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double integral test

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antonl 2026-04-22 20:04:38 +02:00
parent da72d26496
commit b25dce857e
37 changed files with 208 additions and 4574 deletions
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300
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out/bsplines_knots.dat
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2.560000e+01
2.573333e+01
2.586667e+01
2.600000e+01
2.613333e+01
2.626667e+01
2.640000e+01
2.653333e+01
2.666667e+01
2.680000e+01
2.693333e+01
2.706667e+01
2.720000e+01
2.733333e+01
2.746667e+01
2.760000e+01
2.773333e+01
2.786667e+01
2.800000e+01
2.813333e+01
2.826667e+01
2.840000e+01
2.853333e+01
2.866667e+01
2.880000e+01
2.893333e+01
2.906667e+01
2.920000e+01
2.933333e+01
2.946667e+01
2.960000e+01
2.973333e+01
2.986667e+01
3.000000e+01
3.013333e+01
3.026667e+01
3.040000e+01
3.053333e+01
3.066667e+01
3.080000e+01
3.093333e+01
3.106667e+01
3.120000e+01
3.133333e+01
3.146667e+01
3.160000e+01
3.173333e+01
3.186667e+01
3.200000e+01
3.213333e+01
3.226667e+01
3.240000e+01
3.253333e+01
3.266667e+01
3.280000e+01
3.293333e+01
3.306667e+01
3.320000e+01
3.333333e+01
3.346667e+01
3.360000e+01
3.373333e+01
3.386667e+01
3.400000e+01
3.413333e+01
3.426667e+01
3.440000e+01
3.453333e+01
3.466667e+01
3.480000e+01
3.493333e+01
3.506667e+01
3.520000e+01
3.533333e+01
3.546667e+01
3.560000e+01
3.573333e+01
3.586667e+01
3.600000e+01
3.613333e+01
3.626667e+01
3.640000e+01
3.653333e+01
3.666667e+01
3.680000e+01
3.693333e+01
3.706667e+01
3.720000e+01
3.733333e+01
3.746667e+01
3.760000e+01
3.773333e+01
3.786667e+01
3.800000e+01
3.813333e+01
3.826667e+01
3.840000e+01
3.853333e+01
3.866667e+01
3.880000e+01
3.893333e+01
3.906667e+01
3.920000e+01
3.933333e+01
3.946667e+01
3.960000e+01
3.973333e+01
4.000000e+01

40
out/knotpoints.dat
View File

@ -1,40 +0,0 @@
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
1.212121e+00
2.424242e+00
3.636364e+00
4.848485e+00
6.060606e+00
7.272727e+00
8.484848e+00
9.696970e+00
1.090909e+01
1.212121e+01
1.333333e+01
1.454545e+01
1.575758e+01
1.696970e+01
1.818182e+01
1.939394e+01
2.060606e+01
2.181818e+01
2.303030e+01
2.424242e+01
2.545455e+01
2.666667e+01
2.787879e+01
2.909091e+01
3.030303e+01
3.151515e+01
3.272727e+01
3.393939e+01
3.515152e+01
3.636364e+01
3.757576e+01
3.878788e+01
4.000000e+01
4.000000e+01
4.000000e+01
4.000000e+01

