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gets -0.5 hartree for hydrogen ground state! need refactor and then check other l and plot wavefunctions

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This commit is contained in:
Anton Ljungdahl 2024-11-02 19:47:23 +01:00
parent b950d90719
commit 7bb3a066b4
16 changed files with 890 additions and 503 deletions
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1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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out/bsplines_knots.dat
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out/dBsplines_knots.dat
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48
out/knotpoints.dat
View File

@ -2,22 +2,38 @@
0.000000e+00
0.000000e+00
0.000000e+00
5.882353e-01
1.176471e+00
1.764706e+00
2.352941e+00
2.941176e+00
3.529412e+00
4.117647e+00
4.705882e+00
5.294118e+00
5.882353e+00
6.470588e+00
7.058824e+00
7.647059e+00
8.235294e+00
8.823529e+00
9.411765e+00
3.030303e-01
6.060606e-01
9.090909e-01
1.212121e+00
1.515152e+00
1.818182e+00
2.121212e+00
2.424242e+00
2.727273e+00
3.030303e+00
3.333333e+00
3.636364e+00
3.939394e+00
4.242424e+00
4.545455e+00
4.848485e+00
5.151515e+00
5.454545e+00
5.757576e+00
6.060606e+00
6.363636e+00
6.666667e+00
6.969697e+00
7.272727e+00
7.575758e+00
7.878788e+00
8.181818e+00
8.484848e+00
8.787879e+00
9.090909e+00
9.393939e+00
9.696970e+00
1.000000e+01
1.000000e+01
1.000000e+01

491
src/main.c
View File

@ -19,6 +19,8 @@
#include "os/os_inc.c"
#include "os/os_entry_point.c"
#include <mkl_cblas.h>
#define grid_file_path_bin "D:\\dev\\hf_again\\out\\grid.bin"
#define grid_file_path "D:\\dev\\hf_again\\out\\grid.dat"
#define knotpoints_file_path "D:\\dev\\hf_again\\out\\knotpoints.dat"
@ -27,6 +29,10 @@
#define bspline_knots_array_file_path "D:\\dev\\hf_again\\out\\bsplines_knots.dat"
#define dBspline_knots_array_file_path "D:\\dev\\hf_again\\out\\dBsplines_knots.dat"
// coordinates in Bohr radii
#define GRID_START_POINT 0.0
#define GRID_END_POINT 10.0
// Complex number with double precision
typedef struct Z64 Z64;
struct Z64
@ -35,6 +41,15 @@ struct Z64
F64 im;
};
typedef struct Mat_F64 Mat_F64;
struct Mat_F64
{
U32 size1;
U32 size2;
F64 **matrix;
F64 *data;
};
typedef struct Grid Grid;
struct Grid
{
@ -93,6 +108,66 @@ global GaussLegendre g_gauss_legendre = {0};
global Arena* g_base_arena = 0;
global U32 g_debug_bspline_matrix = 0;
function Mat_F64
mat_F64(U32 size1, U32 size2)
{
Mat_F64 out = {0};
out.size1 = size1;
out.size2 = size2;
out.matrix = (F64 **)malloc(size1 * sizeof(F64 *));
U64 data_byte_size = size1 * size2 * sizeof(F64);
out.data = (F64 *)malloc(data_byte_size);
MemoryZero(out.data, data_byte_size);
for(U32 i = 0; i < size1; i++)
{
out.matrix[i] = &out.data[i * size2];
}
return out;
}
function void
mat_F64_free(Mat_F64 *mat)
{
free(mat->matrix);
free(mat->data);
mat->size1 = 0;
mat->size2 = 0;
mat->matrix = 0;
mat->data = 0;
}
function inline void
mat_F64_set(Mat_F64 *mat, U32 i, U32 j, F64 val)
{
U32 row = i < mat->size1 ? i : mat->size1-1;
U32 col = j < mat->size2 ? j : mat->size2-1;
mat->matrix[row][col] = val;
return;
}
function inline F64
mat_F64_get(Mat_F64 *mat, U32 i, U32 j)
{
U32 row = i < mat->size1 ? i : mat->size1-1;
U32 col = j < mat->size2 ? j : mat->size2-1;
return mat->matrix[row][col];
}
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);
MemoryCopy(out.data, src->data, data_byte_size);
return out;
}
function void
set_up_gauss_legendre_points(Arena* arena)
{
@ -265,8 +340,8 @@ compute_dBspline_F64(F64 x_coord, U32 index)
function void
set_up_grid(Arena *arena)
{
g_grid.start = 0.0;
g_grid.end = 10.0;
g_grid.start = GRID_START_POINT;
g_grid.end = GRID_END_POINT;
g_grid.num_steps = 100;
g_grid.points = PushArray(arena, F64, g_grid.num_steps);
@ -305,7 +380,7 @@ set_up_bspline_context(Arena* arena)
{
// Create knotpoint sequence.
