bool link_sparse_hessian(
size_t size ,
size_t repeat ,
CppAD::vector<double>& x ,
const CppAD::vector<size_t>& row ,
const CppAD::vector<size_t>& col ,
CppAD::vector<double>& hessian )
{
// -----------------------------------------------------
// setup
typedef vector<double> DblVector;
typedef vector< std::set<size_t> > SetVector;
typedef CppAD::AD<double> ADScalar;
typedef vector<ADScalar> ADVector;
size_t i, j, k;
size_t order = 0; // derivative order corresponding to function
size_t m = 1; // number of dependent variables
size_t n = size; // number of independent variables
size_t K = row.size(); // number of non-zeros in lower triangle
ADVector a_x(n); // AD domain space vector
ADVector a_y(m); // AD range space vector
DblVector w(m); // double range space vector
DblVector hes(K); // non-zeros in lower triangle
CppAD::ADFun<double> f; // AD function object
// weights for hessian calculation (only one component of f)
w[0] = 1.;
// use the unspecified fact that size is non-decreasing between calls
static size_t previous_size = 0;
bool print = (repeat > 1) & (previous_size != size);
previous_size = size;
// declare sparsity pattern
# if USE_SET_SPARSITY
SetVector sparsity(n);
# else
typedef vector<bool> BoolVector;
BoolVector sparsity(n * n);
# endif
// initialize all entries as zero
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
hessian[ i * n + j] = 0.;
}
// ------------------------------------------------------
extern bool global_retape;
if( global_retape) while(repeat--)
{ // choose a value for x
CppAD::uniform_01(n, x);
for(j = 0; j < n; j++)
a_x[j] = x[j];
// declare independent variables
Independent(a_x);
// AD computation of f(x)
CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);
// create function object f : X -> Y
f.Dependent(a_x, a_y);
extern bool global_optimize;
if( global_optimize )
{ print_optimize(f, print, "cppad_sparse_hessian_optimize", size);
print = false;
}
// calculate the Hessian sparsity pattern for this function
calc_sparsity(sparsity, f);
// structure that holds some of work done by SparseHessian
CppAD::sparse_hessian_work work;
// calculate this Hessian at this x
f.SparseHessian(x, w, sparsity, row, col, hes, work);
for(k = 0; k < K; k++)
{ hessian[ row[k] * n + col[k] ] = hes[k];
hessian[ col[k] * n + row[k] ] = hes[k];
}
}
else
{ // choose a value for x
CppAD::uniform_01(n, x);
for(j = 0; j < n; j++)
a_x[j] = x[j];
// declare independent variables
Independent(a_x);
// AD computation of f(x)
CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);
// create function object f : X -> Y
f.Dependent(a_x, a_y);
extern bool global_optimize;
if( global_optimize )
{ print_optimize(f, print, "cppad_sparse_hessian_optimize", size);
print = false;
}
// calculate the Hessian sparsity pattern for this function
calc_sparsity(sparsity, f);
// declare structure that holds some of work done by SparseHessian
CppAD::sparse_hessian_work work;
while(repeat--)
{ // choose a value for x
CppAD::uniform_01(n, x);
// calculate sparsity at this x
f.SparseHessian(x, w, sparsity, row, col, hes, work);
for(k = 0; k < K; k++)
{ hessian[ row[k] * n + col[k] ] = hes[k];
hessian[ col[k] * n + row[k] ] = hes[k];
}
}
}
return true;
}
DataType& SparseStorage<DataType>::elem(casadi_int rr, casadi_int cc) {
