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Commit 7df0fde6 authored by Oleg Dzhimiev's avatar Oleg Dzhimiev
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Gauss-Newton algorithm as extension to numbers.js

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js/numbers/numbers.calculus.extra.js 0 → 100644
View file @ 7df0fde6
/**
* @file numbers.calculus.extra.js
* @brief Gauss-Newton
* @copyright Copyright (C) 2017 Elphel Inc.
* @authors Oleg Dzhimiev <oleg@elphel.com>
*
* @license: GPL-3.0
*
* @licstart The following is the entire license notice for the
* JavaScript code in this page.
*
* The JavaScript code in this page is free software: you can
* redistribute it and/or modify it under the terms of the GNU
* General Public License (GNU GPL) as published by the Free Software
* Foundation, either version 3 of the License, or (at your option)
* any later version. The code is distributed WITHOUT ANY WARRANTY;
* without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
*
* As additional permission under GNU GPL version 3 section 7, you
* may distribute non-source (e.g., minimized or compacted) forms of
* that code without the copy of the GNU GPL normally required by
* section 4, provided you include this license notice and a URL
* through which recipients can access the Corresponding Source.
*
* @licend The above is the entire license notice
* for the JavaScript code in this page.
*/
/**
* Gauss-Newton algorithm for minimizing error function which
* is a sum of squared errors for each measurement
*
* @v {Array} vector, initial approximation
* @n {Number} number of measuments
* @r {Function} residual function
* @dr {Array} array of derivative functions
* @eps {Number} precision
*
*/
numbers.calculus.GaussNewton = function(v,n,r,dr,eps){
var epsilon = eps || 1e-8
var limit = 1000
var stop = false
var counter = 0
var v0 = v
while(!stop){
counter++
var v1 = iterate(v0,n,r,dr)
var s0 = sigma(v0,n,r)
var s1 = sigma(v1,n,r)
if((Math.abs(s1-s0)<epsilon)||(counter==limit)){
stop = true
}
v0 = v1
}
return {
count: counter,
error: s1,
v: v0
}
//functions
function iterate(v,n,r,dr){
var J = jacobian(v,n,dr)
var Jt = numbers.matrix.transpose(J)
// JtJ
J = numbers.matrix.multiply(Jt,J)
// (Jt x J)^-1
J = numbers.matrix.inverse(J)
// (Jt x J)^-1 x Jt
J = numbers.matrix.multiply(J,Jt)
var V = []
for(var i=0;i<n;i++){
V.push([r(i,v)])
}
var delta = numbers.matrix.multiply(J,V)
var res = []
for(var i=0;i<v.length;i++){
res[i] = v[i]-delta[i][0]
}
return res
}
function sigma(v,n,r){
var sum = 0;
for(var i=0;i<n;i++){
sum += r(i,v)*r(i,v)
}
sum = Math.sqrt(sum/n)
return sum
}
function jacobian(v,n,dr){
var J = []
for(var i=0;i<n;i++){
var row = []
for(var j=0;j<dr.length;j++){
row.push(dr[j](i,v))
}
J[i] = row
}
return J
}
}
js/numbers/numbers.js 0 → 100644
View file @ 7df0fde6
This diff is collapsed.
