Matrix transposeMultiplyMatrixR(const Matrix A, const Matrix B) {
/** creates a new matrix that is the product of the A and (B transpose) */
int i, j, k; /* Variables used as indices */
Matrix P = makeMatrix(A->row_dim, B->row_dim); /* Product A * B */
DEBUG(10, "Multiplying Matrix");
assert(A->row_dim == B->row_dim); /* Verify that the Matrices can be multiplied */
/* Optimized code */
for ( i = 0; i < A->row_dim; i++) {
for ( j = 0; j < B->row_dim; j++) {
ME( P, i, j) = 0;
}
}
for (k = 0; k < A->col_dim; k++) {
for ( i = 0; i < A->row_dim; i++) {
for ( j = 0; j < B->row_dim; j++) {
ME( P, i, j) += ME(A, i, k) * ME(B, j, k);
}
}
}
return P;
}
/* This method performs an L2 based distance measure
after solving for a best fit transformation. The
best fit transformation is a combination of a 2D
scale, rotation and translation. The algorithm
solves for this transformation using a least squares
solution to a set of transformation aproximations. */
FTYPE GeometrySimLeastSquaresNLS(FaceGraph f1, FaceGraph f2){
int i;
FTYPE dist = 0.0;
Matrix g1 = makeMatrix(f1->geosize*2,1);
Matrix g2 = makeMatrix(f1->geosize*2,1);
for (i = 0; i < f1->geosize; i++) {
FTYPE dedx=0, dedy=0;
DENarrowingLocalSearch(f1->jets[i],f2->jets[i],&dedx,&dedy);
ME(g1,2*i,0) = f1->jets[i]->x ;
ME(g1,2*i+1,0) = f1->jets[i]->y ;
ME(g2,2*i,0) = f2->jets[i]->x + dedx;
ME(g2,2*i+1,0) = f2->jets[i]->y + dedy;
}
TransformLeastSquares(g1,g2);
dist = L2Dist(g1, g2);
freeMatrix(g1);
freeMatrix(g2);
return dist;
}
void rowMultAdd(Matrix m, int rSrc, int rDest, FTYPE value) {
int col = 0;
for(col = 0; col < m->col_dim; col++) {
ME(m,rDest,col) += value*ME(m,rSrc,col);
}
}
void fisherVerify(Matrix fisherBasis, Matrix fisherValues, Matrix Sw, Matrix Sb) {
Matrix SbW = multiplyMatrix(Sb, fisherBasis);
Matrix SwW = multiplyMatrix(Sw, fisherBasis);
Matrix D = makeIdentityMatrix(fisherBasis->row_dim);
Matrix DSwW;
Matrix zeroMat;
int i, j;
MESSAGE("Verifying Fisher Basis.");
for (i = 0; i < D->row_dim; i++) {
ME(D, i, i) = ME(fisherValues, i, 0);
}
DSwW = multiplyMatrix(D, SwW);
zeroMat = subtractMatrix(SbW, DSwW);
for (i = 0; i < zeroMat->row_dim; i++) {
for (j = 0; j < zeroMat->col_dim; j++) {
if (!EQUAL_ZERO(ME(zeroMat, i, j), 0.000001)) {
DEBUG( -1, "Fisher validation failed.");
printf("Element: (%d,%d) value = %f", i, j, ME(zeroMat, i, j));
exit(1);
}
}
}
}
/* Return a scale Matrix */
Matrix scaleMatrix(double s){
Matrix transform = makeIdentityMatrix(3);
ME(transform,0,0) = s;
ME(transform,1,1) = s;
return transform;
}
/* invert a matrix using Gaussian Elimination */
Matrix invertRREF(Matrix m) {
int prealloc = alloc_matrix;
int i,j;
Matrix tmp = makeZeroMatrix(m->row_dim, m->col_dim*2);
Matrix inverse = makeMatrix(m->row_dim, m->col_dim);
DEBUG_CHECK(m->row_dim == m->col_dim,"Matrix can only be inverted if it is square");
/* build the tmp Matrix which will be passed to RREF */
for( i = 0; i < m->row_dim; i++) {
for( j = 0; j < m->col_dim; j++) {
ME(tmp,i,j) = ME(m,i,j);
if(i == j) {
ME(tmp,i,j+m->col_dim) = 1;
}
}
}
matrixRREF(tmp);
for( i = 0; i < m->row_dim; i++) {
for( j = 0; j < m->col_dim; j++) {
