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-rw-r--r--thirdparty/thekla_atlas/nvmath/Fitting.cpp1205
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diff --git a/thirdparty/thekla_atlas/nvmath/Fitting.cpp b/thirdparty/thekla_atlas/nvmath/Fitting.cpp
deleted file mode 100644
index 6cd5cb0f32..0000000000
--- a/thirdparty/thekla_atlas/nvmath/Fitting.cpp
+++ /dev/null
@@ -1,1205 +0,0 @@
-// This code is in the public domain -- Ignacio Castaño <castano@gmail.com>
-
-#include "Fitting.h"
-#include "Vector.inl"
-#include "Plane.inl"
-
-#include "nvcore/Array.inl"
-#include "nvcore/Utils.h" // max, swap
-
-#include <float.h> // FLT_MAX
-//#include <vector>
-#include <string.h>
-
-using namespace nv;
-
-// @@ Move to EigenSolver.h
-
-// @@ We should be able to do something cheaper...
-static Vector3 estimatePrincipalComponent(const float * __restrict matrix)
-{
- const Vector3 row0(matrix[0], matrix[1], matrix[2]);
- const Vector3 row1(matrix[1], matrix[3], matrix[4]);
- const Vector3 row2(matrix[2], matrix[4], matrix[5]);
-
- float r0 = lengthSquared(row0);
- float r1 = lengthSquared(row1);
- float r2 = lengthSquared(row2);
-
- if (r0 > r1 && r0 > r2) return row0;
- if (r1 > r2) return row1;
- return row2;
-}
-
-
-static inline Vector3 firstEigenVector_PowerMethod(const float *__restrict matrix)
-{
- if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
- {
- return Vector3(0.0f);
- }
-
- Vector3 v = estimatePrincipalComponent(matrix);
-
- const int NUM = 8;
- for (int i = 0; i < NUM; i++)
- {
- float x = v.x * matrix[0] + v.y * matrix[1] + v.z * matrix[2];
- float y = v.x * matrix[1] + v.y * matrix[3] + v.z * matrix[4];
- float z = v.x * matrix[2] + v.y * matrix[4] + v.z * matrix[5];
-
- float norm = max(max(x, y), z);
-
- v = Vector3(x, y, z) / norm;
- }
-
- return v;
-}
-
-
-Vector3 nv::Fit::computeCentroid(int n, const Vector3 *__restrict points)
-{
- Vector3 centroid(0.0f);
-
- for (int i = 0; i < n; i++)
- {
- centroid += points[i];
- }
- centroid /= float(n);
-
- return centroid;
-}
-
-Vector3 nv::Fit::computeCentroid(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric)
-{
- Vector3 centroid(0.0f);
- float total = 0.0f;
-
- for (int i = 0; i < n; i++)
- {
- total += weights[i];
- centroid += weights[i]*points[i];
- }
- centroid /= total;
-
- return centroid;
-}
-
-Vector4 nv::Fit::computeCentroid(int n, const Vector4 *__restrict points)
-{
- Vector4 centroid(0.0f);
-
- for (int i = 0; i < n; i++)
- {
- centroid += points[i];
- }
- centroid /= float(n);
-
- return centroid;
-}
-
-Vector4 nv::Fit::computeCentroid(int n, const Vector4 *__restrict points, const float *__restrict weights, Vector4::Arg metric)
-{
- Vector4 centroid(0.0f);
- float total = 0.0f;
-
- for (int i = 0; i < n; i++)
- {
- total += weights[i];
- centroid += weights[i]*points[i];
- }
- centroid /= total;
-
- return centroid;
-}
-
-
-
-Vector3 nv::Fit::computeCovariance(int n, const Vector3 *__restrict points, float *__restrict covariance)
-{
- // compute the centroid
- Vector3 centroid = computeCentroid(n, points);
-
- // compute covariance matrix
- for (int i = 0; i < 6; i++)
- {
- covariance[i] = 0.0f;
- }
-
- for (int i = 0; i < n; i++)
- {
- Vector3 v = points[i] - centroid;
-
- covariance[0] += v.x * v.x;
- covariance[1] += v.x * v.y;
- covariance[2] += v.x * v.z;
- covariance[3] += v.y * v.y;
- covariance[4] += v.y * v.z;
- covariance[5] += v.z * v.z;
- }
-
- return centroid;
-}
-
-Vector3 nv::Fit::computeCovariance(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric, float *__restrict covariance)