casadi_int oldsize = sparsity().nnz();
casadi_int ind = sparsity_.add_nz(rr, cc);
if (oldsize != sparsity().nnz())
nonzeros().insert(nonzeros().begin()+ind, DataType(0));
return nonzeros().at(ind);
}
DataType& SparseStorage<DataType>::elem(int rr, int cc) {
int oldsize = sparsity().size();
int ind = sparsityRef().getNZ(rr, cc);
if (oldsize != sparsity().size())
data().insert(begin()+ind, DataType(0));
return at(ind);
}
void Multiplication::generateOperation(std::ostream &stream, const std::vector<std::string>& arg, const std::vector<std::string>& res, CodeGenerator& gen) const{
// Clear the result
stream << " casadi_fill(" << sparsity().size() << ",0.0," << res.front() << ",1);" << endl;
// Perform sparse matrix multiplication
stream << " casadi_mm_nt_sparse(";
for(int i=0; i<2; ++i){
stream << arg.at(i) << ",s" << gen.getSparsity(dep(i).sparsity()) << ",";
}
stream << res.front() << ",s" << gen.getSparsity(sparsity()) << ");" << endl;
}
std::string Reshape::print(const std::vector<std::string>& arg) const {
// For vectors, reshape is also a transpose
if (dep().is_vector() && sparsity().is_vector()) {
// Print as transpose: X'
return arg.at(0) + "'";
} else {
// Print as reshape(X) or vec(X)
if (sparsity().is_column()) {
return "vec(" + arg.at(0) + ")";
} else {
return "reshape(" + arg.at(0) + ")";
}
}
}
const DataType& SparseStorage<DataType>::elem(int rr, int cc) const {
int ind = sparsity().getNZ(rr, cc);
if (ind==-1)
return casadi_limits<DataType>::zero;
else
return at(ind);
}
void Project::evalFwd(const std::vector<std::vector<MX> >& fseed,
std::vector<std::vector<MX> >& fsens) {
int nfwd = fsens.size();
for (int d=0; d<nfwd; ++d) {
fsens[d][0] = project(fseed[d][0], sparsity(), true);
}
}
void HorzRepsum::spAdj(bvec_t** arg, bvec_t** res, int* iw, bvec_t* w, int mem) {
int nnz = sparsity().nnz();
for (int i=0;i<n_;++i) {
std::transform(res[0], res[0]+nnz, arg[0]+i*nnz, arg[0]+i*nnz, &Orring);
}
std::fill(res[0], res[0]+nnz, 0);
}
std::string Project::print(const std::vector<std::string>& arg) const {
if (sparsity().isdense()) {
return "dense(" + arg.at(0) + ")";
} else {
return "project(" + arg.at(0) + ")";
}
}
MX Reshape::getTranspose() const {
// For vectors, reshape is also a transpose
if (dep().is_vector() && sparsity().is_vector()) {
return dep();
} else {
return MXNode::getTranspose();
}
}
void UnaryMX::generateOperation(std::ostream &stream, const std::vector<std::string>& arg, const std::vector<std::string>& res, CodeGenerator& gen) const{
stream << " for(i=0; i<" << sparsity().size() << "; ++i) ";
stream << res.at(0) << "[i]=";
casadi_math<double>::printPre(op_,stream);
stream << arg.at(0) << "[i]";
casadi_math<double>::printPost(op_,stream);
stream << ";" << endl;
}
void Transpose::generate(const std::vector<int>& arg, const std::vector<int>& res,
CodeGenerator& g) const {
g.addAuxiliary(CodeGenerator::AUX_TRANS);
g.body << " trans("
<< g.work(arg[0], nnz()) << ", " << g.sparsity(dep().sparsity()) << ", "
<< g.work(res[0], nnz()) << ", " << g.sparsity(sparsity()) << ", iw);" << endl;
}
void HorzRepsum::evalGen(const T** arg, T** res, int* iw, T* w, int mem,
R reduction) const {
int nnz = sparsity().nnz();
fill_n(res[0], nnz, 0);
for (int i=0;i<n_;++i) {
std::transform(arg[0]+i*nnz, arg[0]+(i+1)*nnz, res[0], res[0], reduction);