js/numbers/numbers.matrix.extra.js 0 → 100644
View file @ 7df0fde6
numbers.matrix.toString = function(a){
var res = ""
for(var i=0;i<a.length;i++){
res += a[i].join(" ")+"\n"
}
return res
}
js/ui_align.js
View file @ 7df0fde6
......@@ -43,8 +43,8 @@ function align_init(){
//align_heading();
//test_markers_set1();
//if (DEBUG_ALIGN) test_markers_set1();
//if (DEBUG_ALIGN) test_markers_set2();
if (DEBUG_ALIGN) test_markers_set3();
if (DEBUG_ALIGN) test_markers_set2();
//if (DEBUG_ALIGN) test_markers_set3();
x3dom_align_GN();
});
......@@ -123,61 +123,15 @@ function x3dom_align_GN(){
var x0 = Data.camera.kml.latitude;
var y0 = Data.camera.kml.longitude;
var h0 = Data.camera.kml.heading;
var epsilon = 1e-8;
//if (h0>180) h0 = h0 - 360;
//tests
//test_AxB();
//test_At();
//test_AxV();
//test_Ainv();
var ε = 0.000000001;
var iterate = true;
var counter = 0;
var result = 0;
var xyh = [x0,y0,(h0>180)?h0-360:h0];
while(iterate){
if (DEBUG_ALIGN){
// functions values
for(var i=0;i<Data.markers.length;i++){
console.log(f1_3d_i(i,xyh[0],xyh[1],xyh[2])+" - "+f2_map_i(i,xyh[0],xyh[1],xyh[2])+" = "+r_i(i,xyh[0],xyh[1],xyh[2]));
}
}
counter++;
var result = numbers.calculus.GaussNewton(xyh,Data.markers.length,r_i,[dr_dx_i,dr_dy_i,dr_dh_i],epsilon);
//console.log("Interation: "+counter+" for "+xyh[0]+" "+xyh[1]+" "+xyh[2]);
xyh_new = GaussNewtonAlgorithm(xyh[0],xyh[1],xyh[2]);
//if (xyh_new[2]<-180) xyh_new[2] += 360;
//if (xyh_new[2]> 180) xyh_new[2] -= 360;
var s0 = sigma(xyh[0],xyh[1],xyh[2]);
var s1 = sigma(xyh_new[0],xyh_new[1],xyh_new[2]);
//if ((s1>s0)||((s0-s1)<ε)){
if (Math.abs(s0-s1)<ε){
iterate = false;
}
if(DEBUG_ALIGN){
console.log("Errors: "+(xyh_new[0]-xyh[0])+" "+(xyh_new[1]-xyh[1])+" "+(xyh_new[2]-xyh[2]));
console.log("Iteration "+counter+" result: "+xyh_new[0]+" "+xyh_new[1]+" "+xyh_new[2]);
console.log("Error function value: "+sigma(xyh_new[0],xyh_new[1],xyh_new[2]));
}
if (counter==1000){
iterate = false;
}
xyh[0] = xyh_new[0];
xyh[1] = xyh_new[1];
xyh[2] = xyh_new[2];
}
xyh = result.v;
var s1 = result.error;
var counter = result.count;
//calc distance error
de = distance_error(x0,y0,(h0>180)?h0-360:h0);
......@@ -188,51 +142,14 @@ function x3dom_align_GN(){
}
/*
* calc the next iteration values
*/
function GaussNewtonAlgorithm(x,y,h){
var J = Jacobian(x,y,h);
var Jt = At(J);
var JtJ = AxB(Jt,J);
var JtJi = Ainv(JtJ);
var JtJixJt = AxB(JtJi,Jt);
var Vr = [];
for(var i=0;i<Data.markers.length;i++){
Vr[i] = r_i(i,x,y,h);
}
var d = AxV(JtJixJt,Vr);
var k = 1;
return [x-k*d[0], y-k*d[1], h-k*d[2]];
}
/*
* sum of squared residuals - criterion for stopping
*/
function sigma(x,y,h){
var sum = 0
for(var i=0;i<Data.markers.length;i++){
sum += r_i(i,x,y,h)*r_i(i,x,y,h);
}
sum = Math.sqrt(sum/Data.markers.length);
return sum;
}
/*
* heading in degrees from 3D model
*/
function f1_3d_i(i,x,y,h){
function f1_3d_i(i,v){
var base = Data.camera;
var mark = Data.markers[i];
var v = new x3dom.fields.SFVec3f(mark.align.x-base.x,0,mark.align.z-base.z);