ME(inverse,i,j) = ME(tmp,i,j+m->col_dim);
}
}
freeMatrix(tmp);
if(prealloc != alloc_matrix - 1) {
printf("Error deallocating matricies <%s>: pre=%d post=%d",__FUNCTION__, prealloc, alloc_matrix);
exit(1);
}
return inverse;
}
Matrix reflectMatrix(int bool_x, int bool_y){
Matrix transform = makeIdentityMatrix(3);
if(bool_x) ME(transform,0,0) = -1;
if(bool_y) ME(transform,1,1) = -1;
return transform;
}
/* Return a translation matrix */
Matrix translateMatrix(double dx, double dy){
Matrix transform = makeIdentityMatrix(3);
ME(transform,0,2) = dx;
ME(transform,1,2) = dy;
return transform;
}
void
mean_subtract_images (Matrix images, Matrix mean)
{
int i, j;
for (i = 0; i < images->row_dim; i++) {
for (j = 0; j < images->col_dim; j++) {
ME(images, i, j) -= ME(mean, i, 0);
}
}
}
/* Return a rotation matrix */
Matrix rotateMatrix(double theta){
Matrix transform = makeIdentityMatrix(3);
ME(transform,0,0) = cos(theta);
ME(transform,1,1) = cos(theta);
ME(transform,0,1) = -sin(theta);
ME(transform,1,0) = sin(theta);
return transform;
}
void rowSwap(Matrix m, int rSrc, int rDest) {
int col = 0;
FTYPE tmp;
for(col = 0; col < m->col_dim; col++) {
tmp = ME(m,rSrc,col);
ME(m,rSrc,col) = ME(m,rDest,col);
ME(m,rDest,col) = tmp;
}
}
Matrix duplicateMatrix(const Matrix mat) {
Matrix dup = makeMatrix(mat->row_dim, mat->col_dim);
int i, j;
for (i = 0; i < mat->row_dim; i++) {
for (j = 0; j < mat->col_dim; j++) {
ME(dup, i, j) = ME(mat, i, j);
}
}
return dup;
}
FTYPE L2Dist(Matrix g1, Matrix g2){
FTYPE dist = 0.0;
int i;
for (i = 0; i < g1->row_dim/2; i++) {
dist += SQR(ME(g1,2*i,0) - ME(g2,2*i,0));
dist += SQR(ME(g1,2*i+1,0) - ME(g2,2*i+1,0));
}
return sqrt(dist);
}
/*
This function reads images in to a vector. That vector is then mean subtracted
and then projected onto an optimal basis (PCA, LDA or LPP). Returned is a matrix
that contains the images after they have been projected onto the subspace.
*/
Matrix
readAndProjectImages (Subspace *s, char *imageNamesFile, char *imageDirectory, int *numImages, ImageList **srt)
{
int i, j;
Matrix images, vector, smallVector;
char name[FILE_LINE_LENGTH];
ImageList *subject, *replicate;
DEBUG(1, "Reading training file names from file");
*srt = getImageNames(imageNamesFile, numImages);
DEBUG_CHECK(*srt, "Error: header no imagenames found in file image list file");
/* Automatically determine number of pixels in images */
sprintf(name, "%s/%s", imageDirectory, (*srt)->filename);
DEBUG(1, "Autodetecting number of pixels, i.e. vector length based on the size of image 0.");
DEBUG_CHECK (autoFileLength(name) == s->numPixels, "Images sizes do not match subspace basis vector size");
DEBUG_INT(1, "Vector length", s->numPixels);
DEBUG_CHECK(s->numPixels > 0, "Error positive value required for a Vector Length");
/*Images stored in the columns of a matrix */
DEBUG(1, "Allocating image matrix");
images = makeMatrix(s->basis->col_dim, *numImages);
vector = makeMatrix(s->numPixels, 1);
i = 0;
for (subject = *srt; subject; subject = subject->next_subject) {
for (replicate = subject; replicate; replicate = replicate->next_replicate) {
