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more eigenvectors and some refactoring

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Anton Ljungdahl 2024-11-12 12:56:55 +01:00
parent 1ae83767ff
commit 519a5c1dd0
37 changed files with 3600 additions and 492 deletions
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out/bsplines_grid.dat
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6
out/bsplines_knots.dat
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7.303793e-02
2.480886e-02

34
out/eigvec_n5_l1.dat Normal file
View File

@ -0,0 +1,34 @@
-1.682028e-02
-6.591512e-02
-1.491203e-01
-1.764547e-01
-1.368580e-01
-4.961758e-02
5.416827e-02
1.455414e-01
2.042909e-01
2.208419e-01
1.953490e-01
1.353609e-01
5.298347e-02
-3.786093e-02
-1.237346e-01
-1.933820e-01
-2.387867e-01
-2.556333e-01
-2.432683e-01
-2.042800e-01
-1.438204e-01
-6.878683e-02
1.303469e-02
9.378116e-02
1.662185e-01
2.243006e-01
2.635604e-01
2.813280e-01
2.767849e-01
2.508730e-01
2.060847e-01
1.461643e-01
6.806116e-02
2.307003e-02

BIN
out/grid.bin
View File

Binary file not shown.

378
out/grid.dat
View File

@ -1,100 +1,300 @@
0.000000e+00
1.300000e-01
2.600000e-01
3.900000e-01
5.200000e-01
6.500000e-01
7.800000e-01
9.100000e-01
1.040000e+00
1.170000e+00
1.000000e-01
2.000000e-01
3.000000e-01
4.000000e-01
5.000000e-01
6.000000e-01
7.000000e-01
8.000000e-01
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1.430000e+00
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2.210000e+00
2.340000e+00
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1.400000e+00
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2.000000e+00
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2.140000e+01
2.150000e+01
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2.180000e+01
2.190000e+01
2.200000e+01
2.210000e+01
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2.230000e+01
2.240000e+01
2.250000e+01
2.260000e+01
2.270000e+01
2.280000e+01
2.290000e+01
2.300000e+01
2.310000e+01
2.320000e+01
2.330000e+01
2.340000e+01
2.350000e+01
2.360000e+01
2.370000e+01
2.380000e+01
2.390000e+01
2.400000e+01
2.410000e+01
2.420000e+01
2.430000e+01
2.440000e+01
2.450000e+01
2.460000e+01
2.470000e+01
2.480000e+01
2.490000e+01
2.500000e+01
2.510000e+01
2.520000e+01
2.530000e+01
2.540000e+01
2.550000e+01
2.560000e+01
2.570000e+01
2.580000e+01
2.590000e+01
2.600000e+01
2.610000e+01
2.620000e+01
2.630000e+01
2.640000e+01
2.650000e+01
2.660000e+01
2.670000e+01
2.680000e+01
2.690000e+01
2.700000e+01
2.710000e+01
2.720000e+01
2.730000e+01
2.740000e+01
2.750000e+01
2.760000e+01
2.770000e+01
2.780000e+01
2.790000e+01
2.800000e+01
2.810000e+01
2.820000e+01
2.830000e+01
2.840000e+01
2.850000e+01
2.860000e+01
2.870000e+01
2.880000e+01
2.890000e+01
2.900000e+01
2.910000e+01
2.920000e+01
2.930000e+01
2.940000e+01
2.950000e+01
2.960000e+01
2.970000e+01
2.980000e+01
3.000000e+01

34
out/ground_state_coeffs.dat
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@ -1,34 +0,0 @@
1.133340e-01
2.694214e-01
4.439444e-01
4.595803e-01
4.179690e-01
3.547308e-01
2.883617e-01
2.276047e-01
1.758416e-01
1.336568e-01
1.003007e-01
7.449632e-02
5.486226e-02
4.011609e-02
2.915634e-02
2.108062e-02
1.517274e-02
1.087716e-02
7.770252e-03
5.533336e-03
3.929222e-03
2.782933e-03
1.966331e-03
1.386158e-03
9.748959e-04
6.838729e-04
4.781267e-04
3.326017e-04
2.293545e-04
1.555076e-04
1.017495e-04
6.122882e-05
2.593097e-05
8.380605e-06