-{
- // compute the centroid
- Vector3 centroid = computeCentroid(n, points, weights, metric);
-
- // compute covariance matrix
- for (int i = 0; i < 6; i++)
- {
- covariance[i] = 0.0f;
- }
-
- for (int i = 0; i < n; i++)
- {
- Vector3 a = (points[i] - centroid) * metric;
- Vector3 b = weights[i]*a;
-
- covariance[0] += a.x * b.x;
- covariance[1] += a.x * b.y;
- covariance[2] += a.x * b.z;
- covariance[3] += a.y * b.y;
- covariance[4] += a.y * b.z;
- covariance[5] += a.z * b.z;
- }
-
- return centroid;
-}
-
-Vector4 nv::Fit::computeCovariance(int n, const Vector4 *__restrict points, float *__restrict covariance)
-{
- // compute the centroid
- Vector4 centroid = computeCentroid(n, points);
-
- // compute covariance matrix
- for (int i = 0; i < 10; i++)
- {
- covariance[i] = 0.0f;
- }
-
- for (int i = 0; i < n; i++)
- {
- Vector4 v = points[i] - centroid;
-
- covariance[0] += v.x * v.x;
- covariance[1] += v.x * v.y;
- covariance[2] += v.x * v.z;
- covariance[3] += v.x * v.w;
-
- covariance[4] += v.y * v.y;
- covariance[5] += v.y * v.z;
- covariance[6] += v.y * v.w;
-
- covariance[7] += v.z * v.z;
- covariance[8] += v.z * v.w;
-
- covariance[9] += v.w * v.w;
- }
-
- return centroid;
-}
-
-Vector4 nv::Fit::computeCovariance(int n, const Vector4 *__restrict points, const float *__restrict weights, Vector4::Arg metric, float *__restrict covariance)
-{
- // compute the centroid
- Vector4 centroid = computeCentroid(n, points, weights, metric);
-
- // compute covariance matrix
- for (int i = 0; i < 10; i++)
- {
- covariance[i] = 0.0f;
- }
-
- for (int i = 0; i < n; i++)
- {
- Vector4 a = (points[i] - centroid) * metric;
- Vector4 b = weights[i]*a;
-
- covariance[0] += a.x * b.x;
- covariance[1] += a.x * b.y;
- covariance[2] += a.x * b.z;
- covariance[3] += a.x * b.w;
-
- covariance[4] += a.y * b.y;
- covariance[5] += a.y * b.z;
- covariance[6] += a.y * b.w;
-
- covariance[7] += a.z * b.z;
- covariance[8] += a.z * b.w;
-
- covariance[9] += a.w * b.w;
- }
-
- return centroid;
-}
-
-
-
-Vector3 nv::Fit::computePrincipalComponent_PowerMethod(int n, const Vector3 *__restrict points)
-{
- float matrix[6];
- computeCovariance(n, points, matrix);
-
- return firstEigenVector_PowerMethod(matrix);
-}
-
-Vector3 nv::Fit::computePrincipalComponent_PowerMethod(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric)
-{
- float matrix[6];
- computeCovariance(n, points, weights, metric, matrix);
-
- return firstEigenVector_PowerMethod(matrix);
-}
-
-
-
-static inline Vector3 firstEigenVector_EigenSolver3(const float *__restrict matrix)
-{
- if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
- {
- return Vector3(0.0f);
- }
-
- float eigenValues[3];
- Vector3 eigenVectors[3];
- if (!nv::Fit::eigenSolveSymmetric3(matrix, eigenValues, eigenVectors))
- {
- return Vector3(0.0f);
- }
-
- return eigenVectors[0];
-}
-
-Vector3 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector3 *__restrict points)
-{
- float matrix[6];
- computeCovariance(n, points, matrix);
-
- return firstEigenVector_EigenSolver3(matrix);
-}
-
-Vector3 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric)
-{
- float matrix[6];
- computeCovariance(n, points, weights, metric, matrix);
-
- return firstEigenVector_EigenSolver3(matrix);
-}
-
-
-
-static inline Vector4 firstEigenVector_EigenSolver4(const float *__restrict matrix)
-{
- if (matrix[0] == 0 && matrix[4] == 0 && matrix[7] == 0&& matrix[9] == 0)
- {
- return Vector4(0.0f);
- }
-
- float eigenValues[4];
- Vector4 eigenVectors[4];