}
}
void Transpose::spFwd(const bvec_t** arg,
bvec_t** res, int* iw, bvec_t* w) {
// Shortands
const bvec_t *x = arg[0];
bvec_t *xT = res[0];
// Get sparsity
int nz = nnz();
const int* x_row = dep().row();
const int* xT_colind = sparsity().colind();
int xT_ncol = sparsity().size2();
// Loop over the nonzeros of the argument
copy(xT_colind, xT_colind+xT_ncol+1, iw);
for (int el=0; el<nz; ++el) {
xT[iw[*x_row++]++] = *x++;
}
}
void Transpose::evalGen(const T* const* arg, T* const* res,
int* iw, T* w) {
// Get sparsity patterns
//const vector<int>& x_colind = input[0]->colind();
const int* x_row = dep(0).row();
int x_sz = dep(0).nnz();
const int* xT_colind = sparsity().colind();
int xT_ncol = sparsity().size2();
const T* x = arg[0];
T* xT = res[0];
// Transpose
copy(xT_colind, xT_colind+xT_ncol+1, iw);
for (int el=0; el<x_sz; ++el) {
xT[iw[x_row[el]]++] = x[el];
}
}
void HorzRepmat::generate(CodeGenerator& g, const std::string& mem,
const std::vector<int>& arg, const std::vector<int>& res) const {
int nnz = dep(0).nnz();
g.body << " for (i=0;i<" << n_ << ";++i) {" << endl;
g.body << " " << g.copy(g.work(arg[0], dep(0).nnz()), nnz,
g.work(res[0], sparsity().nnz()) + "+ i*" + g.to_string(nnz))
<< endl
<< " }" << endl;
}
void HorzRepsum::generate(CodeGenerator& g, const std::string& mem,
const std::vector<int>& arg, const std::vector<int>& res) const {
int nnz = sparsity().nnz();
g.body << " " << g.fill(g.work(res[0], nnz), nnz, "0") << endl;
g.body << " for (i=0;i<" << n_ << ";++i) {" << endl;
g.body << " for (j=0;j<" << nnz << ";++j) {" << endl;
g.body << " " << g.work(res[0], nnz)<< "[j] += " <<
g.work(arg[0], dep(0).nnz()) << "[j+i*" << nnz << "];" << endl;
g.body << " }" << endl;
g.body << " }" << endl;
}
void Split::spFwd(const bvec_t** arg, bvec_t** res, int* iw, bvec_t* w, int mem) {
int nx = offset_.size()-1;
for (int i=0; i<nx; ++i) {
if (res[i]!=0) {
const bvec_t *arg_ptr = arg[0] + offset_[i];
int n_i = sparsity(i).nnz();
bvec_t *res_i_ptr = res[i];
for (int k=0; k<n_i; ++k) {
*res_i_ptr++ = *arg_ptr++;
}
}
}
}
bool GetNonzerosSlice::isIdentity() const {
// Check sparsity
if (!(sparsity() == dep().sparsity()))
return false;
// Check if the nonzeros follow in increasing order
if (s_.start_ != 0) return false;
if (s_.step_ != 1) return false;
if (s_.stop_ != size()) return false;
// True if reached this point
return true;
}
void Split::spAdj(const pv_bvec_t& arg,
const pv_bvec_t& res, int* itmp, bvec_t* rtmp) {
int nx = offset_.size()-1;
for (int i=0; i<nx; ++i) {
if (res[i]!=0) {
bvec_t *arg_ptr = arg[0] + offset_[i];
int n_i = sparsity(i).nnz();
bvec_t *res_i_ptr = res[i];
for (int k=0; k<n_i; ++k) {
*arg_ptr++ |= *res_i_ptr;
*res_i_ptr++ = 0;
}
}
}
}
void Multiplication<TrX,TrY>::generateOperation(std::ostream &stream, const std::vector<std::string>& arg, const std::vector<std::string>& res, CodeGenerator& gen) const{
// Check if inplace
bool inplace = arg.at(0).compare(res.front())==0;
// Copy first argument if not inplace
if(!inplace){
stream << " for(i=0; i<" << this->size() << "; ++i) " << res.front() << "[i]=" << arg.at(0) << "[i];" << endl;
}
// Perform sparse matrix multiplication
gen.addAuxiliary(CodeGenerator::AUX_MM_TN_SPARSE);
stream << " casadi_mm_tn_sparse(";
