cv::PCA *PCA_LoadData(int blocks)
{
char path[40];
int rows, cols;
sprintf(path, "./PCAeigenvectors%d.mat", blocks);
FILE *fd = fopen(path, "r+");
if (!fd) {
perror("Error opening file for loading\n");
return NULL;
}
fscanf(fd, "%d", &rows);
fscanf(fd, "%d", &cols);
cv::Mat eigenvectors(rows, cols, CV_64FC1);
for (int j=0; j < eigenvectors.rows; j++) {
for (int i=0; i < eigenvectors.cols; i++) {
fscanf(fd, "%lf", &(eigenvectors.at<double>(j,i)));
}
}
fclose(fd);
sprintf(path, "./PCAmean%d.mat", blocks);
fd = fopen(path, "r+");
if (!fd) {
printf("blah %s\n", path);
perror("Error opening file for loading huh\n");
return NULL;
}
fscanf(fd, "%d", &rows);
fscanf(fd, "%d", &cols);
cv::Mat mean(rows, cols, CV_64FC1);
for (int j=0; j < mean.rows; j++) {
for (int i=0; i < mean.cols; i++) {
fscanf(fd, "%lf", &(mean.at<double>(j,i)));
}
}
fclose(fd);
cv::PCA *pca_obj = new cv::PCA();
pca_obj->eigenvectors = eigenvectors;
pca_obj->mean = mean;
return pca_obj;
}
bool eigen(const Mat2& M, Vec2& evals, Vec2 evecs[2])
{
bool result = eigenvalues(M, evals);
if( result )
eigenvectors(M, evals, evecs);
return result;
}
/**
Compute the natural frequencies of the structure
Arguments:
n - number of natural frequencies to return (unless n exceeds the total DOF of the structure,
in which case all computed natural frequencies will be returned.
Return:
freq - a numpy array of frequencies (not necessarily of length n as described above).
**/
py::tuple computeNaturalFrequenciesAndEigenvectors(int n){
Vector freqs(n);
Matrix eigenvectors(0, 0);
beam->computeNaturalFrequencies(n, freqs, eigenvectors);
return py::make_tuple(freqs, eigenvectors);
}
Vector rmvn_robust_mt(RNG &rng, const Vector &mu, const SpdMatrix &V) {
uint n = V.nrow();
Matrix eigenvectors(n, n);
Vector eigenvalues = eigen(V, eigenvectors);
for (uint i = 0; i < n; ++i) {
// We're guaranteed that eigenvalues[i] is real and non-negative. We
// can take the absolute value of eigenvalues[i] to guard against
// spurious negative numbers close to zero.
eigenvalues[i] = sqrt(fabs(eigenvalues[i])) * rnorm_mt(rng, 0, 1);
}
Vector ans(eigenvectors * eigenvalues);
ans += mu;
return ans;
}
int Zoltan_Get_Coordinates(
ZZ *zz,
int num_obj, /* Input: number of objects */
ZOLTAN_ID_PTR global_ids, /* Input: global IDs of objects */
ZOLTAN_ID_PTR local_ids, /* Input: local IDs of objects; may be NULL. */
int *num_dim, /* Output: dimension of coordinates */
double **coords /* Output: array of coordinates; malloc'ed by
fn if NULL upon input. */
)
{
char *yo = "Zoltan_Get_Coordinates";
int i,j,rc;
int num_gid_entries = zz->Num_GID;
int num_lid_entries = zz->Num_LID;
int alloced_coords = 0;
ZOLTAN_ID_PTR lid; /* Temporary pointers to local IDs; used to pass
NULL to query functions when NUM_LID_ENTRIES == 0. */
double dist[3];
double im[3][3];
double deg_ratio;
double x;
int order[3];
int reduce_dimensions, d, axis_aligned;
int target_dim;
int ierr = ZOLTAN_OK;
char msg[256];
ZZ_Transform *tran;
ZOLTAN_TRACE_ENTER(zz, yo);
/* Error check -- make sure needed callback functions are registered. */
if (zz->Get_Num_Geom == NULL ||
(zz->Get_Geom == NULL && zz->Get_Geom_Multi == NULL)) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo, "Must register ZOLTAN_NUM_GEOM_FN and "
"either ZOLTAN_GEOM_MULTI_FN or ZOLTAN_GEOM_FN");
goto End;
}
/* Get problem dimension. */
*num_dim = zz->Get_Num_Geom(zz->Get_Num_Geom_Data, &ierr);
if (ierr != ZOLTAN_OK && ierr != ZOLTAN_WARN) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo,
"Error returned from ZOLTAN_GET_NUM_GEOM_FN");
goto End;
}
if (*num_dim < 0 || *num_dim > 3) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo,
"Invalid dimension returned from ZOLTAN_NUM_GEOM_FN");
goto End;
}
/* Get coordinates for object; allocate memory if not already provided. */
if (*num_dim > 0 && num_obj > 0) {
if (*coords == NULL) {
alloced_coords = 1;
*coords = (double *) ZOLTAN_MALLOC(num_obj * (*num_dim) * sizeof(double));
if (*coords == NULL) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo, "Memory error");
goto End;
}
}
if (zz->Get_Geom_Multi != NULL) {
zz->Get_Geom_Multi(zz->Get_Geom_Multi_Data, zz->Num_GID, zz->Num_LID,
num_obj, global_ids, local_ids, *num_dim, *coords,
&ierr);
if (ierr != ZOLTAN_OK && ierr != ZOLTAN_WARN) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo,
"Error returned from ZOLTAN_GET_GEOM_MULTI_FN");
goto End;
}
}
else {
for (i = 0; i < num_obj; i++) {
lid = (num_lid_entries ? &(local_ids[i*num_lid_entries]) : NULL);
zz->Get_Geom(zz->Get_Geom_Data, num_gid_entries, num_lid_entries,
global_ids + i*num_gid_entries, lid,
(*coords) + i*(*num_dim), &ierr);
if (ierr != ZOLTAN_OK && ierr != ZOLTAN_WARN) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo,
"Error returned from ZOLTAN_GET_GEOM_FN");
goto End;
}
}
}
}
/*
* For RCB, RIB, and HSFC: if REDUCE_DIMENSIONS was selected, compute the
* center of mass and inertial matrix of the coordinates.
*
* For 3D problems: If the geometry is "flat", transform the points so the
* two primary directions lie along the X and Y coordinate axes and project
* to the Z=0 plane. If in addition the geometry is "skinny", project to
* the X axis. (This creates a 2D or 1D problem respectively.)
*
* For 2D problems: If the geometry is essentially a line, transform it's
* primary direction to the X axis and project to the X axis, yielding a
* 1D problem.
*
* Return these points to the partitioning algorithm, in effect partitioning
* in only the 2 (or 1) significant dimensions.
*/
if (((*num_dim == 3) || (*num_dim == 2)) &&
((zz->LB.Method==RCB) || (zz->LB.Method==RIB) || (zz->LB.Method==HSFC))){
Zoltan_Bind_Param(Reduce_Dim_Params, "KEEP_CUTS", (void *)&i);
Zoltan_Bind_Param(Reduce_Dim_Params, "REDUCE_DIMENSIONS",
(void *)&reduce_dimensions);
Zoltan_Bind_Param(Reduce_Dim_Params, "DEGENERATE_RATIO", (void *)°_ratio);
i = 0;
reduce_dimensions = 0;
deg_ratio = 10.0;
Zoltan_Assign_Param_Vals(zz->Params, Reduce_Dim_Params, zz->Debug_Level,
zz->Proc, zz->Debug_Proc);
if (reduce_dimensions == 0){
goto End;
}
if (deg_ratio <= 1){
if (zz->Proc == 0){
ZOLTAN_PRINT_WARN(0, yo, "DEGENERATE_RATIO <= 1, setting it to 10.0");
}
deg_ratio = 10.0;
}
if (zz->LB.Method == RCB){
tran = &(((RCB_STRUCT *)(zz->LB.Data_Structure))->Tran);
}
else if (zz->LB.Method == RIB){
tran = &(((RIB_STRUCT *)(zz->LB.Data_Structure))->Tran);
}
else{
tran = &(((HSFC_Data*)(zz->LB.Data_Structure))->tran);
}
d = *num_dim;
if (tran->Target_Dim >= 0){
/*
* On a previous load balancing call, we determined whether
* or not the geometry was degenerate. If the geometry was
* determined to be not degenerate, then we assume it is still
* not degenerate, and we skip the degeneracy calculation.
*/
if (tran->Target_Dim > 0){
/*
* The geometry *was* degenerate. We test the extent
* of the geometry along the principal directions determined
* last time to determine if it is still degenerate with that
* orientation. If so, we transform the coordinates using the
* same transformation we used last time. If not, we do the
* entire degeneracy calculation again.
