021, 0.27148, 0.04427, 0.00547, 0.00052, 0.00004),
+           tol = 1e-5)
[1] TRUE
> 
> x <- seq(-1, 1, length.out=7)
> y <- chebApprox(x, function(x) x^2, -1, 1, 6)
> all.equal(x^2, y, tol = 1e-7)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.06    0.09    0.14