if (debuglevel > 0)
printf("%s ", replicate->filename);
sprintf(name, "%s/%s", imageDirectory, replicate->filename);
replicate->imageIndex = i;
readFile(name, 0, vector);
writeProgress("Reading images", i,*numImages);
smallVector = centerThenProjectImages(s, vector);
/* Copy the smaller vector into the image matrix*/
for (j = 0; j < smallVector->row_dim; j++) {
ME(images, j, i) = ME(smallVector, j, 0);
}
freeMatrix(smallVector);
i++; /* increament the image index */
}
if (debuglevel > 0)
printf("\n");
}
return images;
}
void matrixRREF(Matrix m) {
int prealloc = alloc_matrix;
int pivotCol = 0;
int pivotRow = 0;
int row;
FTYPE absVal;
int tmp = 0;
while(1) {
/* Select the row with the largest absolute value, or move to the next row
if there is no value int the column */
absVal = 0.0;
while( absVal == 0.0 && pivotCol < m->col_dim) {
absVal = ABS(ME(m,pivotRow,pivotCol));
tmp = pivotRow;
for(row = pivotRow+1; row < m->row_dim; row++) {
if( ABS(ME(m,row,pivotCol)) > absVal ) {
absVal = ABS(ME(m,row,pivotCol));
tmp = row;
}
}
if(absVal == 0) {
pivotCol++;
}
}
/* return if the RREF has been found */
if( pivotCol >= m->col_dim || pivotRow >= m->row_dim) return;
/* make sure that the pivot row is in the correct position */
if(pivotRow != tmp) rowSwap(m,tmp,pivotRow);
/* rescale the Pivot Row */
rowMult( m, pivotRow,1.0/ME(m,pivotRow,pivotCol) );
/* This part of the algorithm is not as effecent as it could be,
but it works for now. */
for(row = 0; row < m->row_dim; row++) {
if(row != pivotRow) {
rowMultAdd(m,pivotRow,row,-ME(m,row,pivotCol));
}
}
pivotRow++;
pivotCol++;
}
if(prealloc != alloc_matrix) {
printf("Error deallocating matricies <%s>: pre=%d post=%d",__FUNCTION__, prealloc, alloc_matrix);
exit(1);
}
}
/**
Verify properties of the eigen basis used for pca.
The eigenbasis should be ortonormal: U'*U - I == 0
The basis should be decomposed such that: X == U*D*V'
returns true if tests fail.
*/
int basis_verify(Matrix X, Matrix U) {
Matrix UtX = transposeMultiplyMatrixL(U, X);
Matrix UUtX = multiplyMatrix(U, UtX);
Matrix UtU = transposeMultiplyMatrixL(U, U);
Matrix identity = makeIdentityMatrix(U->col_dim);
Matrix test;
int i, j;
int failed = 0;
const double tol = 1.0e-7;
freeMatrix(UtX);
DEBUG(2, "Checking orthogonality of eigenbasis");
test = subtractMatrix(UtU, identity);
freeMatrix(UtU);
freeMatrix(identity);
for (i = 0; i < test->row_dim; i++) {
for (j = 0; j < test->col_dim; j++) {
if (!EQUAL_ZERO(ME(test, i, j), tol)) {
failed = 1;
MESSAGE("Eigenbasis is not orthogonal to within tolerance.");
DEBUG_DOUBLE(1, "Matrix Element", ME(test, i, j));
DEBUG_DOUBLE(1, "Tolerance", tol);
exit(1);
}
}
}
freeMatrix(test);
DEBUG(2, "Checking reconstruction property of the eigen decomposition");
test = subtractMatrix(X, UUtX);
freeMatrix(UUtX);
for (i = 0; i < test->row_dim; i++) {
for (j = 0; j < test->col_dim; j++) {
if (!EQUAL_ZERO(ME(test, i, j), tol)) {
failed = 1;
MESSAGE("Data matrix is not reconstructable to within tolerance.");
DEBUG_DOUBLE(1, "Matrix Element", ME(test, i, j));
DEBUG_DOUBLE(1, "Tolarence", tol);
exit(1);
}
}
}