70
out/knotpoints.dat
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@ -2,39 +2,39 @@
0.000000e+00
0.000000e+00
0.000000e+00
3.939394e-01
7.878788e-01
1.181818e+00
1.575758e+00
1.969697e+00
2.363636e+00
2.757576e+00
3.151515e+00
3.545455e+00
3.939394e+00
4.333333e+00
4.727273e+00
5.121212e+00
5.515152e+00
5.909091e+00
6.303030e+00
6.696970e+00
7.090909e+00
7.484848e+00
7.878788e+00
8.272727e+00
8.666667e+00
9.060606e+00
9.454545e+00
9.848485e+00
1.024242e+01
1.063636e+01
1.103030e+01
1.142424e+01
9.090909e-01
1.818182e+00
2.727273e+00
3.636364e+00
4.545455e+00
5.454545e+00
6.363636e+00
7.272727e+00
8.181818e+00
9.090909e+00
1.000000e+01
1.090909e+01
1.181818e+01
1.221212e+01
1.260606e+01
1.300000e+01
1.300000e+01
1.300000e+01
1.300000e+01
1.272727e+01
1.363636e+01
1.454545e+01
1.545455e+01
1.636364e+01
1.727273e+01
1.818182e+01
1.909091e+01
2.000000e+01
2.090909e+01
2.181818e+01
2.272727e+01
2.363636e+01
2.454545e+01
2.545455e+01
2.636364e+01
2.727273e+01
2.818182e+01
2.909091e+01
3.000000e+01
3.000000e+01
3.000000e+01
3.000000e+01

2
src/hf/bsplines_and_grid.c
View File

@ -74,7 +74,7 @@ set_up_grid(Arena *arena)
{
g_grid.start = GRID_START_POINT;
g_grid.end = GRID_END_POINT;
g_grid.num_steps = 100;
g_grid.num_steps = GRID_NUM_STEPS;
g_grid.points = PushArray(arena, F64, g_grid.num_steps);
F64 step_size = (g_grid.end-g_grid.start)/(F64)g_grid.num_steps;

5
src/hf/bsplines_and_grid.h
View File

@ -3,7 +3,8 @@
// coordinates in Bohr radii
#define GRID_START_POINT 0.0
#define GRID_END_POINT 10.0
#define GRID_END_POINT 30.0
#define GRID_NUM_STEPS 300
typedef struct Grid Grid;
struct Grid
@ -29,8 +30,6 @@ struct BSplineCtx
F64 *dBsplines; // First deriv in knotpoints
};
function void set_up_grid(Arena *arena);
//~ Bspline functions
function F64 bspline_recursion(F64 x, U32 k, U32 i);

10
src/hf/file_io.c
View File

@ -22,6 +22,7 @@ write_array_binary_F64(String8 path_to_file, F64 *values, U32 array_size)
join.post = str8_lit("\n");
String8 log_msg = str8_list_join(scratch.arena, log_list, &join);
LOG(log_msg.str);
scratch_release(scratch);
}
OS_file_close(file_handle);
}
@ -60,4 +61,13 @@ write_array_F64(String8 path_to_file, F64 *values, U32 array_size, char* fmt)
str8_list_pushf(scratch.arena, &list, fmt, values[i]);
}
write_string_list_to_file(scratch.arena, path_to_file, &list);
scratch_release(scratch);
}
function String8
get_eigenvector_filename(Arena *arena, U32 energy_idx, U32 angular_momentum_idx)
{
String8 out = str8_pushf(arena, "D:\\dev\\hf_again\\out\\eigvec_n%i_l%i.dat", energy_idx, angular_momentum_idx);
return out;
}

1
src/hf/file_io.h
View File

@ -13,5 +13,6 @@
function void write_string_list_to_file(Arena *arena, String8 path, String8List *list);
function void write_array_F64(String8 path_to_file, F64 *values, U32 array_size, char* fmt);
function void write_array_binary_F64(String8 path_to_file, F64 *values, U32 array_size);
function String8 get_eigenvector_filename(Arena *arena, U32 energy_index, U32 angular_momentum_idx);
#endif /* FILE_IO_H */

