vec diag(DistMat & mat){
assert(info.is_square());
vec ret = zeros(info.total());
for (int i=0; i< info.total(); i++){
ret[i] = latent_factors_inmem[i].A_ii;
}
return ret;
}
void init_lanczos(bipartite_graph_descriptor & info){
data_size = nsv + nv+1 + max_iter;
actual_vector_len = data_size;
#pragma omp parallel for
for (int i=0; i< info.total(); i++){
latent_factors_inmem[i].pvec = zeros(actual_vector_len);
}
logstream(LOG_INFO)<<"Allocated a total of: " << ((double)actual_vector_len * info.total() * sizeof(double)/ 1e6) << " MB for storing vectors." << std::endl;
}
vec diag(DistMat & mat){
assert(info.is_square());
vec ret = zeros(info.total());
for (int i=0; i< info.total(); i++){
//TODO ret[i] = pgraph->vertex_data(i).A_ii;
assert(false);
}
return ret;
}
/**
* Vertex update function.
*/
void update(graphchi_vertex<VertexDataType, EdgeDataType> &vertex, graphchi_context &gcontext) {
if (vertex.id() < (uint)mi.start || vertex.id() >= (uint)mi.end)
return;
vertex_data& user = latent_factors_inmem[vertex.id()];
bool rows = vertex.id() < (uint)info.get_start_node(false);
if (info.is_square())
rows = mi.A_transpose;
(void) rows; // unused
assert(mi.r_offset >=0);
//store previous value for convergence detection
if (mi.prev_offset >= 0)
user.pvec[mi.prev_offset ] = user.pvec[mi.r_offset];
double val = 0;
assert(mi.x_offset >=0 || mi.y_offset>=0);
/*** COMPUTE r = c*A*x ********/
if (mi.A_offset && mi.x_offset >= 0){
for(int e=0; e < vertex.num_edges(); e++) {
const edge_data & edge = vertex.edge(e)->get_data();
const vertex_data & movie = latent_factors_inmem[vertex.edge(e)->vertex_id()];
val += (edge.weight * movie.pvec[mi.x_offset]);
}
if (info.is_square() && mi.use_diag)// add the diagonal term
val += (/*mi.c**/ (user.A_ii+ regularization) * user.pvec[mi.x_offset]);
val *= mi.c;
}
/***** COMPUTE r = c*I*x *****/
else if (!mi.A_offset && mi.x_offset >= 0){
val = mi.c*user.pvec[mi.x_offset];
}
/**** COMPUTE r+= d*y (optional) ***/
if (mi.y_offset>= 0){
val += mi.d*user.pvec[mi.y_offset];
}
/***** compute r = (... ) / div */
if (mi.div_offset >= 0){
val /= user.pvec[mi.div_offset];
}
assert(mi.r_offset>=0 && mi.r_offset < user.pvec.size());
user.pvec[mi.r_offset] = val;
} //end update
DistVec& DistVec::operator=(DistMat &mat){
mi.r_offset = offset;
assert(prev_offset < data_size);
mi.prev_offset = prev_offset;
transpose = mat.transpose;
mi.start = info.get_start_node(!transpose);
mi.end = info.get_end_node(!transpose);
//graphchi_engine<VertexDataType, EdgeDataType> engine(training, nshards, false, m);
//set_engine_flags(engine);
//Axb program;
pengine->run(program, 1);
debug_print(name);
mi.reset_offsets();
mat.transpose = false;
return *this;
}
DistVec& operator=(const DistVec & vec){
assert(offset < (info.is_square() ? 2*data_size: data_size));
if (mi.x_offset == -1 && mi.y_offset == -1){
mi.y_offset = vec.offset;
}
mi.r_offset = offset;
assert(prev_offset < data_size);
mi.prev_offset = prev_offset;
if (mi.d == 0.0)
mi.d=1.0;
transpose = vec.transpose;
end = vec.end;
start = vec.start;
mi.start = start;
mi.end = end;
graphchi_engine<VertexDataType, EdgeDataType> engine(training, nshards, false, m);
engine.set_disable_vertexdata_storage();
engine.set_modifies_inedges(false);
engine.set_modifies_outedges(false);
Axb program;
engine.run(program, 1);
debug_print(name);
mi.reset_offsets();
return *this;
}
DistVec& operator=(const vec & pvec){
assert(offset >= 0);
assert(pvec.size() == info.num_nodes(true) || pvec.size() == info.num_nodes(false));