stream << arg.at(1) << ",s" << gen.getSparsity(dep(1).sparsity()) << ",";
stream << arg.at(2) << ",s" << gen.getSparsity(dep(2).sparsity()) << ",";
stream << res.front() << ",s" << gen.getSparsity(sparsity()) << ");" << endl;
}
int main(int argc, char *argv[])
{
// tests();
// srand(time(10));
srand(10);
if(argc < 4)
{
std::cout << "Input arguments:\n\t1: Filename for A matrix (as in A ~= WH)\n\t2: New desired dimension\n\t3: Max NMF iterations\n\t4: Max NNLS iterations\n\t5 (optional): delimiter (space is default)\n";
}
else
{
std::string filename = argv[1];
int newDimension = atoi(argv[2]);
int max_iter_nmf = atoi(argv[3]);
int max_iter_nnls = atoi(argv[4]);
char delimiter = (argc > 5) ? *argv[5] : ' ';
DenseMatrix* A = readMatrix(filename,delimiter);
A->copyColumnToRow();
printf("Sparsity of A: %f\n",sparsity(A));
DenseMatrix W = DenseMatrix(A->rows,newDimension);
DenseMatrix H = DenseMatrix(newDimension,A->cols);
NMF_Input input = NMF_Input(&W,&H,A,max_iter_nmf,max_iter_nnls);
std::cout << "Starting NMF computation." << std::endl;
std::clock_t start = std::clock();
double duration;
// nmf_cpu(input);
nmf_cpu_profile(input);
duration = ( std::clock() - start ) / (double) CLOCKS_PER_SEC;
std::cout << "NMF computation complete. Time: " << duration << " s." << std::endl;
W.copyColumnToRow();
dtype AF = FrobeniusNorm(A);
dtype WH_AF = Fnorm(W,H,*A);
printf("Objective value: %f\n",WH_AF/AF);
// DenseMatrix z1 = DenseMatrix(A->rows,newDimension);
// DenseMatrix z2 = DenseMatrix(newDimension,A->cols);
// printf("Calculated solution approximate Frobenius norm: %f\n",Fnorm(z1,z2,*A));
// printcolmajor(H.colmajor,H.rows,H.cols);
if(A) delete A;
}
return 0;
}
void EvaluationMX::generateOperation(std::ostream &stream, const std::vector<std::string>& arg, const std::vector<std::string>& res, CodeGenerator& gen) const{
// Get the index of the function
int f = gen.getDependency(fcn_);
stream << " f" << f << "_buffered(";
// Pass inputs to the function input buffers
for(int i=0; i<arg.size(); ++i){
// Pass argument to the function
stream << arg.at(i) << ",";
// Pass argument sparsity to the function
if(dep(i).isNull()){
stream << "0";
} else {
int sp_i = gen.getSparsity(dep(i).sparsity());
stream << "s" << sp_i;
}
// Separate with a space to visualize argument grouping
if(i+1<arg.size()+res.size()) stream << ", ";
}
// Separate arguments and results with two extra spaces
stream << " ";
// Pass results to the function input buffers
for(int i=0; i<res.size(); ++i){
// Pass results buffer to the function
stream << res.at(i) << ",";
// Pass argument sparsity to the function
int sp_i = gen.getSparsity(sparsity(i));
stream << "s" << sp_i;
// Separate with a space to visualize argument grouping
if(i+1<res.size()) stream << ", ";
}
// Finalize the function call
stream << ");" << endl;
}
void Project::spAdj(bvec_t** arg, bvec_t** res, int* iw, bvec_t* w) {
dep().sparsity().bor(arg[0], res[0], sparsity());
fill(res[0], res[0]+nnz(), 0);
}
void Project::generate(const std::vector<int>& arg, const std::vector<int>& res,
CodeGenerator& g) const {
g.body << " " << g.project(g.work(arg.front(), dep().nnz()), dep(0).sparsity(),
g.work(res.front(), nnz()), sparsity(), "w") << endl;
}
void SetNonzeros<Add>::eval_mx(const std::vector<MX>& arg, std::vector<MX>& res) {