15
src/hf/hf_base.c
View File

@ -74,11 +74,24 @@ function Mat_F64
mat_F64_copy(Mat_F64 *src)
{
Mat_F64 out = mat_F64(src->size1, src->size2);
U32 data_byte_size = src->size1 * src->size2 * sizeof(F64);
U64 data_byte_size = src->size1 * src->size2 * sizeof(F64);
MemoryCopy(out.data, src->data, data_byte_size);
return out;
}
function void
mat_F64_copy_to_dst(Mat_F64 *dst, Mat_F64 *src)
{
U64 data_byte_size = src->size1 * src->size2 * sizeof(F64);
MemoryCopy(dst->data, src->data, data_byte_size);
}
function void
mat_F64_zero(Mat_F64 *mat)
{
MemoryZero(mat->data, mat->size1 * mat->size2 * sizeof(F64));
}
function void
set_up_gauss_legendre_points(Arena* arena)

254
src/main.c
View File

@ -31,12 +31,23 @@
#include "hf/tests.c"
typedef struct Eigensolution_F64 Eigensolution_F64;
struct Eigensolution_F64
{
F64 *eigenvalues_re;
F64 *eigenvalues_im;
Mat_F64 right_eigenvectors;
Mat_F64 left_eigenvectors;
};
typedef struct Orbital Orbital;
struct Orbital
{
U32 n;
U32 l;
U32 j;
Eigensolution_F64 eigensolution;
};
@ -54,18 +65,11 @@ struct SortPair_F64
U64 original_index;
};
typedef struct Eigensolution_F64 Eigensolution_F64;
struct Eigensolution_F64
{
F64 *eigenvalues_re;
F64 *eigenvalues_im;
Mat_F64 right_eigenvectors;
Mat_F64 left_eigenvectors;
};
global Arena* g_base_arena = 0;
global Arena* g_filename_arena = 0;
#define NUM_ANGULAR_MOMENTA 3
global F64 angular_momenta[NUM_ANGULAR_MOMENTA] = {0.0, 1.0, 2.0};
U64 qsort_partition_F64(SortPair_F64 *array, U64 size, U64 low, U64 high)
{
@ -164,39 +168,8 @@ print_eigenvalues( char* desc, int n, F64* wr, F64* wi)
scratch_release(scratch);
}
function void EntryPoint(void)
function void set_up_first_matrices(Mat_F64 *H, Mat_F64 *H_l, Mat_F64 *B_inv)
{
OS_InitReceipt os_receipt = OS_init();
OS_InitGfxReceipt os_gfx_receipt = OS_gfx_init(os_receipt);
g_base_arena = m_make_arena();
set_up_gauss_legendre_points(g_base_arena);
//- Set up grid and write to file.
set_up_grid(g_base_arena);
write_array_binary_F64(str8_lit(grid_file_path_bin), g_grid.points, g_grid.num_steps);
write_array_F64(str8_lit(grid_file_path), g_grid.points, g_grid.num_steps, "%13.6e\n");
//- The BSpline context is the knotpoints and the BSpline order etc.
set_up_bspline_context(g_base_arena);
write_array_F64(str8_lit(knotpoints_file_path),
g_bspline_ctx.knotpoints, g_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(g_base_arena);
U32 N = g_bspline_ctx.num_knotpoints;
U32 k = g_bspline_ctx.order;
U32 mat_size1 = N - k - 2;
U32 mat_size2 = mat_size1;
Mat_F64 H = mat_F64(mat_size1, mat_size2);
Mat_F64 H_l = mat_F64(mat_size1, mat_size2);
// This will be the inverse of B, but to start with we construct B.
Mat_F64 B_inv = mat_F64(mat_size1, mat_size2);
// 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:
@ -213,14 +186,13 @@ function void EntryPoint(void)
/* } */
F64 *t = g_bspline_ctx.knotpoints;
F64 l = 0.0;
F64 Z = 1.0;
U32 k = g_bspline_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++)