assert(start < end);
if (!info.is_square() && pvec.size() == info.num_nodes(false)){
transpose = true;
}
else {
transpose = false;
}
for (int i=start; i< end; i++){
latent_factors_inmem[i].pvec[offset] = pvec[i-start];
}
debug_print(name);
return *this;
}
DistVec& DistVec::operator=(DistMat &mat){
mi.r_offset = offset;
assert(prev_offset < data_size);
mi.prev_offset = prev_offset;
transpose = mat.transpose;
mi.start = info.get_start_node(!transpose);
mi.end = info.get_end_node(!transpose);
graphchi_engine<VertexDataType, EdgeDataType> engine(training, nshards, false, m);
engine.set_disable_vertexdata_storage();
Axb program;
engine.set_modifies_inedges(false);
engine.set_modifies_outedges(false);
engine.run(program, 1);
debug_print(name);
mi.reset_offsets();
mat.transpose = false;
return *this;
}
/* Gather the weighted rank of the adjacent page */
double gather(icontext_type& context, const vertex_type& vertex,
edge_type& edge) const {
if (edge.data().role == edge_data::PREDICT)
return 0;
bool brows = vertex.id() < (uint)info.get_start_node(false);
if (info.is_square())
brows = !mi.A_transpose;
if (mi.A_offset && mi.x_offset >= 0){
double val = edge.data().obs * (brows ? edge.target().data().pvec[mi.x_offset] :
edge.source().data().pvec[mi.x_offset]);
//printf("gather edge on vertex %d val %lg obs %lg\n", vertex.id(), val, edge.data().obs);
return val;
}
//printf("edge on vertex %d val %lg\n", vertex.id(), 0.0);
return 0;
}
DistVec& DistVec::operator=(DistMat &mat){
mi.r_offset = offset;
assert(prev_offset < data_size);
mi.prev_offset = prev_offset;
transpose = mat.transpose;
mi.start = info.get_start_node(!transpose);
mi.end = info.get_end_node(!transpose);
INITIALIZE_TRACER(Axbtrace, "Axb update function");
BEGIN_TRACEPOINT(Axbtrace);
pcurrent = this;
int old_start = start; int old_end = end;
start = mi.start; end = mi.end;
start_engine();
start = old_start; end = old_end;
END_TRACEPOINT(Axbtrace);
debug_print(name);
mi.reset_offsets();
mat.transpose = false;
return *this;
}
DistSlicedMat(int _start_offset, int _end_offset, bool _transpose, const bipartite_graph_descriptor &_info, std::string _name){
//assert(_start_offset < _end_offset);
assert(_start_offset >= 0);
assert(_info.total() > 0);
transpose = _transpose;
info = _info;
init();
start_offset = _start_offset;
end_offset = _end_offset;
name = _name;
}
void multiply(DistSlicedMat & mat, int curoffset, double a){
assert(a>0);
DistVec current = mat[curoffset];
assert(mat.start_offset <= current.offset);
vec result = zeros(curoffset);
if (curoffset > 0){
#pragma omp parallel for
for (int i=mat.start_offset; i< current.offset; i++){
for (int k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
result[i-mat.start_offset] += latent_factors_inmem[k].pvec[i] * latent_factors_inmem[k].pvec[current.offset];
}
}
#pragma omp parallel for
for (int k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
latent_factors_inmem[k].pvec[curoffset] /= a;
}
for (int i=mat.start_offset; i< current.offset; i++){
#pragma omp parallel for
for (int k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
latent_factors_inmem[k].pvec[current.offset] -= result[i-mat.start_offset]/a * latent_factors_inmem[k].pvec[i];
}
}
}
current.debug_print(current.name);
}
void orthogonalize_vs_all(DistSlicedMat & mat, int curoffset, double &alpha){
assert(mi.ortho_repeats >=1 && mi.ortho_repeats <= 3);
bool old_debug = debug;
debug = false;
DistVec current = mat[curoffset];
