switch to rational numbers + add variable type matrix library
This commit is contained in:
Florian Stecker
parent
c19f61b714
commit
c566a8741e
15
Makefile
15
Makefile
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@ -1,16 +1,16 @@
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HEADERS=triangle.h linalg.h queue.h
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HEADERS=triangle.h linalg.h queue.h mat.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=-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: singular_values.o triangle.o linalg.o mat.o
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gcc $(OPTIONS) -o singular_values triangle.o linalg.o singular_values.o mat.o -lm -lgsl -lcblas -lgmp
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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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@ -21,5 +21,8 @@ linalg.o: linalg.c $(HEADERS)
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triangle.o: triangle.c $(HEADERS)
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gcc $(OPTIONS) -c triangle.c
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mat.o: mat.c $(HEADERS)
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gcc $(OPTIONS) -c mat.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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rm -f singular_values triangle.o linalg.o singular_values.o mat.o
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@ -0,0 +1,158 @@
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#include "mat.h"
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mat_workspace *mat_workspace_init(int n)
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{
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mat_workspace *ws = (mat_workspace*)malloc(sizeof(mat_workspace));
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mat_init(ws->tmp_mat, n);
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INIT(ws->tmp_num);
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INIT(ws->tmp_num2);
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return ws;
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}
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void mat_workspace_clear(mat_workspace *ws)
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{
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mat_clear(ws->tmp_mat);
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CLEAR(ws->tmp_num);
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CLEAR(ws->tmp_num2);
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free(ws);
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}
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void mat_init(mat m, int n)
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{
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m->n = n;
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m->x = malloc(n*n*sizeof(NUMBER));
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LOOP(i,n) LOOP(j,n) INIT(m->x[i+j*n]);
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}
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void mat_get(NUMBER out, mat m, int i, int j)
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{
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SET(out, M(m,i,j));
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}
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void mat_set(mat m, int i, int j, NUMBER x)
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{
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SET(M(m,i,j), x);
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}
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NUMBER *mat_ref(mat m, int i, int j)
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{
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return &M(m,i,j);
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}
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void mat_zero(mat m)
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{
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LOOP(i,m->n) LOOP(j,m->n) SET_ZERO(M(m,i,j));
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}
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void mat_identity(mat m)
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{
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LOOP(i,m->n) LOOP(j,m->n) {
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if(i == j)
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SET_ONE(M(m,i,j));
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else
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SET_ZERO(M(m,i,j));
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}
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}
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void mat_copy(mat to, mat from)
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{
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LOOP(i,from->n) LOOP(j,from->n) SET(M(to,i,j), M(from,i,j));
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}
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void mat_clear(mat m)
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{
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LOOP(i,m->n) LOOP(j,m->n) CLEAR(M(m,i,j));
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free(m->x);
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}
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int mat_same(mat m1, mat m2)
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{
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return m1 == m2;
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}
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static void mat_multiply_outofplace(mat_workspace *ws, mat out, mat in1, mat in2)
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{
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int n = out->n;
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NUMBER *tmp = &(ws->tmp_num);
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LOOP(i,n) LOOP(j,n) {
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SET_ZERO(M(out,i,j));
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LOOP(k,n) {
