public static void vmul(out Vec3 Out, DMat3 a, Vec3 v) { Out = new Vec3( (float)((a.m00 * v.X) + (a.m01 * v.Y) + (a.m02 * v.Z)), (float)((a.m10 * v.X) + (a.m11 * v.Y) + (a.m12 * v.Z)), (float)((a.m20 * v.X) + (a.m21 * v.Y) + (a.m22 * v.Z))); }
public static double calcError(DMat3 A, Vec3 x, Vec3 b) { Vec3 vtmp; MatUtils.vmul(out vtmp, A, x); vtmp = b - vtmp; return(vtmp.Dot(vtmp)); }
public static double calcError(SMat3 origA, Vec3 x, Vec3 b) { var A = new DMat3(); Vec3 vtmp; A.setSymmetric(origA); MatUtils.vmul(out vtmp, A, x); vtmp = b - vtmp; return(vtmp.Dot(vtmp)); }
public static void mmul_ata(out SMat3 Out, DMat3 a) { Out = new SMat3(); Out.setSymmetric(a.m00 * a.m00 + a.m10 * a.m10 + a.m20 * a.m20, a.m00 * a.m01 + a.m10 * a.m11 + a.m20 * a.m21, a.m00 * a.m02 + a.m10 * a.m12 + a.m20 * a.m22, a.m01 * a.m01 + a.m11 * a.m11 + a.m21 * a.m21, a.m01 * a.m02 + a.m11 * a.m12 + a.m21 * a.m22, a.m02 * a.m02 + a.m12 * a.m12 + a.m22 * a.m22); }
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 solveLeastSquares(DMat3 a, Vec3 b, Vec3 x, double svd_tol, int svd_sweeps, double pinv_tol) { DMat3 at; SMat3 ata; Vec3 atb; MatUtils.transpose(out at, a); MatUtils.mmul_ata(out ata, a); MatUtils.vmul(out atb, at, b); return(solveSymmetric(ata, atb, x, svd_tol, svd_sweeps, pinv_tol)); }
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 mmul(out DMat3 Out, DMat3 a, DMat3 b) { Out = new DMat3(); Out.set(a.m00 * b.m00 + a.m01 * b.m10 + a.m02 * b.m20, a.m00 * b.m01 + a.m01 * b.m11 + a.m02 * b.m21, a.m00 * b.m02 + a.m01 * b.m12 + a.m02 * b.m22, a.m10 * b.m00 + a.m11 * b.m10 + a.m12 * b.m20, a.m10 * b.m01 + a.m11 * b.m11 + a.m12 * b.m21, a.m10 * b.m02 + a.m11 * b.m12 + a.m12 * b.m22, a.m20 * b.m00 + a.m21 * b.m10 + a.m22 * b.m20, a.m20 * b.m01 + a.m21 * b.m11 + a.m22 * b.m21, a.m20 * b.m02 + a.m21 * b.m12 + a.m22 * b.m22); }
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 void transpose(out DMat3 Out, DMat3 a) { Out = new DMat3(); Out.set(a.m00, a.m10, a.m20, a.m01, a.m11, a.m21, a.m02, a.m12, a.m22); }
public static double fnorm(DMat3 a) { return(Math.Sqrt((a.m00 * a.m00) + (a.m01 * a.m01) + (a.m02 * a.m02) + (a.m10 * a.m10) + (a.m11 * a.m11) + (a.m12 * a.m12) + (a.m20 * a.m20) + (a.m21 * a.m21) + (a.m22 * a.m22))); }
public static double off(DMat3 a) { return(Math.Sqrt((a.m01 * a.m01) + (a.m02 * a.m02) + (a.m10 * a.m10) + (a.m12 * a.m12) + (a.m20 * a.m20) + (a.m21 * a.m21))); }