Eigen::SparseMatrix<double> Condi2Joint(Eigen::SparseMatrix<double> Condi, Eigen::SparseVector<double> Pa)
{ // second dimension of Condi is the parent
Eigen::SparseMatrix<double> Joint;
Joint.resize(Condi.rows(), Condi.cols());
for (int cols = 0; cols < Condi.cols(); cols++)
{
Eigen::SparseVector<double> tmp_vec = Condi.block(0, cols, Condi.rows(), 1)*Pa.coeff(cols);
for (int id_rows = 0; id_rows < tmp_vec.size(); id_rows++)
{
Joint.coeffRef(id_rows, cols) = tmp_vec.coeff(id_rows);
}
}
Joint.prune(TOLERANCE);
return Joint;
}
matrix<Type> invertSparseMatrix(Eigen::SparseMatrix<Type> A){
matrix<Type> I(A.rows(),A.cols());
I.setIdentity();
Eigen::SimplicialLDLT< Eigen::SparseMatrix<Type> > ldlt(A);
matrix<Type> ans = ldlt.solve(I);
return ans;
}
IGL_INLINE void igl::slice_into(
const Eigen::SparseMatrix<T>& X,
const Eigen::Matrix<int,Eigen::Dynamic,1> & R,
const Eigen::Matrix<int,Eigen::Dynamic,1> & C,
Eigen::SparseMatrix<T>& Y)
{
int xm = X.rows();
int xn = X.cols();
assert(R.size() == xm);
assert(C.size() == xn);
#ifndef NDEBUG
int ym = Y.size();
int yn = Y.size();
assert(R.minCoeff() >= 0);
assert(R.maxCoeff() < ym);
assert(C.minCoeff() >= 0);
assert(C.maxCoeff() < yn);
#endif
// create temporary dynamic sparse matrix
Eigen::DynamicSparseMatrix<T, Eigen::RowMajor> dyn_Y(Y);
// Iterate over outside
for(int k=0; k<X.outerSize(); ++k)
{
// Iterate over inside
for(typename Eigen::SparseMatrix<T>::InnerIterator it (X,k); it; ++it)
{
dyn_Y.coeffRef(R(it.row()),C(it.col())) = it.value();
}
}
Y = Eigen::SparseMatrix<T>(dyn_Y);
}
ColCompressedMatrix convert_from_Eigen(const Eigen::SparseMatrix<double> &m)
{
assert(m.rows() == m.cols());
assert(m.isCompressed());
return ColCompressedMatrix(m.rows, m.nonZeros(),
m.valuePtr(), m.outerIndexPtr(), m.innerIndexPtr());
}
void place::erodeSparse(const Eigen::SparseMatrix<double> &src,
Eigen::SparseMatrix<double> &dst) {
dst = Eigen::SparseMatrix<double>(src.rows(), src.cols());
std::vector<Eigen::Triplet<double>> tripletList;
Eigen::MatrixXd srcNS = Eigen::MatrixXd(src);
for (int i = 0; i < srcNS.cols(); ++i) {
for (int j = 0; j < srcNS.rows(); ++j) {
double value = 0.0;
for (int k = -1; k < 1; ++k) {
for (int l = -1; l < 1; ++l) {
if (i + k < 0 || i + k >= srcNS.cols() || j + l < 0 ||
j + l >= srcNS.rows())
continue;
else
value = std::max(value, srcNS(j + l, i + k));
}
}
if (value != 0)
tripletList.push_back(Eigen::Triplet<double>(j, i, value));
}
}
dst.setFromTriplets(tripletList.begin(), tripletList.end());
}
IGL_INLINE void igl::matlab::prepare_lhs_double(
const Eigen::SparseMatrix<Vtype> & M,
mxArray *plhs[])
{
using namespace std;
const int m = M.rows();
const int n = M.cols();
// THIS WILL NOT WORK FOR ROW-MAJOR
assert(n==M.outerSize());
const int nzmax = M.nonZeros();
plhs[0] = mxCreateSparse(m, n, nzmax, mxREAL);
mxArray * mx_data = plhs[0];
// Copy data immediately
double * pr = mxGetPr(mx_data);
mwIndex * ir = mxGetIr(mx_data);
mwIndex * jc = mxGetJc(mx_data);
// Iterate over outside
int k = 0;
for(int j=0; j<M.outerSize(); j++)
{
jc[j] = k;
// Iterate over inside
for(typename Eigen::SparseMatrix<Vtype>::InnerIterator it (M,j); it; ++it)
{
// copy (cast to double)
pr[k] = it.value();
ir[k] = it.row();
k++;
}
}
jc[M.outerSize()] = k;
}
IGL_INLINE void igl::min(
const Eigen::SparseMatrix<AType> & A,
const int dim,