*/
if ((tran->Axis_Order[0] >= 0) &&
(tran->Axis_Order[1] >= 0) && (tran->Axis_Order[2] >= 0)){
axis_aligned = 1;
}
else{
axis_aligned = 0;
}
projected_distances(zz, *coords, num_obj, tran->CM,
tran->Evecs, dist, d, axis_aligned, tran->Axis_Order);
target_dim = get_target_dimension(dist, order, deg_ratio, d);
if (target_dim > 0){
transform_coordinates(*coords, num_obj, d, tran);
}
else{
/* Set's Target_Dim to -1, flag to recompute degeneracy */
Zoltan_Initialize_Transformation(tran);
}
}
}
if (tran->Target_Dim < 0){
tran->Target_Dim = 0;
/*
* Get the center of mass and inertial matrix of coordinates. Ignore
* vertex weights, we are only interested in geometry. Global operation.
*/
if (d == 2){
inertial_matrix2D(zz, *coords, num_obj, tran->CM, im);
}
else{
inertial_matrix3D(zz, *coords, num_obj, tran->CM, im);
}
/*
* The inertial matrix is a 3x3 or 2x2 real symmetric matrix. Get its
* three or two orthonormal eigenvectors. These usually indicate the
* orientation of the geometry.
*/
rc = eigenvectors(im, tran->Evecs, d);
if (rc){
if (zz->Proc == 0){
ZOLTAN_PRINT_WARN(0, yo, "REDUCE_DIMENSIONS calculation failed");
}
goto End;
}
/*
* Here we check to see if the eigenvectors are very close
* to the coordinate axes. If so, we can more quickly
* determine whether the geometry is degenerate, and also more
* quickly transform the geometry to the lower dimensional
* space.
*/
axis_aligned = 0;
for (i=0; i<d; i++){
tran->Axis_Order[i] = -1;
}
for (j=0; j<d; j++){
for (i=0; i<d; i++){
x = fabs(tran->Evecs[i][j]);
if (NEAR_ONE(x)){
tran->Axis_Order[j] = i; /* e'vector j is very close to i axis */
break;
}
}
if (tran->Axis_Order[j] < 0){
break;
}
}
if ((tran->Axis_Order[0] >= 0) &&
(tran->Axis_Order[1] >= 0) && (tran->Axis_Order[2] >= 0)){
axis_aligned = 1;
}
/*
* Calculate the extent of the geometry along the three lines defined
* by the direction of the eigenvectors through the center of mass.
*/
projected_distances(zz, *coords, num_obj, tran->CM, tran->Evecs, dist,
d, axis_aligned, tran->Axis_Order);
/*
* Decide whether these distances indicate the geometry is
* very flat in one or two directions.
*/
target_dim = get_target_dimension(dist, order, deg_ratio, d);
if (target_dim > 0){
/*
* Yes, geometry is degenerate
*/
if ((zz->Debug_Level > 0) && (zz->Proc == 0)){
if (d == 2){
sprintf(msg,
"Geometry (~%lf x %lf), exceeds %lf to 1.0 ratio",
dist[order[0]], dist[order[1]], deg_ratio);
}
else{
sprintf(msg,
"Geometry (~%lf x %lf x %lf), exceeds %lf to 1.0 ratio",
dist[order[0]], dist[order[1]], dist[order[2]], deg_ratio);
}
ZOLTAN_PRINT_INFO(zz->Proc, yo, msg);
sprintf(msg, "We'll treat it as %d dimensional",target_dim);
ZOLTAN_PRINT_INFO(zz->Proc, yo, msg);
}
if (axis_aligned){
/*
** Create new geometry, transforming the primary direction
** to the X-axis, and the secondary to the Y-axis.
*/
tran->Permutation[0] = tran->Axis_Order[order[0]];
if (target_dim == 2){
tran->Permutation[1] = tran->Axis_Order[order[1]];
}
}
else{
/*
* Reorder the eigenvectors (they're the columns of evecs) from
* longest projected distance to shorted projected distance. Compute
* the transpose (the inverse) of the matrix. This will transform
* the geometry to align along the X-Y plane, or along the X axis.
*/
for (i=0; i< target_dim; i++){
tran->Transformation[i][2] = 0.0;
for (j=0; j<d; j++){
tran->Transformation[i][j] = tran->Evecs[j][order[i]];
}
}
for (i=target_dim; i< 3; i++){
for (j=0; j<3; j++){
tran->Transformation[i][j] = 0.0;
}
}
}
tran->Target_Dim = target_dim;
transform_coordinates(*coords, num_obj, d, tran);
} /* If geometry is very flat */
} /* If REDUCE_DIMENSIONS is true */
} /* If 2-D or 3-D rcb, rib or hsfc */
End:
if (ierr != ZOLTAN_OK && ierr != ZOLTAN_WARN) {
ZOLTAN_PRINT_ERROR(zz->Proc, yo, "Error found; no coordinates returned.");
if (alloced_coords) ZOLTAN_FREE(coords);
}
ZOLTAN_TRACE_EXIT(zz, yo);
return ierr;
}
static void
ambHessian( /* anisotropic radii & pos. gradient */
AMBHEMI *hp,
FVECT uv[2], /* returned */
float ra[2], /* returned (optional) */
float pg[2] /* returned (optional) */
)
{
static char memerrmsg[] = "out of memory in ambHessian()";
FVECT (*hessrow)[3] = NULL;
FVECT *gradrow = NULL;
FVECT hessian[3];
FVECT gradient;
FFTRI fftr;
int i, j;
/* be sure to assign unit vectors */
VCOPY(uv[0], hp->ux);
VCOPY(uv[1], hp->uy);
/* clock-wise vertex traversal from sample POV */
if (ra != NULL) { /* initialize Hessian row buffer */
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
if (hessrow == NULL)
error(SYSTEM, memerrmsg);
memset(hessian, 0, sizeof(hessian));
} else if (pg == NULL) /* bogus call? */
return;
if (pg != NULL) { /* initialize form factor row buffer */
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
if (gradrow == NULL)
error(SYSTEM, memerrmsg);
memset(gradient, 0, sizeof(gradient));
}
/* compute first row of edges */
for (j = 0; j < hp->ns-1; j++) {
comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
if (hessrow != NULL)
comp_hessian(hessrow[j], &fftr, hp->rp->ron);
if (gradrow != NULL)
comp_gradient(gradrow[j], &fftr, hp->rp->ron);
}
/* sum each row of triangles */
for (i = 0; i < hp->ns-1; i++) {
FVECT hesscol[3]; /* compute first vertical edge */
FVECT gradcol;
comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
if (hessrow != NULL)
comp_hessian(hesscol, &fftr, hp->rp->ron);
if (gradrow != NULL)
comp_gradient(gradcol, &fftr, hp->rp->ron);
for (j = 0; j < hp->ns-1; j++) {
FVECT hessdia[3]; /* compute triangle contributions */
FVECT graddia;
double backg;
backg = back_ambval(hp, AI(hp,i,j),
AI(hp,i,j+1), AI(hp,i+1,j));
/* diagonal (inner) edge */
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
if (hessrow != NULL) {
comp_hessian(hessdia, &fftr, hp->rp->ron);
rev_hessian(hesscol);
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
}
if (gradrow != NULL) {
comp_gradient(graddia, &fftr, hp->rp->ron);
rev_gradient(gradcol);
add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
}
/* initialize edge in next row */
comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
if (hessrow != NULL)
comp_hessian(hessrow[j], &fftr, hp->rp->ron);
if (gradrow != NULL)
comp_gradient(gradrow[j], &fftr, hp->rp->ron);
/* new column edge & paired triangle */
backg = back_ambval(hp, AI(hp,i+1,j+1),
AI(hp,i+1,j), AI(hp,i,j+1));
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
if (hessrow != NULL) {
comp_hessian(hesscol, &fftr, hp->rp->ron);
rev_hessian(hessdia);
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
if (i < hp->ns-2)
rev_hessian(hessrow[j]);
}
if (gradrow != NULL) {
comp_gradient(gradcol, &fftr, hp->rp->ron);
rev_gradient(graddia);