freeMatrix(test);
return failed;
}
Matrix matrixCols( const Matrix mat, int col1, int col2) {
Matrix cols = makeMatrix(mat->row_dim, col2 - col1 + 1);
int i, j;
DEBUG_CHECK(col1 <= col2 && col2 < mat->col_dim, "Poorly chosen columns for extract columns operation");
for (i = col1; i <= col2; i++) {
for (j = 0; j < mat->row_dim; j++) {
ME(cols, j, i - col1) = ME(mat, j, i);
}
}
return cols;
}
void addMatrixEquals(Matrix A, const Matrix B) {
/** output A += B */
int i, j;
DEBUG(10, "Adding Matrix");
assert(A->row_dim == B->row_dim);
assert(A->col_dim == B->col_dim);
for (i = 0; i < A->row_dim; i++) {
for (j = 0; j < A->col_dim; j++) {
ME(A, i, j) += ME(B, i, j);
}
}
}
Matrix transposeMatrix(const Matrix A) {
/* creates a new matrix that is the transpose of A */
int i, j; /* Variables used as indices */
Matrix T = makeMatrix(A->col_dim, A->row_dim); /* Transpose of A */
DEBUG(10, "Transposing Matrix");
/** Transpose data */
for ( i = 0; i < A->row_dim; i++) {
for ( j = 0; j < A->col_dim; j++) {
ME(T, j, i) = ME(A, i, j);
}
}
return T;
}
void test_multipole_forces_stackel(int p=0, int q=0,std::string qq="No"){
TestDensity_Stackel rho(1.,-30.,-10.);
TriaxialPotential T(&rho,1e8);
MultipoleExpansion ME(&rho,100,30,16,-1,10.,0.01,100.,false,true,true);
ME.visualize("me.vis");
int NMAX = 50;
VecDoub xx(NMAX,0), exact(NMAX,0), triaxial(NMAX,0), multipole(NMAX,0);
#pragma omp parallel for schedule(dynamic)
for(int xn = 0; xn<NMAX; xn++){
double x = (double)xn+.1;
xx[xn] = x;
VecDoub X(3,1);
X[p]=x;
if(qq=="general"){
X[0]=x/2.;X[1]=x/3.;X[2]=x;
}
exact[xn] = rho.Forces(X)[q];
triaxial[xn] = T.Forces(X)[q];
multipole[xn] = ME.Forces(X)[q];
}
Gnuplot G("lines ls 1");
G.set_xrange(0.9*Min(xx),1.1*Max(xx));
G.set_yrange(0.9*Min(exact),1.1*Max(exact));
G.set_xlabel("x").set_ylabel("Potential");
G.savetotex("multipole_density_test").plot_xy(xx,exact);
G.set_style("lines ls 2").plot_xy(xx,triaxial);
G.set_style("lines ls 3").plot_xy(xx,multipole);
G.outputpdf("multipole_density_test");
}
void test_multipole_forces(int p=0, int q=0, std::string qq = "No"){
TestDensity_Hernquist rho(1.,10.,{1.,0.6,0.3});
// TestDensity_Isochrone rho(1.,10.,{1.,0.9,0.7});
TriaxialPotential T(&rho,1e6);
MultipoleExpansion ME(&rho,200,20,8,-1,10.,0.001,5000.,false,true,true);
int NMAX = 100;
VecDoub xx(NMAX,0), exact(NMAX,0), multipole(NMAX,0), triaxial(NMAX,0);
// #pragma omp parallel for schedule(dynamic)
for(int xn = 0; xn<NMAX; xn++){
double x = 0.01*(double)xn+1e-3;
xx[xn] = x;
VecDoub X(3,1e-4);
X[p]=x;
if(qq=="general"){
X[0]=x/2.;X[1]=x;X[2]=x/4.;
}
exact[xn] = rho.Forces(X)[q];
triaxial[xn] = T.Forces(X)[q];
multipole[xn] = ME.Forces(X)[q];
}
Gnuplot G("lines ls 1");
G.set_xrange(0.9*Min(xx),1.1*Max(xx));
G.set_yrange(1.1*Min(exact),1e-6);
G.set_xlabel("x").set_ylabel("Force");
G.savetotex("multipole_density_test").plot_xy(xx,multipole);
G.set_style("lines ls 3").plot_xy(xx,triaxial);
G.outputpdf("multipole_density_test");
}
void rowMult(Matrix m, int rSrc, FTYPE value) {
int col = 0;
for(col = 0; col < m->col_dim; col++) {
ME(m,rSrc,col) *= value;
}
}
