compute jordan projection for triangle rotation group
This commit is contained in:
Florian Stecker
commit
0c07494110
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@ -0,0 +1,25 @@
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HEADERS=triangle.h linalg.h queue.h
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#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
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#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
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SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
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#SPECIAL_OPTIONS=
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OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
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all: singular_values
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singular_values: singular_values.o triangle.o linalg.o
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gcc $(OPTIONS) -o singular_values triangle.o linalg.o singular_values.o -lm -lgsl -lcblas
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singular_values.o: singular_values.c $(HEADERS)
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gcc $(OPTIONS) -c singular_values.c
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linalg.o: linalg.c $(HEADERS)
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gcc $(OPTIONS) -c linalg.c
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triangle.o: triangle.c $(HEADERS)
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gcc $(OPTIONS) -c triangle.c
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clean:
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rm -f singular_values triangle.o linalg.o singular_values.o
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@ -0,0 +1,353 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_eigen.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_complex_math.h>
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#include <memory.h>
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#include <math.h>
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#include "linalg.h"
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#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
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#define FCMP(x, y) gsl_fcmp(x, y, 1e-10)
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/*********************************************** temporary storage ********************************************************/
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workspace_t *workspace_alloc(int n)
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{
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workspace_t *result = (workspace_t*)malloc(sizeof(workspace_t));
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result->n = n;
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result->work_nonsymmv = gsl_eigen_nonsymmv_alloc(n);
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result->work_symmv = gsl_eigen_symmv_alloc(n);
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result->work_sv = gsl_vector_alloc(n);
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result->eval_complex = gsl_vector_complex_alloc(n);
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result->evec_complex = gsl_matrix_complex_alloc(n, n);
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result->eval_real = gsl_vector_alloc(n);
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result->evec_real = gsl_matrix_alloc(n, n);
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result->permutation = gsl_permutation_alloc(n);
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result->tmp_mat = malloc(MAX_TEMP_MATRICES*sizeof(gsl_matrix*));
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for(int i = 0; i < MAX_TEMP_MATRICES; i++)
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result->tmp_mat[i] = gsl_matrix_alloc(3, 3);
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result->tmp_mat_used = 0;
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result->tmp_vec = malloc(MAX_TEMP_MATRICES*sizeof(gsl_vector*));
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for(int i = 0; i < MAX_TEMP_MATRICES; i++)
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result->tmp_vec[i] = gsl_vector_alloc(3);
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result->tmp_vec_used = 0;
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return result;
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}
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void workspace_free(workspace_t *workspace)
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{
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gsl_eigen_nonsymmv_free(workspace->work_nonsymmv);
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gsl_eigen_symmv_free(workspace->work_symmv);
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gsl_vector_free(workspace->work_sv);
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gsl_vector_complex_free(workspace->eval_complex);
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gsl_matrix_complex_free(workspace->evec_complex);
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gsl_vector_free(workspace->eval_real);
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gsl_matrix_free(workspace->evec_real);
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gsl_permutation_free(workspace->permutation);
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for(int i = 0; i < MAX_TEMP_MATRICES; i++)
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gsl_matrix_free(workspace->tmp_mat[i]);
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free(workspace->tmp_mat);
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for(int i = 0; i < MAX_TEMP_VECTORS; i++)
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gsl_vector_free(workspace->tmp_vec[i]);
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free(workspace->tmp_vec);
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}
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/************************************************** basic operations ********************************************************/
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void invert(gsl_matrix *in, gsl_matrix *out, workspace_t *ws)
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{
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int s;
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, in);
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gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
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gsl_linalg_LU_invert(tmp, ws->permutation, out);
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releaseTempMatrices(ws, 1);
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}
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void solve(gsl_matrix *A, gsl_vector *b, gsl_vector *result, workspace_t *ws)
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{
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int s;
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, A);
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gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
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gsl_linalg_LU_solve(tmp, ws->permutation, b, result);
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releaseTempMatrices(ws, 1);
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}
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void conjugate(gsl_matrix *in, gsl_matrix *conjugator, gsl_matrix *out, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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invert(conjugator, out, ws); // use out to temporarily store inverse conjugator
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, in, out, 0.0, tmp); // in * conjugator^{-1}
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, conjugator, tmp, 0.0, out);
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releaseTempMatrices(ws, 1);
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}
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void multiply(gsl_matrix *a, gsl_matrix *b, gsl_matrix *out)
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{
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, out);
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}
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void multiply_right(gsl_matrix *a, gsl_matrix *b, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, tmp);
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gsl_matrix_memcpy(a, tmp);
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releaseTempMatrices(ws, 1);
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}
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void multiply_left(gsl_matrix *a, gsl_matrix *b, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, tmp);
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gsl_matrix_memcpy(b, tmp);
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releaseTempMatrices(ws, 1);
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}
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void multiply_many(workspace_t *ws, gsl_matrix *out, int n, ...)