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MULTIPLY(*tmp, M(in1,i,k), M(in2,k,j));
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ADD(M(out,i,j), M(out,i,j), *tmp);
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}
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}
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}
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void mat_multiply(mat_workspace *ws, mat out, mat in1, mat in2)
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{
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if(mat_same(out, in1) || mat_same(out, in2)) {
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mat_multiply_outofplace(ws, ws->tmp_mat, in1, in2);
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mat_copy(out, ws->tmp_mat);
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} else {
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mat_multiply_outofplace(ws, out, in1, in2);
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}
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}
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void mat_det(mat_workspace *ws, NUMBER out, mat in)
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{
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// let's just assume n = 3 for the moment
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NUMBER *tmp = &(ws->tmp_num);
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int n = 3;
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SET_ZERO(out);
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LOOP(i,n) {
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MULTIPLY(*tmp, M(in,0,i), M(in,1,(i+1)%3));
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MULTIPLY(*tmp, *tmp, M(in,2,(i+2)%3));
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ADD(out, out, *tmp);
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MULTIPLY(*tmp, M(in,0,(i+2)%3), M(in,1,(i+1)%3));
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MULTIPLY(*tmp, *tmp, M(in,2,i));
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SUB(out, out, *tmp);
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}
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}
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static void mat_pseudoinverse_outofplace(mat_workspace *ws, mat out, mat in)
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{
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// let's just assume n = 3 for the moment
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NUMBER *tmp = &(ws->tmp_num);
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NUMBER *tmp2 = &(ws->tmp_num2);
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int n = 3;
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LOOP(i,n) LOOP(j,n) {
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MULTIPLY(*tmp, M(in,(i+1)%3,(j+1)%3), M(in,(i+2)%3,(j+2)%3));
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MULTIPLY(*tmp2, M(in,(i+1)%3,(j+2)%3), M(in,(i+2)%3,(j+1)%3));
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SUB(M(out,j,i), *tmp, *tmp2);
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}
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}
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void mat_pseudoinverse(mat_workspace *ws, mat out, mat in)
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{
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if(mat_same(out, in)) {
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mat_pseudoinverse_outofplace(ws, ws->tmp_mat, in);
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mat_copy(out, ws->tmp_mat);
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} else {
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mat_pseudoinverse_outofplace(ws, out, in);
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}
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}
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void mat_trace(NUMBER out, mat in)
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{
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SET_ZERO(out);
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ADD(out, out, M(in,0,0));
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ADD(out, out, M(in,1,1));
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ADD(out, out, M(in,2,2));
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}
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void mat_print(mat in)
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{
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int n = in->n;
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LOOP(i,n) {
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LOOP(j,n) {
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PRINT(M(in,i,j));
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fputc(j == n - 1 ? '\n' : ' ', stdout);
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}
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}
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}
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@ -0,0 +1,66 @@
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#ifndef MAT_H
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#define MAT_H
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#include <gmp.h>
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#include <malloc.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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// library for matrix computations in variable rings (based on GMP types)
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/*
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needed features:
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x multiply matrices
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- inverse
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- pseudoinverse
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x set
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- eigenvalues
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*/
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#define NUMBER mpq_t
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#define INIT mpq_init