assert(mat.start_offset <= current.offset);
double * alphas = new double[curoffset];
//DistDouble * alphas = new DistDouble[curoffset];
//cout<<current.to_vec().transpose() << endl;
if (curoffset > 0){
for (int j=0; j < mi.ortho_repeats; j++){
memset(alphas, 0, sizeof(double)*curoffset);
#pragma omp parallel for
for (int i=mat.start_offset; i< current.offset; i++){
for (int k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
assert(i-mat.start_offset>=0 && i-mat.start_offset < curoffset);
assert(i < latent_factors_inmem[k].pvec.size());
assert(k < (int)latent_factors_inmem.size());
assert(current.offset < latent_factors_inmem[k].pvec.size());
alphas[i-mat.start_offset] += latent_factors_inmem[k].pvec[i] * latent_factors_inmem[k].pvec[current.offset];
}
}
for (int i=mat.start_offset; i< current.offset; i++){
#pragma omp parallel for
for (int k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
latent_factors_inmem[k].pvec[current.offset] -= alphas[i-mat.start_offset] * latent_factors_inmem[k].pvec[i];
}
}
} //for ortho_repeast
}
delete [] alphas;
debug = old_debug;
current.debug_print(current.name);
// alpha = 0;
double sum = 0;
int k;
//#pragma omp parallel for private(k) reduction(+: sum)
for (k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
sum = sum + pow(latent_factors_inmem[k].pvec[current.offset],2);
}
alpha = sqrt(sum);
if (alpha >= 1e-10 ){
#pragma omp parallel for
for (int k=info.get_start_node(!current.transpose); k< info.get_end_node(!current.transpose); k++){
latent_factors_inmem[k].pvec[current.offset]/=alpha;
}
}
}
DistVec& DistVec::operator=(const vec & pvec){
assert(offset >= 0);
assert(pvec.size() == info.num_nodes(true) || pvec.size() == info.num_nodes(false));
assert(start < end);
if (!info.is_square() && pvec.size() == info.num_nodes(false)){
transpose = true;
}
else {
transpose = false;
}
//#pragma omp parallel for
INITIALIZE_TRACER(vecequals, "vector assignment");
BEGIN_TRACEPOINT(vecequals);
//for (int i=start; i< end; i++){
// pgraph->vertex_data(i).pvec[offset] = pvec[i-start];
//}
pcurrent = this;
curvec = pvec;
graphlab::vertex_set nodes = pgraph->select(select_in_range);
pgraph->transform_vertices(assign_vec, nodes);
END_TRACEPOINT(vecequals);
debug_print(name);
return *this;
}
/* Use the total rank of adjacent pages to update this page */
void apply(icontext_type& context, vertex_type& vertex,
const double& total) {
//printf("Entered apply on node %d value %lg\n", vertex.id(), total);
vertex_data & user = vertex.data();
assert(mi.x_offset >=0 || mi.y_offset >= 0);
assert(mi.r_offset >=0);
/* perform orthogonalization of current vector */
if (mi.orthogonalization){
for (int i=mi.mat_offset; i< mi.vec_offset; i++){
vertex.data().pvec[mi.vec_offset] -= alphas.pvec[i-mi.mat_offset] * vertex.data().pvec[i];
}
return;
}
double val = total;
//assert(total != 0 || mi.y_offset >= 0);
//store previous value for convergence detection
if (mi.prev_offset >= 0)
user.pvec[mi.prev_offset ] = user.pvec[mi.r_offset];
assert(mi.x_offset >=0 || mi.y_offset>=0);
if (mi.A_offset && mi.x_offset >= 0){
if (info.is_square() && mi.use_diag)// add the diagonal term
val += (/*mi.c**/ (user.A_ii+ regularization) * user.pvec[mi.x_offset]);
//printf("node %d added diag term: %lg\n", vertex.id(), user.A_ii);
val *= mi.c;
}
/***** COMPUTE r = c*I*x *****/
else if (!mi.A_offset && mi.x_offset >= 0){
val = mi.c*user.pvec[mi.x_offset];
}
/**** COMPUTE r+= d*y (optional) ***/
if (mi.y_offset>= 0){