Eigen::PlainObjectBase<DerivedB> & B,
Eigen::PlainObjectBase<DerivedI> & I)
{
const int n = A.cols();
const int m = A.rows();
B.resize(dim==1?n:m);
B.setConstant(std::numeric_limits<typename DerivedB::Scalar>::max());
I.resize(dim==1?n:m);
for_each(A,[&B,&I,&dim](int i, int j,const typename DerivedB::Scalar v)
{
if(dim == 2)
{
std::swap(i,j);
}
// Coded as if dim == 1, assuming swap for dim == 2
if(v < B(j))
{
B(j) = v;
I(j) = i;
}
});
Eigen::VectorXi Z;
find_zero(A,dim,Z);
for(int j = 0;j<I.size();j++)
{
if(Z(j) != (dim==1?m:n) && 0 < B(j))
{
B(j) = 0;
I(j) = Z(j);
}
}
}
/// return the extremal eigenvalues of Ax=cBx
std::pair<double, double>
generalized_extreme_eigenvalues(const Eigen::SparseMatrix<double> &Ain,
const Eigen::SparseMatrix<double> &Bin) {
assert(Ain.rows() == Ain.cols());
assert(Ain.rows() == Ain.cols());
assert(Ain.rows() == Bin.rows());
assert(Ain.isCompressed());
assert(Bin.isCompressed());
const int N = static_cast<int>(Ain.rows());
/* mkl_sparse_d_gv input parameters */
char which =
'S'; /* Which eigenvalues to calculate. ('L' - largest (algebraic)
eigenvalues, 'S' - smallest (algebraic) eigenvalues) */
int pm[128]; /* This array is used to pass various parameters to Extended
Eigensolver Extensions routines. */
int k0 = 1; /* Desired number of max/min eigenvalues */
/* mkl_sparse_d_gv output parameters */
int k; /* Number of eigenvalues found (might be less than k0). */
double E_small[3]; /* Eigenvalues */
double E_large[3]; /* Eigenvalues */
double X[3]; /* Eigenvectors */
double res[3]; /* Residual */
/* Local variables */
int compute_vectors = 0; /* Flag to compute eigenvectors */
int tol = 7; /* Tolerance */
/* Sparse BLAS IE variables */
sparse_status_t status;
ConvertToMklResult A = to_mkl(Ain, status); // TODO: check A.status;
ConvertToMklResult B = to_mkl(Bin, status); // TODO: check B.status;
/* Step 2. Call mkl_sparse_ee_init to define default input values */
mkl_sparse_ee_init(pm);
pm[1] = tol; /* Set tolerance */
pm[6] = compute_vectors;
/* Step 3. Solve the standard Ax = ex eigenvalue problem. */
which = 'S';
const int infoS = mkl_sparse_d_gv(&which, pm, A.matrix, A.descr, B.matrix,
B.descr, k0, &k, E_small, X, res);
assert(infoS == 0);
which = 'L';
const int infoL = mkl_sparse_d_gv(&which, pm, A.matrix, A.descr, B.matrix,
B.descr, k0, &k, E_large, X, res);
assert(infoL == 0);
mkl_sparse_destroy(A.matrix);
mkl_sparse_destroy(B.matrix);
return {E_small[0], E_large[0]}; // todo: return the right thing
}
Mat::Mat(vector<string> _row_names, vector<string> _col_names,
Eigen::SparseMatrix<double> _matrix,MatType _mattype)
{
row_names = _row_names;
col_names = _col_names;
assert(row_names.size() == _matrix.rows());
assert(col_names.size() == _matrix.cols());
matrix = _matrix;
mattype = _mattype;
}
IGL_INLINE void igl::components(
const Eigen::SparseMatrix<AScalar> & A,
Eigen::PlainObjectBase<DerivedC> & C,
Eigen::PlainObjectBase<Derivedcounts> & counts)
{
using namespace Eigen;
using namespace std;
assert(A.rows() == A.cols() && "A should be square.");
const size_t n = A.rows();
Array<bool,Dynamic,1> seen = Array<bool,Dynamic,1>::Zero(n,1);
C.resize(n,1);
typename DerivedC::Scalar id = 0;
vector<typename Derivedcounts::Scalar> vcounts;
// breadth first search
for(int k=0; k<A.outerSize(); ++k)
{
if(seen(k))
{
continue;
}
queue<int> Q;