U32 k = 4;
U32 bspl_N = 24;
U32 bspl_N = 40;
g_bspline_ctx.order = k;
g_bspline_ctx.num_knotpoints = bspl_N;
g_bspline_ctx.num_bsplines = bspl_N-k;
@ -485,77 +560,6 @@ set_up_bsplines_at_points_and_write_matrix_F64(Arena *arena)
num_knotpoints,
num_bsplines,
str8_lit(dBspline_knots_array_file_path));
/**
// Write grid bsplines
{
ArenaTemp scratch = scratch_get(0, 0);
// First line is just the bspline indices.
String8List first_line_list = {0};
StringJoin join = {0};
join.sep = str8_lit("\t\t");
for(U32 i = 0; i < num_bsplines; i++)
{
str8_list_pushf(scratch.arena, &first_line_list, " %i", i);
}
str8_list_push(scratch.arena, &first_line_list, str8_lit("\n"));
String8 first_line = str8_list_join(scratch.arena, first_line_list, &join);
String8List bspline_array_list = {0};
str8_list_push(scratch.arena, &bspline_array_list, first_line);
for(U32 i = 0; i < g_grid.num_steps; i++)
{
String8List row = {0};
for(U32 j = 0; j < num_bsplines; j++)
{
U32 index = g_grid.num_steps * i + j;
F64 bspline_value = g_bspline_ctx.bsplines_grid[index];
str8_list_pushf(scratch.arena, &row, "%13.6e", bspline_value);
}
StringJoin bspl_join = {0};
bspl_join.sep = str8_lit(" ");
bspl_join.post = str8_lit("\n");
String8 row_joined = str8_list_join(scratch.arena, row, &bspl_join);
str8_list_push(scratch.arena, &bspline_array_list, row_joined);
}
write_string_list_to_file(scratch.arena, str8_lit(bspline_grid_array_file_path), &bspline_array_list);
}
// Write knots bsplines
{
ArenaTemp scratch = scratch_get(0, 0);
// First line is just the bspline indices.
String8List first_line_list = {0};
StringJoin join = {0};
join.sep = str8_lit("\t\t");
for(U32 i = 0; i < num_bsplines; i++)
{
str8_list_pushf(scratch.arena, &first_line_list, " %i", i);
}
str8_list_push(scratch.arena, &first_line_list, str8_lit("\n"));
String8 first_line = str8_list_join(scratch.arena, first_line_list, &join);
String8List bspline_array_list = {0};
str8_list_push(scratch.arena, &bspline_array_list, first_line);
for(U32 i = 0; i < num_knotpoints; i++)
{
String8List row = {0};
for(U32 j = 0; j < num_bsplines; j++)
{
U32 index = num_knotpoints * i + j;
F64 bspline_value = g_bspline_ctx.bsplines[index];
str8_list_pushf(scratch.arena, &row, "%13.6e", bspline_value);
}
StringJoin bspl_join = {0};
bspl_join.sep = str8_lit(" ");
bspl_join.post = str8_lit("\n");
String8 row_joined = str8_list_join(scratch.arena, row, &bspl_join);
str8_list_push(scratch.arena, &bspline_array_list, row_joined);
}
write_string_list_to_file(scratch.arena, str8_lit(bspline_knots_array_file_path), &bspline_array_list);
}
**/
}
@ -583,15 +587,61 @@ print_matrix_Z64( char* desc, int m, int n, Z64* a, int lda )
scratch_release(scratch);
}
/* Auxiliary routine: printing a matrix */
function void
print_matrix_F64( char* desc, int m, int n, F64* a, int lda )
{
ArenaTemp scratch = scratch_get(0,0);
int i, j;
String8 newline = str8_lit("\n");
String8 header = str8_pushf(scratch.arena, "\n %s\n", desc );
LOG(header.str);
//printf("\n %s \n", desc);
for( i = 0; i < m; i++ ) {
for( j = 0; j < n; j++ ) {
String8 outstr = str8_pushf(scratch.arena, " %6.2f", a[i+j*lda], a[i+j*lda]);
LOG(outstr.str);
//printf(" (%6.2f,%6.2f)", a[i+j*lda].real, a[i+j*lda].imag );
}
LOG(newline.str);
//printf("\n");
}
scratch_release(scratch);
}
/* Auxiliary routine: printing a matrix */
function void
print_eigenvalues( char* desc, int n, F64* wr, F64* wi)
