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 CeedVector X, X_q, U, U_q; 18 CeedBasis basis_x_lobatto, basis_u_lobatto, basis_x_gauss, basis_u_gauss; 19 CeedInt Q = 6; 20 const CeedScalar p[6] = {1, 2, 3, 4, 5, 6}; // 1 + 2x + 3x^2 + ... 21 const CeedScalar *xq, *uuq; 22 CeedScalar x[2], uq[Q]; 23 24 CeedInit(argv[1], &ceed); 25 26 CeedVectorCreate(ceed, 2, &X); 27 CeedVectorCreate(ceed, Q, &X_q); 28 CeedVectorSetValue(X_q, 0); 29 CeedVectorCreate(ceed, Q, &U); 30 CeedVectorSetValue(U, 0); 31 CeedVectorCreate(ceed, Q, &U_q); 32 33 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS_LOBATTO, &basis_x_lobatto); 34 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS_LOBATTO, &basis_u_lobatto); 35 36 for (int i = 0; i < 2; i++) x[i] = CeedIntPow(-1, i + 1); 37 CeedVectorSetArray(X, CEED_MEM_HOST, CEED_USE_POINTER, (CeedScalar *)&x); 38 39 CeedBasisApply(basis_x_lobatto, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, X, X_q); 40 41 CeedVectorGetArrayRead(X_q, CEED_MEM_HOST, &xq); 42 for (CeedInt i = 0; i < Q; i++) uq[i] = PolyEval(xq[i], ALEN(p), p); 43 CeedVectorRestoreArrayRead(X_q, &xq); 44 CeedVectorSetArray(U_q, CEED_MEM_HOST, CEED_USE_POINTER, (CeedScalar *)&uq); 45 46 // This operation is the identity because the quadrature is collocated 47 CeedBasisApply(basis_u_lobatto, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, U_q, U); 48 49 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, Q, CEED_GAUSS, &basis_x_gauss); 50 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, Q, Q, CEED_GAUSS, &basis_u_gauss); 51 52 CeedBasisApply(basis_x_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, X, X_q); 53 CeedBasisApply(basis_u_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, U, U_q); 54 55 CeedVectorGetArrayRead(X_q, CEED_MEM_HOST, &xq); 56 CeedVectorGetArrayRead(U_q, CEED_MEM_HOST, &uuq); 57 for (CeedInt i = 0; i < Q; i++) { 58 CeedScalar px = PolyEval(xq[i], ALEN(p), p); 59 if (fabs(uuq[i] - px) > 100. * CEED_EPSILON) printf("%f != %f = p(%f)\n", uuq[i], px, xq[i]); 60 } 61 CeedVectorRestoreArrayRead(X_q, &xq); 62 CeedVectorRestoreArrayRead(U_q, &uuq); 63 64 CeedVectorDestroy(&X); 65 CeedVectorDestroy(&X_q); 66 CeedVectorDestroy(&U); 67 CeedVectorDestroy(&U_q); 68 CeedBasisDestroy(&basis_x_lobatto); 69 CeedBasisDestroy(&basis_u_lobatto); 70 CeedBasisDestroy(&basis_x_gauss); 71 CeedBasisDestroy(&basis_u_gauss); 72 CeedDestroy(&ceed); 73 return 0; 74 } 75