val += mi.d*user.pvec[mi.y_offset];
}
/***** compute r = (... ) / div */
if (mi.div_offset >= 0){
val /= user.pvec[mi.div_offset];
}
user.pvec[mi.r_offset] = val;
//printf("Exit apply on node %d value %lg\n", vertex.id(), val);
}
DistVec& DistVec::operator=(const DistVec & vec){
assert(offset < (info.is_square() ? 2*data_size: data_size));
if (mi.x_offset == -1 && mi.y_offset == -1){
mi.y_offset = vec.offset;
}
mi.r_offset = offset;
assert(prev_offset < data_size);
mi.prev_offset = prev_offset;
if (mi.d == 0.0)
mi.d=1.0;
transpose = vec.transpose;
end = vec.end;
start = vec.start;
mi.start = start;
mi.end = end;
INITIALIZE_TRACER(Axbtrace2, "Update function Axb");
BEGIN_TRACEPOINT(Axbtrace2);
pcurrent = (DistVec*)&vec;
start_engine();
debug_print(name);
mi.reset_offsets();
return *this;
}
DistVec& operator=(const DistVec & vec){
assert(offset < (info.is_square() ? 2*data_size: data_size));
if (mi.x_offset == -1 && mi.y_offset == -1){
mi.y_offset = vec.offset;
}
mi.r_offset = offset;
assert(prev_offset < data_size);
mi.prev_offset = prev_offset;
if (mi.d == 0.0)
mi.d=1.0;
transpose = vec.transpose;
end = vec.end;
start = vec.start;
mi.start = start;
mi.end = end;
//graphchi_engine<VertexDataType, EdgeDataType> engine(training, nshards, false, m);
//set_engine_flags(engine);
//Axb program;
pengine->run(program, 1);
debug_print(name);
mi.reset_offsets();
return *this;
}
void assign_vec(graph_type::vertex_type & vertex){
if (!info.is_square())
assert(vertex.id() - pcurrent->start >= 0 && vertex.id() - pcurrent->start < curvec.size());
vertex.data().pvec[pcurrent->offset] = curvec[vertex.id() - pcurrent->start];
}
void init(){
start = info.get_start_node(!transpose);
end = info.get_end_node(!transpose);
assert(start < end && start >= 0 && end >= 1);
//debug_print(name);
};
bool selected_node(const graph_type::vertex_type& vertex){
if (info.is_square())
return true;
else return ((vertex.id() >= (uint)info.get_start_node(!pcurrent->transpose)) &&
(vertex.id() < (uint)info.get_end_node(!pcurrent->transpose)));
}
vec lanczos( bipartite_graph_descriptor & info, timer & mytimer, vec & errest,
const std::string & vecfile){
int nconv = 0;
int its = 1;
DistMat A(info);
DistSlicedMat U(info.is_square() ? data_size : 0, info.is_square() ? 2*data_size : data_size, true, info, "U");
DistSlicedMat V(0, data_size, false, info, "V");
vec alpha, beta, b;
vec sigma = zeros(data_size);
errest = zeros(nv);
DistVec v_0(info, 0, false, "v_0");
if (vecfile.size() == 0)
v_0 = randu(size(A,2));
PRINT_VEC2("svd->V", v_0);
DistDouble vnorm = norm(v_0);
v_0=v_0/vnorm;
PRINT_INT(nv);
while(nconv < nsv && its < max_iter){
std::cout<<"Starting iteration: " << its << " at time: " << mytimer.current_time() << std::endl;
int k = nconv;
int n = nv;
PRINT_INT(k);
PRINT_INT(n);
alpha = zeros(n);
beta = zeros(n);
U[k] = V[k]*A._transpose();
orthogonalize_vs_all(U, k, alpha(0));
//alpha(0)=norm(U[k]).toDouble();
PRINT_VEC3("alpha", alpha, 0);
//U[k] = U[k]/alpha(0);
for (int i=k+1; i<n; i++){
std::cout <<"Starting step: " << i << " at time: " << mytimer.current_time() << std::endl;
PRINT_INT(i);
V[i]=U[i-1]*A;
orthogonalize_vs_all(V, i, beta(i-k-1));
//beta(i-k-1)=norm(V[i]).toDouble();
//V[i] = V[i]/beta(i-k-1);
PRINT_VEC3("beta", beta, i-k-1);
U[i] = V[i]*A._transpose();
orthogonalize_vs_all(U, i, alpha(i-k));
//alpha(i-k)=norm(U[i]).toDouble();
//U[i] = U[i]/alpha(i-k);
PRINT_VEC3("alpha", alpha, i-k);
}
V[n]= U[n-1]*A;
orthogonalize_vs_all(V, n, beta(n-k-1));