Q.push(k);
vcounts.push_back(0);
while(!Q.empty())
{
const int f = Q.front();
Q.pop();
if(seen(f))
{
continue;
}
seen(f) = true;
C(f,0) = id;
vcounts[id]++;
// Iterate over inside
for(typename SparseMatrix<AScalar>::InnerIterator it (A,f); it; ++it)
{
const int g = it.index();
if(!seen(g) && it.value())
{
Q.push(g);
}
}
}
id++;
}
assert((size_t) id == vcounts.size());
const size_t ncc = vcounts.size();
assert((size_t)C.maxCoeff()+1 == ncc);
counts.resize(ncc,1);
for(size_t i = 0;i<ncc;i++)
{
counts(i) = vcounts[i];
}
}
inline
void
space_operator(
Eigen::SparseMatrix<double>& result,
Eigen::SparseMatrix<double>& laplace,
const double multiplier,
Eigen::SparseMatrix<double>& unit_matrix)
{
result.resize(unit_matrix.rows(), unit_matrix.cols());
result = laplace*multiplier+unit_matrix;
}
Eigen::SparseMatrix<double> joint2conditional(Eigen::SparseMatrix<double> edgePot)// pa is the second dimension
{ // second dimension of edgePot is the parent
Eigen::SparseMatrix<double> Conditional;
Conditional.resize(edgePot.rows(), edgePot.cols());
Eigen::SparseVector<double> Parent_Marginal;
Parent_Marginal.resize(edgePot.cols());
for (int id_col = 0; id_col < edgePot.cols(); id_col++)
{
Eigen::SparseVector<double> tmp_vec = edgePot.block(0, id_col, edgePot.rows(), 1);
Parent_Marginal.coeffRef(id_col) = tmp_vec.sum();
if (Parent_Marginal.coeff(id_col)>TOLERANCE)
for (int id_row = 0; id_row < edgePot.rows(); id_row++)
{
Conditional.coeffRef(id_row, id_col) = edgePot.coeff(id_row, id_col) / Parent_Marginal.coeff(id_col);
}
}
Conditional.makeCompressed();
Conditional.prune(TOLERANCE);
return Conditional;
}
TEST(slice_into, sparse_identity)
{
Eigen::SparseMatrix<double> A = Eigen::MatrixXd::Random(10,9).sparseView();
Eigen::VectorXi I = Eigen::VectorXi::LinSpaced(A.rows(),0,A.rows()-1);
Eigen::VectorXi J = Eigen::VectorXi::LinSpaced(A.cols(),0,A.cols()-1);
{
Eigen::SparseMatrix<double> B(I.maxCoeff()+1,J.maxCoeff()+1);
igl::slice_into(A,I,J,B);
test_common::assert_eq(A,B);
}
{
Eigen::SparseMatrix<double> B(I.maxCoeff()+1,A.cols());
igl::slice_into(A,I,1,B);
test_common::assert_eq(A,B);
}
{
Eigen::SparseMatrix<double> B(A.rows(),J.maxCoeff()+1);
igl::slice_into(A,J,2,B);
test_common::assert_eq(A,B);
}
}
TEST(slice, sparse_identity)
{
Eigen::SparseMatrix<double> A = Eigen::MatrixXd::Random(10,9).sparseView();
Eigen::VectorXi I = igl::LinSpaced<Eigen::VectorXi >(A.rows(),0,A.rows()-1);
Eigen::VectorXi J = igl::LinSpaced<Eigen::VectorXi >(A.cols(),0,A.cols()-1);
{
Eigen::SparseMatrix<double> B;
igl::slice(A,I,J,B);
test_common::assert_eq(A,B);
}
{
Eigen::SparseMatrix<double> B;
igl::slice(A,I,1,B);
test_common::assert_eq(A,B);
}
{
Eigen::SparseMatrix<double> B;
igl::slice(A,J,2,B);
test_common::assert_eq(A,B);
}
}
IGL_INLINE void igl::cat(
const int dim,
const Eigen::SparseMatrix<Scalar> & A,
const Eigen::SparseMatrix<Scalar> & B,
Eigen::SparseMatrix<Scalar> & C)
{
assert(dim == 1 || dim == 2);
using namespace Eigen;
// Special case if B or A is empty
if(A.size() == 0)
{
C = B;
return;
}
if(B.size() == 0)
{
C = A;
return;
}
DynamicSparseMatrix<Scalar, RowMajor> dyn_C;
if(dim == 1)
{
assert(A.cols() == B.cols());
dyn_C.resize(A.rows()+B.rows(),A.cols());
}else if(dim == 2)
{
assert(A.rows() == B.rows());
dyn_C.resize(A.rows(),A.cols()+B.cols());
}else
{
