1 /// @file 2 /// Test polynomial interpolation transpose from arbitrary points in 1D 3 /// \test Test polynomial interpolation transpose from arbitrary points 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 *c) { 11 CeedScalar y = c[n - 1]; 12 for (CeedInt i = n - 2; i >= 0; i--) y = y * x + c[i]; 13 return y; 14 } 15 16 int main(int argc, char **argv) { 17 Ceed ceed; 18 CeedVector x, x_nodes, x_points, x_point, u, v, u_point, v_point; 19 CeedBasis basis_x, basis_u; 20 const CeedInt p = 5, q = 5, num_points = 4; 21 const CeedScalar c[4] = {1, 2, 3, 4}; // 1 + 2x + 3x^2 + ... 22 23 CeedInit(argv[1], &ceed); 24 25 CeedVectorCreate(ceed, 2, &x); 26 CeedVectorCreate(ceed, p, &x_nodes); 27 CeedVectorCreate(ceed, num_points, &x_points); 28 CeedVectorCreate(ceed, 1, &x_point); 29 CeedVectorCreate(ceed, p, &u); 30 CeedVectorCreate(ceed, num_points, &v); 31 CeedVectorCreate(ceed, p, &u_point); 32 CeedVectorCreate(ceed, 1, &v_point); 33 CeedVectorSetValue(v_point, 1.0); 34 35 // Get nodal coordinates 36 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, 2, p, CEED_GAUSS_LOBATTO, &basis_x); 37 { 38 CeedScalar x_array[2]; 39 40 for (CeedInt i = 0; i < 2; i++) x_array[i] = CeedIntPow(-1, i + 1); 41 CeedVectorSetArray(x, CEED_MEM_HOST, CEED_COPY_VALUES, x_array); 42 } 43 CeedBasisApply(basis_x, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x, x_nodes); 44 45 // Set values of u at nodes 46 { 47 const CeedScalar *x_array; 48 CeedScalar u_array[p]; 49 50 CeedVectorGetArrayRead(x_nodes, CEED_MEM_HOST, &x_array); 51 for (CeedInt i = 0; i < p; i++) u_array[i] = Eval(x_array[i], ALEN(c), c); 52 CeedVectorRestoreArrayRead(x_nodes, &x_array); 53 CeedVectorSetArray(u, CEED_MEM_HOST, CEED_COPY_VALUES, (CeedScalar *)&u_array); 54 } 55 56 // Interpolate to arbitrary points 57 CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, p, q, CEED_GAUSS, &basis_u); 58 { 59 CeedScalar x_array[4] = {-0.33, -0.65, 0.16, 0.99}; 60 61 CeedVectorSetArray(x_points, CEED_MEM_HOST, CEED_COPY_VALUES, x_array); 62 } 63 CeedBasisApplyAtPoints(basis_u, num_points, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, x_points, u, v); 64 65 for (CeedInt i = 0; i < num_points; i++) { 66 CeedScalar fx = 0.0; 67 const CeedScalar *x_array, *u_array, *v_array, *u_point_array; 68 69 CeedVectorGetArrayRead(x_points, CEED_MEM_HOST, &x_array); 70 CeedVectorGetArrayRead(u, CEED_MEM_HOST, &u_array); 71 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 72 CeedVectorSetValue(x_point, x_array[i]); 73 CeedBasisApplyAtPoints(basis_u, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, x_point, v_point, u_point); 74 CeedVectorGetArrayRead(u_point, CEED_MEM_HOST, &u_point_array); 75 for (CeedInt j = 0; j < p; j++) fx += u_array[j] * u_point_array[j]; 76 if (fabs(v_array[i] - fx) > 100. * CEED_EPSILON) printf("%f != %f = f(%f)\n", v_array[i], fx, x_array[i]); 77 CeedVectorRestoreArrayRead(u_point, &u_point_array); 78 CeedVectorRestoreArrayRead(x_points, &x_array); 79 CeedVectorRestoreArrayRead(u, &u_array); 80 CeedVectorRestoreArrayRead(v, &v_array); 81 } 82 83 CeedVectorDestroy(&x); 84 CeedVectorDestroy(&x_nodes); 85 CeedVectorDestroy(&x_points); 86 CeedVectorDestroy(&x_point); 87 CeedVectorDestroy(&u); 88 CeedVectorDestroy(&v); 89 CeedVectorDestroy(&u_point); 90 CeedVectorDestroy(&v_point); 91 CeedBasisDestroy(&basis_x); 92 CeedBasisDestroy(&basis_u); 93 CeedDestroy(&ceed); 94 return 0; 95 } 96