- if (!nv::Fit::eigenSolveSymmetric4(matrix, eigenValues, eigenVectors))
- {
- return Vector4(0.0f);
- }
-
- return eigenVectors[0];
-}
-
-Vector4 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector4 *__restrict points)
-{
- float matrix[10];
- computeCovariance(n, points, matrix);
-
- return firstEigenVector_EigenSolver4(matrix);
-}
-
-Vector4 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector4 *__restrict points, const float *__restrict weights, Vector4::Arg metric)
-{
- float matrix[10];
- computeCovariance(n, points, weights, metric, matrix);
-
- return firstEigenVector_EigenSolver4(matrix);
-}
-
-
-
-void ArvoSVD(int rows, int cols, float * Q, float * diag, float * R);
-
-Vector3 nv::Fit::computePrincipalComponent_SVD(int n, const Vector3 *__restrict points)
-{
- // Store the points in an n x n matrix
- Array<float> Q; Q.resize(n*n, 0.0f);
- for (int i = 0; i < n; ++i)
- {
- Q[i*n+0] = points[i].x;
- Q[i*n+1] = points[i].y;
- Q[i*n+2] = points[i].z;
- }
-
- // Alloc space for the SVD outputs
- Array<float> diag; diag.resize(n, 0.0f);
- Array<float> R; R.resize(n*n, 0.0f);
-
- ArvoSVD(n, n, &Q[0], &diag[0], &R[0]);
-
- // Get the principal component
- return Vector3(R[0], R[1], R[2]);
-}
-
-Vector4 nv::Fit::computePrincipalComponent_SVD(int n, const Vector4 *__restrict points)
-{
- // Store the points in an n x n matrix
- Array<float> Q; Q.resize(n*n, 0.0f);
- for (int i = 0; i < n; ++i)
- {
- Q[i*n+0] = points[i].x;
- Q[i*n+1] = points[i].y;
- Q[i*n+2] = points[i].z;
- Q[i*n+3] = points[i].w;
- }
-
- // Alloc space for the SVD outputs
- Array<float> diag; diag.resize(n, 0.0f);
- Array<float> R; R.resize(n*n, 0.0f);
-
- ArvoSVD(n, n, &Q[0], &diag[0], &R[0]);
-
- // Get the principal component
- return Vector4(R[0], R[1], R[2], R[3]);
-}
-
-
-
-Plane nv::Fit::bestPlane(int n, const Vector3 *__restrict points)
-{
- // compute the centroid and covariance
- float matrix[6];
- Vector3 centroid = computeCovariance(n, points, matrix);
-
- if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
- {
- // If no plane defined, then return a horizontal plane.
- return Plane(Vector3(0, 0, 1), centroid);
- }
-
- float eigenValues[3];
- Vector3 eigenVectors[3];
- if (!eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
- // If no plane defined, then return a horizontal plane.
- return Plane(Vector3(0, 0, 1), centroid);
- }
-
- return Plane(eigenVectors[2], centroid);
-}
-
-bool nv::Fit::isPlanar(int n, const Vector3 * points, float epsilon/*=NV_EPSILON*/)
-{
- // compute the centroid and covariance
- float matrix[6];
- computeCovariance(n, points, matrix);
-
- float eigenValues[3];
- Vector3 eigenVectors[3];
- if (!eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
- return false;
- }
-
- return eigenValues[2] < epsilon;
-}
-
-
-
-// Tridiagonal solver from Charles Bloom.
-// Householder transforms followed by QL decomposition.
-// Seems to be based on the code from Numerical Recipes in C.
-
-static void EigenSolver3_Tridiagonal(float mat[3][3], float * diag, float * subd);
-static bool EigenSolver3_QLAlgorithm(float mat[3][3], float * diag, float * subd);
-
-bool nv::Fit::eigenSolveSymmetric3(const float matrix[6], float eigenValues[3], Vector3 eigenVectors[3])
-{
- nvDebugCheck(matrix != NULL && eigenValues != NULL && eigenVectors != NULL);
-
- float subd[3];
- float diag[3];
- float work[3][3];
-
- work[0][0] = matrix[0];
- work[0][1] = work[1][0] = matrix[1];
- work[0][2] = work[2][0] = matrix[2];
- work[1][1] = matrix[3];
- work[1][2] = work[2][1] = matrix[4];
- work[2][2] = matrix[5];
-