for(U32 j = 0; j < H->size2; j++)
{
U32 bspl_index_i = i+1; // The second Bspline has index 1 in our array etc.
U32 bspl_index_j = j+1;
@ -277,9 +249,9 @@ function void EntryPoint(void)
/* String8 debug = str8_pushf(scratch.arena, "(i=%i,j=%i,t_i=%4.4f,t_i=%4.4f,term1=%.4e,term2=%.4e,term3=%.4e,term_sum=%.4e) \n", */
/* bspl_index_i, bspl_index_j, t[bspl_index_i+k-1],t[bspl_index_j+k-1],term1,term2,term3,term_sum); */
/* LOG(debug.str); */
mat_F64_set(&H, i, j, H_term_sum);
mat_F64_set(&H_l, i, j, H_l_term);
mat_F64_set(&B_inv, i, j, Bmat_term);
mat_F64_set(H, i, j, H_term_sum);
mat_F64_set(H_l, i, j, H_l_term);
mat_F64_set(B_inv, i, j, Bmat_term);
//mat_F64_set(&H, i, j, abs_index_diff);
}
//mat_F64_set(&H, i, j, abs_index_diff);
@ -293,71 +265,149 @@ function void EntryPoint(void)
//LOG("\n");
//print_mat_F64(&B);
}
}
Arena *mkl_arena = m_make_arena();
function void
EntryPoint(void)
{
OS_InitReceipt os_receipt = OS_init();
OS_InitGfxReceipt os_gfx_receipt = OS_gfx_init(os_receipt);
g_filename_arena = m_make_arena_reserve(Megabytes(2));
g_base_arena = m_make_arena();
set_up_gauss_legendre_points(g_base_arena);
//- Set up grid and write to file.
set_up_grid(g_base_arena);
write_array_binary_F64(str8_lit(grid_file_path_bin), g_grid.points, g_grid.num_steps);
write_array_F64(str8_lit(grid_file_path), g_grid.points, g_grid.num_steps, "%13.6e\n");
//- The BSpline context is the knotpoints and the BSpline order etc.
set_up_bspline_context(g_base_arena);
write_array_F64(str8_lit(knotpoints_file_path),
g_bspline_ctx.knotpoints, g_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(g_base_arena);
U32 N = g_bspline_ctx.num_knotpoints;
U32 k = g_bspline_ctx.order;
U32 mat_size1 = N - k - 2;
U32 mat_size2 = mat_size1;
Mat_F64 H_base = mat_F64(mat_size1, mat_size2);
Mat_F64 H_l_base = mat_F64(mat_size1, mat_size2);
Mat_F64 H_l = mat_F64(mat_size1, mat_size2);
Mat_F64 H = mat_F64(mat_size1, mat_size2);
// This will be the inverse of B, but to start with we construct B.
Mat_F64 B_inv = mat_F64(mat_size1, mat_size2);
// A is the actual matrix for each eigenvalue problem.
Mat_F64 A = mat_F64(H.size1, H.size2);
set_up_first_matrices(&H_base, &H_l_base, &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_F64 A = mat_F64(H.size1, H.size2);
mat_invert_F64(&B_inv);
// Multiply to get A = B^-1 H
// For each angular momentum
for(U32 ang_mom_idx = 0; ang_mom_idx < NUM_ANGULAR_MOMENTA; ang_mom_idx++)
{
S32 n = A.size1;
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
n, n, n, 1.0, B_inv.data, n, H.data, n, 0.0, A.data, n);
LOG("Matrix A: \n");
print_mat_F64(&A);
}
Eigensolution_F64 eigensolution = {0};
// Solve generalised eigenvalue problem
{
S32 n = A.size1;
S32 lda = n;
S32 ldvl = n;
S32 ldvr = n;
S32 info;
S32 lwork;
F64 wkopt;
F64 *work;
F64 *wr = PushArray(mkl_arena, F64, n);
F64 *wi = PushArray(mkl_arena, F64, n);
F64 *vl = PushArray(mkl_arena, F64, ldvl*n);
F64 *vr = PushArray(mkl_arena, F64, ldvr*n);
lwork = -1;
F64 *a = A.data;