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{
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va_list args;
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va_start(args, n);
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gsl_matrix_set_identity(out);
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for(int i = 0; i < n; i++) {
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gsl_matrix *cur = va_arg(args, gsl_matrix *);
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multiply_right(out, cur, ws);
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}
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va_end(args);
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}
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void cartan_calc(gsl_matrix *g, double *mu, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, g);
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gsl_linalg_SV_decomp(tmp, ws->evec_real, ws->eval_real, ws->work_sv);
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for(int i = 0; i < ws->n - 1; i++)
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mu[i] = log(gsl_vector_get(ws->eval_real, i) / gsl_vector_get(ws->eval_real, i+1));
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releaseTempMatrices(ws, 1);
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}
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void initialize(gsl_matrix *g, double *data, int x, int y)
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{
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gsl_matrix_view view = gsl_matrix_view_array(data, x, y);
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gsl_matrix_memcpy(g, &view.matrix);
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}
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void rotation_matrix(gsl_matrix *g, double *vector)
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{
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double normalized[3];
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double norm = sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]);
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for(int i = 0; i < 3; i++)
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normalized[i] = vector[i] / norm;
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gsl_matrix_set_identity(g);
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gsl_matrix_set(g, 0, 0, cos(norm));
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gsl_matrix_set(g, 0, 1, -sin(norm) * normalized[2]);
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gsl_matrix_set(g, 0, 2, +sin(norm) * normalized[1]);
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gsl_matrix_set(g, 1, 0, +sin(norm) * normalized[2]);
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gsl_matrix_set(g, 1, 1, cos(norm));
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gsl_matrix_set(g, 1, 2, -sin(norm) * normalized[0]);
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gsl_matrix_set(g, 2, 0, -sin(norm) * normalized[1]);
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gsl_matrix_set(g, 2, 1, +sin(norm) * normalized[0]);
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gsl_matrix_set(g, 2, 2, cos(norm));
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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g->data[i * g->tda + j] += (1 - cos(norm)) * normalized[i] * normalized[j];
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}
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double trace(gsl_matrix *g)
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{
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return gsl_matrix_get(g, 0, 0) + gsl_matrix_get(g, 1, 1) + gsl_matrix_get(g, 2, 2);
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}
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double determinant(gsl_matrix *g, workspace_t *ws)
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{
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int s;
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double result;
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, g);
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gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
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result = gsl_linalg_LU_det(tmp, s);
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releaseTempMatrices(ws, 1);
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return result;
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}
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int eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
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{
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gsl_matrix *g_ = getTempMatrix(ws);
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int success = 0;
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gsl_matrix_memcpy(g_, g);
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gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
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int r = gsl_eigen_nonsymmv(g_, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
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ERROR(r, "gsl_eigen_nonsymmv failed!\n");
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gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
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int real = 1;
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for(int i = 0; i < ws->n; i++)
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if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, i)), 0) != 0)
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real = 0;
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if(!real)
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goto eigenvectors_out;
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for(int i = 0; i < ws->n; i++)
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for(int j = 0; j < ws->n; j++)
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gsl_matrix_set(evec_real, i, j, GSL_REAL(gsl_matrix_complex_get(ws->evec_complex, i, j)));
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success = 1;
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eigenvectors_out:
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releaseTempMatrices(ws, 1);
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return success;
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}
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// only fills in the real eigenvectors and returns their count