- EigenSolver3_Tridiagonal(work, diag, subd);
- if (!EigenSolver3_QLAlgorithm(work, diag, subd))
- {
- for (int i = 0; i < 3; i++) {
- eigenValues[i] = 0;
- eigenVectors[i] = Vector3(0);
- }
- return false;
- }
-
- for (int i = 0; i < 3; i++) {
- eigenValues[i] = (float)diag[i];
- }
-
- // eigenvectors are the columns; make them the rows :
-
- for (int i=0; i < 3; i++)
- {
- for (int j = 0; j < 3; j++)
- {
- eigenVectors[j].component[i] = (float) work[i][j];
- }
- }
-
- // shuffle to sort by singular value :
- if (eigenValues[2] > eigenValues[0] && eigenValues[2] > eigenValues[1])
- {
- swap(eigenValues[0], eigenValues[2]);
- swap(eigenVectors[0], eigenVectors[2]);
- }
- if (eigenValues[1] > eigenValues[0])
- {
- swap(eigenValues[0], eigenValues[1]);
- swap(eigenVectors[0], eigenVectors[1]);
- }
- if (eigenValues[2] > eigenValues[1])
- {
- swap(eigenValues[1], eigenValues[2]);
- swap(eigenVectors[1], eigenVectors[2]);
- }
-
- nvDebugCheck(eigenValues[0] >= eigenValues[1] && eigenValues[0] >= eigenValues[2]);
- nvDebugCheck(eigenValues[1] >= eigenValues[2]);
-
- return true;
-}
-
-static void EigenSolver3_Tridiagonal(float mat[3][3], float * diag, float * subd)
-{
- // Householder reduction T = Q^t M Q
- // Input:
- // mat, symmetric 3x3 matrix M
- // Output:
- // mat, orthogonal matrix Q
- // diag, diagonal entries of T
- // subd, subdiagonal entries of T (T is symmetric)
- const float epsilon = 1e-08f;
-
- float a = mat[0][0];
- float b = mat[0][1];
- float c = mat[0][2];
- float d = mat[1][1];
- float e = mat[1][2];
- float f = mat[2][2];
-
- diag[0] = a;
- subd[2] = 0.f;
- if (fabsf(c) >= epsilon)
- {
- const float ell = sqrtf(b*b+c*c);
- b /= ell;
- c /= ell;
- const float q = 2*b*e+c*(f-d);
- diag[1] = d+c*q;
- diag[2] = f-c*q;
- subd[0] = ell;
- subd[1] = e-b*q;
- mat[0][0] = 1; mat[0][1] = 0; mat[0][2] = 0;
- mat[1][0] = 0; mat[1][1] = b; mat[1][2] = c;
- mat[2][0] = 0; mat[2][1] = c; mat[2][2] = -b;
- }
- else
- {
- diag[1] = d;
- diag[2] = f;
- subd[0] = b;
- subd[1] = e;
- mat[0][0] = 1; mat[0][1] = 0; mat[0][2] = 0;
- mat[1][0] = 0; mat[1][1] = 1; mat[1][2] = 0;
- mat[2][0] = 0; mat[2][1] = 0; mat[2][2] = 1;
- }
-}
-
-static bool EigenSolver3_QLAlgorithm(float mat[3][3], float * diag, float * subd)
-{
- // QL iteration with implicit shifting to reduce matrix from tridiagonal
- // to diagonal
- const int maxiter = 32;
-
- for (int ell = 0; ell < 3; ell++)
- {
- int iter;
- for (iter = 0; iter < maxiter; iter++)
- {
- int m;
- for (m = ell; m <= 1; m++)
- {
- float dd = fabsf(diag[m]) + fabsf(diag[m+1]);
- if ( fabsf(subd[m]) + dd == dd )
- break;
- }
- if ( m == ell )
- break;
-
- float g = (diag[ell+1]-diag[ell])/(2*subd[ell]);
- float r = sqrtf(g*g+1);
- if ( g < 0 )
- g = diag[m]-diag[ell]+subd[ell]/(g-r);
- else
- g = diag[m]-diag[ell]+subd[ell]/(g+r);
- float s = 1, c = 1, p = 0;
- for (int i = m-1; i >= ell; i--)
- {
- float f = s*subd[i], b = c*subd[i];
- if ( fabsf(f) >= fabsf(g) )
- {
- c = g/f;
- r = sqrtf(c*c+1);
- subd[i+1] = f*r;
- c *= (s = 1/r);
- }
- else
- {
- s = f/g;
- r = sqrtf(s*s+1);
- subd[i+1] = g*r;
- s *= (c = 1/r);
- }
- g = diag[i+1]-p;
- r = (diag[i]-g)*s+2*b*c;
- p = s*r;
- diag[i+1] = g+p;
- g = c*r-b;
-
- for (int k = 0; k < 3; k++)
- {
- f = mat[k][i+1];
- mat[k][i+1] = s*mat[k][i]+c*f;
- mat[k][i] = c*mat[k][i]-s*f;
- }
- }
- diag[ell] -= p;
- subd[ell] = g;
- subd[m] = 0;
- }
-
- if ( iter == maxiter )
- // should not get here under normal circumstances
- return false;
- }
-
- return true;
-}
-
-
-
-// Tridiagonal solver for 4x4 symmetric matrices.
