diff --git a/out/bspline0.dat b/out/bspline0.dat index 80a4923..22d9708 100644 --- a/out/bspline0.dat +++ b/out/bspline0.dat @@ -1,9 +1,9 @@ 1.000000e+00 - 5.717870e-01 - 2.874960e-01 - 1.176490e-01 - 3.276800e-02 - 3.375000e-03 + 3.007630e-01 + 3.930400e-02 + 1.000000e-06 + 0.000000e+00 + 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 diff --git a/out/bspline1.dat b/out/bspline1.dat index 7502b2a..318e80c 100644 --- a/out/bspline1.dat +++ b/out/bspline1.dat @@ -1,15 +1,15 @@ 0.000000e+00 - 3.885478e-01 - 5.685820e-01 - 5.916892e-01 - 5.094560e-01 - 3.734688e-01 - 2.352980e-01 - 1.328603e-01 - 6.553600e-02 - 2.595575e-02 - 6.750000e-03 - 5.492500e-04 + 5.628398e-01 + 5.229180e-01 + 2.575732e-01 + 7.860800e-02 + 1.071875e-02 + 2.000000e-06 + 0.000000e+00 + 0.000000e+00 + 0.000000e+00 + 0.000000e+00 + 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 diff --git a/out/bspline2.dat b/out/bspline2.dat index 02dcf51..515563c 100644 --- a/out/bspline2.dat +++ b/out/bspline2.dat @@ -1,21 +1,21 @@ 0.000000e+00 - 3.884642e-02 - 1.373713e-01 - 2.685532e-01 - 4.053707e-01 - 5.208021e-01 - 5.878380e-01 - 5.897094e-01 - 5.385493e-01 - 4.515533e-01 - 3.459167e-01 - 2.388351e-01 - 1.474560e-01 - 8.217317e-02 - 3.972133e-02 - 1.518750e-02 - 3.658667e-03 - 2.218333e-04 + 1.304078e-01 + 3.898620e-01 + 5.807092e-01 + 5.544480e-01 + 3.779063e-01 + 1.768620e-01 + 5.475150e-02 + 7.776000e-03 + 4.500000e-06 + 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 diff --git a/out/bspline3.dat b/out/bspline3.dat index f3457db..5db3571 100644 --- a/out/bspline3.dat +++ b/out/bspline3.dat @@ -1,27 +1,27 @@ 0.000000e+00 - 8.188333e-04 - 6.550667e-03 - 2.210850e-02 - 5.240533e-02 - 1.023542e-01 - 1.768627e-01 - 2.762872e-01 + 5.989500e-03 + 4.791600e-02 + 1.617165e-01 + 3.614827e-01 + 5.656042e-01 + 6.662707e-01 + 5.854622e-01 3.881387e-01 - 4.976782e-01 - 5.901667e-01 - 6.508652e-01 - 6.650987e-01 - 6.271972e-01 - 5.497027e-01 - 4.473542e-01 - 3.348907e-01 - 2.270512e-01 - 1.384307e-01 - 7.608883e-02 - 3.600000e-02 - 1.325117e-02 - 2.929333e-03 - 1.215000e-04 + 1.821032e-01 + 5.716667e-02 + 8.442167e-03 + 1.066667e-05 + 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 diff --git a/out/bspline9.dat b/out/bspline9.dat index 43c64c2..fe18c58 100644 --- a/out/bspline9.dat +++ b/out/bspline9.dat @@ -17,6 +17,29 @@ 0.000000e+00 0.000000e+00 0.000000e+00 + 3.280500e-03 + 3.600000e-02 + 1.340595e-01 + 3.216787e-01 + 5.330272e-01 + 6.605227e-01 + 6.119792e-01 + 4.278227e-01 + 2.153522e-01 + 7.316267e-02 + 1.325117e-02 + 1.666667e-04 + 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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0.000000e+00 0.000000e+00 -9.900000e+00 9.900000e+00 diff --git a/out/dBspline0.dat b/out/dBspline0.dat index 76a71f4..f50c6c4 100644 --- a/out/dBspline0.dat +++ b/out/dBspline0.dat @@ -1,9 +1,9 @@ --5.100000e+00 --3.513390e+00 --2.221560e+00 --1.224510e+00 --5.222400e-01 --1.147500e-01 +-9.900000e+00 +-4.444110e+00 +-1.144440e+00 +-9.900000e-04 + 0.000000e+00 + 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 diff --git a/out/dBspline1.dat b/out/dBspline1.dat index b43890e..33f7b47 100644 --- a/out/dBspline1.dat +++ b/out/dBspline1.dat @@ -1,15 +1,15 @@ - 5.100000e+00 - 2.756933e+00 - 9.297300e-01 --3.816075e-01 --1.177080e+00 --1.456687e+00 --1.224510e+00 --8.365275e-01 --5.222400e-01 --2.816475e-01 --1.147500e-01 --2.154750e-02 + 9.900000e+00 + 1.985693e+00 +-2.155230e+00 +-2.522767e+00 +-1.144440e+00 +-3.031875e-01 +-9.900000e-04 + 0.000000e+00 + 0.000000e+00 + 0.000000e+00 + 0.000000e+00 + 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 diff --git a/out/dBspline2.dat b/out/dBspline2.dat index af7f61b..cc84627 100644 --- a/out/dBspline2.dat +++ b/out/dBspline2.dat @@ -1,21 +1,21 @@ 0.000000e+00 - 7.318925e-01 - 1.193570e+00 - 1.385033e+00 - 1.306280e+00 - 9.573125e-01 - 3.411900e-01 --2.751025e-01 --7.194400e-01 --9.918225e-01 --1.092250e+00 --1.020723e+00 --7.833600e-01 --5.304850e-01 --3.267400e-01 --1.721250e-01 --6.664000e-02 --1.028500e-02 + 2.278733e+00 + 2.580930e+00 + 9.065925e-01 +-1.223640e+00 +-2.097562e+00 +-1.713690e+00 +-7.855650e-01 +-2.138400e-01 +-1.485000e-03 + 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 diff --git a/out/dBspline3.dat b/out/dBspline3.dat index 15af4bd..3f18315 100644 --- a/out/dBspline3.dat +++ b/out/dBspline3.dat @@ -1,27 +1,27 @@ 0.000000e+00 - 2.456500e-02 - 9.826000e-02 - 2.210850e-01 - 3.930400e-01 - 6.141250e-01 - 8.829800e-01 - 1.080945e+00 - 1.131520e+00 - 1.034705e+00 - 7.905000e-01 - 3.989050e-01 --1.319200e-01 --6.015450e-01 --9.237800e-01 --1.098625e+00 --1.126080e+00 --1.006145e+00 --7.510600e-01 --5.039650e-01 --3.060000e-01 --1.571650e-01 --5.746000e-02 --6.885000e-03 + 1.796850e-01 + 7.187400e-01 + 1.617165e+00 + 2.199120e+00 + 1.703625e+00 + 1.300200e-01 +-1.570305e+00 +-2.196480e+00 +-1.744545e+00 +-8.085000e-01 +-2.258850e-01 +-2.640000e-03 + 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 diff --git a/out/dBspline9.dat b/out/dBspline9.dat index c1d5d09..be012df 100644 --- a/out/dBspline9.dat +++ b/out/dBspline9.dat @@ -6,6 +6,29 @@ 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 + 1.202850e-01 + 5.940000e-01 + 1.427085e+00 + 2.173380e+00 + 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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 0.000000e+00 0.000000e+00 0.000000e+00 diff --git a/out/knotpoints.dat b/out/knotpoints.dat index 34ce0ed..02d5aed 100644 --- a/out/knotpoints.dat +++ b/out/knotpoints.dat @@ -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 diff --git a/src/main.c b/src/main.c index dd53945..d1eef77 100644 --- a/src/main.c +++ b/src/main.c @@ -19,6 +19,8 @@ #include "os/os_inc.c" #include "os/os_entry_point.c" +#include + #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 ); */ + +/* } */