200
src/hf/hf_base.c
View File

@ -2,7 +2,7 @@
GaussLegendre g_gauss_legendre = {0};
function inline U32
mat_get_col_major_idx(U32 i, U32 j, U32 size1) {
mat_ij_to_index(U32 i, U32 j, U32 size1) {
return j * size1 + i;
}
@ -21,7 +21,7 @@ mat_F64(Arena *arena, U32 size1, U32 size2)
function inline void
mat_F64_set(Mat_F64 *mat, U32 i, U32 j, F64 val)
{
U32 index = mat_get_col_major_idx(i, j, mat->size1);
U32 index = mat_ij_to_index(i, j, mat->size1);
mat->data[index] = val;
return;
}
@ -29,7 +29,7 @@ mat_F64_set(Mat_F64 *mat, U32 i, U32 j, F64 val)
function inline F64
mat_F64_get(Mat_F64 *mat, U32 i, U32 j)
{
U32 index = mat_get_col_major_idx(i, j, mat->size1);
U32 index = mat_ij_to_index(i, j, mat->size1);
return mat->data[index];
}
@ -233,7 +233,11 @@ function void print_eigenvalues(S32 l, S32 n, F64 *wr, F64 *wi) {
}
function void
set_up_first_matrices(Problem *problem, Mat_F64 *H, Mat_F64 *H_l, Mat_F64 *B_inv) {
set_up_base_matrices(Problem *problem,
Mat_F64 *H,
Mat_F64 *H_l,
Mat_F64 *B_inv) {
// We work in units hbar = 1, bohr radius a0 = 1, electron mass m_e = 1, and
// charge e = 1, and 1/(4piepsilon_0) = 1. Set up Hamiltonian: H =
// -0.5*d^2/dr^2 + l(l+1)/(2r^2) - Z/r
@ -245,7 +249,7 @@ set_up_first_matrices(Problem *problem, Mat_F64 *H, Mat_F64 *H_l, Mat_F64 *B_inv
U32 k = bspl_ctx->order;
// Skipping first bspline
for (U32 i = 0; i < H->size1; i++) {
for (U32 i = 0; i < H->size1; i++) {
for (U32 j = 0; j < H->size2; j++) {
U32 bspl_index_i =
i + 1; // The second Bspline has index 1 in our array etc.
@ -359,11 +363,31 @@ compute_wf_norm_F64(F64 *coeffs, U64 coeff_size, U64 n, U64 l) {
scratch_release(scratch);
}
function F64 naive_kernel(F64 r1, F64 r2, F64 k, F64 alpha, F64 beta) {
if(r1 < r2) {
return pow(r1, 2.0*k+1.0)*exp(-alpha*r1)*exp(-beta*r2);
} else {
return exp(-alpha*r1)*pow(r2, 2.0*k+1.0)*exp(-beta*r2);
}
}
function F64 factorial(S32 k) {
if(k == 0) {
return 1.0;
} else if(k == 1) {
return 1.0;
} else {
F64 kf = (F64)k;
S32 next = k - 1;
return kf * factorial(next);
}
}
/////////////////////////////////////////////////////////////////////////////////////////
//~
// Main problem function, called from entry point.
//~ Testing HF integrals.
function void
hf_main(void) {
hf_coulomb_integrals_test(void)
{
Problem problem = problem_create();
LOG(str8_pushf(problem.arena, "Created Problem-struct for %s \n", problem.atom.name.str).str);
@ -397,52 +421,172 @@ hf_main(void) {
U32 k = problem.bspline_ctx.order;
U32 mat_size1 = N - k - 2;
U32 mat_size2 = mat_size1;
Mat_F64 H_base = mat_F64(problem.arena, mat_size1, mat_size2);
Mat_F64 H_l_base = mat_F64(problem.arena, mat_size1, mat_size2);
Mat_F64 H_l = mat_F64(problem.arena, mat_size1, mat_size2);
Mat_F64 H = mat_F64(problem.arena, mat_size1, mat_size2);
LOG(" *** Running tests for coulomb operator integrals! *** \n ");
Mat_F64 test_mat = mat_F64(problem.arena, mat_size1, mat_size2);
Mat_F64 double_int_mat = mat_F64(problem.arena, mat_size1, mat_size2);
// We want to compute integrals over two r-coordinates r1 and r2, of the form
// int1(int2( F(r1) (r^k_smaller / r^(k+1)_greater) G(r2) )
// We will test with analytic functions
// F(r) = r^(k+1) exp(-alpha*r)
// G(r) = r^(k+1) exp(-beta*r)
// Because then whenever r1 < r2 the kernel will be
// r1^(2k+1)exp(-alpha*r1)*exp(-beta*r2)