-
-static void EigenSolver4_Tridiagonal(float mat[4][4], float * diag, float * subd);
-static bool EigenSolver4_QLAlgorithm(float mat[4][4], float * diag, float * subd);
-
-bool nv::Fit::eigenSolveSymmetric4(const float matrix[10], float eigenValues[4], Vector4 eigenVectors[4])
-{
- nvDebugCheck(matrix != NULL && eigenValues != NULL && eigenVectors != NULL);
-
- float subd[4];
- float diag[4];
- float work[4][4];
-
- work[0][0] = matrix[0];
- work[0][1] = work[1][0] = matrix[1];
- work[0][2] = work[2][0] = matrix[2];
- work[0][3] = work[3][0] = matrix[3];
- work[1][1] = matrix[4];
- work[1][2] = work[2][1] = matrix[5];
- work[1][3] = work[3][1] = matrix[6];
- work[2][2] = matrix[7];
- work[2][3] = work[3][2] = matrix[8];
- work[3][3] = matrix[9];
-
- EigenSolver4_Tridiagonal(work, diag, subd);
- if (!EigenSolver4_QLAlgorithm(work, diag, subd))
- {
- for (int i = 0; i < 4; i++) {
- eigenValues[i] = 0;
- eigenVectors[i] = Vector4(0);
- }
- return false;
- }
-
- for (int i = 0; i < 4; i++) {
- eigenValues[i] = (float)diag[i];
- }
-
- // eigenvectors are the columns; make them the rows
-
- for (int i = 0; i < 4; i++)
- {
- for (int j = 0; j < 4; j++)
- {
- eigenVectors[j].component[i] = (float) work[i][j];
- }
- }
-
- // sort by singular value
-
- for (int i = 0; i < 3; ++i)
- {
- for (int j = i+1; j < 4; ++j)
- {
- if (eigenValues[j] > eigenValues[i])
- {
- swap(eigenValues[i], eigenValues[j]);
- swap(eigenVectors[i], eigenVectors[j]);
- }
- }
- }
-
- nvDebugCheck(eigenValues[0] >= eigenValues[1] && eigenValues[0] >= eigenValues[2] && eigenValues[0] >= eigenValues[3]);
- nvDebugCheck(eigenValues[1] >= eigenValues[2] && eigenValues[1] >= eigenValues[3]);
- nvDebugCheck(eigenValues[2] >= eigenValues[2]);
-
- return true;
-}
-
-#include "nvmath/Matrix.inl"
-
-inline float signNonzero(float x)
-{
- return (x >= 0.0f) ? 1.0f : -1.0f;
-}
-
-static void EigenSolver4_Tridiagonal(float mat[4][4], float * diag, float * subd)
-{
- // Householder reduction T = Q^t M Q
- // Input:
- // mat, symmetric 3x3 matrix M
- // Output:
- // mat, orthogonal matrix Q
- // diag, diagonal entries of T
- // subd, subdiagonal entries of T (T is symmetric)
-
- static const int n = 4;
-
- // Set epsilon relative to size of elements in matrix
- static const float relEpsilon = 1e-6f;
- float maxElement = FLT_MAX;
- for (int i = 0; i < n; ++i)
- for (int j = 0; j < n; ++j)
- maxElement = max(maxElement, fabsf(mat[i][j]));
- float epsilon = relEpsilon * maxElement;
-
- // Iterative algorithm, works for any size of matrix but might be slower than
- // a closed-form solution for symmetric 4x4 matrices. Based on this article:
- // http://en.wikipedia.org/wiki/Householder_transformation#Tridiagonalization
-
- Matrix A, Q(identity);
- memcpy(&A, mat, sizeof(float)*n*n);
-
- // We proceed from left to right, making the off-tridiagonal entries zero in
- // one column of the matrix at a time.