void computeDistanceMatrix(Matrix distance, FaceGraph* graphs, int mini, int maxi, int minj, int maxj, FaceGraphSimilarity distMeasure) {
int i,j;
static time_t current_time = 0;
if( (maxi - mini > MAX_BLOCK_SIZE) || (maxi - mini > MAX_BLOCK_SIZE) ) {
int sizei = maxi - mini;
int sizej = maxj - minj;
computeDistanceMatrix(distance, graphs, mini, mini+sizei/2, minj, minj+sizej/2, distMeasure);
computeDistanceMatrix(distance, graphs, mini+sizei/2, maxi, minj, minj+sizej/2, distMeasure);
computeDistanceMatrix(distance, graphs, mini, mini+sizei/2, minj+sizej/2, maxj, distMeasure);
computeDistanceMatrix(distance, graphs, mini+sizei/2, maxi, minj+sizej/2, maxj, distMeasure);
if(current_time + 10 < time(NULL)) {
/* Estimate the remaining time and print status report */
int hour, min, sec;
double remaining_time;
current_time = time(NULL);
remaining_time = ((double)total - completed)*((double)current_time - start_time) / completed;
hour = ((int)remaining_time)/3600;
min = (((int)remaining_time)%3600)/60;
sec = ((int)remaining_time)%60;
printf("Measuring: %010d of %010d (%5.2f%%) ETR = %02dh %02dm %02ds\r",completed, total, completed*100.0/total, hour, min, sec);
fflush(stdout);
}
return;
}
for(i = mini; i < maxi; i++) {
for(j = minj; j < maxj; j++) {
ME(distance,i,j) = distMeasure(graphs[i], graphs[j]);
completed++;
}
}
}
void
memcheck_guest_query_malloc(target_ulong guest_address)
{
MallocDescQuery qdesc;
MallocDescEx* found;
ProcDesc* proc;
// Copy free descriptor from guest to emulator.
memcheck_get_query_descriptor(&qdesc, guest_address);
proc = get_process_from_pid(qdesc.query_pid);
if (proc == NULL) {
ME("memcheck: Unable to obtain process for pid=%u on query_%s",
qdesc.query_pid, qdesc.routine == 1 ? "free" : "realloc");
memcheck_fail_query(guest_address);
return;
}
// Find allocation entry for the given address.
found = procdesc_find_malloc(proc, qdesc.ptr);
if (found == NULL) {
av_invalid_pointer(proc, qdesc.ptr, qdesc.routine);
memcheck_fail_query(guest_address);
return;
}
// Copy allocation descriptor back to the guest's space.
memcheck_set_malloc_descriptor(qdesc.desc, &found->malloc_desc);
}
/* get_mean_image
This function takes a matrix of images and returns the mean of
all of the images in the matrix.
*/
Matrix
get_mean_image (Matrix images)
{
int i, j;
Matrix mean = makeMatrix(images->row_dim, 1);
for (i = 0; i < images->row_dim; i++)
{
ME(mean, i, 0) = 0.0;
for (j = 0; j < images->col_dim; j++)
ME(mean, i, 0) += ME(images, i, j);
ME(mean, i, 0) = ME(mean, i, 0) / images->col_dim;
}
return mean;
}
int tfsignature_extract(struct mailbox_transaction_context *t,
struct mail *mail, const char **signature)
{
const char *const *signatures;
signatures = get_mail_headers(mail, tfsignature_hdr);
if (!signatures || !signatures[0]) {
if (!tfsignature_nosig_ignore) {
mail_storage_set_error(t->box->storage,
ME(NOTPOSSIBLE)
"antispam signature not found");
return -1;
} else {
*signature = NULL;
return 0;
}
}
while (signatures[1])
signatures++;
*signature = signatures[0];
return 0;
}
void test_multipole_spherical(int p=0){
TestDensity_Hernquist rho(1.,1.,{1.,1.,1.});
