public static void rotate12(SMat3 vtav, DMat3 v)
{
if (vtav.m12 == 0)
{
return;
}
double c = 0, s = 0;
Schur2.rot12(vtav, c, s);
Givens.rot12_post(v, c, s);
}
public static void rotate01(SMat3 vtav, DMat3 v)
{
if (vtav.m01 == 0)
{
return;
}
double c = 0, s = 0;
Schur2.rot01(vtav, c, s);
Givens.rot01_post(v, c, s);
}
public static double solveSymmetric(SMat3 A, Vec3 b, Vec3 x, double svd_tol, int svd_sweeps,
double pinv_tol)
{
DMat3 pinv;
var V = new DMat3();
var VTAV = new SMat3();
getSymmetricSvd(A, VTAV, V, svd_tol, svd_sweeps);
pseudoinverse(out pinv, VTAV, V, pinv_tol);
MatUtils.vmul(out x, pinv, b);
return(calcError(A, x, b));
}
public static void getSymmetricSvd(SMat3 a, SMat3 vtav, DMat3 v, double tol, int max_sweeps)
{
vtav.setSymmetric(a);
v.set(1, 0, 0, 0, 1, 0, 0, 0, 1);
var delta = tol * MatUtils.fnorm(vtav);
for (var i = 0; i < max_sweeps && MatUtils.off(vtav) > delta; ++i)
{
rotate01(vtav, v);
rotate02(vtav, v);
rotate12(vtav, v);
}
}
public static void pseudoinverse(out DMat3 Out, SMat3 d, DMat3 v, double tol)
{
double d0 = pinv(d.m00, tol), d1 = pinv(d.m11, tol), d2 = pinv(d.m22, tol);
Out = new DMat3();
Out.set(v.m00 * d0 * v.m00 + v.m01 * d1 * v.m01 + v.m02 * d2 * v.m02,
v.m00 * d0 * v.m10 + v.m01 * d1 * v.m11 + v.m02 * d2 * v.m12,
v.m00 * d0 * v.m20 + v.m01 * d1 * v.m21 + v.m02 * d2 * v.m22,
v.m10 * d0 * v.m00 + v.m11 * d1 * v.m01 + v.m12 * d2 * v.m02,
v.m10 * d0 * v.m10 + v.m11 * d1 * v.m11 + v.m12 * d2 * v.m12,
v.m10 * d0 * v.m20 + v.m11 * d1 * v.m21 + v.m12 * d2 * v.m22,
v.m20 * d0 * v.m00 + v.m21 * d1 * v.m01 + v.m22 * d2 * v.m02,
v.m20 * d0 * v.m10 + v.m21 * d1 * v.m11 + v.m22 * d2 * v.m12,
v.m20 * d0 * v.m20 + v.m21 * d1 * v.m21 + v.m22 * d2 * v.m22);
}
public static double off(SMat3 a)
{
return(Math.Sqrt(2 * ((a.m01 * a.m01) + (a.m02 * a.m02) + (a.m12 * a.m12))));
}
public static double fnorm(SMat3 a)
{
return(Math.Sqrt((a.m00 * a.m00) + (a.m01 * a.m01) + (a.m02 * a.m02)
+ (a.m01 * a.m01) + (a.m11 * a.m11) + (a.m12 * a.m12)
+ (a.m02 * a.m02) + (a.m12 * a.m12) + (a.m22 * a.m22)));
}
