1 /// @file 2 /// Test polynomial interpolation in 1D 3 /// \test Test polynomial interpolation in 1D 4 #include <ceed.h> 5 #include <math.h> 6 7 #define ALEN(a) (sizeof(a) / sizeof((a)[0])) 8 9 static CeedScalar PolyEval(CeedScalar x, CeedInt n, const CeedScalar *p) { 10 CeedScalar y = p[n-1]; 11 for (CeedInt i=n-2; i>=0; i--) y = y*x + p[i]; 12 return y; 13 } 14 15 int main(int argc, char **argv) { 16 Ceed ceed; 17 CeedBasis bxl, bxg, bug; 18 CeedInt Q = 6; 19 const CeedScalar p[] = {1, 2, 3, 4, 5, 6}; // 1 + 2x + 3x^2 + ... 20 const CeedScalar x[] = {-1, 1}; 21 CeedScalar xq[Q], u[Q], uq[Q], w[Q], sum, error, pint[ALEN(p)+1]; 22 23 CeedInit(argv[1], &ceed); 24 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS_LOBATTO, &bxl); 25 CeedBasisApply(bxl, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, xq); 26 for (CeedInt i=0; i<Q; i++) u[i] = PolyEval(xq[i], ALEN(p), p); 27 28 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS, &bxg); 29 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS, &bug); 30 CeedBasisApply(bxg, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, xq); 31 CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, uq); 32 CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, NULL, w); 33 sum = 0; 34 for (CeedInt i=0; i<Q; i++) { 35 sum += w[i] * uq[i]; 36 } 37 pint[0] = 0; 38 for (CeedInt i=0; i<(CeedInt)ALEN(p); i++) pint[i+1] = p[i] / (i+1); 39 error = sum - PolyEval(1, ALEN(pint), pint) + PolyEval(-1, ALEN(pint), pint); 40 if (!(error < 1e-10)) 41 printf("Error %e sum %g exact %g\n", error, sum, 42 PolyEval(1, ALEN(pint), pint) - PolyEval(-1, ALEN(pint), pint)); 43 44 CeedBasisDestroy(&bxl); 45 CeedBasisDestroy(&bxg); 46 CeedBasisDestroy(&bug); 47 CeedDestroy(&ceed); 48 return 0; 49 } 50