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#define CLEAR mpq_clear
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#define SET mpq_set
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#define SET_ZERO(x) mpq_set_ui(x,0,1)
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#define SET_ONE(x) mpq_set_ui(x,1,1)
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#define ADD mpq_add
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#define SUB mpq_sub
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#define MULTIPLY mpq_mul
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#define DIV mpq_div
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#define PRINT(x) gmp_printf("%Qd", x)
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#define M(m,i,j) ((m)->x[(i)+(m)->n*(j)])
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struct _mat{
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int n;
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NUMBER *x;
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} ;
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typedef struct _mat mat[1];
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typedef struct _mat_workspace {
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mat tmp_mat;
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NUMBER tmp_num;
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NUMBER tmp_num2;
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} mat_workspace;
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mat_workspace *mat_workspace_init(int n);
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void mat_workspace_clear(mat_workspace *ws);
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void mat_init(mat m, int n);
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void mat_get(NUMBER out, mat m, int i, int j);
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void mat_set(mat m, int i, int j, NUMBER x);
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NUMBER *mat_ref(mat m, int i, int j);
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void mat_zero(mat m);
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void mat_identity(mat m);
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void mat_copy(mat to, mat from);
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void mat_clear(mat m);
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int mat_same(mat m1, mat m2);
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static void mat_multiply_outofplace(mat_workspace *ws, mat out, mat in1, mat in2);
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void mat_multiply(mat_workspace *ws, mat out, mat in1, mat in2);
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void mat_det(mat_workspace *ws, NUMBER out, mat in);
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static void mat_pseudoinverse_outofplace(mat_workspace *ws, mat out, mat in);
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void mat_pseudoinverse(mat_workspace *ws, mat out, mat in);
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void mat_trace(NUMBER out, mat in);
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void mat_print(mat in);
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#endif
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@ -1,60 +1,69 @@
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#include "triangle.h"
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#include "linalg.h"
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#include "mat.h"
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#include <gsl/gsl_poly.h>
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//#define MAX_ELEMENTS 2800000
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//#define MAX_ELEMENTS 720000
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#define MAX_ELEMENTS 14000
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//#define DRAW_PICTURE 1
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void initialize_triangle_generators(workspace_t *ws, gsl_matrix **gen, double a1, double a2, double a3, double s, double t)
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void mpq_quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
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{
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gsl_matrix **tmp;
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tmp = getTempMatrices(ws, 6);
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mpq_t tmp;
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mpq_init(tmp);
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double rho1sqrt = sqrt(s*(s+2*cos(2*M_PI*a1))+1);
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double rho2sqrt = sqrt(s*(s+2*cos(2*M_PI*a2))+1);
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double rho3sqrt = sqrt(s*(s+2*cos(2*M_PI*a3))+1);
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mpq_set_si(out, a, 1);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, b, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, c, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, d, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, e, 1);
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mpq_add(out, out, tmp);
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for(int i = 0; i < 6; i++)
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gsl_matrix_set_zero(tmp[i]);
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mpq_clear(tmp);
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}
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gsl_matrix_set(tmp[0], 0, 0, 1);
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gsl_matrix_set(tmp[0], 1, 0, -rho3sqrt/t);
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gsl_matrix_set(tmp[0], 2, 0, -rho2sqrt*t);
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gsl_matrix_set(tmp[0], 1, 1, -1);
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gsl_matrix_set(tmp[0], 2, 2, -1);
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void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t t)
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{