MultipoleExpansion_Spherical ME(&rho,100,1.,0.01,200.);
VecDoub X = {1e-5,1e-5,1e-5};
double centre2 = rho.Phi(X);
double centre3 = ME.Phi(X);
int NMAX = 200;
VecDoub xx(NMAX,0), exact(NMAX,0), triaxial(NMAX,0), multipole(NMAX,0);
// #pragma omp parallel for schedule(dynamic)
for(int xn = 0; xn<NMAX; xn++){
double x = 0.0001*(double)xn+.0001;
xx[xn] = x;
VecDoub X2 = X;
X2[p]=x;
exact[xn] = rho.Phi(X2);
multipole[xn] = ME.Phi(X2);
}
Gnuplot G("lines ls 1");
G.set_xrange(0.9*Min(xx),1.1*Max(xx));
G.set_yrange(0.9*Min(multipole),1.1*Max(multipole));
G.set_xlabel("x").set_ylabel("Potential");
G.savetotex("multipole_density_test").plot_xy(xx,exact);
G.set_style("lines ls 3").plot_xy(xx,multipole);
G.outputpdf("multipole_density_test");
}
void test_multipole(int p=0,std::string qq="No"){
TestDensity_Hernquist rho(1.,10.,{1.,0.9,0.7});
TriaxialPotential T(&rho,1e6);
MultipoleExpansion ME2(&rho,100,30,16,6,1.,0.01,2000.,false,true,true);
ME2.output_to_file("me.tmp");
ME2.visualize("me.vis");
MultipoleExpansion ME("me.tmp");
VecDoub X = {0.001,0.001,0.01};
double centre2 = 0.;//T.Phi(X);
double centre3 = 0.;//ME2.Phi(X);
int NMAX = 200;
VecDoub xx(NMAX,0), exact(NMAX,0), triaxial(NMAX,0), multipole(NMAX,0);
#pragma omp parallel for schedule(dynamic)
for(int xn = 0; xn<NMAX; xn++){
double x = (double)xn+1.;
xx[xn] = x;
VecDoub X2=X;
X2[p]=x;
if(qq=="general"){
X[0]=x/2.;X[1]=x/3.;X[2]=x/2.;
}
triaxial[xn] = (T.Phi(X2)-centre2);
multipole[xn] = (ME2.Phi(X2)-centre3);
}
Gnuplot G("lines ls 1");
G.set_xrange(0.9*Min(xx),1.1*Max(xx));
G.set_yrange(0.9*Min(multipole),1.1*Max(multipole));
G.set_xlabel("x").set_ylabel("Potential");
G.savetotex("multipole_density_test").plot_xy(xx,triaxial);
G.set_style("lines ls 3").plot_xy(xx,multipole);
G.outputpdf("multipole_density_test");
}
void test_multipole_axisymmetric(int p=0){
Miyamoto_NagaiDensity rho(1.,1.,0.7);
MultipoleExpansion_Axisymmetric ME2(&rho,100,30,16,1.,0.01,100.);
ME2.output_to_file("me.tmp");
ME2.visualize("me.vis");
MultipoleExpansion ME("me.tmp");
VecDoub X = {0.001,0.001,0.01};
double centre2 = rho.Phi(X);
double centre3 = ME2.Phi(X);
int NMAX = 50;
VecDoub xx(NMAX,0), exact(NMAX,0), triaxial(NMAX,0), multipole(NMAX,0);
#pragma omp parallel for schedule(dynamic)
for(int xn = 0; xn<NMAX; xn++){
double x = 0.1*(double)xn;
xx[xn] = x;
VecDoub X2=X;
X2[p]=x;
triaxial[xn] = (rho.Phi(X2)-centre2);
multipole[xn] = (ME2.Phi(X2)-centre3);
}
Gnuplot G("lines ls 1");
G.set_xrange(0.9*Min(xx),1.1*Max(xx));
G.set_yrange(0.9*Min(multipole),1.1*Max(multipole));
G.set_xlabel("x").set_ylabel("Potential");
G.savetotex("multipole_density_test").plot_xy(xx,triaxial);
G.set_style("lines ls 3").plot_xy(xx,multipole);
G.outputpdf("multipole_density_test");
}
Matrix addMatrix( const Matrix A, const Matrix B) {
/** output A + B */
Matrix sum = makeMatrix(A->row_dim, A->col_dim);
int i, j;
DEBUG(10, "Adding Matrix");
assert(A->row_dim == B->row_dim);
assert(A->col_dim == B->col_dim);
for (i = 0; i < A->row_dim; i++) {
for (j = 0; j < A->col_dim; j++) {
ME(sum, i, j) = ME(A, i, j) + ME(B, i, j);
}
}
return sum;
}
