Least-squares line fitting: Difference between revisions
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A WASSERMANN (talk | contribs) No edit summary |
A WASSERMANN (talk | contribs) No edit summary |
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<jsxgraph width="600" height="600"> | <jsxgraph width="600" height="600"> | ||
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5], keepaspectratio:true, axis:true}); | var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5], keepaspectratio:true, axis:true}); | ||
var i, p = [], angle, xr, yr, delta = 0.1; | var i, j, p = [], angle, xr, yr, delta = 0.1; | ||
// Random points are constructed which lie roughly on a line | // Random points are constructed which lie roughly on a line | ||
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brd.unsuspendUpdate(); | brd.unsuspendUpdate(); | ||
var | var r = [], rbar = [], x = [], y = [], z = [], A = [[0,0,0],[0,0,0],[0,0,0]], n, d; | ||
n = p.length; | n = p.length; | ||
for (i=0;i<n;i++) { | for (i=0;i<n;i++) { | ||
r.push([1.0, p[i].X(), p[i].Y()]); | |||
d = r[0]*r[0] + r[1]*r[1] + r[2]*r[2]; | |||
r[0] = 1.0 - r[0]/d; | |||
r[1] /= d; | |||
r[2] /= d; | |||
} | } | ||
for (j=0;j<3;j++) { | |||
for (i=0,d=0;i<n;i++) { | |||
d += r[i][j]; | |||
} | |||
d /= n; | |||
rbar[j] = d; | |||
for (i=0;i<n;i++) { | |||
r[i][j] -= d; | |||
} | |||
} | |||
for (i=0;i<n;i++) { | |||
A[0][0] += r[i][0]*r[i][0]; | |||
A[0][1] += r[i][0]*r[i][1]; | |||
A[0][2] += r[i][0]*r[i][2]; | |||
A[1][0] += r[i][1]*r[i][0]; | |||
A[1][1] += r[i][1]*r[i][1]; | |||
A[1][2] += r[i][1]*r[i][2]; | |||
A[2][0] += r[i][2]*r[i][0]; | |||
A[2][1] += r[i][2]*r[i][1]; | |||
A[2][2] += r[i][2]*r[i][2]; | |||
} | |||
console.log(A); | |||
/* | |||
// Now, the general linear least-square fitting problem | // Now, the general linear least-square fitting problem | ||
// min_z || M*z - y||_2^2 | // min_z || M*z - y||_2^2 | ||
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brd.create('circle',[ [xm,ym], r]); | brd.create('circle',[ [xm,ym], r]); | ||
//alert([xm,ym,r].toString()); | //alert([xm,ym,r].toString()); | ||
// Having constructed the points, we can fit a line described | // Having constructed the points, we can fit a line described | ||
// by homogeneous coordinates | // by homogeneous coordinates | ||
Revision as of 16:50, 9 November 2010
This little JXSGraph application finds the line - described by homogeneous coordinates [a,b,c] - that minimizes
- [math]\displaystyle{ \sum_{i=1}^n (ax_i+by_i+cz_i)^2. }[/math]
Coming soon...