// and whenever r2 > r1 we have
// exp(-alpha*r1)*r2^(2k+1)exp(-beta*r2)
// That is we cancel the denominator.
// In particular we can get an analytic result as a function of k, alpha and beta:
// (2k+1)! / ((alpha*beta)(alpha+beta)^(2k+1))
// The reason is so that we can
// 1) Make sure that we are integrating over two r-coordinates properly.
// 2) Compare a "fast" method to just brute force double integral loop to make sur
// it is correct.
// 3) Expand the method to the general spline case to compute the Coulomb matrix
// element with confidence that it is correct.
{
BSplineCtx *bspl_ctx = &problem.bspline_ctx;
U32 bspl_order = bspl_ctx->order;
F64 *t1 = bspl_ctx->knotpoints;
F64 k_mpole = 1.0;
F64 alpha = 2.0;
F64 beta = 3.0;
// The set of r coordinates will be all knotpoints and the quadrature points in
// between them
F64 result = 0.0;
U32 phys_point_first_index = bspl_ctx->first_phys_index;;
U32 phys_point_last_index = bspl_ctx->num_phys_points + k-1;
for(S32 r1_i = phys_point_first_index; r1_i < phys_point_last_index-1; r1_i += 1)
{
F64 a1 = t1[r1_i];
F64 b1 = t1[r1_i + 1];
F64 c1 = (a1+b1);
F64 h1 = (b1-a1);
for(S32 r2_i = phys_point_first_index; r2_i < phys_point_last_index-1; r2_i += 1)
{
F64 a2 = t1[r2_i];
F64 b2 = t1[r2_i + 1];
F64 c2 = (a2+b2);
F64 h2 = (b2-a2);
for(S32 q1 = 0; q1 < g_gauss_legendre.order; q1 += 1) {
F64 w1 = 0.5 * h1 * g_gauss_legendre.weights[q1];
F64 z1 = g_gauss_legendre.abscissae[q1];
F64 r1 = (z1 * (0.5 * h1)) + (c1 * 0.5);
for(S32 q2 = 0; q2 < g_gauss_legendre.order; q2 += 1) {
F64 w2 = 0.5 * h2 * g_gauss_legendre.weights[q2];
F64 z2 = g_gauss_legendre.abscissae[q2];
F64 r2 = (z2 * (0.5 * h2)) + (c2 * 0.5);
F64 kernel = naive_kernel(r1, r2, k_mpole, alpha, beta);
result += w1 * w2 * kernel;
}
}
}
}
ArenaTemp scratch = scratch_get(0,0);
// Analytic
S32 k_mpole_int = 1;
F64 fact = factorial(2*k_mpole_int + 1);
F64 reference = fact / ((alpha*beta)*pow((alpha+beta),2.0*k_mpole+1.0));
LOG(str8_pushf(scratch.arena, "Reference: %.12f \n", reference).str);
LOG(str8_pushf(scratch.arena, "Computed: %.12f \n", result).str);
scratch_release(scratch);
}
}
/////////////////////////////////////////////////////////////////////////////////////////
//~
// Main problem function, called from entry point.
function void
hf_eigenvalues_main(void)
{
Problem problem = problem_create();
LOG(str8_pushf(problem.arena, "Created Problem-struct for %s \n", problem.atom.name.str).str);
set_up_gauss_legendre_points(problem.arena);
//- Set up grid and write to file.
grid_assign(&problem.grid);
set_up_grid(problem.arena);
write_array_binary_F64(str8_lit(grid_file_path_bin),
problem.grid.points,
problem.grid.num_steps);
write_array_F64(str8_lit(grid_file_path),
problem.grid.points,
problem.grid.num_steps,
"%13.6e\n");
//- The BSpline context is the knotpoints and the BSpline order etc.
bspline_ctx_assign(&problem.bspline_ctx);
set_up_bspline_context(problem.arena);
write_array_F64(str8_lit(knotpoints_file_path), problem.bspline_ctx.knotpoints,
problem.bspline_ctx.num_knotpoints, "%13.6e\n");
//- Then we generate the BSplines and save them off for reference and
// debugging.
set_up_bsplines_at_points_and_write_matrix_F64(problem.arena);
U32 N = problem.bspline_ctx.num_knotpoints;
U32 k = problem.bspline_ctx.order;
U32 mat_size1 = N - k - 2;
U32 mat_size2 = mat_size1;