dgeev("Vectors", "Vectors", &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr,
&wkopt, &lwork, &info);
lwork = (S32)wkopt;
work = (F64 *)malloc(lwork * sizeof(F64) );
dgeev("Vectors", "Vectors", &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr,
work, &lwork, &info);
if(info > 0)
{
LOG("Failed to compute eigenvalues in dgeev\n");
exit( 1 );
mat_F64_copy_to_dst(&H, &H_base);
F64 l = angular_momenta[ang_mom_idx];
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);
// Multiply l(l+1)
cblas_dscal(mat_size, l_factor, H_l.data, 1);
// Add H = H_base + H_l
cblas_daxpy(mat_size, 1.0, H_l.data, 1, H.data, 1);
}
eigensolution.right_eigenvectors = mat_F64_from_data(ldvr, n, vr);
print_eigenvalues( "Eigenvalues unsorted:", n, wr, wi );
U64 *sorted_indices = PushArray(mkl_arena, U64, n);
sort_and_get_indices_F64(wr, sorted_indices, n);
sort_by_indices_F64(wi, sorted_indices, n);
print_eigenvalues( "Eigenvalues sorted: ", n, wr, wi );
// Multiply to get A = B^-1 H
{
S32 n = A.size1;
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
n, n, n, 1.0, B_inv.data, n, H.data, n, 0.0, A.data, n);
LOG("Matrix A: \n");
print_mat_F64(&A);
}
U64 lowest_energy_index = sorted_indices[0];
write_array_F64(str8_lit("D:\\dev\\hf_again\\out\\ground_state_coeffs.dat"), eigensolution.right_eigenvectors.matrix[lowest_energy_index], n, "%13.6e\n");
// This arena is used to push results from f. ex eigenvalue computations.
Arena *mkl_arena = m_make_arena();
Eigensolution_F64 eigensolution = {0};
// Solve generalised eigenvalue problem
{
S32 size1 = A.size1;
S32 lda = size1;
S32 ldvl = size1;
S32 ldvr = size1;
S32 info;
S32 lwork;
free( (void*)work );
F64 wkopt;
F64 *work;
F64 *wr = PushArray(mkl_arena, F64, size1);
F64 *wi = PushArray(mkl_arena, F64, size1);
F64 *vl = PushArray(mkl_arena, F64, ldvl*size1);
F64 *vr = PushArray(mkl_arena, F64, ldvr*size1);
lwork = -1;
F64 *a = A.data;
dgeev("Vectors", "Vectors", &size1, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr,
&wkopt, &lwork, &info);
lwork = (S32)wkopt;
work = (F64 *)malloc(lwork * sizeof(F64) );
dgeev("Vectors", "Vectors", &size1, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr,
work, &lwork, &info);
if(info > 0)
{
LOG("Failed to compute eigenvalues in dgeev\n");
exit( 1 );
}
eigensolution.right_eigenvectors = mat_F64_from_data(ldvr, size1, vr);
U64 *sorted_indices = PushArray(mkl_arena, U64, size1);
sort_and_get_indices_F64(wr, sorted_indices, size1);
sort_by_indices_F64(wi, sorted_indices, size1);
print_eigenvalues( "Eigenvalues sorted: ", size1, wr, wi );
U32 i = 0;
F64 energy = -1000.0;
U32 counter = 0;
while(energy < 0.0)
{
energy = wr[i];
U64 energy_index = sorted_indices[i];
U64 n = 1 + i;
if(ang_mom_idx > 0)
{
n = 2 + i;
}
write_array_F64(get_eigenvector_filename(g_filename_arena, n, ang_mom_idx),
eigensolution.right_eigenvectors.matrix[energy_index], size1, "%13.6e\n");
i += 1;
counter += 1;
if(counter > 10)
{
break;
}
}
free( (void*)work );
}
}
}