add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
if (i < hp->ns-2)
rev_gradient(gradrow[j]);
}
}
}
/* release row buffers */
if (hessrow != NULL) free(hessrow);
if (gradrow != NULL) free(gradrow);
if (ra != NULL) /* extract eigenvectors & radii */
eigenvectors(uv, ra, hessian);
if (pg != NULL) { /* tangential position gradient */
pg[0] = DOT(gradient, uv[0]);
pg[1] = DOT(gradient, uv[1]);
}
}
void pclbo::LBOEstimation<PointT, NormalT>::compute() {
typename pcl::KdTreeFLANN<PointT>::Ptr kdt(new pcl::KdTreeFLANN<PointT>());
kdt->setInputCloud(_cloud);
const double avg_dist = pclbo::avg_distance<PointT>(10, _cloud, kdt);
const double h = 5 * avg_dist;
std::cout << "Average distance between points: " << avg_dist << std::endl;
int points_with_mass = 0;
double avg_mass = 0.0;
B.resize(_cloud->size());
std::cout << "Computing the Mass matrix..." << std::flush;
// Compute the mass matrix diagonal B
for (int i = 0; i < _cloud->size(); i++) {
const auto& point = _cloud->at(i);
const auto& normal = _normals->at(i);
const auto& normal_vector = normal.getNormalVector3fMap().template cast<double>();
if (!pcl::isFinite(point)) continue;
std::vector<int> indices;
std::vector<float> distances;
kdt->radiusSearch(point, h, indices, distances);
if (indices.size() < 4) {
B[i] = 0.0;
continue;
}
// Project the neighbor points in the tangent plane at p_i with normal n_i
std::vector<Eigen::Vector3d> projected_points;
for (const auto& neighbor_index : indices) {
if (neighbor_index != i) {
const auto& neighbor_point = _cloud->at(neighbor_index);
projected_points.push_back(project(point, normal, neighbor_point));
}
}
assert(projected_points.size() >= 3);
// Use the first vector to create a 2D basis
Eigen::Vector3d u = projected_points[0];
u.normalize();
Eigen::Vector3d v = (u.cross(normal_vector));
v.normalize();
// Add the points to a 2D plane
std::vector<Eigen::Vector2d> plane;
// Add the point at the center
plane.push_back(Eigen::Vector2d::Zero());
// Add the rest of the points
for (const auto& projected : projected_points) {
double x = projected.dot(u);
double y = projected.dot(v);
// Add the 2D point to the vector
plane.push_back(Eigen::Vector2d(x, y));
}
assert(plane.size() >= 4);
// Compute the voronoi cell area of the point
double area = VoronoiDiagram::area(plane);
B[i] = area;
avg_mass += area;
points_with_mass++;
}
// Average mass
if (points_with_mass > 0) {
avg_mass /= static_cast<double>(points_with_mass);
}
// Set border points to have average mass
for (auto& b : B) {
if (b == 0.0) {
b = avg_mass;
}
}
std::cout << "done" << std::endl;
std::cout << "Computing the stiffness matrix..." << std::flush;
std::vector<double> diag(_cloud->size(), 0.0);
// Compute the stiffness matrix Q
for (int i = 0; i < _cloud->size(); i++) {
const auto& point = _cloud->at(i);
if (!pcl::isFinite(point)) continue;
std::vector<int> indices;
std::vector<float> distances;
kdt->radiusSearch(point, h, indices, distances);
for (const auto& j : indices) {
if (j != i) {
const auto& neighbor = _cloud->at(j);
double d = (neighbor.getVector3fMap() - point.getVector3fMap()).norm();
double w = B[i] * B[j] * (1.0 / (4.0 * M_PI * h * h)) * exp(-(d * d) / (4.0 * h));
I.push_back(i);
J.push_back(j);
S.push_back(w);
diag[i] += w;
}
}
}
// Fill the diagonal as the negative sum of the rows
for (int i = 0; i < diag.size(); i++) {
I.push_back(i);
J.push_back(i);
S.push_back(-diag[i]);
}
// Compute the B^{-1}Q matrix
Eigen::MatrixXd Q = Eigen::MatrixXd::Zero(_cloud->size(), _cloud->size());
for (int i = 0; i < I.size(); i++) {
const int row = I[i];
const int col = J[i];
Q(row, col) = S[i];
}
std::cout << "done" << std::endl;
std::cout << "Computing eigenvectors" << std::endl;
Eigen::Map<Eigen::VectorXd> B_vec(B.data(), B.size());
Eigen::GeneralizedSelfAdjointEigenSolver<Eigen::MatrixXd> ges;
ges.compute(Q, B_vec.asDiagonal());
eigenvalues = ges.eigenvalues();
eigenfunctions = ges.eigenvectors();
// Sort the eigenvalues by magnitude
std::vector<std::pair<double, int> > map_vector(eigenvalues.size());
for (auto i = 0; i < eigenvalues.size(); i++) {
map_vector[i].first = std::abs(eigenvalues(i));
map_vector[i].second = i;
}
std::sort(map_vector.begin(), map_vector.end());
// truncate the first 100 eigenfunctions
Eigen::MatrixXd eigenvectors(eigenfunctions.rows(), eigenfunctions.cols());
Eigen::VectorXd eigenvals(eigenfunctions.cols());
eigenvalues.resize(map_vector.size());
for (auto i = 0; i < map_vector.size(); i++) {
const auto& pair = map_vector[i];
eigenvectors.col(i) = eigenfunctions.col(pair.second);
eigenvals(i) = pair.first;
}
eigenfunctions = eigenvectors;
eigenvalues = eigenvals;
}
/**
* Description not yet available.
* \param
*/
void laplace_approximation_calculator::
do_newton_raphson_banded(function_minimizer * pfmin,double f_from_1,
int& no_converge_flag)
{
//quadratic_prior * tmpptr=quadratic_prior::ptr[0];
//cout << tmpptr << endl;
laplace_approximation_calculator::where_are_we_flag=2;
double maxg=fabs(evaluate_function(uhat,pfmin));
laplace_approximation_calculator::where_are_we_flag=0;
dvector uhat_old(1,usize);
for(int ii=1;ii<=num_nr_iters;ii++)
{
// test newton raphson
switch(hesstype)
{
case 3:
bHess->initialize();
break;
case 4:
Hess.initialize();
break;
default:
cerr << "Illegal value for hesstype here" << endl;
ad_exit(1);
}
grad.initialize();
//int check=initial_params::stddev_scale(scale,uhat);
//check=initial_params::stddev_curvscale(curv,uhat);
//max_separable_g=0.0;
sparse_count = 0;
step=get_newton_raphson_info_banded(pfmin);
//if (bHess)
// cout << "norm(*bHess) = " << norm(*bHess) << endl;
//cout << "norm(Hess) = " << norm(Hess) << endl;
//cout << grad << endl;
//check_pool_depths();
if (!initial_params::mc_phase)
cout << "Newton raphson " << ii << " ";
if (quadratic_prior::get_num_quadratic_prior()>0)
{
quadratic_prior::get_cHessian_contribution(Hess,xsize);
quadratic_prior::get_cgradient_contribution(grad,xsize);
}
int ierr=0;
if (hesstype==3)
{
if (use_dd_nr==0)
{
banded_lower_triangular_dmatrix bltd=choleski_decomp(*bHess,ierr);
if (ierr && no_converge_flag ==0)
{
no_converge_flag=1;
//break;
}
if (ierr)
{
double oldval;
evaluate_function(oldval,uhat,pfmin);
uhat=banded_calculations_trust_region_approach(uhat,pfmin);
}
else
{
if (dd_nr_flag==0)
{
dvector v=solve(bltd,grad);
step=-solve_trans(bltd,v);
//uhat_old=uhat;
uhat+=step;
}
else
{
#if defined(USE_DD_STUFF)
int n=grad.indexmax();
maxg=fabs(evaluate_function(uhat,pfmin));
uhat=dd_newton_raphson2(grad,*bHess,uhat);
#else
cerr << "high precision Newton Raphson not implemented" << endl;
ad_exit(1);
#endif
}
maxg=fabs(evaluate_function(uhat,pfmin));
