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