1*4411cf47Sjeremylt /// @file 2*4411cf47Sjeremylt /// Test polynomial interpolation in 1D 3*4411cf47Sjeremylt /// \test Test polynomial interpolation in 1D 457c64913Sjeremylt #include <ceed.h> 557c64913Sjeremylt #include <math.h> 657c64913Sjeremylt 757c64913Sjeremylt #define ALEN(a) (sizeof(a) / sizeof((a)[0])) 857c64913Sjeremylt 957c64913Sjeremylt static CeedScalar PolyEval(CeedScalar x, CeedInt n, const CeedScalar *p) { 1057c64913Sjeremylt CeedScalar y = p[n-1]; 1157c64913Sjeremylt for (CeedInt i=n-2; i>=0; i--) y = y*x + p[i]; 1257c64913Sjeremylt return y; 1357c64913Sjeremylt } 1457c64913Sjeremylt 1557c64913Sjeremylt int main(int argc, char **argv) { 1657c64913Sjeremylt Ceed ceed; 1757c64913Sjeremylt CeedBasis bxl, bxg, bug; 1857c64913Sjeremylt CeedInt Q = 6; 1957c64913Sjeremylt const CeedScalar p[] = {1, 2, 3, 4, 5, 6}; // 1 + 2x + 3x^2 + ... 2057c64913Sjeremylt const CeedScalar x[] = {-1, 1}; 2157c64913Sjeremylt CeedScalar xq[Q], u[Q], uq[Q], w[Q], sum, error, pint[ALEN(p)+1]; 2257c64913Sjeremylt 2357c64913Sjeremylt CeedInit(argv[1], &ceed); 2457c64913Sjeremylt CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS_LOBATTO, &bxl); 2557c64913Sjeremylt CeedBasisApply(bxl, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, xq); 2657c64913Sjeremylt for (CeedInt i=0; i<Q; i++) u[i] = PolyEval(xq[i], ALEN(p), p); 2757c64913Sjeremylt 2857c64913Sjeremylt CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS, &bxg); 2957c64913Sjeremylt CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS, &bug); 3057c64913Sjeremylt CeedBasisApply(bxg, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, xq); 3157c64913Sjeremylt CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, uq); 3257c64913Sjeremylt CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, NULL, w); 3357c64913Sjeremylt sum = 0; 3457c64913Sjeremylt for (CeedInt i=0; i<Q; i++) { 3557c64913Sjeremylt sum += w[i] * uq[i]; 3657c64913Sjeremylt } 3757c64913Sjeremylt pint[0] = 0; 3857c64913Sjeremylt for (CeedInt i=0; i<(CeedInt)ALEN(p); i++) pint[i+1] = p[i] / (i+1); 3957c64913Sjeremylt error = sum - PolyEval(1, ALEN(pint), pint) + PolyEval(-1, ALEN(pint), pint); 4057c64913Sjeremylt if (!(error < 1e-10)) 4157c64913Sjeremylt printf("Error %e sum %g exact %g\n", error, sum, 4257c64913Sjeremylt PolyEval(1, ALEN(pint), pint) - PolyEval(-1, ALEN(pint), pint)); 4357c64913Sjeremylt 4457c64913Sjeremylt CeedBasisDestroy(&bxl); 4557c64913Sjeremylt CeedBasisDestroy(&bxg); 4657c64913Sjeremylt CeedBasisDestroy(&bug); 4757c64913Sjeremylt CeedDestroy(&ceed); 4857c64913Sjeremylt return 0; 4957c64913Sjeremylt } 50