if (f_from_1< pfmin->lapprox->fmc1.fbest)
{
uhat=banded_calculations_trust_region_approach(uhat,pfmin);
maxg=fabs(evaluate_function(uhat,pfmin));
}
}
}
else
{
cout << "error not used" << endl;
ad_exit(1);
/*
banded_symmetric_ddmatrix bHessdd=banded_symmetric_ddmatrix(*bHess);
ddvector gradd=ddvector(grad);
//banded_lower_triangular_ddmatrix bltdd=choleski_decomp(bHessdd,ierr);
if (ierr && no_converge_flag ==0)
{
no_converge_flag=1;
break;
}
if (ierr)
{
double oldval;
evaluate_function(oldval,uhat,pfmin);
uhat=banded_calculations_trust_region_approach(uhat,pfmin);
maxg=fabs(evaluate_function(uhat,pfmin));
}
else
{
ddvector v=solve(bHessdd,gradd);
step=-make_dvector(v);
//uhat_old=uhat;
uhat=make_dvector(ddvector(uhat)+step);
maxg=fabs(evaluate_function(uhat,pfmin));
if (f_from_1< pfmin->lapprox->fmc1.fbest)
{
uhat=banded_calculations_trust_region_approach(uhat,pfmin);
maxg=fabs(evaluate_function(uhat,pfmin));
}
}
*/
}
if (maxg < 1.e-13)
{
break;
}
}
else if (hesstype==4)
{
dvector step;
# if defined(USE_ATLAS)
if (!ad_comm::no_atlas_flag)
{
step=-atlas_solve_spd(Hess,grad,ierr);
}
else
{
dmatrix A=choleski_decomp_positive(Hess,ierr);
if (!ierr)
{
step=-solve(Hess,grad);
//step=-solve(A*trans(A),grad);
}
}
if (!ierr) break;
# else
if (sparse_hessian_flag)
{
//step=-solve(*sparse_triplet,Hess,grad,*sparse_symbolic);
dvector temp=solve(*sparse_triplet2,grad,*sparse_symbolic2,ierr);
if (ierr)
{
step=-temp;
}
else
{
cerr << "matrix not pos definite in sparse choleski" << endl;
pfmin->bad_step_flag=1;
int on;
int nopt;
if ((on=option_match(ad_comm::argc,ad_comm::argv,"-ieigvec",nopt))
>-1)
{
dmatrix M=make_dmatrix(*sparse_triplet2);
ofstream ofs3("inner-eigvectors");
ofs3 << "eigenvalues and eigenvectors " << endl;
dvector v=eigenvalues(M);
dmatrix ev=trans(eigenvectors(M));
ofs3 << "eigenvectors" << endl;
int i;
for (i=1;i<=ev.indexmax();i++)
{
ofs3 << setw(4) << i << " "
<< setshowpoint() << setw(14) << setprecision(10) << v(i)
<< " "
<< setshowpoint() << setw(14) << setprecision(10)
<< ev(i) << endl;
}
}
}
//cout << norm2(step-tmpstep) << endl;
//dvector step1=-solve(Hess,grad);
//cout << norm2(step-step1) << endl;
}
else
{
step=-solve(Hess,grad);
}
# endif
if (pmin->bad_step_flag)
break;
uhat_old=uhat;
uhat+=step;
double maxg_old=maxg;
maxg=fabs(evaluate_function(uhat,pfmin));
if (maxg>maxg_old)
{
uhat=uhat_old;
evaluate_function(uhat,pfmin);
break;
}
if (maxg < 1.e-13)
{
break;
}
}
if (sparse_hessian_flag==0)
{
for (int i=1;i<=usize;i++)
{
y(i+xsize)=uhat(i);
}
}
else
{
for (int i=1;i<=usize;i++)
{
value(y(i+xsize))=uhat(i);
}
}
}
}
/**
Symmetrize and invert the hessian
*/
void function_minimizer::hess_inv(void)
{
initial_params::set_inactive_only_random_effects();
int nvar=initial_params::nvarcalc(); // get the number of active parameters
independent_variables x(1,nvar);
initial_params::xinit(x); // get the initial values into the x vector
//double f;
dmatrix hess(1,nvar,1,nvar);
uistream ifs("admodel.hes");
int file_nvar = 0;
ifs >> file_nvar;
if (nvar != file_nvar)
{
cerr << "Number of active variables in file mod_hess.rpt is wrong"
<< endl;
}
for (int i = 1;i <= nvar; i++)
{
ifs >> hess(i);
if (!ifs)
{
cerr << "Error reading line " << i << " of the hessian"
<< " in routine hess_inv()" << endl;
exit(1);
}
}
int hybflag = 0;
ifs >> hybflag;
dvector sscale(1,nvar);
ifs >> sscale;
if (!ifs)
{
cerr << "Error reading sscale"
<< " in routine hess_inv()" << endl;
}
double maxerr=0.0;
for (int i = 1;i <= nvar; i++)
{
for (int j=1;j<i;j++)
{
double tmp=(hess(i,j)+hess(j,i))/2.;
double tmp1=fabs(hess(i,j)-hess(j,i));
tmp1/=(1.e-4+fabs(hess(i,j))+fabs(hess(j,i)));
if (tmp1>maxerr) maxerr=tmp1;
hess(i,j)=tmp;
hess(j,i)=tmp;
}
}
/*
if (maxerr>1.e-2)
{
cerr << "warning -- hessian aprroximation is poor" << endl;
}
*/
for (int i = 1;i <= nvar; i++)
{
int zero_switch=0;
for (int j=1;j<=nvar;j++)
{
if (hess(i,j)!=0.0)
{
zero_switch=1;
}
}
if (!zero_switch)
{
cerr << " Hessian is 0 in row " << i << endl;
cerr << " This means that the derivative if probably identically 0 "
" for this parameter" << endl;
}
}
int ssggnn;
ln_det(hess,ssggnn);
int on1=0;
{
ofstream ofs3((char*)(ad_comm::adprogram_name + adstring(".eva")));
{
dvector se=eigenvalues(hess);
ofs3 << setshowpoint() << setw(14) << setprecision(10)
<< "unsorted:\t" << se << endl;
se=sort(se);
ofs3 << setshowpoint() << setw(14) << setprecision(10)
<< "sorted:\t" << se << endl;
if (se(se.indexmin())<=0.0)
{
negative_eigenvalue_flag=1;
cout << "Warning -- Hessian does not appear to be"
" positive definite" << endl;
}
}
ivector negflags(0,hess.indexmax());
int num_negflags=0;
{
int on = option_match(ad_comm::argc,ad_comm::argv,"-eigvec");
on1=option_match(ad_comm::argc,ad_comm::argv,"-spmin");
if (on > -1 || on1 >-1 )
{
ofs3 << setshowpoint() << setw(14) << setprecision(10)
<< eigenvalues(hess) << endl;
dmatrix ev=trans(eigenvectors(hess));
ofs3 << setshowpoint() << setw(14) << setprecision(10)
<< ev << endl;
for (int i=1;i<=ev.indexmax();i++)
{
double lam=ev(i)*hess*ev(i);
ofs3 << setshowpoint() << setw(14) << setprecision(10)
<< lam << " " << ev(i)*ev(i) << endl;
if (lam<0.0)
{
num_negflags++;
negflags(num_negflags)=i;
}
}
if ( (on1>-1) && (num_negflags>0)) // we will try to get away from
{ // saddle point
negative_eigenvalue_flag=0;
spminflag=1;
if(negdirections)
{
delete negdirections;
}
negdirections = new dmatrix(1,num_negflags);
for (int i=1;i<=num_negflags;i++)
{
(*negdirections)(i)=ev(negflags(i));
}
}
int on2 = option_match(ad_comm::argc,ad_comm::argv,"-cross");
if (on2>-1)
{ // saddle point
dmatrix cross(1,ev.indexmax(),1,ev.indexmax());
for (int i = 1;i <= ev.indexmax(); i++)
{
for (int j=1;j<=ev.indexmax();j++)
{
cross(i,j)=ev(i)*ev(j);
}
}
ofs3 << endl << " e(i)*e(j) ";
ofs3 << endl << cross << endl;
}
}
}
if (spminflag==0)
{
if (num_negflags==0)
{
hess=inv(hess);
int on=0;
if ( (on=option_match(ad_comm::argc,ad_comm::argv,"-eigvec"))>-1)
{
int i;
ofs3 << "choleski decomp of correlation" << endl;
dmatrix ch=choleski_decomp(hess);
for (i=1;i<=ch.indexmax();i++)
ofs3 << ch(i)/norm(ch(i)) << endl;
ofs3 << "parameterization of choleski decomnp of correlation" << endl;
for (i=1;i<=ch.indexmax();i++)
{
dvector tmp=ch(i)/norm(ch(i));
ofs3 << tmp(1,i)/tmp(i) << endl;
}
}
}
}
}
if (spminflag==0)
{
if (on1<0)
{
for (int i = 1;i <= nvar; i++)
{
if (hess(i,i) <= 0.0)
{
hess_errorreport();
ad_exit(1);
}
}
}
{
adstring tmpstring="admodel.cov";
if (ad_comm::wd_flag)
tmpstring = ad_comm::adprogram_name + ".cov";
uostream ofs((char*)tmpstring);
ofs << nvar << hess;
ofs << gradient_structure::Hybrid_bounded_flag;
ofs << sscale;
}
}
}
/// Execute algorithm.