- for (int k = 0; k < n - 2; ++k)
- {
- float sum = 0.0f;
- for (int j = k+1; j < n; ++j)
- sum += A(j,k)*A(j,k);
- float alpha = -signNonzero(A(k+1,k)) * sqrtf(sum);
- float r = sqrtf(0.5f * (alpha*alpha - A(k+1,k)*alpha));
-
- // If r is zero, skip this column - already in tridiagonal form
- if (fabsf(r) < epsilon)
- continue;
-
- float v[n] = {};
- v[k+1] = 0.5f * (A(k+1,k) - alpha) / r;
- for (int j = k+2; j < n; ++j)
- v[j] = 0.5f * A(j,k) / r;
-
- Matrix P(identity);
- for (int i = 0; i < n; ++i)
- for (int j = 0; j < n; ++j)
- P(i,j) -= 2.0f * v[i] * v[j];
-
- A = mul(mul(P, A), P);
- Q = mul(Q, P);
- }
-
- nvDebugCheck(fabsf(A(2,0)) < epsilon);
- nvDebugCheck(fabsf(A(0,2)) < epsilon);
- nvDebugCheck(fabsf(A(3,0)) < epsilon);
- nvDebugCheck(fabsf(A(0,3)) < epsilon);
- nvDebugCheck(fabsf(A(3,1)) < epsilon);
- nvDebugCheck(fabsf(A(1,3)) < epsilon);
-
- for (int i = 0; i < n; ++i)
- diag[i] = A(i,i);
- for (int i = 0; i < n - 1; ++i)
- subd[i] = A(i+1,i);
- subd[n-1] = 0.0f;
-
- memcpy(mat, &Q, sizeof(float)*n*n);
-}
-
-static bool EigenSolver4_QLAlgorithm(float mat[4][4], float * diag, float * subd)
-{
- // QL iteration with implicit shifting to reduce matrix from tridiagonal
- // to diagonal
- const int maxiter = 32;
-
- for (int ell = 0; ell < 4; ell++)
- {
- int iter;
- for (iter = 0; iter < maxiter; iter++)
- {
- int m;
- for (m = ell; m < 3; m++)
- {
- float dd = fabsf(diag[m]) + fabsf(diag[m+1]);
- if ( fabsf(subd[m]) + dd == dd )
- break;
- }
- if ( m == ell )
- break;
-
- float g = (diag[ell+1]-diag[ell])/(2*subd[ell]);
- float r = sqrtf(g*g+1);
- if ( g < 0 )
- g = diag[m]-diag[ell]+subd[ell]/(g-r);
- else
- g = diag[m]-diag[ell]+subd[ell]/(g+r);
- float s = 1, c = 1, p = 0;
- for (int i = m-1; i >= ell; i--)
- {
- float f = s*subd[i], b = c*subd[i];
- if ( fabsf(f) >= fabsf(g) )
- {
- c = g/f;
- r = sqrtf(c*c+1);
- subd[i+1] = f*r;
- c *= (s = 1/r);
- }
- else
- {
- s = f/g;
- r = sqrtf(s*s+1);
- subd[i+1] = g*r;
- s *= (c = 1/r);
- }
- g = diag[i+1]-p;
- r = (diag[i]-g)*s+2*b*c;
- p = s*r;
- diag[i+1] = g+p;
- g = c*r-b;
-
- for (int k = 0; k < 4; k++)
- {
- f = mat[k][i+1];
- mat[k][i+1] = s*mat[k][i]+c*f;
- mat[k][i] = c*mat[k][i]-s*f;
- }
- }
- diag[ell] -= p;
- subd[ell] = g;
- subd[m] = 0;
- }
-
- if ( iter == maxiter )
- // should not get here under normal circumstances
- return false;
- }
-
- return true;
-}
-
-
-
-int nv::Fit::compute4Means(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric, Vector3 *__restrict cluster)
-{
- // Compute principal component.
- float matrix[6];
- Vector3 centroid = computeCovariance(n, points, weights, metric, matrix);
- Vector3 principal = firstEigenVector_PowerMethod(matrix);
-
- // Pick initial solution.
- int mini, maxi;
- mini = maxi = 0;
-
- float mindps, maxdps;
- mindps = maxdps = dot(points[0] - centroid, principal);
-
- for (int i = 1; i < n; ++i)
- {
- float dps = dot(points[i] - centroid, principal);
-
- if (dps < mindps) {
- mindps = dps;
- mini = i;
- }
- else {
- maxdps = dps;
- maxi = i;
- }
- }
-
- cluster[0] = centroid + mindps * principal;
- cluster[1] = centroid + maxdps * principal;
- cluster[2] = (2.0f * cluster[0] + cluster[1]) / 3.0f;
- cluster[3] = (2.0f * cluster[1] + cluster[0]) / 3.0f;
-
- // Now we have to iteratively refine the clusters.
- while (true)
- {
- Vector3 newCluster[4] = { Vector3(0.0f), Vector3(0.0f), Vector3(0.0f), Vector3(0.0f) };
- float total[4] = {0, 0, 0, 0};
-
- for (int i = 0; i < n; ++i)
- {
- // Find nearest cluster.
- int nearest = 0;
- float mindist = FLT_MAX;
- for (int j = 0; j < 4; j++)
- {
- float dist = lengthSquared((cluster[j] - points[i]) * metric);
- if (dist < mindist)
- {
- mindist = dist;
- nearest = j;
- }
- }
-
- newCluster[nearest] += weights[i] * points[i];
- total[nearest] += weights[i];
- }
-
- for (int j = 0; j < 4; j++)
- {
- if (total[j] != 0)
- newCluster[j] /= total[j];
- }
-
- if (equal(cluster[0], newCluster[0]) && equal(cluster[1], newCluster[1]) &&
- equal(cluster[2], newCluster[2]) && equal(cluster[3], newCluster[3]))
- {
- return (total[0] != 0) + (total[1] != 0) + (total[2] != 0) + (total[3] != 0);
- }
-
- cluster[0] = newCluster[0];
- cluster[1] = newCluster[1];
- cluster[2] = newCluster[2];
- cluster[3] = newCluster[3];
-
- // Sort clusters by weight.