problem.H_base = mat_F64(problem.arena, mat_size1, mat_size2);
problem.H_l_base = mat_F64(problem.arena, mat_size1, mat_size2);
problem.H_l = mat_F64(problem.arena, mat_size1, mat_size2);
problem.H = mat_F64(problem.arena, mat_size1, mat_size2);
// This will be the inverse of B, but to start with we construct B.
Mat_F64 B_inv = mat_F64(problem.arena, mat_size1, mat_size2);
problem.B_inv = mat_F64(problem.arena, mat_size1, mat_size2);
// A is the actual matrix for each eigenvalue problem.
Mat_F64 A = mat_F64(problem.arena, H.size1, H.size2);
set_up_first_matrices(&problem, &H_base, &H_l_base, &B_inv);
problem.A = mat_F64(problem.arena, problem.H.size1, problem.H.size2);
set_up_base_matrices(&problem,
&problem.H_base,
&problem.H_l_base,
&problem.B_inv);
// Our problem is Hc = EBc, but we want to solve B^-1Hc = Ec,
// so we invert the B matrix and compute the product A = B^-1H before calling
// zgeev
mat_invert_F64(&B_inv);
mat_invert_F64(&problem.B_inv);
// This arena is used to push results from f. ex eigenvalue computations.
// For each angular momentum
for (U32 ang_mom_idx = 0; ang_mom_idx < MAX_NUM_ANGULAR_MOMENTA; ang_mom_idx++) {
ArenaTemp scratch = scratch_get(0, 0);
mat_F64_copy_to_dst(&H, &H_base);
mat_F64_copy_to_dst(&problem.H, &problem.H_base);
F64 l = problem.angular_momentum_l[ang_mom_idx];
Eigensolution_F64 *eigsol = &problem.eigsols[ang_mom_idx];
eigsol->l = (U32)l;
if (l > 1e-16) {
F64 l_factor = l * (l + 1.0);
U64 mat_size = H_l.size1 * H_l.size2;
mat_F64_copy_to_dst(&H_l, &H_l_base);
U64 mat_size = problem.H_l.size1 * problem.H_l.size2;
mat_F64_copy_to_dst(&problem.H_l, &problem.H_l_base);
// Multiply l(l+1)
cblas_dscal(mat_size, l_factor, H_l.data, 1);
cblas_dscal(mat_size, l_factor, problem.H_l.data, 1);
// Add H = H_base + H_l
cblas_daxpy(mat_size, 1.0, H_l.data, 1, H.data, 1);
cblas_daxpy(mat_size, 1.0, problem.H_l.data, 1, problem.H.data, 1);
}
//LOG("Matrix H: \n");
//print_mat_F64(&problem.H);
// Multiply to get A = B^-1 H
{
S32 n = A.size1;
S32 n = problem.A.size1;
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
B_inv.data, n, H.data, n, 0.0, A.data, n);
problem.B_inv.data, n, problem.H.data, n, 0.0, problem.A.data, n);
//LOG("Matrix A: \n");
//print_mat_F64(&A);
//print_mat_F64(&problem.A);
}
// Solve generalised eigenvalue problem
{
S32 size1 = A.size1;
S32 size1 = problem.A.size1;
S32 lda = size1;
S32 ldvl = size1;
S32 ldvr = size1;
@ -462,7 +606,7 @@ hf_main(void) {
F64 *vr = eigsol->right_eigvecs.data;
lwork = -1;
F64 *a = A.data;
F64 *a = problem.A.data;
dgeev("Vectors", "Vectors", &size1, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr,
&wkopt, &lwork, &info);
lwork = (S32)wkopt;
@ -482,7 +626,7 @@ hf_main(void) {
print_eigenvalues((U32)l, size1, wr, wi );
U32 i = 0;
F64 energy = -1000.0;
F64 energy = -1.0*(F64)(U32Max); // Just have an unreasonable energy bound
U32 counter = 0;
while (energy < 0.0) {
energy = wr[i];
@ -495,7 +639,7 @@ hf_main(void) {
// compute_wf_norm_F64(eigensolution.right_eigenvectors.matrix[energy_index],
// size1, n, ang_mom_idx);
U64 eigvec_idx = mat_get_col_major_idx(0, energy_index, size1);
U64 eigvec_idx = mat_ij_to_index(0, energy_index, size1);
F64 *eigvecs = &eigsol->right_eigvecs.data[eigvec_idx];
write_array_F64(
get_eigenvector_filename(scratch.arena, n, ang_mom_idx),