void Schrodinger1D::exec()
{
double startX = get("StartX");
double endX = get("EndX");
if (endX <= startX)
{
throw std::invalid_argument("StartX must be <= EndX");
}
IFunction_sptr VPot = getClass("VPot");
chebfun vpot( 0, startX, endX );
vpot.bestFit( *VPot );
size_t nBasis = vpot.n() + 1;
std::cerr << "n=" << nBasis << std::endl;
//if (n < 3)
{
nBasis = 200;
vpot.resize( nBasis );
}
const double beta = get("Beta");
auto kinet = new ChebCompositeOperator;
kinet->addRight( new ChebTimes(-beta) );
kinet->addRight( new ChebDiff2 );
auto hamiltonian = new ChebPlus;
hamiltonian->add('+', kinet );
hamiltonian->add('+', new ChebTimes(VPot) );
GSLMatrix L;
hamiltonian->createMatrix( vpot.getBase(), L );
GSLVector d;
GSLMatrix v;
L.diag( d, v );
std::vector<double> norms = vpot.baseNorm();
assert(norms.size() == L.size1());
assert(norms.size() == L.size2());
for(size_t i = 0; i < norms.size(); ++i)
{
double factor = 1.0 / norms[i];
for(size_t j = i; j < norms.size(); ++j)
{
v.multiplyBy(i,j,factor);
}
}
// eigenvectors orthogonality check
// GSLMatrix v1 = v;
// GSLMatrix tst;
// tst = Tr(v1) * v;
// std::cerr << tst << std::endl;
std::vector<size_t> indx(L.size1());
getSortedIndex( d, indx );
auto eigenvalues = API::TableWorkspace_ptr(dynamic_cast<API::TableWorkspace*>(
API::WorkspaceFactory::instance().create("TableWorkspace"))
);
eigenvalues->setRowCount(nBasis);
setProperty("Eigenvalues", eigenvalues);
eigenvalues->addColumn("double","N");
auto nColumn = static_cast<API::TableColumn<double>*>(eigenvalues->getColumn("N").get());
nColumn->asNumeric()->setPlotRole(API::NumericColumn::X);
auto& nc = nColumn->data();
eigenvalues->addDoubleColumn("Energy");
auto eColumn = static_cast<API::TableColumn<double>*>(eigenvalues->getColumn("Energy").get());
eColumn->asNumeric()->setPlotRole(API::NumericColumn::Y);
auto& ec = eigenvalues->getDoubleData("Energy");
boost::scoped_ptr<ChebfunVector> eigenvectors(new ChebfunVector);
chebfun fun0(nBasis,startX,endX);
ChebFunction_sptr theSum(new ChebFunction(fun0));
// collect indices of spurious eigenvalues to move them to the back
std::vector<size_t> spurious;
// index for good eigenvalues
size_t n = 0;
for(size_t j = 0; j < nBasis; ++j)
{
size_t i = indx[j];
chebfun fun(fun0);
fun.setP(v,i);
// check eigenvalues for spurious ones
chebfun dfun(fun);
dfun.square();
double norm = dfun.integr();
// I am not sure that it's a solid condition
if ( norm < 0.999999 )
{
// bad eigenvalue
spurious.push_back(j);
}
else
{
nc[n] = double(n);
ec[n] = d[i];
eigenvectors->add(ChebFunction_sptr(new ChebFunction(fun)));
// test sum of functions squares
*theSum += dfun;
// chebfun dfun(fun);
// hamiltonian->apply(fun,dfun);
// dfun *= fun;
// std::cerr << "ener["<<n<<"]=" << ec[n] << ' ' << norm << ' ' << dfun.integr() << std::endl;
++n;
}
}
GSLVector eigv;
ChebfunVector *eigf = NULL;
improve(hamiltonian, eigenvectors.get(), eigv, &eigf);
eigenvalues->setRowCount( eigv.size() );
for(size_t i = 0; i < eigv.size(); ++i)
{
nc[i] = double(i);
ec[i] = eigv[i];
}
eigf->add(theSum);
setProperty("Eigenvectors",ChebfunVector_sptr(eigf));
//makeQuadrature(eigf);
}
// This is the model equation for the timeframe RANSAC
// B.K.P. Horn's closed form Absolute Orientation method (1987 paper)
// The convention used here is: right = (1/scale) * RMat * left + TMat
int Photogrammetry::absoluteOrientation(vector<cv::Point3d> & left, vector<cv::Point3d> & right, cv::Mat & RMat, cv::Mat & TMat, double & scale) {
//check if both vectors have the same number of size
if (left.size() != right.size()) {
cerr << "Sizes don't match" << endl;
return -1;
}
//compute the mean of the left and right set of points
cv::Point3d leftmean, rightmean;
leftmean.x = 0;
leftmean.y = 0;
leftmean.z = 0;
rightmean.x = 0;
rightmean.y = 0;
rightmean.z = 0;
for (int i = 0; i < left.size(); i++) {
leftmean.x += left[i].x;
leftmean.y += left[i].y;
leftmean.z += left[i].z;
rightmean.x += right[i].x;
rightmean.y += right[i].y;
rightmean.z += right[i].z;
}
leftmean.x /= left.size();
leftmean.y /= left.size();
leftmean.z /= left.size();
rightmean.x /= right.size();
rightmean.y /= right.size();
rightmean.z /= right.size();
cv::Mat leftmeanMat(3,1,CV_64F);
cv::Mat rightmeanMat(3,1,CV_64F);
leftmeanMat.at<double>(0,0) = leftmean.x;
leftmeanMat.at<double>(0,1) = leftmean.y;
leftmeanMat.at<double>(0,2) = leftmean.z;
rightmeanMat.at<double>(0,0) = rightmean.x;
rightmeanMat.at<double>(0,1) = rightmean.y;
rightmeanMat.at<double>(0,2) = rightmean.z;
//normalize all points
for (int i = 0; i < left.size(); i++) {
left[i].x -= leftmean.x;
left[i].y -= leftmean.y;
left[i].z -= leftmean.z;
right[i].x -= rightmean.x;
right[i].y -= rightmean.y;
right[i].z -= rightmean.z;
}
//compute scale (use the symmetrical solution)
double Sl = 0;
double Sr = 0;
// this is the symmetrical version of the scale !
for (int i = 0; i < left.size(); i++) {
Sl += left[i].x*left[i].x + left[i].y*left[i].y + left[i].z*left[i].z;
Sr += right[i].x*right[i].x + right[i].y*right[i].y + right[i].z*right[i].z;
}
scale = sqrt(Sr/Sl);
// cout << "Scale: " << scale << endl;
//create M matrix
double M[3][3];// = {0.0};
/*
// I believe this is wrong, since not summing over all left right elements, just for the last element ! KM Nov 21
for (int i = 0; i < left.size(); i++) {
M[0][0] = left[i].x*right[i].x;
M[0][1] = left[i].x*right[i].y;
M[0][2] = left[i].x*right[i].z;
M[1][0] = left[i].y*right[i].x;
M[1][1] = left[i].y*right[i].y;
M[1][2] = left[i].y*right[i].z;
M[2][0] = left[i].z*right[i].x;
M[2][1] = left[i].z*right[i].y;
M[2][2] = left[i].z*right[i].z;
}
*/
M[0][0] = 0;
M[0][1] = 0;
M[0][2] = 0;
M[1][0] = 0;
M[1][1] = 0;
M[1][2] = 0;
M[2][0] = 0;
M[2][1] = 0;
M[2][2] = 0;
for (int i = 0; i < left.size(); i++)
{
M[0][0] += left[i].x*right[i].x;
M[0][1] += left[i].x*right[i].y;
M[0][2] += left[i].x*right[i].z;
M[1][0] += left[i].y*right[i].x;
M[1][1] += left[i].y*right[i].y;
M[1][2] += left[i].y*right[i].z;
M[2][0] += left[i].z*right[i].x;
M[2][1] += left[i].z*right[i].y;
M[2][2] += left[i].z*right[i].z;
}
//create N matrix
cv::Mat N = cv::Mat::zeros(4,4,CV_64F);
N.at<double>(0,0) = M[0][0] + M[1][1] + M[2][2];
N.at<double>(0,1) = M[1][2] - M[2][1];
N.at<double>(0,2) = M[2][0] - M[0][2];
N.at<double>(0,3) = M[0][1] - M[1][0];
N.at<double>(1,0) = M[1][2] - M[2][1];
N.at<double>(1,1) = M[0][0] - M[1][1] - M[2][2];
N.at<double>(1,2) = M[0][1] + M[1][0];
N.at<double>(1,3) = M[2][0] + M[0][2];
N.at<double>(2,0) = M[2][0] - M[0][2];
N.at<double>(2,1) = M[0][1] + M[1][0];
N.at<double>(2,2) = -M[0][0] + M[1][1] - M[2][2];
N.at<double>(2,3) = M[1][2] + M[2][1];
N.at<double>(3,0) = M[0][1] - M[1][0];
N.at<double>(3,1) = M[2][0] + M[0][2];
N.at<double>(3,2) = M[1][2] + M[2][1];
N.at<double>(3,3) = -M[0][0] - M[1][1] + M[2][2];
// cout << "N: " << N << endl;
//compute eigenvalues
cv::Mat eigenvalues(1,4,CV_64FC1);
cv::Mat eigenvectors(4,4,CV_64FC1);
// cout << "eigenvalues: \n" << eigenvalues << endl;
if (!cv::eigen(N, eigenvalues, eigenvectors)) {
cerr << "eigen failed" << endl;
return -1;
}
// cout << "Eigenvalues:\n" << eigenvalues << endl;
// cout << "Eigenvectors:\n" << eigenvectors << endl;
//compute quaterion as maximum eigenvector
double q[4];
q[0] = eigenvectors.at<double>(0,0);
q[1] = eigenvectors.at<double>(0,1);
q[2] = eigenvectors.at<double>(0,2);
q[3] = eigenvectors.at<double>(0,3);
/* // I believe this changed with the openCV implementation, eigenvectors are stored in row-order !