- for (int i = 0; i < 4; i++)
- {
- for (int j = i; j > 0 && total[j] > total[j - 1]; j--)
- {
- swap( total[j], total[j - 1] );
- swap( cluster[j], cluster[j - 1] );
- }
- }
- }
-}
-
-
-
-// Adaptation of James Arvo's SVD code, as found in ZOH.
-
-inline float Sqr(float x) { return x*x; }
-
-inline float svd_pythag( float a, float b )
-{
- float at = fabsf(a);
- float bt = fabsf(b);
- if( at > bt )
- return at * sqrtf( 1.0f + Sqr( bt / at ) );
- else if( bt > 0.0f )
- return bt * sqrtf( 1.0f + Sqr( at / bt ) );
- else return 0.0f;
-}
-
-inline float SameSign( float a, float b )
-{
- float t;
- if( b >= 0.0f ) t = fabsf( a );
- else t = -fabsf( a );
- return t;
-}
-
-void ArvoSVD(int rows, int cols, float * Q, float * diag, float * R)
-{
- static const int MaxIterations = 30;
-
- int i, j, k, l, p, q, iter;
- float c, f, h, s, x, y, z;
- float norm = 0.0f;
- float g = 0.0f;
- float scale = 0.0f;
-
- Array<float> temp; temp.resize(cols, 0.0f);
-
- for( i = 0; i < cols; i++ )
- {
- temp[i] = scale * g;
- scale = 0.0f;
- g = 0.0f;
- s = 0.0f;
- l = i + 1;
-
- if( i < rows )
- {
- for( k = i; k < rows; k++ ) scale += fabsf( Q[k*cols+i] );
- if( scale != 0.0f )
- {
- for( k = i; k < rows; k++ )
- {
- Q[k*cols+i] /= scale;
- s += Sqr( Q[k*cols+i] );
- }
- f = Q[i*cols+i];
- g = -SameSign( sqrtf(s), f );
- h = f * g - s;
- Q[i*cols+i] = f - g;
- if( i != cols - 1 )
- {
- for( j = l; j < cols; j++ )
- {
- s = 0.0f;
- for( k = i; k < rows; k++ ) s += Q[k*cols+i] * Q[k*cols+j];
- f = s / h;
- for( k = i; k < rows; k++ ) Q[k*cols+j] += f * Q[k*cols+i];
- }
- }
- for( k = i; k < rows; k++ ) Q[k*cols+i] *= scale;
- }
- }
-
- diag[i] = scale * g;
- g = 0.0f;
- s = 0.0f;
- scale = 0.0f;
-
- if( i < rows && i != cols - 1 )
- {
- for( k = l; k < cols; k++ ) scale += fabsf( Q[i*cols+k] );
- if( scale != 0.0f )
- {
- for( k = l; k < cols; k++ )
- {
- Q[i*cols+k] /= scale;
- s += Sqr( Q[i*cols+k] );
- }
- f = Q[i*cols+l];
- g = -SameSign( sqrtf(s), f );
- h = f * g - s;
- Q[i*cols+l] = f - g;
- for( k = l; k < cols; k++ ) temp[k] = Q[i*cols+k] / h;
- if( i != rows - 1 )
- {
- for( j = l; j < rows; j++ )
- {
- s = 0.0f;
- for( k = l; k < cols; k++ ) s += Q[j*cols+k] * Q[i*cols+k];
- for( k = l; k < cols; k++ ) Q[j*cols+k] += s * temp[k];
- }
- }
- for( k = l; k < cols; k++ ) Q[i*cols+k] *= scale;
- }
- }
- norm = max( norm, fabsf( diag[i] ) + fabsf( temp[i] ) );
- }
-
-
- for( i = cols - 1; i >= 0; i-- )
- {
- if( i < cols - 1 )
- {
- if( g != 0.0f )
- {
- for( j = l; j < cols; j++ ) R[i*cols+j] = ( Q[i*cols+j] / Q[i*cols+l] ) / g;
- for( j = l; j < cols; j++ )
- {
- s = 0.0f;
- for( k = l; k < cols; k++ ) s += Q[i*cols+k] * R[j*cols+k];
- for( k = l; k < cols; k++ ) R[j*cols+k] += s * R[i*cols+k];
- }
- }
- for( j = l; j < cols; j++ )
- {
- R[i*cols+j] = 0.0f;
- R[j*cols+i] = 0.0f;
- }
- }
- R[i*cols+i] = 1.0f;
- g = temp[i];
- l = i;
- }
-
-
- for( i = cols - 1; i >= 0; i-- )
- {
- l = i + 1;
- g = diag[i];
- if( i < cols - 1 ) for( j = l; j < cols; j++ ) Q[i*cols+j] = 0.0f;