fprintf(stderr,"cat.h: Error: Unsupported dimension %d\n",dim);
}
dyn_C.reserve(A.nonZeros()+B.nonZeros());
// Iterate over outside of A
for(int k=0; k<A.outerSize(); ++k)
{
// Iterate over inside
for(typename SparseMatrix<Scalar>::InnerIterator it (A,k); it; ++it)
{
dyn_C.coeffRef(it.row(),it.col()) += it.value();
}
}
// Iterate over outside of B
for(int k=0; k<B.outerSize(); ++k)
{
// Iterate over inside
for(typename SparseMatrix<Scalar>::InnerIterator it (B,k); it; ++it)
{
int r = (dim == 1 ? A.rows()+it.row() : it.row());
int c = (dim == 2 ? A.cols()+it.col() : it.col());
dyn_C.coeffRef(r,c) += it.value();
}
}
C = SparseMatrix<Scalar>(dyn_C);
}
IGL_INLINE void igl::repdiag(
const Eigen::SparseMatrix<T>& A,
const int d,
Eigen::SparseMatrix<T>& B)
{
using namespace std;
using namespace Eigen;
int m = A.rows();
int n = A.cols();
vector<Triplet<T> > IJV;
IJV.reserve(A.nonZeros()*d);
// Loop outer level
for (int k=0; k<A.outerSize(); ++k)
{
// loop inner level
for (typename Eigen::SparseMatrix<T>::InnerIterator it(A,k); it; ++it)
{
for(int i = 0;i<d;i++)
{
IJV.push_back(Triplet<T>(i*m+it.row(),i*n+it.col(),it.value()));
}
}
}
B.resize(m*d,n*d);
B.setFromTriplets(IJV.begin(),IJV.end());
// Q: Why is this **Very** slow?
//int m = A.rows();
//int n = A.cols();
//B.resize(m*d,n*d);
//// Reserve enough space for new non zeros
//B.reserve(d*A.nonZeros());
//// loop over reps
//for(int i=0;i<d;i++)
//{
// // Loop outer level
// for (int k=0; k<A.outerSize(); ++k)
// {
// // loop inner level
// for (typename Eigen::SparseMatrix<T>::InnerIterator it(A,k); it; ++it)
// {
// B.insert(i*m+it.row(),i*n+it.col()) = it.value();
// }
// }
//}
//B.makeCompressed();
}
IGL_INLINE void igl::harwell_boeing(
const Eigen::SparseMatrix<Scalar> & A,
int & num_rows,
std::vector<Scalar> & V,
std::vector<Index> & R,
std::vector<Index> & C)
{
num_rows = A.rows();
int num_cols = A.cols();
int nnz = A.nonZeros();
V.resize(nnz);
R.resize(nnz);
C.resize(num_cols+1);
// Assumes outersize is columns
assert(A.cols() == A.outerSize());
int column_pointer = 0;
int i = 0;
int k = 0;
// Iterate over outside
for(; k<A.outerSize(); ++k)
{
C[k] = column_pointer;
// Iterate over inside
for(typename Eigen::SparseMatrix<Scalar>::InnerIterator it (A,k); it; ++it)
{
V[i] = it.value();
R[i] = it.row();
i++;
// Also increment column pointer
column_pointer++;
}
}
// by convention C[num_cols] = nnz
C[k] = column_pointer;
}
Eigen::SparseMatrix<Type> kronecker(Eigen::SparseMatrix<Type> x,
Eigen::SparseMatrix<Type> y){
typedef Eigen::Triplet<Type> T;
typedef typename Eigen::SparseMatrix<Type>::InnerIterator Iterator;
std::vector<T> tripletList;
int n1=x.rows(),n2=x.cols(),n3=y.rows(),n4=y.cols();
int i,j,k,l;
// Loop over nonzeros of x
for (int cx=0; cx<x.outerSize(); cx++)
for (Iterator itx(x,cx); itx; ++itx)
// Loop over nonzeros of y
for (int cy=0; cy<y.outerSize(); cy++)
for (Iterator ity(y,cy); ity; ++ity)
{
i=itx.row();
j=itx.col();
k=ity.row();
l=ity.col();
tripletList.push_back(T(i*n3+k,j*n4+l, itx.value()*ity.value() ));
}
Eigen::SparseMatrix<Type> mat(n1*n3,n2*n4);
mat.setFromTriplets(tripletList.begin(), tripletList.end());
return mat;
}
inline void fastSparseDiagProduct(const Eigen::SparseMatrix<double>& lhs,
const std::vector<double>& rhs,
Eigen::SparseMatrix<double>& res)
{
res = lhs;
// Multiply columns by diagonal rhs.