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mpq_set_ui(*mat_ref(gen[0], 0, 0), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 0, 1), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 0, 2), 1, 1);
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mpq_set_ui(*mat_ref(gen[0], 1, 0), 1, 1);
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mpq_set_ui(*mat_ref(gen[0], 1, 1), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 1, 2), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 2, 0), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 2, 1), 1, 1);
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mpq_set_ui(*mat_ref(gen[0], 2, 2), 0, 1);
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gsl_matrix_set(tmp[1], 0, 0, -1);
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gsl_matrix_set(tmp[1], 0, 1, -rho3sqrt*t);
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gsl_matrix_set(tmp[1], 1, 1, 1);
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gsl_matrix_set(tmp[1], 2, 1, -rho1sqrt/t);
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gsl_matrix_set(tmp[1], 2, 2, -1);
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mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
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mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
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mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
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mpq_quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
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mpq_quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
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mpq_quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
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mpq_quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
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mpq_quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
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mpq_quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
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gsl_matrix_set(tmp[2], 0, 0, -1);
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gsl_matrix_set(tmp[2], 1, 1, -1);
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gsl_matrix_set(tmp[2], 0, 2, -rho2sqrt/t);
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gsl_matrix_set(tmp[2], 1, 2, -rho1sqrt*t);
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gsl_matrix_set(tmp[2], 2, 2, 1);
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mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
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mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
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mat_multiply(ws, gen[2], gen[4], gen[3]); // r = q^{-1}p^{-1}
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mat_pseudoinverse(ws, gen[5], gen[2]);
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gsl_matrix_set(tmp[3], 0, 0, 1);
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gsl_matrix_set(tmp[3], 1, 1, s);
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gsl_matrix_set(tmp[3], 2, 2, 1/s);
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gsl_matrix_set(tmp[4], 0, 0, 1/s);
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gsl_matrix_set(tmp[4], 1, 1, 1);
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gsl_matrix_set(tmp[4], 2, 2, s);
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gsl_matrix_set(tmp[5], 0, 0, s);
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gsl_matrix_set(tmp[5], 1, 1, 1/s);
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gsl_matrix_set(tmp[5], 2, 2, 1);
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multiply_many(ws, gen[0], 3, tmp[2], tmp[3], tmp[1]);
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multiply_many(ws, gen[1], 3, tmp[0], tmp[4], tmp[2]);
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multiply_many(ws, gen[2], 3, tmp[1], tmp[5], tmp[0]);
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invert(gen[0], gen[3], ws);
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invert(gen[1], gen[4], ws);
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invert(gen[2], gen[5], ws);
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releaseTempMatrices(ws, 6);
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// mat_print(gen[0]);
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// mat_print(gen[1]);
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// mat_print(gen[2]);
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// mat_print(gen[3]);
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// mat_print(gen[4]);
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// mat_print(gen[5]);
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}
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char *print_word(groupelement_t *g, char *str)
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@ -73,138 +82,92 @@ char *print_word(groupelement_t *g, char *str)
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int main(int argc, char *argv[])
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{
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groupelement_t *group;
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workspace_t *ws;
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gsl_matrix **matrices;
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gsl_matrix *gen[6];
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gsl_matrix *tmp, *tmp2, *coxeter;
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double mu[6], tr, trinv;
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char buf[100];
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/*
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if(argc < 2) {
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fprintf(stderr, "Too few arguments!\n");
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return 1;
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}
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*/
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mat_workspace *ws;
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mat *matrices;