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int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
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{
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gsl_matrix *g_ = getTempMatrix(ws);
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gsl_matrix_memcpy(g_, g);
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gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
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int r = gsl_eigen_nonsymmv(g_, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
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ERROR(r, "gsl_eigen_nonsymmv failed!\n");
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gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
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int real = 0;
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for(int i = 0; i < ws->n; i++) {
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if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, i)), 0) == 0) {// real
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if(evec_real) {
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for(int j = 0; j < ws->n; j++)
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gsl_matrix_set(evec_real, j, real, GSL_REAL(gsl_matrix_complex_get(ws->evec_complex, j, i)));
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}
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real++;
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}
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}
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releaseTempMatrices(ws, 1);
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return real;
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}
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void eigensystem_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws)
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{
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gsl_matrix *g_ = getTempMatrix(ws);
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gsl_matrix_memcpy(g_, g);
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int r = gsl_eigen_symmv (g_, eval, evec, ws->work_symmv);
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ERROR(r, "gsl_eigen_symmv failed!\n");
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gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_ABS_DESC);
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releaseTempMatrices(ws, 1);
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}
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// returns number of positive directions and matrix transforming TO diagonal basis
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int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws)
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{
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gsl_matrix *A_ = getTempMatrix(ws);
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gsl_matrix_memcpy(A_, A);
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int r = gsl_eigen_symmv (A_, ws->eval_real, cob, ws->work_symmv);
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ERROR(r, "gsl_eigen_symmv failed!\n");
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gsl_eigen_symmv_sort(ws->eval_real, cob, GSL_EIGEN_SORT_VAL_ASC);
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gsl_matrix_transpose(cob);
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int positive = 0;
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for(int i = 0; i < ws->n; i++) {
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if(gsl_vector_get(ws->eval_real, i) > 0)
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positive++;
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for(int j = 0; j < ws->n; j++)
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*gsl_matrix_ptr(cob, i, j) *= sqrt(fabs(gsl_vector_get(ws->eval_real, i)));
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}
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releaseTempMatrices(ws, 1);
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return positive;
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}
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// computes a matrix in SL(3, R) which projectively transforms (e1, e2, e3, e1+e2+e3) to the 4 given vectors
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void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_vector *coeff = getTempVector(ws);
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int s;
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double det, scale;
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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gsl_matrix_set(tmp, i, j, gsl_vector_get(vertices[j], i));
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gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
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gsl_linalg_LU_solve(tmp, ws->permutation, vertices[3], coeff);
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det = gsl_linalg_LU_det(tmp, s);
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for(int i = 0; i < 3; i++)
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det *= gsl_vector_get(coeff, i);
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scale = 1/cbrt(det);
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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gsl_matrix_set(result, i, j, scale*gsl_vector_get(vertices[j], i)*gsl_vector_get(coeff, j));
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releaseTempMatrices(ws, 1);
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releaseTempVectors(ws, 1);
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}
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void rotation_frame(gsl_matrix *rotation, gsl_matrix *result, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix *rot_basis = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, rotation);
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gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
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int r = gsl_eigen_nonsymmv(tmp, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
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ERROR(r, "gsl_eigen_nonsymmv failed!\n");
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double arg, minarg = 5; // greater than pi
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int minidx;
