1 /// @file 2 /// Test polynomial interpolation in 1D 3 /// \test Test polynomial interpolation in 1D 4 #include <ceed.h> 5 #include <math.h> 6 #include <stdio.h> 7 8 #define ALEN(a) (sizeof(a) / sizeof((a)[0])) 9 10 static CeedScalar Eval(CeedScalar x, CeedInt n, const CeedScalar *p) { 11 CeedScalar y = p[n - 1]; 12 for (CeedInt i = n - 2; i >= 0; i--) y = y * x + p[i]; 13 return y; 14 } 15 16 int main(int argc, char **argv) { 17 Ceed ceed; 18 CeedVector x, x_q, u, u_q; 19 CeedBasis basis_x_lobatto, basis_u_lobatto, basis_x_gauss, basis_u_gauss; 20 CeedInt q = 6; 21 const CeedScalar p[6] = {1, 2, 3, 4, 5, 6}; // 1 + 2x + 3x^2 + ... 22 23 CeedInit(argv[1], &ceed); 24 25 CeedVectorCreate(ceed, 2, &x); 26 CeedVectorCreate(ceed, q, &x_q); 27 CeedVectorSetValue(x_q, 0); 28 CeedVectorCreate(ceed, q, &u); 29 CeedVectorSetValue(u, 0); 30 CeedVectorCreate(ceed, q, &u_q); 31 32 { 33 CeedScalar x_array[2]; 34 35 for (int i = 0; i < 2; i++) x_array[i] = CeedIntPow(-1, i + 1); 36 CeedVectorSetArray(x, CEED_MEM_HOST, CEED_COPY_VALUES, x_array); 37 } 38 39 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, q, CEED_GAUSS_LOBATTO, &basis_x_lobatto); 40 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, q, q, CEED_GAUSS_LOBATTO, &basis_u_lobatto); 41 42 CeedBasisApply(basis_x_lobatto, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, x_q); 43 { 44 const CeedScalar *x_q_array; 45 CeedScalar u_array[q]; 46 47 CeedVectorGetArrayRead(x_q, CEED_MEM_HOST, &x_q_array); 48 for (CeedInt i = 0; i < q; i++) u_array[i] = Eval(x_q_array[i], ALEN(p), p); 49 CeedVectorRestoreArrayRead(x_q, &x_q_array); 50 CeedVectorSetArray(u_q, CEED_MEM_HOST, CEED_COPY_VALUES, (CeedScalar *)&u_array); 51 } 52 53 // This operation is the identity because the quadrature is collocated 54 CeedBasisApply(basis_u_lobatto, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, u_q, u); 55 56 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, q, CEED_GAUSS, &basis_x_gauss); 57 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, q, q, CEED_GAUSS, &basis_u_gauss); 58 59 CeedBasisApply(basis_x_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, x_q); 60 CeedBasisApply(basis_u_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, u_q); 61 62 { 63 const CeedScalar *x_q_array, *u_q_array; 64 65 CeedVectorGetArrayRead(x_q, CEED_MEM_HOST, &x_q_array); 66 CeedVectorGetArrayRead(u_q, CEED_MEM_HOST, &u_q_array); 67 for (CeedInt i = 0; i < q; i++) { 68 CeedScalar px = Eval(x_q_array[i], ALEN(p), p); 69 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]); 70 } 71 CeedVectorRestoreArrayRead(x_q, &x_q_array); 72 CeedVectorRestoreArrayRead(u_q, &u_q_array); 73 } 74 75 CeedVectorDestroy(&x); 76 CeedVectorDestroy(&x_q); 77 CeedVectorDestroy(&u); 78 CeedVectorDestroy(&u_q); 79 CeedBasisDestroy(&basis_x_lobatto); 80 CeedBasisDestroy(&basis_u_lobatto); 81 CeedBasisDestroy(&basis_x_gauss); 82 CeedBasisDestroy(&basis_u_gauss); 83 CeedDestroy(&ceed); 84 return 0; 85 } 86