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 Eval(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 22 CeedInit(argv[1], &ceed); 23 24 CeedVectorCreate(ceed, 2, &x); 25 CeedVectorCreate(ceed, q, &x_q); 26 CeedVectorSetValue(x_q, 0); 27 CeedVectorCreate(ceed, q, &u); 28 CeedVectorSetValue(u, 0); 29 CeedVectorCreate(ceed, q, &u_q); 30 31 { 32 CeedScalar x_array[2]; 33 34 for (int i = 0; i < 2; i++) x_array[i] = CeedIntPow(-1, i + 1); 35 CeedVectorSetArray(x, CEED_MEM_HOST, CEED_COPY_VALUES, x_array); 36 } 37 38 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, q, CEED_GAUSS_LOBATTO, &basis_x_lobatto); 39 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, q, q, CEED_GAUSS_LOBATTO, &basis_u_lobatto); 40 41 CeedBasisApply(basis_x_lobatto, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, x_q); 42 { 43 const CeedScalar *x_q_array; 44 CeedScalar u_array[q]; 45 46 CeedVectorGetArrayRead(x_q, CEED_MEM_HOST, &x_q_array); 47 for (CeedInt i = 0; i < q; i++) u_array[i] = Eval(x_q_array[i], ALEN(p), p); 48 CeedVectorRestoreArrayRead(x_q, &x_q_array); 49 CeedVectorSetArray(u_q, CEED_MEM_HOST, CEED_COPY_VALUES, (CeedScalar *)&u_array); 50 } 51 52 // This operation is the identity because the quadrature is collocated 53 CeedBasisApply(basis_u_lobatto, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, u_q, u); 54 55 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, q, CEED_GAUSS, &basis_x_gauss); 56 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, q, q, CEED_GAUSS, &basis_u_gauss); 57 58 CeedBasisApply(basis_x_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, x_q); 59 CeedBasisApply(basis_u_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, u_q); 60 61 { 62 const CeedScalar *x_q_array, *u_q_array; 63 64 CeedVectorGetArrayRead(x_q, CEED_MEM_HOST, &x_q_array); 65 CeedVectorGetArrayRead(u_q, CEED_MEM_HOST, &u_q_array); 66 for (CeedInt i = 0; i < q; i++) { 67 CeedScalar px = Eval(x_q_array[i], ALEN(p), p); 68 if (fabs(u_q_array[i] - px) > 100. * CEED_EPSILON) printf("%f != %f = p(%f)\n", u_q_array[i], px, x_q_array[i]); 69 } 70 CeedVectorRestoreArrayRead(x_q, &x_q_array); 71 CeedVectorRestoreArrayRead(u_q, &u_q_array); 72 } 73 74 CeedVectorDestroy(&x); 75 CeedVectorDestroy(&x_q); 76 CeedVectorDestroy(&u); 77 CeedVectorDestroy(&u_q); 78 CeedBasisDestroy(&basis_x_lobatto); 79 CeedBasisDestroy(&basis_u_lobatto); 80 CeedBasisDestroy(&basis_x_gauss); 81 CeedBasisDestroy(&basis_u_gauss); 82 CeedDestroy(&ceed); 83 return 0; 84 } 85