var res = Math.atan2(v.x,-v.z)*180/Math.PI + h;
var vec = new x3dom.fields.SFVec3f(mark.align.x-base.x,0,mark.align.z-base.z);
var res = Math.atan2(vec.x,-vec.z)*180/Math.PI + v[2];
if (res> 180) res = res - 360;
if (res<-180) res = res + 360;
......@@ -243,10 +160,10 @@ function f1_3d_i(i,x,y,h){
/*
* heading in degrees from map
*/
function f2_map_i(i,x,y,h){
function f2_map_i(i,v){
var mark = Data.markers[i];
var p1_ll = new L.LatLng(x,y);
var p1_ll = new L.LatLng(v[0],v[1]);
var p2_ll = new L.LatLng(mark.align.latitude,mark.align.longitude);
//console.log(p1_ll);
......@@ -275,9 +192,9 @@ function f2_map_i(i,x,y,h){
/*
* residuals function
*/
function r_i(i,x,y,h){
var f1 = f1_3d_i(i,x,y,h);
var f2 = f2_map_i(i,x,y,h);
function r_i(i,v){
var f1 = f1_3d_i(i,v);
var f2 = f2_map_i(i,v);
//return (f1-f2+360)%360;
return (f1-f2);
}
......@@ -285,10 +202,10 @@ function r_i(i,x,y,h){
/*
* dr/dx(i)
*/
function dr_dx_i(i,x,y,h){
function dr_dx_i(i,v){
var mark = Data.markers[i];
var p1_ll = new L.LatLng(x,y);
var p1_ll = new L.LatLng(v[0],v[1]);
var p2_ll = new L.LatLng(mark.align.latitude,mark.align.longitude);
p1_ll.lat = p1_ll.lat*Math.PI/180;
......@@ -316,10 +233,10 @@ function dr_dx_i(i,x,y,h){
/*
* dr/dy(i)
*/
function dr_dy_i(i,x,y,h){
function dr_dy_i(i,v){
var mark = Data.markers[i];
var p1_ll = new L.LatLng(x,y);
var p1_ll = new L.LatLng(v[0],v[1]);
var p2_ll = new L.LatLng(mark.align.latitude,mark.align.longitude);
p1_ll.lat = p1_ll.lat*Math.PI/180;
......@@ -347,175 +264,10 @@ function dr_dy_i(i,x,y,h){
/*
* dr/dh(i)
*/
function dr_dh_i(i,x,y,h){
function dr_dh_i(i,v){
return 1;
}
/*
* Jacobi matrix
*/
function Jacobian(x,y,h){
var J = [];
var base = Data.camera;
for(var i=0;i<Data.markers.length;i++){
var mark = Data.markers[i];
J[i]=[ dr_dx_i(i,x,y,h), dr_dy_i(i,x,y,h), dr_dh_i(i,x,y,h)];
/*
e0 = 0.000000001;
e1 = 0.000000001;
e2 = 0.00001;
dri_dx_cal = dr_dx_i(i,x,y,h);
dri_dy_cal = dr_dy_i(i,x,y,h);
dri_dh_cal = dr_dh_i(i,x,y,h);
dri_dx_num = (r_i(i,x+e0,y ,h )-r_i(i,x-e0,y ,h ))/e0/2;
dri_dy_num = (r_i(i,x ,y+e1,h )-r_i(i,x ,y-e1,h ))/e1/2;
dri_dh_num = (r_i(i,x ,y ,h+e2)-r_i(i,x ,y ,h-e2))/e2/2;
console.log("CALC: "+dri_dx_cal.toFixed(10)+" "+dri_dy_cal.toFixed(10)+" "+dri_dh_cal.toFixed(4));
console.log("NUME: "+dri_dx_num.toFixed(10)+" "+dri_dy_num.toFixed(10)+" "+dri_dh_num.toFixed(4));
*/
}
return J;
}
/*
* Utility functions
*/
/*
* AxB, any dimensions
*/
function AxB(A,B){
var m1 = A.length;
var n1 = A[0].length;
var m2 = B.length;
var n2 = B[0].length;
if(n1!=m2){
console.log("M=AxB: cannot multiply matrices A_"+m1+"_"+n1+" x B_"+m2+"_"+n2);
return [];
}
var R = [];
for(var i=0;i<m1;i++){
R[i] = [];
for(var j=0;j<n2;j++){
R[i][j] = 0;
for(var k=0;k<n1;k++){
R[i][j] += A[i][k]*B[k][j];
}
}
}
return R;
}
/*
* Determinant for 3x3 only
*/
function Adet(A){
var m = A.length;
var n = A[0].length;
if ((m!=3)||(n!=3)){
console.log("Matrix inverting works only for 3x3 dimension");
}
var M = new x3dom.fields.SFMatrix4f(
A[0][0],A[0][1],A[0][2],0,
