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, bul, 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], uq[Q], u[Q]; 22 23 CeedInit(argv[1], &ceed); 24 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS_LOBATTO, &bxl); 25 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS_LOBATTO, &bul); 26 CeedBasisApply(bxl, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, xq); 27 for (CeedInt i=0; i<Q; i++) uq[i] = PolyEval(xq[i], ALEN(p), p); 28 29 // This operation is the identity because the quadrature is collocated 30 CeedBasisApply(bul, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, uq, u); 31 32 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS, &bxg); 33 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS, &bug); 34 CeedBasisApply(bxg, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, xq); 35 CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, uq); 36 for (CeedInt i=0; i<Q; i++) { 37 CeedScalar px = PolyEval(xq[i], ALEN(p), p); 38 if (!(fabs(uq[i] - px) < 1e-14)) { 39 printf("%f != %f=p(%f)\n", uq[i], px, xq[i]); 40 } 41 } 42 43 CeedBasisDestroy(&bxl); 44 CeedBasisDestroy(&bul); 45 CeedBasisDestroy(&bxg); 46 CeedBasisDestroy(&bug); 47 CeedDestroy(&ceed); 48 return 0; 49 } 50