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for(int i = 0; i < 3; i++) {
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arg = gsl_complex_arg(gsl_vector_complex_get(ws->eval_complex, i));
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if(abs(arg) < minarg)
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{
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minidx = i;
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minarg = abs(arg);
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}
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}
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ERROR(FCMP(minarg, 0.0) != 0, "rotation_frame() failed! No eigenvalue was 1.\n");
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for(int i = 0; i < 3; i++) {
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gsl_complex x = gsl_matrix_complex_get(ws->evec_complex, i, (minidx+1)%3);
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gsl_complex y = gsl_matrix_complex_get(ws->evec_complex, i, (minidx+2)%3);
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gsl_complex z = gsl_matrix_complex_get(ws->evec_complex, i, minidx);
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gsl_matrix_set(result, i, 0, GSL_REAL(x)+GSL_REAL(y));
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gsl_matrix_set(result, i, 1, GSL_IMAG(x)-GSL_IMAG(y));
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gsl_matrix_set(result, i, 2, GSL_REAL(z));
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}
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releaseTempMatrices(ws, 2);
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}
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@ -0,0 +1,98 @@
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#ifndef LINALG_H
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#define LINALG_H
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#include <stdio.h>
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#include <stdlib.h>
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#include <stdarg.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_eigen.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_linalg.h>
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#include <memory.h>
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#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
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#define FCMP(x, y) gsl_fcmp(x, y, 1e-10)
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#define MAX_TEMP_MATRICES 10
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#define MAX_TEMP_VECTORS 10
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typedef struct _workspace {
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int n;
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gsl_eigen_nonsymmv_workspace *work_nonsymmv;
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gsl_eigen_symmv_workspace *work_symmv;
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gsl_vector *work_sv;
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gsl_vector_complex *eval_complex;
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gsl_matrix_complex *evec_complex;
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gsl_vector *eval_real;
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gsl_matrix *evec_real;
|
||||
gsl_permutation *permutation;
|
||||
|
||||
gsl_matrix **tmp_mat;
|
||||
int tmp_mat_used;
|
||||
gsl_vector **tmp_vec;
|
||||
int tmp_vec_used;
|
||||
} workspace_t;
|
||||
|
||||
workspace_t *workspace_alloc(int n);
|
||||
void workspace_free(workspace_t *workspace);
|
||||
void solve(gsl_matrix *A, gsl_vector *b, gsl_vector *result, workspace_t *ws);
|
||||
void invert(gsl_matrix *in, gsl_matrix *out, workspace_t *ws);
|
||||
void conjugate(gsl_matrix *in, gsl_matrix *conjugator, gsl_matrix *out, workspace_t *ws);
|
||||
void multiply(gsl_matrix *a, gsl_matrix *b, gsl_matrix *out);
|
||||
void multiply_right(gsl_matrix *a, gsl_matrix *b, workspace_t *ws);
|
||||
void multiply_left(gsl_matrix *a, gsl_matrix *b, workspace_t *ws);
|
||||
void multiply_many(workspace_t *ws, gsl_matrix *out, int n, ...);
|
||||
void cartan_calc(gsl_matrix *g, double *mu, workspace_t *ws);
|
||||
void initialize(gsl_matrix *g, double *data, int x, int y);
|
||||
void rotation_matrix(gsl_matrix *g, double *vector);
|
||||
int jordan_calc(gsl_matrix *g, double *mu, workspace_t *ws);
|
||||
double trace(gsl_matrix *g);
|
||||
double determinant(gsl_matrix *g, workspace_t *ws);
|
||||
int eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
|
||||
int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
|
||||
void eigenvectors_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws);
|
||||
int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws);
|
||||
void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws);
|
||||
void rotation_frame(gsl_matrix *rotation, gsl_matrix *result, workspace_t *ws);
|
||||
|
||||
// matrix allocation stuff
|
||||
|
||||
static gsl_matrix **getTempMatrices(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_mat_used + n > MAX_TEMP_MATRICES, "Ran out of temporary matrices. Consider increasing MAX_TEMP_MATRICES\n");
|
||||
int index = ws->tmp_mat_used;
|
||||
ws->tmp_mat_used += n;
|
||||
return ws->tmp_mat + index;
|
||||
}
|
||||
|
||||
static gsl_matrix *getTempMatrix(workspace_t *ws)
|
||||
{
|
||||
return *getTempMatrices(ws, 1);
|
||||
}
|
||||
|
||||
static void releaseTempMatrices(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_mat_used - n < 0, "Released more matrices then in use\n");
|
||||
ws->tmp_mat_used -= n;
|
||||
}
|
||||
|
||||
static gsl_vector **getTempVectors(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_vec_used + n > MAX_TEMP_VECTORS, "Ran out of temporary vectors. Consider increasing MAX_TEMP_VECTORS\n");
|
||||
int index = ws->tmp_vec_used;
|
||||
ws->tmp_vec_used += n;
|
||||
return ws->tmp_vec + index;
|
||||
}
|
||||
|
||||
static gsl_vector *getTempVector(workspace_t *ws)
|
||||
{
|
||||
return *getTempVectors(ws, 1);
|
||||
}
|
||||
|
||||
static void releaseTempVectors(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_vec_used - n < 0, "Released more vectors then in use\n");
|
||||
ws->tmp_vec_used -= n;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
#ifndef QUEUE_H
|
||||
#define QUEUE_H
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#define QUEUE_SIZE 1500000
|
||||
|
||||
#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
|
||||
#ifdef _DEBUG
|
||||
#define LOG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
|
||||
#else
|
||||
#define LOG(msg, ...)