A[1][0],A[1][1],A[1][2],0,
A[2][0],A[2][1],A[2][2],0,
0,0,0,1
);
return M.det();
}
/*
* Inverted matrix for 3x3 only
*/
function Ainv(A){
var m = A.length;
var n = A[0].length;
if ((m!=3)||(n!=3)){
console.log("Matrix inverting works only for 3x3 dimension");
}
var M = new x3dom.fields.SFMatrix4f(
A[0][0],A[0][1],A[0][2],0,
A[1][0],A[1][1],A[1][2],0,
A[2][0],A[2][1],A[2][2],0,
0,0,0,1
);
var R = M.inverse();
return [
[R._00,R._01,R._02],
[R._10,R._11,R._12],
[R._20,R._21,R._22]
];
}
/*
* Transposed matrix, any dimensions
*/
function At(A){
var R = [];
for(var i=0;i<A[0].length;i++){
R[i] = [];
for(var j=0;j<A.length;j++){
R[i][j] = A[j][i];
}
}
return R;
}
/*
* Matrix x Vector - any dimensions
*/
function AxV(A,V){
var Vr = [];
var m1 = A.length;
var n1 = A[0].length;
var m2 = V.length;
var n2 = 1;
if (n1!=m2){
console.log("Matrix or vector dimension errors, too bad");
return [];
}
for(var i=0;i<m1;i++){
Vr[i] = 0;
for(var j=0;j<m2;j++){
Vr[i] += A[i][j]*V[j];
}
}
return Vr;
}
/*
* ui dialog to apply or cancel results
......@@ -614,7 +366,7 @@ function distance_error(x,y,h){
for(var i=0;i<Data.markers.length;i++){
var angle0 = h;
var angle1 = f2_map_i(i,x,y,h);
var angle1 = f2_map_i(i,[x,y,h]);
var z_map = Math.cos(Math.PI/180*(angle0-angle1))*Data.markers[i].d_map;
var z_x3d = -Data.markers[i].align.z;
sum += 1/z_map-1/z_x3d;
......@@ -647,92 +399,6 @@ function align_tilt(){
}
function test_Ainv(){
var A = [
[0,0,1],
[1,0,0],
[0,1,0]
];
console.log(A);
console.log(Ainv(A));
}
function test_AxV(){
var A = [
[1,2,3,4],
[5,6,7,8],
[9,10,11,12]
];
var V1 = [
13,
14,
15,
16
];
var V2 = [
13,
14,
15
];
console.log(AxV(A,V1));
console.log(AxV(A,V2));
}
function test_At(){
console.log("testing At: begin");
var A = [
[1,2,3,4],
[5,6,7,8],
[9,10,11,12]
];
console.log(A);
console.log(At(A));
console.log("testing At: end");
}
function test_AxB(){
console.log("testing AxB: begin");
var A = [
[1,2,3,4],
[5,6,7,8],
[9,10,11,12]
];
var B = [
[13,14,15],
[16,17,18],
[19,20,21],
[22,23,24],
];
var C = [
[2,2],
[1,1]
];
//test1: 3x4 x 4x3 = 3x3
console.log(AxB(A,B));
//test2: fail test case
console.log(AxB(A,C));
console.log("testing AxB: end");
}
function test_markers_set1(){
Data.camera.kml.latitude = 40.7233861;
......
test.html
View file @ 7df0fde6
......@@ -25,6 +25,10 @@
<script type='text/javascript' src='js/leaflet/leaflet.camera-view-marker.js'></script>
<script type='text/javascript' src='js/leaflet/leaflet.camera-view-marker.measure.js'></script>
<script type='text/javascript' src='js/numbers/numbers.js'></script>
<script type='text/javascript' src='js/numbers/numbers.matrix.extra.js'></script>
<script type='text/javascript' src='js/numbers/numbers.calculus.extra.js'></script>
<!---script type='text/javascript' src='js/x3dom/x3dom-full.debug.js'></script-->
<script type='text/javascript' src='js/x3dom_init.js'></script>
<script type='text/javascript' src='js/x3dom_functions.js'></script>
......
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