// Get all the nonzeros
vector<int> nz = all();
// Output sparsity
const Sparsity &osp = sparsity();
const int* orow = osp.row();
vector<int> ocol = osp.get_col();
// Input sparsity (first input same as output)
const Sparsity &isp = dep(1).sparsity();
vector<int> icol = isp.get_col();
// We next need to resort the assignment vector by outputs instead of inputs
// Start by counting the number of output nonzeros corresponding to each input nonzero
vector<int> onz_count(osp.nnz()+2, 0);
for (vector<int>::const_iterator it=nz.begin(); it!=nz.end(); ++it) {
onz_count[*it+2]++;
}
// Cumsum to get index offset for output nonzero
for (int i=0; i<onz_count.size()-1; ++i) {
onz_count[i+1] += onz_count[i];
}
// Get the order of assignments
vector<int> nz_order(nz.size());
for (int k=0; k<nz.size(); ++k) {
// Save the new index
nz_order[onz_count[1+nz[k]]++] = k;
}
// Find out which elements are being set
vector<int>& with_duplicates = onz_count; // Reuse memory
onz_count.resize(nz.size());
for (int k=0; k<nz.size(); ++k) {
// Get output nonzero
int onz_k = nz[nz_order[k]];
// Get element (note: may contain duplicates)
if (onz_k>=0) {
with_duplicates[k] = ocol[onz_k]*osp.size1() + orow[onz_k];
} else {
with_duplicates[k] = -1;
}
}
// Get all output elements (this time without duplicates)
vector<int> el_output;
osp.find(el_output);
// Sparsity pattern being formed and corresponding nonzero mapping
vector<int> r_colind, r_row, r_nz, r_ind;
// Get references to arguments and results
res[0] = arg[0];
// Entries in res with elements zero'ed out
if (!Add) {
// Get the nz locations in res corresponding to the output sparsity pattern
r_nz.resize(with_duplicates.size());
copy(with_duplicates.begin(), with_duplicates.end(), r_nz.begin());
res[0].sparsity().get_nz(r_nz);
// Zero out the corresponding entries
res[0] = MX::zeros(isp)->getSetNonzeros(res[0], r_nz);
}
// Get the nz locations of the elements in arg corresponding to the argument sparsity pattern
arg[1].sparsity().find(r_nz);
isp.get_nz(r_nz);
// Filter out ignored entries and check if there is anything to add at all
bool elements_to_add = false;
for (vector<int>::iterator k=r_nz.begin(); k!=r_nz.end(); ++k) {
if (*k>=0) {
if (nz[*k]>=0) {
elements_to_add = true;
} else {
*k = -1;
}
}
}
// Quick continue of no elements to set/add
if (!elements_to_add) return;
// Get the nz locations in the argument corresponding to the inputs
r_ind.resize(el_output.size());
copy(el_output.begin(), el_output.end(), r_ind.begin());
res[0].sparsity().get_nz(r_ind);
// Enlarge the sparsity pattern of the arguments if not all assignments fit
for (vector<int>::iterator k=r_nz.begin(); k!=r_nz.end(); ++k) {
if (*k>=0 && nz[*k]>=0 && r_ind[nz[*k]]<0) {
// Create a new pattern which includes both the the previous seed
// and the addition/assignment
Sparsity sp = res[0].sparsity().unite(osp);
res[0] = res[0]->getProject(sp);
// Recalculate the nz locations in the arguments corresponding to the inputs
copy(el_output.begin(), el_output.end(), r_ind.begin());
res[0].sparsity().get_nz(r_ind);
break;
}
}
// Have r_nz point to locations in the result instead of the output
for (vector<int>::iterator k=r_nz.begin(); k!=r_nz.end(); ++k) {
if (*k>=0) {
*k = r_ind[nz[*k]];
}
}
// Add to the element to the sensitivity, if any