|
||||
#endif
|
||||
|
||||
typedef struct {
|
||||
unsigned int start;
|
||||
unsigned int end;
|
||||
int data[QUEUE_SIZE];
|
||||
} queue_t;
|
||||
|
||||
static void queue_init(queue_t *q)
|
||||
{
|
||||
q->start = q->end = 0;
|
||||
}
|
||||
|
||||
static void queue_put(queue_t *q, int x)
|
||||
{
|
||||
q->data[q->end++] = x;
|
||||
q->end %= QUEUE_SIZE;
|
||||
|
||||
ERROR(q->start == q->end, "The queue is full! Increase QUEUE_SIZE\n");
|
||||
}
|
||||
|
||||
static int queue_get(queue_t *q)
|
||||
{
|
||||
if(q->start == q->end)
|
||||
return -1;
|
||||
|
||||
int result = q->data[q->start++];
|
||||
q->start %= QUEUE_SIZE;
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,210 @@
|
|||
#include "triangle.h"
|
||||
#include "linalg.h"
|
||||
|
||||
#define MAX_ELEMENTS 14000
|
||||
//#define DRAW_PICTURE 1
|
||||
|
||||
void initialize_triangle_generators(workspace_t *ws, gsl_matrix **gen, double a1, double a2, double a3, double s, double t)
|
||||
{
|
||||
gsl_matrix **tmp;
|
||||
tmp = getTempMatrices(ws, 6);
|
||||
|
||||
double rho1sqrt = sqrt(s*(s+2*cos(2*M_PI*a1))+1);
|
||||
double rho2sqrt = sqrt(s*(s+2*cos(2*M_PI*a2))+1);
|
||||
double rho3sqrt = sqrt(s*(s+2*cos(2*M_PI*a3))+1);
|
||||
|
||||
for(int i = 0; i < 6; i++)
|
||||
gsl_matrix_set_zero(tmp[i]);
|
||||
|
||||
gsl_matrix_set(tmp[0], 0, 0, 1);
|
||||
gsl_matrix_set(tmp[0], 1, 0, -rho3sqrt/t);
|
||||
gsl_matrix_set(tmp[0], 2, 0, -rho2sqrt*t);
|
||||
gsl_matrix_set(tmp[0], 1, 1, -1);
|
||||
gsl_matrix_set(tmp[0], 2, 2, -1);
|
||||
|
||||
gsl_matrix_set(tmp[1], 0, 0, -1);
|
||||
gsl_matrix_set(tmp[1], 0, 1, -rho3sqrt*t);
|
||||
gsl_matrix_set(tmp[1], 1, 1, 1);
|
||||
gsl_matrix_set(tmp[1], 2, 1, -rho1sqrt/t);
|
||||
gsl_matrix_set(tmp[1], 2, 2, -1);
|
||||
|
||||
gsl_matrix_set(tmp[2], 0, 0, -1);
|
||||
gsl_matrix_set(tmp[2], 1, 1, -1);
|
||||
gsl_matrix_set(tmp[2], 0, 2, -rho2sqrt/t);
|
||||
gsl_matrix_set(tmp[2], 1, 2, -rho1sqrt*t);
|
||||
gsl_matrix_set(tmp[2], 2, 2, 1);
|
||||
|
||||
gsl_matrix_set(tmp[3], 0, 0, 1);
|
||||
gsl_matrix_set(tmp[3], 1, 1, s);
|
||||
gsl_matrix_set(tmp[3], 2, 2, 1/s);
|
||||
|
||||
gsl_matrix_set(tmp[4], 0, 0, 1/s);
|
||||
gsl_matrix_set(tmp[4], 1, 1, 1);
|
||||
gsl_matrix_set(tmp[4], 2, 2, s);
|
||||
|
||||
gsl_matrix_set(tmp[5], 0, 0, s);
|
||||
gsl_matrix_set(tmp[5], 1, 1, 1/s);
|
||||
gsl_matrix_set(tmp[5], 2, 2, 1);
|
||||
|
||||
multiply_many(ws, gen[0], 3, tmp[2], tmp[3], tmp[1]);
|
||||
multiply_many(ws, gen[1], 3, tmp[0], tmp[4], tmp[2]);
|
||||
multiply_many(ws, gen[2], 3, tmp[1], tmp[5], tmp[0]);
|
||||
|
||||
invert(gen[0], gen[3], ws);
|
||||
invert(gen[1], gen[4], ws);
|
||||
invert(gen[2], gen[5], ws);
|
||||
|
||||
releaseTempMatrices(ws, 6);