- if( g != 0.0f )
- {
- g = 1.0f / g;
- if( i != cols - 1 )
- {
- for( j = l; j < cols; j++ )
- {
- s = 0.0f;
- for( k = l; k < rows; k++ ) s += Q[k*cols+i] * Q[k*cols+j];
- f = ( s / Q[i*cols+i] ) * g;
- for( k = i; k < rows; k++ ) Q[k*cols+j] += f * Q[k*cols+i];
- }
- }
- for( j = i; j < rows; j++ ) Q[j*cols+i] *= g;
- }
- else
- {
- for( j = i; j < rows; j++ ) Q[j*cols+i] = 0.0f;
- }
- Q[i*cols+i] += 1.0f;
- }
-
-
- for( k = cols - 1; k >= 0; k-- )
- {
- for( iter = 1; iter <= MaxIterations; iter++ )
- {
- int jump = 0;
-
- for( l = k; l >= 0; l-- )
- {
- q = l - 1;
- if( fabsf( temp[l] ) + norm == norm ) { jump = 1; break; }
- if( fabsf( diag[q] ) + norm == norm ) { jump = 0; break; }
- }
-
- if( !jump )
- {
- c = 0.0f;
- s = 1.0f;
- for( i = l; i <= k; i++ )
- {
- f = s * temp[i];
- temp[i] *= c;
- if( fabsf( f ) + norm == norm ) break;
- g = diag[i];
- h = svd_pythag( f, g );
- diag[i] = h;
- h = 1.0f / h;
- c = g * h;
- s = -f * h;
- for( j = 0; j < rows; j++ )
- {
- y = Q[j*cols+q];
- z = Q[j*cols+i];
- Q[j*cols+q] = y * c + z * s;
- Q[j*cols+i] = z * c - y * s;
- }
- }
- }
-
- z = diag[k];
- if( l == k )
- {
- if( z < 0.0f )
- {
- diag[k] = -z;
- for( j = 0; j < cols; j++ ) R[k*cols+j] *= -1.0f;
- }
- break;
- }
- if( iter >= MaxIterations ) return;
- x = diag[l];
- q = k - 1;
- y = diag[q];
- g = temp[q];
- h = temp[k];
- f = ( ( y - z ) * ( y + z ) + ( g - h ) * ( g + h ) ) / ( 2.0f * h * y );
- g = svd_pythag( f, 1.0f );
- f = ( ( x - z ) * ( x + z ) + h * ( ( y / ( f + SameSign( g, f ) ) ) - h ) ) / x;
- c = 1.0f;
- s = 1.0f;
- for( j = l; j <= q; j++ )
- {
- i = j + 1;
- g = temp[i];
- y = diag[i];
- h = s * g;
- g = c * g;
- z = svd_pythag( f, h );
- temp[j] = z;
- c = f / z;
- s = h / z;
- f = x * c + g * s;
- g = g * c - x * s;
- h = y * s;
- y = y * c;
- for( p = 0; p < cols; p++ )
- {
- x = R[j*cols+p];
- z = R[i*cols+p];
- R[j*cols+p] = x * c + z * s;
- R[i*cols+p] = z * c - x * s;
- }
- z = svd_pythag( f, h );
- diag[j] = z;
- if( z != 0.0f )
- {
- z = 1.0f / z;
- c = f * z;
- s = h * z;
- }
- f = c * g + s * y;
- x = c * y - s * g;
- for( p = 0; p < rows; p++ )
- {
- y = Q[p*cols+j];
- z = Q[p*cols+i];
- Q[p*cols+j] = y * c + z * s;
- Q[p*cols+i] = z * c - y * s;
- }
- }
- temp[l] = 0.0f;
- temp[k] = f;
- diag[k] = x;
- }
- }
-
- // Sort the singular values into descending order.
-
- for( i = 0; i < cols - 1; i++ )
- {
- float biggest = diag[i]; // Biggest singular value so far.
- int bindex = i; // The row/col it occurred in.
- for( j = i + 1; j < cols; j++ )
- {
- if( diag[j] > biggest )
- {
- biggest = diag[j];
- bindex = j;
- }
- }
- if( bindex != i ) // Need to swap rows and columns.
- {
- // Swap columns in Q.
- for (int j = 0; j < rows; ++j)
- swap(Q[j*cols+i], Q[j*cols+bindex]);
-
- // Swap rows in R.
- for (int j = 0; j < rows; ++j)
- swap(R[i*cols+j], R[bindex*cols+j]);
-
- // Swap elements in diag.
- swap(diag[i], diag[bindex]);
- }
- }
-}
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