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mat tmp;
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mat gen[6];
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char buf[100], buf2[100], buf3[100];
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mpq_t s,t;
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mpq_t det, tr, trinv;
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// allocate stuff
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group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
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ws = workspace_alloc(3);
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matrices = malloc(MAX_ELEMENTS*sizeof(gsl_matrix*));
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ws = mat_workspace_init(3);
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matrices = malloc(MAX_ELEMENTS*sizeof(mat));
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for(int i = 0; i < MAX_ELEMENTS; i++)
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matrices[i] = gsl_matrix_alloc(3, 3);
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mat_init(matrices[i], 3);
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for(int i = 0; i < 6; i++)
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gen[i] = gsl_matrix_alloc(3, 3);
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tmp = gsl_matrix_alloc(3, 3);
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tmp2 = gsl_matrix_alloc(3, 3);
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coxeter = gsl_matrix_alloc(3, 3);
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mat_init(gen[i], 3);
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mat_init(tmp, 3);
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#ifdef DRAW_PICTURE
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int width = 800;
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int height = 800;
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printf("P3\n%d %d\n255\n", width, height);
|
||||
mpq_inits(s, t, det, tr, trinv, NULL);
|
||||
|
||||
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
|
||||
mpq_set_ui(s,1,1);
|
||||
double t_ = atof(argv[1]);
|
||||
mpq_set_ui(t,(int)(t_*100),100);
|
||||
mpq_canonicalize(s);
|
||||
mpq_canonicalize(t);
|
||||
|
||||
// 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);
|
||||
// the real action
|
||||
generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
|
||||
initialize_triangle_generators(ws, gen, s, t);
|
||||
|
||||
gsl_matrix_set_identity(matrices[0]);
|
||||
for(int i = 1; i < MAX_ELEMENTS; i++) {
|
||||
if(group[i].length % 2 != 0)
|
||||
continue;
|
||||
mat_identity(matrices[0]);
|
||||
for(int i = 1; i < MAX_ELEMENTS; i++) {
|
||||
if(group[i].length % 2 != 0)
|
||||
continue;
|
||||
if(!group[i].inverse)
|
||||
continue;
|
||||
|
||||
int parent = group[i].parent->id;
|
||||
int grandparent = group[i].parent->parent->id;
|
||||
int letter;
|
||||
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
|
||||
if(group[parent].letter == 1 && group[i].letter == 2)
|
||||
letter = 0; // p = bc
|
||||
else if(group[parent].letter == 2 && group[i].letter == 0)
|
||||
letter = 1; // q = ca
|
||||
else if(group[parent].letter == 0 && group[i].letter == 1)
|
||||
letter = 2; // r = ab
|
||||
if(group[parent].letter == 2 && group[i].letter == 1)
|
||||
letter = 3; // p^{-1} = cb
|
||||
else if(group[parent].letter == 0 && group[i].letter == 2)
|
||||
letter = 4; // q^{-1} = ac
|
||||
else if(group[parent].letter == 1 && group[i].letter == 0)
|
||||
letter = 5; // r^{-1} = ba
|
||||
|
||||
mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
|
||||
}
|
||||
|
||||
for(int i = 0; i < MAX_ELEMENTS; i++) {
|
||||
if(group[i].length % 2 != 0)
|
||||
continue;
|
||||
if(!group[i].inverse)
|
||||
continue;
|
||||
|
||||
mat_trace(tr, matrices[i]);
|
||||
mat_trace(trinv, matrices[group[i].inverse->id]);
|
||||
|
||||
double lambda1, lambda2, lambda3;
|
||||
// int realevs = gsl_poly_solve_cubic(-mpq_get_d(tr), mpq_get_d(trinv), -1, &lambda3, &lambda2, &lambda1);
|
||||
// if(realevs != 3)
|
||||
// continue;
|
||||
// if(lambda1 < 0 || lambda2 < 0 || lambda3 < 0)
|
||||
// continue;
|
||||
|
||||
// gmp_printf("%d %d %s %Qd %Qd\n", i, group[i].length, print_word(&group[i], buf), tr, trinv);
|
||||
printf("%d %d %s %f %f %f\n", i, group[i].length, print_word(&group[i], buf), log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
|
||||
|
||||
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]);
|
||||
mat_clear(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);
|
||||
mat_clear(gen[i]);
|
||||
mat_clear(tmp);
|
||||
mpq_clears(s, t, det, tr, trinv, NULL);
|
||||
mat_workspace_clear(ws);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,20 +1,38 @@
|
|||
if(!exists("logt")) logt = log(1.5)
|
||||
if(!exists("logt")) logt = log(7)
|
||||
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))
|
||||
file = sprintf("< ./singular_values %f", exp(logt))
|
||||
#title = sprintf("s = %f, t = %f", exp(logs), exp(logt))
|
||||
title = sprintf("t = %.3f", floor(exp(logt)*100)/100.0)
|
||||
# print title
|
||||
|
||||
set zeroaxis
|
||||
set samples 1000
|
||||
set size square
|
||||
set xrange [0:25]
|
||||
set yrange [0:25]
|
||||
set xrange [0:20]
|
||||
set yrange [0:20]
|
||||
set trange [0:20]
|
||||
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
|
||||
|
||||
#tr(a,b) = exp((2*a+b)/3) + exp((b-a)/3) + exp(-(a+2*b)/3)
|
||||
#trinv(a,b) = exp(-(2*a+b)/3) + exp((a-b)/3) + exp((a+2*b)/3)
|
||||
|
||||
tr(a,b) = exp(a) + exp(b-a) + exp(-b)
|
||||
trinv(a,b) = exp(-a) + exp(a-b) + exp(b)
|
||||
|
||||
plot file using 4:5 w p pt 7 ps 0.5 lc 1 t title, \
|
||||
log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \
|
||||
log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t ""
|
||||
|
||||
#plot for[i=-10:10] log(tr(t,t*exp(log(2)*i/10.0))),log(trinv(t,t*exp(log(2)*i/10.0))) w l lw 2 t ""
|
||||
|
||||
#plot for[i=-10:10] t,log(tr(t,t*exp(log(2)*i/10.0)))-t w l lw 2 t ""
|
||||
|
||||
##plot for[i=20:20] t,log(tr(1/t,exp(2*log(2)*i/20.0-log(2)))) w l lw 2 t ""
|
||||
|
||||
pause mouse keypress
|
||||
if(MOUSE_KEY == 60) logt=logt-0.02
|
||||
if(MOUSE_KEY == 62) logt=logt+0.02
|
||||
|
|
|
|||
Loading…
Reference in New Issue