int n = res.cols();
for (int col = 0; col < n; ++col) {
typedef Eigen::SparseMatrix<double>::InnerIterator It;
for (It it(res, col); it; ++it) {
it.valueRef() *= rhs[col];
}
}
}
IGL_INLINE void igl::full(
const Eigen::SparseMatrix<T> & A,
Eigen::PlainObjectBase<DerivedB>& B)
{
assert(false && "Obsolete. Just call B = Matrix(A)");
using namespace Eigen;
B = PlainObjectBase<DerivedB >::Zero(A.rows(),A.cols());
// Iterate over outside
for(int k=0; k<A.outerSize(); ++k)
{
// Iterate over inside
for(typename SparseMatrix<T>::InnerIterator it (A,k); it; ++it)
{
B(it.row(),it.col()) = it.value();
}
}
}
inline std::unique_ptr<giss::VectorSparseMatrix> Eigen_to_giss(
Eigen::SparseMatrix<double> const &mat)
{
std::unique_ptr<giss::VectorSparseMatrix> ret(
new giss::VectorSparseMatrix(giss::SparseDescr(
mat.rows(), mat.cols())));
int nz = mat.nonZeros();
ret->reserve(nz);
for (int k=0; k<mat.outerSize(); ++k) {
for (Eigen::SparseMatrix<double>::InnerIterator it(mat,k); it; ++it) {
ret->set(it.row(), it.col(), it.value(), SparseMatrix::DuplicatePolicy::ADD);
}
}
return ret;
}
void NewtonIterationBlackoilInterleaved::formInterleavedSystem(const std::vector<ADB>& eqs,
const Eigen::SparseMatrix<double, Eigen::RowMajor>& A,
Mat& istlA) const
{
const int np = eqs.size();
// Find sparsity structure as union of basic block sparsity structures,
// corresponding to the jacobians with respect to pressure.
// Use addition to get to the union structure.
Eigen::SparseMatrix<double> structure = eqs[0].derivative()[0];
for (int phase = 0; phase < np; ++phase) {
structure += eqs[phase].derivative()[0];
}
Eigen::SparseMatrix<double, Eigen::RowMajor> s = structure;
// Create ISTL matrix with interleaved rows and columns (block structured).