19
src/hf/hf_base.h
View File

@ -81,14 +81,25 @@ struct Problem {
F64 angular_momentum_l[ANGMOM_NUM_MOMENTA];
Eigensolution_F64 eigsols[MAX_NUM_ANGULAR_MOMENTA];
U32 num_eigsols;
// Problem matrices. Since we can perform the "mass" integral once we call that
// "base", and similarly we can compute the integral for the l-dependent part once,
// and call that H_l_base. Then we can add whatever numerical factors we want on the
// base matrices, and finally combine them.
Mat_F64 H_base;
Mat_F64 H;
Mat_F64 H_l_base;
Mat_F64 H_l;
// Our problem is Hc = EBc, but we want to solve B^-1Hc = Ec,
// so we invert the B matrix and compute the product A = B^-1H before calling
// zgeev for Ac = Ec
Mat_F64 B_inv;
Mat_F64 A;
};
//~ Base math and utility functions
// Mat_F64 functions
function inline U32 mat_get_col_major_idx(U32 i, U32 j, U32 size1);
function inline U32 mat_ij_to_index(U32 i, U32 j, U32 size1);
function Mat_F64 mat_F64(Arena* arena, U32 size1, U32 size2);
function inline void mat_F64_set(Mat_F64 *mat, U32 i, U32 j, F64 val);
function inline F64 mat_F64_get(Mat_F64 *mat, U32 i, U32 j);
@ -108,8 +119,10 @@ function void compute_wf_norm_F64(F64 *coeffs, U64 coeff_size, U64 n, U64 l);
// Problem
function Problem problem_create();
function void set_up_first_matrices(Problem *problem, Mat_F64 *H,
Mat_F64 *H_l, Mat_F64 *B_inv);
function void set_up_base_matrices(Problem *problem,
Mat_F64 *H,
Mat_F64 *H_l,
Mat_F64 *B_inv);
function void hf_main();

13
src/hf/hf_bsplines_and_grid.c
View File

@ -121,31 +121,36 @@ set_up_bspline_context(Arena* arena)
{
// Create knotpoint sequence.
U32 k = 4;
U32 bspl_N = 40;
U32 bspl_N = BSPLINES_NUM;
g_bspline_ctx->order = k;
g_bspline_ctx->num_knotpoints = bspl_N;
g_bspline_ctx->num_bsplines = bspl_N-k;
g_bspline_ctx->num_phys_points = bspl_N-(2*k)+2; // Remove k points at each end, and then add back the first and last points.
g_bspline_ctx->num_phys_points = bspl_N-(2*k)+2; // Remove k points at each end,
// and then add back
// the first and last points.
g_bspline_ctx->arena = arena;
g_bspline_ctx->knotpoints = PushArray(arena, F64, g_bspline_ctx->num_knotpoints);
// Set up physical points;
F64 delta = (g_grid->end-g_grid->start)/(g_bspline_ctx->num_phys_points-1);
// Set ghost points including first physical
U32 first_phys_index = k-1;
U32 phys_point_last_index = g_bspline_ctx->num_phys_points + k-1;
for(U32 i = 0; i < k; i++)
for(U32 i = 0; i <= first_phys_index; i++)
{
g_bspline_ctx->knotpoints[i] = g_grid->start;
}
g_bspline_ctx->first_phys_index = first_phys_index;
for(U32 i = k; i < phys_point_last_index; i++)
{
g_bspline_ctx->knotpoints[i] = g_bspline_ctx->knotpoints[i-1] + delta;
}
// Set the last points
// Set the last points. including last physical point
F64 last_physical = g_grid->end;
for(U32 i = phys_point_last_index; i < g_bspline_ctx->num_knotpoints; i++)
{
g_bspline_ctx->knotpoints[i] = last_physical;
}
g_bspline_ctx->last_phys_index = phys_point_last_index;
}
function void

10
src/hf/hf_bsplines_and_grid.h
View File

@ -3,8 +3,12 @@
// coordinates in Bohr radii
#define GRID_START_POINT 0.0
#define GRID_END_POINT 40.0
#define GRID_NUM_STEPS 300
#define GRID_END_POINT 300.0
#define GRID_NUM_STEPS 100 // Just for plotting/writing,
// else we stick to knotpts and quadrature
#define BSPLINES_NUM 2000
typedef struct Grid Grid;
struct Grid
@ -24,6 +28,8 @@ struct BSplineCtx
U32 num_knotpoints;
U32 num_bsplines;
U32 num_phys_points;
U32 first_phys_index;
U32 last_phys_index;
F64 *bsplines_grid; // In grid points
F64 *dBsplines_grid; // First deriv in grid points
F64 *bsplines; // In knotpoints

4
src/main.c
View File

@ -39,6 +39,6 @@ function void EntryPoint(void) {
OS_InitGfxReceipt os_gfx_receipt = OS_gfx_init(os_receipt);
// Main program
hf_main();
//hf_main();
hf_coulomb_integrals_test();
}