q[0] = eigenvectors.at<double>(0,0);
q[1] = eigenvectors.at<double>(1,0);
q[2] = eigenvectors.at<double>(2,0);
q[3] = eigenvectors.at<double>(3,0);
*/
double absOfEigVec = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
q[0] /= absOfEigVec;
q[1] /= absOfEigVec;
q[2] /= absOfEigVec;
q[3] /= absOfEigVec;
cv::Mat qMat(4,1,CV_64F,q);
// cout << "q: " << qMat << endl;
//compute Rotation matrix
RMat.at<double>(0,0) = q[0]*q[0] + q[1]*q[1] - q[2]*q[2] - q[3]*q[3];
RMat.at<double>(0,1) = 2*(q[1]*q[2] - q[0]*q[3]);
RMat.at<double>(0,2) = 2*(q[1]*q[3] + q[0]*q[2]);
RMat.at<double>(1,0) = 2*(q[2]*q[1] + q[0]*q[3]);
RMat.at<double>(1,1) = q[0]*q[0] - q[1]*q[1] + q[2]*q[2] - q[3]*q[3];
RMat.at<double>(1,2) = 2*(q[2]*q[3] - q[0]*q[1]);
RMat.at<double>(2,0) = 2*(q[3]*q[1] - q[0]*q[2]);
RMat.at<double>(2,1) = 2*(q[2]*q[3] + q[0]*q[1]);
RMat.at<double>(2,2) = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
// cout <<"R:\n" << RMat << endl;
// cout << "Det: " << determinant(RMat) << endl;
//find translation
cv::Mat tempMat(3,1,CV_64F);
//gemm(RMat, leftmeanMat, -1.0, rightmeanMat, 1.0, TMat); // enforcing scale of 1, since same scales in both frames
// The convention used here is: right = (1/scale) * RMat * left + TMat
TMat = -(1/scale) * RMat*leftmeanMat + rightmeanMat;
// gemm(RMat, leftmeanMat, -1.0 * scale, rightmeanMat, 1.0, TMat);
// cout << "Translation: " << TMat << endl;
return 0;
}
bool PivotCalibration2::ComputeSpinCalibration(bool snapRotation)
{
if (this->ToolToReferenceMatrices.size() < 10)
{
this->ErrorText = "Not enough input transforms are available";
return false;
}
if (this->GetMaximumToolOrientationDifferenceDeg() < this->MinimumOrientationDifferenceDeg)
{
this->ErrorText = "Not enough variation in the input transforms";
return false;
}
// Setup our system to find the axis of rotation
unsigned int rows = 3, columns = 3;
vnl_matrix<double> A(rows, columns, 0);
vnl_matrix<double> I(3, 3, 0);
I.set_identity();
vnl_matrix<double> RI(rows, columns);
// this will store the maximum difference in orientation between the first transform and all the other transforms
double maximumOrientationDifferenceDeg = 0;
std::vector< vtkSmartPointer<vtkMatrix4x4> >::const_iterator previt = this->ToolToReferenceMatrices.end();
for (std::vector< vtkSmartPointer<vtkMatrix4x4> >::const_iterator it = this->ToolToReferenceMatrices.begin(); it != this->ToolToReferenceMatrices.end(); it++)
{
if (previt == this->ToolToReferenceMatrices.end())
{
previt = it;
continue; // No comparison to make for the first matrix
}
vtkSmartPointer< vtkMatrix4x4 > itinverse = vtkSmartPointer< vtkMatrix4x4 >::New();
vtkMatrix4x4::Invert((*it), itinverse);
vtkSmartPointer< vtkMatrix4x4 > instRotation = vtkSmartPointer< vtkMatrix4x4 >::New();
vtkMatrix4x4::Multiply4x4(itinverse, (*previt), instRotation);
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
RI(i, j) = instRotation->GetElement(i, j);
}
}
RI = RI - I;
A = A + RI.transpose() * RI;
previt = it;
}
// Note: If the needle orientation protocol changes, only the definitions of shaftAxis and secondaryAxes need to be changed
// Define the shaft axis and the secondary shaft axis
// Current needle orientation protocol dictates: shaft axis -z, orthogonal axis +x
// If StylusX is parallel to ShaftAxis then: shaft axis -z, orthogonal axis +y
vnl_vector<double> shaftAxis_Shaft(columns, 0); shaftAxis_Shaft(0) = 0; shaftAxis_Shaft(1) = 0; shaftAxis_Shaft(2) = -1;
vnl_vector<double> orthogonalAxis_Shaft(columns, 0); orthogonalAxis_Shaft(0) = 1; orthogonalAxis_Shaft(1) = 0; orthogonalAxis_Shaft(2) = 0;
vnl_vector<double> backupAxis_Shaft(columns, 0); backupAxis_Shaft(0) = 0; backupAxis_Shaft(1) = 1; backupAxis_Shaft(2) = 0;
// Find the eigenvector associated with the smallest eigenvalue
// This is the best axis of rotation over all instantaneous rotations
vnl_matrix<double> eigenvectors(columns, columns, 0);
vnl_vector<double> eigenvalues(columns, 0);
vnl_symmetric_eigensystem_compute(A, eigenvectors, eigenvalues);
// Note: eigenvectors are ordered in increasing eigenvalue ( 0 = smallest, end = biggest )
vnl_vector<double> shaftAxis_ToolTip(columns, 0);
shaftAxis_ToolTip(0) = eigenvectors(0, 0);
shaftAxis_ToolTip(1) = eigenvectors(1, 0);
shaftAxis_ToolTip(2) = eigenvectors(2, 0);
shaftAxis_ToolTip.normalize();
// Snap the direction vector to be exactly aligned with one of the coordinate axes
// This is if the sensor is known to be parallel to one of the axis, just not which one
if (snapRotation)
{
int closestCoordinateAxis = element_product(shaftAxis_ToolTip, shaftAxis_ToolTip).arg_max();
shaftAxis_ToolTip.fill(0);
shaftAxis_ToolTip.put(closestCoordinateAxis, 1); // Doesn't matter the direction, will be sorted out in the next step
}
// Make sure it is in the correct direction (opposite the StylusTipToStylus translation)
vnl_vector<double> toolTipToToolTranslation(3);
toolTipToToolTranslation(0) = this->ToolTipToToolMatrix->GetElement(0, 3);
toolTipToToolTranslation(1) = this->ToolTipToToolMatrix->GetElement(1, 3);
toolTipToToolTranslation(2) = this->ToolTipToToolMatrix->GetElement(2, 3);
if (dot_product(shaftAxis_ToolTip, toolTipToToolTranslation) > 0)
{
shaftAxis_ToolTip = shaftAxis_ToolTip * (-1);
}
//set the RMSE
this->SpinRMSE = (A * shaftAxis_ToolTip).rms();
// If the secondary axis 1 is parallel to the shaft axis in the tooltip frame, then use secondary axis 2
vnl_vector<double> orthogonalAxis_ToolTip;
double angle = acos(dot_product(shaftAxis_ToolTip, orthogonalAxis_Shaft));
// Force angle to be between -pi/2 and +pi/2
if (angle > vtkMath::Pi() / 2)
{
angle -= vtkMath::Pi();
}
if (angle < -vtkMath::Pi() / 2)
{
angle += vtkMath::Pi();
}
if (fabs(angle) > vtkMath::RadiansFromDegrees(PARALLEL_ANGLE_THRESHOLD_DEGREES)) // If shaft axis and orthogonal axis are not parallel
{
orthogonalAxis_ToolTip = orthogonalAxis_Shaft;
