lcsim/src/org/lcsim/recon/cluster/util
diff -u -r1.7 -r1.8
--- TensorClusterPropertyCalculator.java 3 Nov 2006 19:17:13 -0000 1.7
+++ TensorClusterPropertyCalculator.java 20 Dec 2007 19:05:35 -0000 1.8
@@ -200,18 +200,104 @@
EV[1] = E2;
EV[2] = E3;
// Now calculate principal axes
- for( int i = 0 ; i < 3 ; i++ )
- {
- double[] C = new double[3];
- C[0] = 1.0;
- C[2] = (Exy*Exy + (Eyy - EV[i])*(EV[i] - Exx))/
- ((Eyy - EV[i])*Exz - Eyz*Exy);
- C[1] = (EV[i] - Exx - Exz*C[2])/Exy;
- double norm = Math.sqrt(C[0]*C[0] + C[1]*C[1] + C[2]*C[2]);
- mm_PA[i][0] = C[0]/norm;
- mm_PA[i][1] = C[1]/norm;
- mm_PA[i][2] = C[2]/norm;
- }
+ // For eigenvalue EV, the axis is (nx, ny, nz) where:
+ // (Exx - EV)nx + (Exy)ny + (Exz)nz = 0
+ // (Eyx)nx + (Eyy - EV)ny + (Eyz)nz = 0
+ // (Ezx)nx + (Ezy)ny + (Ezz - EV)nz = 0
+ // Setting nx = 1, we have:
+ // (Exx - EV) + (Exy)ny + (Exz)nz = 0
+ // (Eyx) + (Eyy - EV)ny + (Eyz)nz = 0
+ // (Ezx) + (Ezy)ny + (Ezz - EV)nz = 0
+ // and so
+ // (Exy)ny = EV - Exx - (Exz)nz => ny = (EV - Exx - Exz*nz)/Exy
+ // What if Exy = 0? Then provided Eyz is non-zero we can write:
+ // (Ezx) + (Ezy)ny + (Ezz - EV)nz = 0
+ // ny = (Exz - (Ezz-EV)*nz)/Eyz
+ // What if Exy = 0 and Eyz = 0 but (Eyy - EV) is non-zero?
+ // (Eyy - EV)ny + (Eyz)nz = 0
+ // ny = -(Eyz*nz)/(Eyy-EV)
+
+ // In the pathological case where Exz = Eyz = Ezz = 0:
+ // (Exx - EV)nx + (Exy)ny = 0 => ny/nx = -(Exx-EV)/Exy
+ // (Eyx)nx + (Eyy - EV)ny = 0 => ny/nx = -Eyx/(Eyy-EV)
+ // (EV)nz = 0
+ // so
+ // -ny/nx = (EV-Exx)/Exy = Eyx/(EV-Eyy)
+ // But watch out for order! Recalculate eigenvalues for this pathological case.
+ // (EV-Exx)(EV-Eyy) = Eyx*Exy
+ // EV^2 - EV(Exx+Eyy) + Exx*Eyy - Eyx*Exy = 0
+ //
+ // In another pathological case, Exz = Exy = 0:
+ // (Exx - EV)nx = 0
+ // (Eyy - EV)ny + (Eyz)nz = 0 => ny/nz = -(Eyz)/(Eyy-EV)
+ // (Ezy)ny + (Ezz - EV)nz = 0 => ny/nz = -(Ezz-EV)/(Ezy)
+ // so we cannot set nx = 1. Instead, write:
+ // -ny/nz = (Eyz)/(Eyy-EV) = (Ezz-EV)/(Ezy)
+ // Then
+ // (Eyz)(Ezy) = (Eyy-EV)(Ezz-EV)
+ // (Eyz)^2 = (Eyy)(Ezz) - (Eyy)(EV) - (Ezz)(EV) + (EV)^2
+ // EV^2 - EV(Eyy+Ezz) + Eyy*Ezz - Eyz*Eyz = 0
+
+ // Handle pathological case
+ if (Exz == 0.0 && Eyz == 0.0) {
+ // Recompute eigenvectors.
+ EV[0] = 0.5*(Exx+Eyy) + 0.5*Math.sqrt((Exx+Eyy)*(Exx+Eyy) + 4.0*Exy*Exy);
+ EV[1] = 0.5*(Exx+Eyy) - 0.5*Math.sqrt((Exx+Eyy)*(Exx+Eyy) + 4.0*Exy*Exy);
+ EV[2] = 0.0;
+ for( int i = 0 ; i < 2 ; i++ ) {
+ double nx_over_ny = Exy / (Exx-EV[i]);
+ double nx_unnormalized = nx_over_ny;
+ double ny_unnormalized = 1.0;
+ double norm = Math.sqrt(nx_unnormalized*nx_unnormalized + ny_unnormalized*ny_unnormalized);
+ mm_PA[i][0] = ny_unnormalized/norm;
+ mm_PA[i][1] = nx_unnormalized/norm;
+ mm_PA[i][2] = 0.0;
+ }
+ // ... and now set third eigenvector to the z direction:
+ mm_PA[2][0] = 0.0;
+ mm_PA[2][1] = 0.0;
+ mm_PA[2][2] = 1.0;
+ } else if (Exz == 0.0 && Exy == 0.0) {
+ // Another pathological case
+ EV[0] = 0.5*(Eyy+Ezz) + 0.5*Math.sqrt((Eyy+Ezz)*(Eyy+Ezz) + 4.0*Eyz*Eyz);
+ EV[1] = 0.5*(Eyy+Ezz) - 0.5*Math.sqrt((Eyy+Ezz)*(Eyy+Ezz) + 4.0*Eyz*Eyz);
+ EV[2] = 0.0;
+ for( int i = 0 ; i < 2 ; i++ ) {
+ double ny_over_nz = Eyz / (Eyy-EV[i]);
+ double ny_unnormalized = ny_over_nz;
+ double nz_unnormalized = 1.0;
+ double norm = Math.sqrt(ny_unnormalized*ny_unnormalized + nz_unnormalized*nz_unnormalized);
+ mm_PA[i][0] = nz_unnormalized/norm;
+ mm_PA[i][1] = ny_unnormalized/norm;
+ mm_PA[i][2] = 0.0;
+ }
+ mm_PA[2][0] = 0.0;
+ mm_PA[2][1] = 0.0;
+ mm_PA[2][2] = 1.0;
+ } else {
+ for( int i = 0 ; i < 3 ; i++ )
+ {
+ double[] C = new double[3];
+ C[0] = 1.0;
+ C[2] = (Exy*Exy + (Eyy - EV[i])*(EV[i] - Exx))/
+ ((Eyy - EV[i])*Exz - Eyz*Exy);
+ C[1] = (EV[i] - Exx - Exz*C[2])/Exy;
+ if (Exy == 0.0) {
+ // Recompute
+ if (Eyz != 0.0) {
+ // ny = (Exz - (Ezz-EV)*nz)/Eyz
+ C[1] = (Exz - (Ezz-EV[i])*C[2])/Eyz;
+ } else {
+ // ny = -(Eyz*nz)/(Eyy-EV)
+ C[1] = -(Eyz*C[2])/(Eyy-EV[i]);
+ }
+ }
+ double norm = Math.sqrt(C[0]*C[0] + C[1]*C[1] + C[2]*C[2]);
+ mm_PA[i][0] = C[0]/norm;
+ mm_PA[i][1] = C[1]/norm;
+ mm_PA[i][2] = C[2]/norm;
+ }
+ }
}
mm_NE[0] = NE1;
mm_NE[1] = NE2;