res[0] = arg[1]->getAddNonzeros(res[0], r_nz);
}
void SetNonzeros<Add>::evalAdj(const std::vector<std::vector<MX> >& aseed,
std::vector<std::vector<MX> >& asens) {
// Get all the nonzeros
vector<int> nz = all();
// Number of derivative directions
int nadj = aseed.size();
// Output sparsity
const Sparsity &osp = sparsity();
const int* orow = osp.row();
vector<int> ocol = osp.get_col();
// Input sparsity (first input same as output)
const Sparsity &isp = dep(1).sparsity();
const int* irow = isp.row();
vector<int> icol = isp.get_col();
// We next need to resort the assignment vector by outputs instead of inputs
// Start by counting the number of output nonzeros corresponding to each input nonzero
vector<int> onz_count(osp.nnz()+2, 0);
for (vector<int>::const_iterator it=nz.begin(); it!=nz.end(); ++it) {
onz_count[*it+2]++;
}
// Cumsum to get index offset for output nonzero
for (int i=0; i<onz_count.size()-1; ++i) {
onz_count[i+1] += onz_count[i];
}
// Get the order of assignments
vector<int> nz_order(nz.size());
for (int k=0; k<nz.size(); ++k) {
// Save the new index
nz_order[onz_count[1+nz[k]]++] = k;
}
// Find out which elements are being set
vector<int>& with_duplicates = onz_count; // Reuse memory
onz_count.resize(nz.size());
for (int k=0; k<nz.size(); ++k) {
// Get output nonzero
int onz_k = nz[nz_order[k]];
// Get element (note: may contain duplicates)
if (onz_k>=0) {
with_duplicates[k] = ocol[onz_k]*osp.size1() + orow[onz_k];
} else {
with_duplicates[k] = -1;
}
}
// Get all output elements (this time without duplicates)
vector<int> el_output;
osp.find(el_output);
// Sparsity pattern being formed and corresponding nonzero mapping
vector<int> r_colind, r_row, r_nz, r_ind;
for (int d=0; d<nadj; ++d) {
// Get the matching nonzeros
r_ind.resize(el_output.size());
copy(el_output.begin(), el_output.end(), r_ind.begin());
aseed[d][0].sparsity().get_nz(r_ind);
// Sparsity pattern for the result
r_colind.resize(isp.size2()+1); // Col count
fill(r_colind.begin(), r_colind.end(), 0);
r_row.clear();
// Perform the assignments
r_nz.clear();
for (int k=0; k<nz.size(); ++k) {
// Get the corresponding nonzero for the input
int el = nz[k];
// Skip if zero assignment
if (el==-1) continue;
// Get the corresponding nonzero in the argument
int el_arg = r_ind[el];
// Skip if no argument
if (el_arg==-1) continue;
// Save the assignment
r_nz.push_back(el_arg);
// Get the corresponding element
int i=icol[k], j=irow[k];
// Add to sparsity pattern
r_row.push_back(j);
r_colind[1+i]++;
}
// col count -> col offset
for (int i=1; i<r_colind.size(); ++i) r_colind[i] += r_colind[i-1];
// If anything to set/add
if (!r_nz.empty()) {
// Create a sparsity pattern from vectors
Sparsity f_sp(isp.size1(), isp.size2(), r_colind, r_row);
asens[d][1] += aseed[d][0]->getGetNonzeros(f_sp, r_nz);
if (!Add) {
asens[d][0] += MX::zeros(f_sp)->getSetNonzeros(aseed[d][0], r_nz);
} else {
asens[d][0] += aseed[d][0];
}
} else {
asens[d][0] += aseed[d][0];
}
}
}
std::vector<MX> SymbolicMX::partial(const std::vector<MX>& x){
return std::vector<MX>(1,MX::eye(sparsity().numel()));
}
/** \brief Get required length of w field */
virtual size_t sz_w() const { return sparsity().size1();}
const std::vector<int>& SparseStorage<DataType>::row() const {
return sparsity().row();
}