{
ArenaTemp scratch = scratch_get(0,0);
int i, j;
String8 newline = str8_lit("\n");
String8 header = str8_pushf(scratch.arena, "\n %s\n", desc );
LOG(header.str);
//printf("\n %s \n", desc);
for( j = 0; j < n; j++ ) {
String8 outstr = str8_pushf(scratch.arena, " (%4.5f, %4.5f)\n", wr[j], wi[j]);
LOG(outstr.str);
//printf(" (%6.2f,%6.2f)", a[i+j*lda].real, a[i+j*lda].imag );
}
LOG(newline.str);
//printf("\n");
scratch_release(scratch);
}
typedef F64 (*func_F64)(F64);
function F64
function F64
cos2(F64 x)
{
return cos(x)*cos(x);
}
function F64
function F64
gq_integration(F64 a, F64 b, func_F64 func)
{
@ -657,6 +707,30 @@ test_gauss_legendre()
}
}
function void
print_mat_F64(Mat_F64 *mat)
{
ArenaTemp scratch = scratch_get(0,0);
for(U32 i = 0; i < mat->size1-1; i++)
{
for(U32 j = 0; j < mat->size2-1; j++)
{
F64 val = mat_F64_get(mat, i, j);
//if(val < 1e-15)
//{
//val = 0.0;
//}
String8 out_str = str8_pushf(scratch.arena, " %.4e", val);
LOG(out_str.str);
}
LOG("\n");
}
scratch_release(scratch);
}
function void EntryPoint(void)
@ -684,13 +758,235 @@ function void EntryPoint(void)
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 B = 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:
// H = -0.5*d^2/dr^2 + l(l+1)/(2r^2) - Z/r
{
ArenaTemp scratch = scratch_get(0, 0);
LOG("Setting up matrices.\n");
String8 setuplog = str8_pushf(scratch.arena,
"Num knotpoints: %i, Bspline order k = %i, Matrix size1 = N-k-2 = %i, size2 = %i\n",
N, k, mat_size1, mat_size2);
LOG(setuplog.str);
F64 *t = g_bspline_ctx.knotpoints;
F64 l = 0.0;
F64 Z = 1.0;
// Skipping first bspline
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.
U32 bspl_index_j = j+1;
// This logic assumes 1-indexed bsplines
F64 abs_index_diff = abs((F64)(bspl_index_i+1) - (F64)(bspl_index_j+1));
if(!(abs_index_diff > ((F64)k-1.0)))
{
// We do Gaussian quadrature between each knot point,
// so we need to figure out where to start.
// We start integration in the first shared knotpoint, which is the one of the highest index.
U32 start_knotpoint_index = bspl_index_i < bspl_index_j ?
bspl_index_j : bspl_index_i;
// And we integrate over the next k knotpoints.
U32 end_knotpoint_index = bspl_index_i < bspl_index_j ?
bspl_index_i+k : bspl_index_j+k;
F64 term1 = 0.0;
F64 term2 = 0.0;
F64 term3 = 0.0;
F64 Bmat_term = 0.0;
for(U32 knotpoint_idx = start_knotpoint_index;
knotpoint_idx < end_knotpoint_index;
knotpoint_idx++)
{
F64 a = t[knotpoint_idx];
F64 b = t[knotpoint_idx+1];
F64 prefac = 0.5*(b-a);
// Skip integrating between ghost points
if(prefac > 1e-16)
{
for(U32 gq_i = 0; gq_i < g_gauss_legendre.order; gq_i++)
{
F64 w = g_gauss_legendre.weights[gq_i];
F64 z = g_gauss_legendre.abscissae[gq_i];
F64 r = (z*prefac)+((a+b)*0.5);
F64 term_prefac = (prefac*w);
F64 dB_i = compute_dBspline_F64(r, bspl_index_i);
F64 dB_j = compute_dBspline_F64(r, bspl_index_j);
F64 B_i = compute_bspline_F64(r, bspl_index_i);
F64 B_j = compute_bspline_F64(r, bspl_index_j);
//F64 r_inv = r > 0.0 ? 1.0/r : 0.0;
term1 += term_prefac*dB_i*dB_j;
term2 += term_prefac*B_i*B_j / (r * r);
term3 += term_prefac*B_i*B_j/r;
Bmat_term += term_prefac*B_i*B_j;
}
}
}
F64 term_sum = 0.5*term1 + (0.5*(l*(l+1.0))*term2) + (-Z)*term3;
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, term_sum);
mat_F64_set(&B, i, j, Bmat_term);
//mat_F64_set(&H, i, j, abs_index_diff);
}
//mat_F64_set(&H, i, j, abs_index_diff);
}
