1a8de75f0Sjeremylt /// @file 252bfb9bbSJeremy L Thompson /// Test polynomial interpolation in 1D 352bfb9bbSJeremy L Thompson /// \test Test polynomial interpolation in 1D 4a8de75f0Sjeremylt #include <ceed.h> 5a8de75f0Sjeremylt #include <math.h> 6a8de75f0Sjeremylt 752bfb9bbSJeremy L Thompson #define ALEN(a) (sizeof(a) / sizeof((a)[0])) 852bfb9bbSJeremy L Thompson 952bfb9bbSJeremy L Thompson static CeedScalar PolyEval(CeedScalar x, CeedInt n, const CeedScalar *p) { 1052bfb9bbSJeremy L Thompson CeedScalar y = p[n-1]; 1152bfb9bbSJeremy L Thompson for (CeedInt i=n-2; i>=0; i--) y = y*x + p[i]; 1252bfb9bbSJeremy L Thompson return y; 13a8de75f0Sjeremylt } 14a8de75f0Sjeremylt 15a8de75f0Sjeremylt int main(int argc, char **argv) { 16a8de75f0Sjeremylt Ceed ceed; 1752bfb9bbSJeremy L Thompson CeedVector X, Xq, U, Uq, W; 1852bfb9bbSJeremy L Thompson CeedBasis bxl, bxg, bug; 1952bfb9bbSJeremy L Thompson CeedInt Q = 6; 2052bfb9bbSJeremy L Thompson const CeedScalar p[6] = {1, 2, 3, 4, 5, 6}; // 1 + 2x + 3x^2 + ... 2152bfb9bbSJeremy L Thompson const CeedScalar *xq, *uq, *w; 2252bfb9bbSJeremy L Thompson CeedScalar u[Q], x[2], sum, error, pint[ALEN(p)+1]; 23a8de75f0Sjeremylt 24a8de75f0Sjeremylt CeedInit(argv[1], &ceed); 25aedaa0e5Sjeremylt 2652bfb9bbSJeremy L Thompson CeedVectorCreate(ceed, 2, &X); 2752bfb9bbSJeremy L Thompson CeedVectorCreate(ceed, Q, &Xq); 2852bfb9bbSJeremy L Thompson CeedVectorSetValue(Xq, 0); 2952bfb9bbSJeremy L Thompson CeedVectorCreate(ceed, Q, &U); 3052bfb9bbSJeremy L Thompson CeedVectorCreate(ceed, Q, &Uq); 3152bfb9bbSJeremy L Thompson CeedVectorSetValue(Uq, 0); 3252bfb9bbSJeremy L Thompson CeedVectorCreate(ceed, Q, &W); 3352bfb9bbSJeremy L Thompson CeedVectorSetValue(W, 0); 34a8de75f0Sjeremylt 3552bfb9bbSJeremy L Thompson CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS_LOBATTO, &bxl); 36aedaa0e5Sjeremylt 3752bfb9bbSJeremy L Thompson for (int i = 0; i < 2; i++) 3852bfb9bbSJeremy L Thompson x[i] = CeedIntPow(-1, i+1); 3952bfb9bbSJeremy L Thompson CeedVectorSetArray(X, CEED_MEM_HOST, CEED_USE_POINTER, x); 40aedaa0e5Sjeremylt 4152bfb9bbSJeremy L Thompson CeedBasisApply(bxl, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, X, Xq); 42a8de75f0Sjeremylt 4352bfb9bbSJeremy L Thompson CeedVectorGetArrayRead(Xq, CEED_MEM_HOST, &xq); 4452bfb9bbSJeremy L Thompson for (CeedInt i=0; i<Q; i++) 4552bfb9bbSJeremy L Thompson u[i] = PolyEval(xq[i], ALEN(p), p); 4652bfb9bbSJeremy L Thompson CeedVectorRestoreArrayRead(Xq, &xq); 4752bfb9bbSJeremy L Thompson CeedVectorSetArray(U, CEED_MEM_HOST, CEED_USE_POINTER, u); 4852bfb9bbSJeremy L Thompson 4952bfb9bbSJeremy L Thompson CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS, &bxg); 5052bfb9bbSJeremy L Thompson CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS, &bug); 5152bfb9bbSJeremy L Thompson 5252bfb9bbSJeremy L Thompson CeedBasisApply(bxg, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, X, Xq); 5352bfb9bbSJeremy L Thompson CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, U, Uq); 54*a7b7f929Sjeremylt CeedBasisApply(bug, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, 55*a7b7f929Sjeremylt CEED_VECTOR_NONE, W); 5652bfb9bbSJeremy L Thompson 5752bfb9bbSJeremy L Thompson CeedVectorGetArrayRead(W, CEED_MEM_HOST, &w); 5852bfb9bbSJeremy L Thompson CeedVectorGetArrayRead(Uq, CEED_MEM_HOST, &uq); 59a8de75f0Sjeremylt sum = 0; 6052bfb9bbSJeremy L Thompson for (CeedInt i=0; i<Q; i++) 6152bfb9bbSJeremy L Thompson sum += w[i] * uq[i]; 6252bfb9bbSJeremy L Thompson CeedVectorRestoreArrayRead(W, &w); 6352bfb9bbSJeremy L Thompson CeedVectorRestoreArrayRead(Uq, &uq); 64a8de75f0Sjeremylt 6552bfb9bbSJeremy L Thompson pint[0] = 0; 6652bfb9bbSJeremy L Thompson for (CeedInt i=0; i<(int)ALEN(p); i++) 6752bfb9bbSJeremy L Thompson pint[i+1] = p[i] / (i+1); 6852bfb9bbSJeremy L Thompson error = sum - PolyEval(1, ALEN(pint), pint) + PolyEval(-1, ALEN(pint), pint); 6952bfb9bbSJeremy L Thompson if (error > 1.e-10) 7052bfb9bbSJeremy L Thompson // LCOV_EXCL_START 7152bfb9bbSJeremy L Thompson printf("Error %e sum %g exact %g\n", error, sum, 7252bfb9bbSJeremy L Thompson PolyEval(1, ALEN(pint), pint) - PolyEval(-1, ALEN(pint), pint)); 7352bfb9bbSJeremy L Thompson // LCOV_EXCL_STOP 7452bfb9bbSJeremy L Thompson 7552bfb9bbSJeremy L Thompson CeedVectorDestroy(&X); 7652bfb9bbSJeremy L Thompson CeedVectorDestroy(&Xq); 7752bfb9bbSJeremy L Thompson CeedVectorDestroy(&U); 7852bfb9bbSJeremy L Thompson CeedVectorDestroy(&Uq); 7952bfb9bbSJeremy L Thompson CeedVectorDestroy(&W); 8052bfb9bbSJeremy L Thompson CeedBasisDestroy(&bxl); 8152bfb9bbSJeremy L Thompson CeedBasisDestroy(&bxg); 8252bfb9bbSJeremy L Thompson CeedBasisDestroy(&bug); 83a8de75f0Sjeremylt CeedDestroy(&ceed); 84a8de75f0Sjeremylt return 0; 85a8de75f0Sjeremylt } 86