|
||||
}
|
||||
|
||||
char *print_word(groupelement_t *g, char *str)
|
||||
{
|
||||
int i = g->length - 1;
|
||||
|
||||
str[g->length] = 0;
|
||||
while(g->parent) {
|
||||
str[i--] = 'a' + g->letter;
|
||||
g = g->parent;
|
||||
}
|
||||
|
||||
return str;
|
||||
}
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
groupelement_t *group;
|
||||
workspace_t *ws;
|
||||
gsl_matrix **matrices;
|
||||
gsl_matrix *gen[6];
|
||||
gsl_matrix *tmp, *tmp2, *coxeter;
|
||||
double mu[6], tr, trinv;
|
||||
char buf[100];
|
||||
|
||||
/*
|
||||
if(argc < 2) {
|
||||
fprintf(stderr, "Too few arguments!\n");
|
||||
return 1;
|
||||
}
|
||||
*/
|
||||
|
||||
// allocate stuff
|
||||
group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
|
||||
ws = workspace_alloc(3);
|
||||
matrices = malloc(MAX_ELEMENTS*sizeof(gsl_matrix*));
|
||||
for(int i = 0; i < MAX_ELEMENTS; i++)
|
||||
matrices[i] = gsl_matrix_alloc(3, 3);
|
||||
for(int i = 0; i < 6; i++)
|
||||
gen[i] = gsl_matrix_alloc(3, 3);
|
||||
tmp = gsl_matrix_alloc(3, 3);
|
||||
tmp2 = gsl_matrix_alloc(3, 3);
|
||||
coxeter = gsl_matrix_alloc(3, 3);
|
||||
|
||||
#ifdef DRAW_PICTURE
|
||||
int width = 800;
|
||||
int height = 800;
|
||||
printf("P3\n%d %d\n255\n", width, height);
|
||||
|
||||
for(int y = 0; y < height; y++) {
|
||||
for(int x = 0; x < width; x++) {
|
||||
double s = exp(((double)x/width-0.5)*4);
|
||||
double t = exp(((double)y/height-0.5)*4);
|
||||
#else
|
||||
double s = atof(argv[1]);
|
||||
double t = atof(argv[2]);
|
||||
#endif
|
||||
|
||||
// the real action
|
||||
generate_triangle_group(group, MAX_ELEMENTS, 5, 6, 7);
|
||||
initialize_triangle_generators(ws, gen, 1.0/5.0, 1.0/6.0, 1.0/7.0, s, t);
|
||||
|
||||
gsl_matrix_set_identity(matrices[0]);
|
||||
for(int i = 1; i < MAX_ELEMENTS; i++) {
|
||||
if(group[i].length % 2 != 0)
|
||||
continue;
|
||||
|
||||
int parent = group[i].parent->id;
|
||||
int grandparent = group[i].parent->parent->id;
|
||||
int letter;
|
||||
|
||||
if(group[parent].letter == 0 && group[i].letter == 1)
|
||||
letter = 3; // p = ab
|
||||
else if(group[parent].letter == 1 && group[i].letter == 2)
|
||||
letter = 4; // q = bc
|
||||
else if(group[parent].letter == 2 && group[i].letter == 0)
|
||||
letter = 5; // r = ca
|
||||
else if(group[parent].letter == 1 && group[i].letter == 0)
|
||||
letter = 0; // p^{-1} = ba
|
||||
else if(group[parent].letter == 2 && group[i].letter == 1)
|
||||
letter = 1; // q^{-1} = cb
|
||||
else if(group[parent].letter == 0 && group[i].letter == 2)
|
||||
letter = 2; // r^{-1} = ac
|
||||
|
||||
multiply(matrices[grandparent], gen[letter], matrices[i]);
|
||||
}
|
||||
|
||||
double excentricity;
|
||||