}
else
{
orthogonalAxis_ToolTip = backupAxis_Shaft;
}
// Do the registration find the appropriate rotation
orthogonalAxis_ToolTip = orthogonalAxis_ToolTip - dot_product(orthogonalAxis_ToolTip, shaftAxis_ToolTip) * shaftAxis_ToolTip;
orthogonalAxis_ToolTip.normalize();
// Register X,Y,O points in the two coordinate frames (only spherical registration - since pure rotation)
vnl_matrix<double> ToolTipPoints(3, 3, 0.0);
vnl_matrix<double> ShaftPoints(3, 3, 0.0);
ToolTipPoints.put(0, 0, shaftAxis_ToolTip(0));
ToolTipPoints.put(0, 1, shaftAxis_ToolTip(1));
ToolTipPoints.put(0, 2, shaftAxis_ToolTip(2));
ToolTipPoints.put(1, 0, orthogonalAxis_ToolTip(0));
ToolTipPoints.put(1, 1, orthogonalAxis_ToolTip(1));
ToolTipPoints.put(1, 2, orthogonalAxis_ToolTip(2));
ToolTipPoints.put(2, 0, 0);
ToolTipPoints.put(2, 1, 0);
ToolTipPoints.put(2, 2, 0);
ShaftPoints.put(0, 0, shaftAxis_Shaft(0));
ShaftPoints.put(0, 1, shaftAxis_Shaft(1));
ShaftPoints.put(0, 2, shaftAxis_Shaft(2));
ShaftPoints.put(1, 0, orthogonalAxis_Shaft(0));
ShaftPoints.put(1, 1, orthogonalAxis_Shaft(1));
ShaftPoints.put(1, 2, orthogonalAxis_Shaft(2));
ShaftPoints.put(2, 0, 0);
ShaftPoints.put(2, 1, 0);
ShaftPoints.put(2, 2, 0);
vnl_svd<double> ShaftToToolTipRegistrator(ShaftPoints.transpose() * ToolTipPoints);
vnl_matrix<double> V = ShaftToToolTipRegistrator.V();
vnl_matrix<double> U = ShaftToToolTipRegistrator.U();
vnl_matrix<double> Rotation = V * U.transpose();
// Make sure the determinant is positve (i.e. +1)
double determinant = vnl_determinant(Rotation);
if (determinant < 0)
{
// Switch the sign of the third column of V if the determinant is not +1
// This is the recommended approach from Huang et al. 1987
V.put(0, 2, -V.get(0, 2));
V.put(1, 2, -V.get(1, 2));
V.put(2, 2, -V.get(2, 2));
Rotation = V * U.transpose();
}
// Set the elements of the output matrix
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
this->ToolTipToToolMatrix->SetElement(i, j, Rotation[i][j]);
}
}
this->ErrorText.empty();
return true;
}
void CCA_logit(bool perm,
vector<vector<int> > & blperm,
Set & S,
Plink & P)
{
///////////////
// Output results
ofstream EPI;
if (!perm)
{
string f = par::output_file_name+".genepi";
P.printLOG("\nWriting gene-based epistasis tests to [ " + f + " ]\n");
EPI.open(f.c_str(), ios::out);
EPI.precision(4);
EPI << setw(12) << "NIND" << " "
<< setw(12) << "GENE1" << " "
<< setw(12) << "GENE2" << " "
<< setw(12) << "NSNP1" << " "
<< setw(12) << "NSNP2" << " "
<< setw(12) << "P" << " "
<< "\n";
}
//////////////////////////////////
// Canonical correlation analysis
int ns = P.snpset.size();
// Consider each pair of genes
for (int s1=0; s1 < ns-1; s1++)
{
for (int s2 = s1+1; s2 < ns; s2++)
{
////////////////////////////////////////////////////////
// Step 1. Construct covariance matrix (cases and controls together)
// And partition covariance matrix:
// S_11 S_21
// S_12 S_22
int n1=0, n2=0;
vector<vector<double> > sigma(0);
vector<double> mean(0);
vector<CSNP*> pSNP(0);
/////////////////////////////
// List of SNPs for both loci
for (int l=0; l<P.snpset[s1].size(); l++)
{
if ( S.cur[s1][l] )
{
pSNP.push_back( P.SNP[ P.snpset[s1][l] ] );
n1++;
}
}
for (int l=0; l<P.snpset[s2].size(); l++)
{
if ( S.cur[s2][l] )
{
pSNP.push_back( P.SNP[ P.snpset[s2][l] ] );
n2++;
}
}
int n12 = n1 + n2;
int ne = n1 < n2 ? n1 : n2;
///////////////////////////////////
// Construct covariance matrix (cases and controls together)
P.setFlags(false);
vector<Individual*>::iterator person = P.sample.begin();
while ( person != P.sample.end() )
{
(*person)->flag = true;
person++;
}
int nind = calcGENEPIMeanVariance(pSNP,
n1,n2,
false,
&P,
mean,
sigma,
P.sample ,
blperm[s1],
blperm[s2] );
///////////////////////////
// Partition covariance matrix
vector<vector<double> > I11;
vector<vector<double> > I11b;
vector<vector<double> > I12;
vector<vector<double> > I21;
vector<vector<double> > I22;
vector<vector<double> > I22b;
sizeMatrix( I11, n1, n1);
sizeMatrix( I11b, n1, n1);
sizeMatrix( I12, n1, n2);
sizeMatrix( I21, n2, n1);
sizeMatrix( I22, n2, n2);
sizeMatrix( I22b, n2, n2); // For step 4b (eigenvectors for gene2)
for (int i=0; i<n1; i++)
for (int j=0; j<n1; j++)
{
I11[i][j] = sigma[i][j];
I11b[i][j] = sigma[i][j];
}
for (int i=0; i<n1; i++)
for (int j=0; j<n2; j++)
I12[i][j] = sigma[i][n1+j];
for (int i=0; i<n2; i++)
for (int j=0; j<n1; j++)
I21[i][j] = sigma[n1+i][j];
for (int i=0; i<n2; i++)
for (int j=0; j<n2; j++)
{
I22[i][j] = sigma[n1+i][n1+j];
I22b[i][j] = sigma[n1+i][n1+j];
}
////////////////////////////////////////////////////////
// Step 2. Calculate the p x p matrix M1 = inv(sqrt(sig11)) %*% sig12 %*% inv(sig22) %*% sig21 %*% inv(sqrt(sig11))
bool flag = true;
I11 = msqrt(I11);
I11 = svd_inverse(I11,flag);
I22 = svd_inverse(I22,flag);
I22b = msqrt(I22b);// For Step 4b
I22b = svd_inverse(I22b,flag);
I11b = svd_inverse(I11b,flag);
matrix_t tmp;
matrix_t M1;
multMatrix(I11, I12, tmp);
multMatrix(tmp, I22, M1);
multMatrix(M1, I21, tmp);
multMatrix(tmp, I11, M1);
////////////////////////////////////////////////////////
// Step 4a. Calculate the p eigenvalues and p x p eigenvectors of
// M (e). These are required to compute the coefficients used to
// build the p canonical variates a[k] for gene1 (see below)
double max_cancor = 0.90;
// Compute evalues and evectors
Eigen gene1_eigen = eigenvectors(M1);
// Sort evalues for gene 1. (the first p of these equal the first p of gene 2 (ie M2), if they are sorted)
vector<double> sorted_eigenvalues_gene1 = gene1_eigen.d;
sort(sorted_eigenvalues_gene1.begin(),sorted_eigenvalues_gene1.end(),greater<double>());
// Position of the largest canonical correlation that is <
// max_cancor in the sorted vector of eigenvalues. This will be
// needed to use the right gene1 and gene2 coefficients to build
// the appropriate canonical variates.