//beta(n-k-1)=norm(V[n]).toDouble();
PRINT_VEC3("beta", beta, n-k-1);
//compute svd of bidiagonal matrix
PRINT_INT(nv);
PRINT_NAMED_INT("svd->nconv", nconv);
n = nv - nconv;
PRINT_INT(n);
alpha.conservativeResize(n);
beta.conservativeResize(n);
PRINT_MAT2("Q",eye(n));
PRINT_MAT2("PT",eye(n));
PRINT_VEC2("alpha",alpha);
PRINT_VEC2("beta",beta);
mat T=diag(alpha);
for (int i=0; i<n-1; i++)
set_val(T, i, i+1, beta(i));
PRINT_MAT2("T", T);
mat a,PT;
svd(T, a, PT, b);
PRINT_MAT2("Q", a);
alpha=b.transpose();
PRINT_MAT2("alpha", alpha);
for (int t=0; t< n-1; t++)
beta(t) = 0;
PRINT_VEC2("beta",beta);
PRINT_MAT2("PT", PT.transpose());
//estiamte the error
int kk = 0;
for (int i=nconv; i < nv; i++){
int j = i-nconv;
PRINT_INT(j);
sigma(i) = alpha(j);
PRINT_NAMED_DBL("svd->sigma[i]", sigma(i));
PRINT_NAMED_DBL("Q[j*n+n-1]",a(n-1,j));
PRINT_NAMED_DBL("beta[n-1]",beta(n-1));
errest(i) = abs(a(n-1,j)*beta(n-1));
PRINT_NAMED_DBL("svd->errest[i]", errest(i));
if (alpha(j) > tol){
errest(i) = errest(i) / alpha(j);
PRINT_NAMED_DBL("svd->errest[i]", errest(i));
}
if (errest(i) < tol){
kk = kk+1;
PRINT_NAMED_INT("k",kk);
}
if (nconv +kk >= nsv){
printf("set status to tol\n");
finished = true;
}
}//end for
PRINT_NAMED_INT("k",kk);
vec v;
if (!finished){
vec swork=get_col(PT,kk);
PRINT_MAT2("swork", swork);
v = zeros(size(A,1));
for (int ttt=nconv; ttt < nconv+n; ttt++){
v = v+swork(ttt-nconv)*(V[ttt].to_vec());
}
PRINT_VEC2("svd->V",V[nconv]);
PRINT_VEC2("v[0]",v);
}
//compute the ritz eigenvectors of the converged singular triplets
if (kk > 0){
PRINT_VEC2("svd->V", V[nconv]);
mat tmp= V.get_cols(nconv,nconv+n)*PT;
V.set_cols(nconv, nconv+kk, get_cols(tmp, 0, kk));
PRINT_VEC2("svd->V", V[nconv]);
PRINT_VEC2("svd->U", U[nconv]);
tmp= U.get_cols(nconv, nconv+n)*a;
U.set_cols(nconv, nconv+kk,get_cols(tmp,0,kk));
PRINT_VEC2("svd->U", U[nconv]);
}
nconv=nconv+kk;
if (finished)
break;
V[nconv]=v;
PRINT_VEC2("svd->V", V[nconv]);
PRINT_NAMED_INT("svd->nconv", nconv);
its++;
PRINT_NAMED_INT("svd->its", its);
PRINT_NAMED_INT("svd->nconv", nconv);
//nv = min(nconv+mpd, N);
//if (nsv < 10)
// nv = 10;
PRINT_NAMED_INT("nv",nv);
} // end(while)
printf(" Number of computed signular values %d",nconv);
printf("\n");
DistVec normret(info, nconv, false, "normret");
DistVec normret_tranpose(info, nconv, true, "normret_tranpose");
for (int i=0; i < nconv; i++){
normret = V[i]*A._transpose() -U[i]*sigma(i);
double n1 = norm(normret).toDouble();
PRINT_DBL(n1);
normret_tranpose = U[i]*A -V[i]*sigma(i);
double n2 = norm(normret_tranpose).toDouble();
PRINT_DBL(n2);
double err=sqrt(n1*n1+n2*n2);
PRINT_DBL(err);
PRINT_DBL(tol);
if (sigma(i)>tol){
err = err/sigma(i);
}
PRINT_DBL(err);
PRINT_DBL(sigma(i));
printf("Singular value %d \t%13.6g\tError estimate: %13.6g\n", i, sigma(i),err);
}
if (save_vectors){
std::cout<<"Going to save output vectors U and V" << std::endl;
if (nconv == 0)
logstream(LOG_FATAL)<<"No converged vectors. Aborting the save operation" << std::endl;
char output_filename[256];
for (int i=0; i< nconv; i++){
sprintf(output_filename, "%s.U.%d", training.c_str(), i);
write_output_vector(output_filename, U[i].to_vec(), false, "GraphLab v2 SVD output. This file contains eigenvector number i of the matrix U");
sprintf(output_filename, "%s.V.%d", training.c_str(), i);
write_output_vector(output_filename, V[i].to_vec(), false, "GraphLab v2 SVD output. This file contains eigenvector number i of the matrix V'");
}
}
return sigma;
}