double max_excentricity = 0;
|
||||
int max_excentricity_index = 0;
|
||||
|
||||
for(int i = 0; i < MAX_ELEMENTS; i++) {
|
||||
if(group[i].length % 2 != 0)
|
||||
continue;
|
||||
|
||||
// jordan projection
|
||||
gsl_matrix_memcpy(tmp, matrices[i]);
|
||||
gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
|
||||
int r = gsl_eigen_nonsymmv(tmp, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
|
||||
ERROR(r, "gsl_eigen_nonsymmv failed!\n");
|
||||
gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
|
||||
|
||||
int real_evs = 0;
|
||||
|
||||
for(int j = 0; j < 3; j++)
|
||||
if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, j)), 0) == 0)
|
||||
real_evs++;
|
||||
|
||||
if(real_evs != 3)
|
||||
continue;
|
||||
|
||||
mu[0] = fabs(GSL_REAL(gsl_vector_complex_get(ws->eval_complex, 0)) / GSL_REAL(gsl_vector_complex_get(ws->eval_complex, 1)));
|
||||
mu[1] = fabs(GSL_REAL(gsl_vector_complex_get(ws->eval_complex, 1)) / GSL_REAL(gsl_vector_complex_get(ws->eval_complex, 2)));
|
||||
|
||||
excentricity = log(mu[1])/log(mu[0]);
|
||||
if(excentricity > max_excentricity + 1e-3) {
|
||||
max_excentricity = excentricity;
|
||||
max_excentricity_index = i;
|
||||
}
|
||||
|
||||
#ifndef DRAW_PICTURE
|
||||
printf("%d %f %f %f %f 0x0000ff %d %s\n", group[i].length, mu[0], mu[1], tr, trinv, i, print_word(&group[i], buf));
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef DRAW_PICTURE
|
||||
int color = (int)((max_excentricity-1)/(max_excentricity+4)*255);
|
||||
if(color < 0)
|
||||
color = 0;
|
||||
if(color > 255)
|
||||
color = 255;
|
||||
printf("%d %d %d\n", color, color, color);
|
||||
}
|
||||
fprintf(stderr, "y = %d\n", y);
|
||||
}
|
||||
#else
|
||||
fprintf(stderr, "max = %f %s\n", max_excentricity, print_word(&group[max_excentricity_index], buf));
|
||||
#endif
|
||||
|
||||
// free stuff
|
||||
for(int i = 0; i < MAX_ELEMENTS; i++)
|
||||
gsl_matrix_free(matrices[i]);
|
||||
for(int i = 0; i < 6; i++)
|
||||
gsl_matrix_free(gen[i]);
|
||||
gsl_matrix_free(tmp);
|
||||
gsl_matrix_free(tmp2);
|
||||
gsl_matrix_free(coxeter);
|
||||
free(matrices);
|
||||
free(group);
|
||||
workspace_free(ws);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,23 @@
|
|||
if(!exists("logt")) logt = log(1.5)
|
||||
if(!exists("logs")) logs = log(1.0)
|
||||
|
||||
file = sprintf("< ./singular_values %f %f", exp(logs), exp(logt))
|
||||
title = sprintf("s = %f, t = %f", exp(logs), exp(logt))
|
||||
# print title
|
||||
|
||||
set zeroaxis
|
||||
set size square
|
||||
set xrange [0:25]
|
||||
set yrange [0:25]
|
||||
set grid
|
||||
set parametric
|
||||
|
||||
plot file using (log($2)):(log($3)) w p pt 7 ps 0.5 lc 1 t title
|
||||