double cancor1=0;
int cancor1_pos;
for (int i=0; i<n1; i++)
{
if ( sqrt(sorted_eigenvalues_gene1[i]) > cancor1 && sqrt(sorted_eigenvalues_gene1[i]) < max_cancor )
{
cancor1 = sqrt(sorted_eigenvalues_gene1[i]);
cancor1_pos = i;
break;
}
}
// Display largest canonical correlation and its position
// cout << "Largest canonical correlation [position]\n"
// << cancor1 << " [" << cancor1_pos << "]" << "\n\n" ;
// Sort evectors. Rows must be ordered according to cancor value (highest first)
matrix_t sorted_eigenvectors_gene1 = gene1_eigen.z;
vector<int> order_eigenvalues_gene1(n1);
for (int i=0; i<n1; i++)
{
// Determine position of the vector associated with the ith cancor
for (int j=0; j<n1; j++)
{
if (gene1_eigen.d[j]==sorted_eigenvalues_gene1[i])
{
if (i==0)
{
order_eigenvalues_gene1[i]=j;
break;
}
else
{
if (j!=order_eigenvalues_gene1[i-1])
{
order_eigenvalues_gene1[i]=j;
break;
}
}
}
}
}
for (int i=0; i<n1; i++)
{
sorted_eigenvectors_gene1[i] = gene1_eigen.z[order_eigenvalues_gene1[i]];
}
// cout << "Eigenvector matrix - unsorted:\n";
// display(gene1_eigen.z);
//cout << "Eigenvector matrix - sorted:\n";
//display(sorted_eigenvectors_gene1);
////////////////////////////////////////////////////////
// Step 4b. Calculate the q x q eigenvectors of M2 (f). These are
// required to compute the coefficients used to build the p
// canonical variates b[k] for gene2 (see below). The first p are
// given by: f[k] = (1/sqrt(eigen[k])) * inv_sqrt_I22 %*% I21 %*%
// inv_sqrt_sig11 %*% e[k] for (k in 1:p) { e.vectors.gene2[,k] =
// (1/sqrt(e.values[k])) * inv.sqrt.sig22 %*% sig21 %*%
// inv.sqrt.sig11 %*% e.vectors.gene1[,k] }
matrix_t M2;
multMatrix(I22b, I21, tmp);
multMatrix(tmp, I11b, M2);
multMatrix(M2, I12, tmp);
multMatrix(tmp, I22b, M2);
Eigen gene2_eigen = eigenvectors(M2);
//cout << "Eigenvalues Gene 2 - unsorted:\n";
//display(gene2_eigen.d);
// Sort evalues for gene2
vector<double> sorted_eigenvalues_gene2 = gene2_eigen.d;
sort(sorted_eigenvalues_gene2.begin(),sorted_eigenvalues_gene2.end(),greater<double>());
// Sort eigenvectors for gene2
matrix_t sorted_eigenvectors_gene2 = gene2_eigen.z;
vector<int> order_eigenvalues_gene2(n2);
for (int i=0; i<n2; i++)
{
// Determine position of the vector associated with the ith cancor
for (int j=0; j<n2; j++)
{
if (gene2_eigen.d[j]==sorted_eigenvalues_gene2[i])
{
if (i==0)
{
order_eigenvalues_gene2[i]=j;
break;
}
else
{
if (j!=order_eigenvalues_gene2[i-1])
{
order_eigenvalues_gene2[i]=j;
break;
}
}
}
}
}
for (int i=0; i<n2; i++)
{
sorted_eigenvectors_gene2[i] = gene2_eigen.z[order_eigenvalues_gene2[i]];
}
//cout << "Eigenvector matrix Gene 2 - unsorted:\n";
//display(gene2_eigen.z);
//cout << "Eigenvector matrix Gene 2 - sorted:\n";
//display(sorted_eigenvectors_gene2);
//exit(0);
//////////////////////////////////////////////////////////////////////////////////
// Step 5 - Calculate the gene1 (pxp) and gene2 (pxq) coefficients
// used to create the canonical variates associated with the p
// canonical correlations
transposeMatrix(gene1_eigen.z);
transposeMatrix(gene2_eigen.z);
matrix_t coeff_gene1;
matrix_t coeff_gene2;
multMatrix(gene1_eigen.z, I11, coeff_gene1);
multMatrix(gene2_eigen.z, I22b, coeff_gene2);
//cout << "Coefficients for Gene 1:\n";
//display(coeff_gene1);
//cout << "Coefficients for Gene 2:\n";
//display(coeff_gene2);
//exit(0);
///////////////////////////////////////////////////////////////////////
// Step 6 - Compute the gene1 and gene2 canonical variates
// associated with the highest canonical correlation NOTE: the
// original variables of data need to have the mean subtracted first!
// Otherwise, the resulting correlation between variate.gene1 and
// variate.gene1 != estimated cancor.
// For each individual, eg compos.gene1 =
// evector.gene1[1]*SNP1.gene1 + evector.gene1[2]*SNP2.gene1 + ...
/////////////////////////////////
// Consider each SNP in gene1
vector<double> gene1(nind);
for (int j=0; j<n1; j++)
{
CSNP * ps = pSNP[j];
///////////////////////////
// Iterate over individuals
for (int i=0; i< P.n ; i++)
{
// Only need to look at one perm set
bool a1 = ps->one[i];
bool a2 = ps->two[i];
if ( a1 )
{
if ( a2 ) // 11 homozygote
{
gene1[i] += (1 - mean[j]) * coeff_gene1[order_eigenvalues_gene1[cancor1_pos]][j];
}
else // 12
{
gene1[i] += (0 - mean[j]) * coeff_gene1[order_eigenvalues_gene1[cancor1_pos]][j];
}
}
else
{
if ( a2 ) // 21
{
gene1[i] += (0 - mean[j]) * coeff_gene1[order_eigenvalues_gene1[cancor1_pos]][j];
}
else // 22 homozygote
{
gene1[i] += (-1 - mean[j]) * coeff_gene1[order_eigenvalues_gene1[cancor1_pos]][j];
}
}
} // Next individual
} // Next SNP in gene1
/////////////////////////////////
// Consider each SNP in gene2
vector<double> gene2(P.n);
int cur_snp = -1;
for (int j=n1; j<n1+n2; j++)
{
cur_snp++;
CSNP * ps = pSNP[j];
// Iterate over individuals
for (int i=0; i<P.n; i++)
{
// Only need to look at one perm set
bool a1 = ps->one[i];
bool a2 = ps->two[i];
if ( a1 )
{
if ( a2 ) // 11 homozygote
{
gene2[i] += (1 - mean[j]) * coeff_gene2[order_eigenvalues_gene2[cancor1_pos]][cur_snp];
}
else // 12
{
gene2[i] += (0 - mean[j]) * coeff_gene2[order_eigenvalues_gene2[cancor1_pos]][cur_snp];
}
}
else
{
if ( a2 ) // 21
{
gene2[i] += (0 - mean[j]) * coeff_gene2[order_eigenvalues_gene2[cancor1_pos]][cur_snp];
}
else // 22 homozygote
{
gene2[i] += (-1 - mean[j]) * coeff_gene2[order_eigenvalues_gene2[cancor1_pos]][cur_snp];
}
}
} // Next individual
} // Next SNP in gene2
// Store gene1.variate and gene2.variate in the multiple_covariates field of P.sample
// TO DO: NEED TO CHECK IF FIELDS ARE EMPTY FIRST!
for (int i=0; i<P.n; i++)
{
P.sample[i]->clist.resize(2);
P.sample[i]->clist[0] = gene1[i];
P.sample[i]->clist[1] = gene2[i];
}
///////////////////////////////////////////////
// STEP 7 - Logistic or linear regression epistasis test
//
Model * lm;
if (par::bt)
{
LogisticModel * m = new LogisticModel(& P);
lm = m;
}
else
{
LinearModel * m = new LinearModel(& P);
lm = m;
}
// No SNPs used
lm->hasSNPs(false);
// Set missing data
lm->setMissing();
// Main effect of GENE1 1. Assumes that the variable is in position 0 of the clist vector
lm->addCovariate(0);
lm->label.push_back("GENE1");
// Main effect of GENE 2. Assumes that the variable is in position 1 of the clist vector
lm->addCovariate(1);
lm->label.push_back("GENE2");
// Epistasis
lm->addInteraction(1,2);
lm->label.push_back("EPI");
// Build design matrix
lm->buildDesignMatrix();
// Prune out any remaining missing individuals
// No longer needed (check)
// lm->pruneY();
// Fit linear model
lm->fitLM();
// Did model fit okay?
lm->validParameters();
// Obtain estimates and statistic
lm->testParameter = 3; // interaction
vector_t b = lm->getCoefs();
double chisq = lm->getStatistic();
double logit_pvalue = chiprobP(chisq,1);
// Clean up
delete lm;
/////////////////////////////
// OUTPUT
EPI << setw(12) << nind << " "
<< setw(12) << P.setname[s1] << " "
<< setw(12) << P.setname[s2] << " "
<< setw(12) << n1 << " "
<< setw(12) << n2 << " "
<< setw(12) << logit_pvalue << " "
<< "\n";
} // End of loop over genes2
} // End of loop over genes1
EPI.close();
} // End of CCA_logit()
Eigen::Eigen()
{
vector <double> eigenvalues(3);
vector<vector <double>> eigenvectors(3,vector<double>(3));
}
ArrayXd BaseSolver::calc_spatial_ldos(float target_energy, float broadening) {
return num::match2sp<ArrayX, ArrayXX>(
eigenvalues(), eigenvectors(),
compute::CalcSpatialLDOS{target_energy, broadening}
);
}