LOG("\n");
}
LOG(str8_pushf(scratch.arena, "H.size1=N-k-2=%i, last bspline index=%i \n", H.size1, g_bspline_ctx.num_bsplines-1).str);
scratch_release(scratch);
print_mat_F64(&H);
LOG("\n");
//print_mat_F64(&B);
}
// 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 B_inv = mat_F64_copy(&B);
Mat_F64 A = mat_F64(H.size1, H.size2);
Arena *mkl_arena = m_make_arena();
//print_mat_F64(&B);
LOG("\n");
//print_mat_F64(&B_inv);
// Invert
{
S32 n = B_inv.size1;
S32 lda = n;
S32 info;
S32 *ipiv = (S32*)malloc(n * sizeof(S32));
F64 *work = (F64 *)malloc(n * sizeof(F64));
S32 lwork = n;
dgetrf_(&n, &n, B_inv.data, &lda, ipiv, &info);
dgetri_(&n, B_inv.data, &lda, ipiv, work, &lwork, &info);
//print_mat_F64(&B_inv);
// Test that inverse worked
/* { */
/* Mat_F64 test = mat_F64(B_inv.size1, B_inv.size2); */
/* cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, */
/* n, n, n, 1.0, B_inv.data, n, B.data, n, 1.0, test.data, n); */
/* LOG("\n"); */
/* print_mat_F64(&test); */
/* mat_F64_free(&test); */
/* } */
free(ipiv);
free(work);
}
// 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);
}
// 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 );
}
/* Print eigenvalues */
print_eigenvalues( "Eigenvalues", n, wr, wi );
/* Free workspace */
free( (void*)work );
}
}
function void
test_matrix()
{
Mat_F64 test_mat = mat_F64(5, 5);
{
ArenaTemp scratch = scratch_get(0,0);
for(U32 i = 0; i < test_mat.size1; i++)
{
for(U32 j = 0; j < test_mat.size2; j++)
{
F64 val = i * test_mat.size2 + j;
mat_F64_set(&test_mat, i, j, val);
}
}
for(U32 i = 0; i < test_mat.size1; i++)
{
for(U32 j = 0; j < test_mat.size2; j++)
{
F64 val = mat_F64_get(&test_mat, i, j);
String8 out_str = str8_pushf(scratch.arena, " %2.2f", val);
LOG(out_str.str);
}
LOG("\n");
}
scratch_release(scratch);
}
}
function void mkl_things(void)
@ -784,3 +1080,46 @@ testing_MKL()
test_mkl_dsyevd();
}
/* function void */
/* dgeev_example() */
/* { */
/* /1* Locals *1/ */
/* MKL_INT n = N, lda = LDA, ldvl = LDVL, ldvr = LDVR, info, lwork; */
/* double wkopt; */
/* double* work; */
/* /1* Local arrays *1/ */
/* double wr[N], wi[N], vl[LDVL*N], vr[LDVR*N]; */
/* double a[LDA*N] = { */
/* -1.01, 3.98, 3.30, 4.43, 7.31, */
/* 0.86, 0.53, 8.26, 4.96, -6.43, */
/* -4.60, -7.04, -3.89, -7.66, -6.16, */
/* 3.31, 5.29, 8.20, -7.33, 2.47, */
/* -4.81, 3.55, -1.51, 6.18, 5.58 */
/* }; */
/* /1* Executable statements *1/ */
/* printf( " DGEEV Example Program Results\n" ); */
/* /1* Query and allocate the optimal workspace *1/ */
/* lwork = -1; */
/* dgeev( "Vectors", "Vectors", &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, */
/* &wkopt, &lwork, &info ); */
/* lwork = (MKL_INT)wkopt; */
/* work = (double*)malloc( lwork*sizeof(double) ); */
/* /1* Solve eigenproblem *1/ */
/* dgeev( "Vectors", "Vectors", &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, */
/* work, &lwork, &info ); */
/* /1* Check for convergence *1/ */
/* if( info > 0 ) { */
/* printf( "The algorithm failed to compute eigenvalues.\n" ); */
/* exit( 1 ); */
/* } */
/* /1* Print eigenvalues *1/ */
/* print_eigenvalues( "Eigenvalues", n, wr, wi ); */
/* /1* Print left eigenvectors *1/ */
/* print_eigenvectors( "Left eigenvectors", n, wi, vl, ldvl ); */
/* /1* Print right eigenvectors *1/ */
/* print_eigenvectors( "Right eigenvectors", n, wi, vr, ldvr ); */
/* /1* Free workspace *1/ */
/* free( (void*)work ); */
/* } */