# plot file using 2:3 w p pt 7 ps 0.5 lc 1 t title
|
||||
|
||||
pause mouse keypress
|
||||
if(MOUSE_KEY == 60) logt=logt-0.02
|
||||
if(MOUSE_KEY == 62) logt=logt+0.02
|
||||
if(MOUSE_KEY == 44) logs=logs-0.02
|
||||
if(MOUSE_KEY == 46) logs=logs+0.02
|
||||
if(MOUSE_KEY != 113) reread
|
||||
|
|
@ -0,0 +1,72 @@
|
|||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
#include <memory.h>
|
||||
|
||||
#include "triangle.h"
|
||||
#include "queue.h"
|
||||
|
||||
static groupelement_t *find_adj(groupelement_t *cur, int gen, int other, int order)
|
||||
{
|
||||
groupelement_t *next = cur->adj[other];
|
||||
for(int i = 0; i < order - 1; i++) {
|
||||
if(!next)
|
||||
break;
|
||||
next = next->adj[gen];
|
||||
if(!next)
|
||||
break;
|
||||
next = next->adj[other];
|
||||
}
|
||||
return next;
|
||||
}
|
||||
|
||||
int generate_triangle_group(groupelement_t *group, int size, int k1, int k2, int k3)
|
||||
{
|
||||
queue_t q;
|
||||
int id, n;
|
||||
groupelement_t *cur, *inv;
|
||||
|
||||
int k[3] = {k1, k2, k3};
|
||||
|
||||
memset(group, 0, size*sizeof(groupelement_t));
|
||||
group[0].letter = -1;
|
||||
n = 1;
|
||||
queue_init(&q);
|
||||
queue_put(&q, 0);
|
||||
|
||||
while((id = queue_get(&q)) != -1) {
|
||||
cur = &group[id];
|
||||
|
||||
for(int gen = 0; gen < 3; gen++) {
|
||||
if(!cur->adj[gen])
|
||||
cur->adj[gen] = find_adj(cur, gen, (gen+2)%3, k[(gen+1)%3]);
|
||||
|
||||
if(!cur->adj[gen])
|
||||
cur->adj[gen] = find_adj(cur, gen, (gen+1)%3, k[(gen+2)%3]);
|
||||
|
||||
if(!cur->adj[gen] && n < size) {
|
||||
cur->adj[gen] = &group[n];
|
||||
cur->adj[gen]->id = n;
|
||||
cur->adj[gen]->parent = cur;
|
||||
cur->adj[gen]->letter = gen;
|
||||
cur->adj[gen]->length = cur->length + 1;
|
||||
queue_put(&q, n);
|
||||
n++;
|
||||
}
|
||||
|
||||
if(cur->adj[gen])
|
||||
cur->adj[gen]->adj[gen] = cur;
|
||||
}
|
||||
}
|
||||
|
||||
for(int i = 0; i < size; i++) {
|
||||
cur = &group[i];
|
||||
inv = &group[0];
|
||||
while(cur->parent && inv) {
|
||||
inv = inv->adj[cur->letter];
|
||||
cur = cur->parent;
|
||||
}
|
||||
group[i].inverse = inv;
|
||||
}
|
||||
|
||||
return n;
|
||||
}
|
||||
|
|
@ -0,0 +1,21 @@
|
|||
#ifndef TRIANGLE_H
|
||||
#define TRIANGLE_H
|
||||
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
#include <memory.h>
|
||||
|
||||
#include "queue.h"
|
||||
|
||||
typedef struct _groupelement {
|
||||
int id;
|
||||
int length;
|
||||
struct _groupelement *adj[3];
|
||||
struct _groupelement *parent;
|
||||
struct _groupelement *inverse;
|
||||
int letter;
|
||||
} groupelement_t;
|
||||
|
||||
int generate_triangle_group(groupelement_t *group, int size, int k1, int k2, int k3);
|
||||
|
||||
#endif
|
||||
Loading…
Reference in New Issue