assert(np == 3);
istlA.setSize(s.rows(), s.cols(), s.nonZeros());
istlA.setBuildMode(Mat::row_wise);
const int* ia = s.outerIndexPtr();
const int* ja = s.innerIndexPtr();
for (Mat::CreateIterator row = istlA.createbegin(); row != istlA.createend(); ++row) {
int ri = row.index();
for (int i = ia[ri]; i < ia[ri + 1]; ++i) {
row.insert(ja[i]);
}
}
const int size = s.rows();
Span span[3] = { Span(size, 1, 0),
Span(size, 1, size),
Span(size, 1, 2*size) };
for (int row = 0; row < size; ++row) {
for (int col_ix = ia[row]; col_ix < ia[row + 1]; ++col_ix) {
const int col = ja[col_ix];
MatrixBlockType block;
for (int p1 = 0; p1 < np; ++p1) {
for (int p2 = 0; p2 < np; ++p2) {
block[p1][p2] = A.coeff(span[p1][row], span[p2][col]);
}
}
istlA[row][col] = block;
}
}
}
Eigen::SparseMatrix<double> normProbMatrix(Eigen::SparseMatrix<double> P)
{
// each column is a probability simplex
Eigen::SparseMatrix<double> P_norm;
P_norm.resize(P.rows(), P.cols());
for (int col = 0; col < P.cols(); col++)
{
//SparseVector<double> A_col_sparse = A_sparse.block(0, i, A_sparse.rows(),1);
SparseVector<double> P_vec = P.block(0, col, P.rows(), 1);
SparseVector<double> P_vec_norm;
P_vec_norm.resize(P_vec.size());
P_vec_norm = normProbVector(P_vec);
for (int id_row = 0; id_row < P.rows(); id_row++)
{
P_norm.coeffRef(id_row, col) = P_vec_norm.coeff(id_row);
}
}
P_norm.makeCompressed();
P_norm.prune(TOLERANCE);
return P_norm;
}
//update random Vectors
void updateMatrix(Eigen::SparseMatrix<double,Eigen::RowMajor>& randomMatrix,
const Eigen::SparseMatrix<int,Eigen::RowMajor>& adjacencyMatrix,
int itr)
{
int numberOfRVector = randomMatrix.rows();
int numberOfVertice = randomMatrix.cols();
std::vector<double> rowSum = getRowSum(adjacencyMatrix);
for(int i=0; i<numberOfRVector;++i){
for(int h=0;h<itr;++h){
Eigen::SparseMatrix<double,Eigen::RowMajor> middleValueMatrix(numberOfVertice,1);
middleValueMatrix.reserve(1);
for(int j = 0; j<numberOfVertice; ++j){
Eigen::SparseMatrix<double,Eigen::RowMajor> v1(1,numberOfVertice), v2(numberOfVertice,1);
v1.reserve(numberOfVertice);
v2.reserve(1);
v1 = adjacencyMatrix.cast<double>().innerVector(j);
v2 = randomMatrix.innerVector(h).transpose();
Eigen::SparseMatrix<double,Eigen::RowMajor> middleValue1 = v1*v2;
double middleValue = 0;
if(rowSum[j] != 0){
middleValue = (*middleValue1.valuePtr())/rowSum[j];
} else
{
middleValue = 1;
}
middleValueMatrix.insert(j,0) = middleValue;
}
Eigen::SparseMatrix<double,Eigen::RowMajor> right = middleValueMatrix.transpose();
Eigen::SparseMatrix<double,Eigen::RowMajor> left = randomMatrix.innerVector(i);
randomMatrix.innerVector(i) = 0.5*(left + right);
}
}
}
double L2R_Huber_SVC::predict(const std::string fileNameLibSVMFormat,
Eigen::VectorXd &w) {
Eigen::SparseMatrix<double, 1> vX;
Eigen::ArrayXd vy;
const char *fn = fileNameLibSVMFormat.c_str();
read_LibSVMdata1(fn, vX, vy);
// loadLib(fileNameLibSVMFormat, vX, vy);
int vl = vX.rows();
int vn = vX.cols();
int success = 0;
if (vn != w.size()) {
w.conservativeResize(vn);
}
Eigen::ArrayXd prob = vy * (vX * w).array();
for (int i = 0; i < vl; ++i) {
if (prob.coeffRef(i) >= 0.0)
++success;
}
return (double)success / vl;
}
IGL_INLINE void igl::components(
const Eigen::SparseMatrix<AScalar> & A,
Eigen::PlainObjectBase<DerivedC> & C)
{
assert(A.rows() == A.cols());
using namespace Eigen;
// THIS IS DENSE:
//boost::adjacency_matrix<boost::undirectedS> bA(A.rows());
boost::adjacency_list<boost::vecS,boost::vecS,boost::undirectedS> bA(A.rows());
for(int j=0; j<A.outerSize();j++)
{
// Iterate over inside
for(typename SparseMatrix<AScalar>::InnerIterator it (A,j); it; ++it)
{
if(0 != it.value())
{
boost::add_edge(it.row(),it.col(),bA);
}
}
}
C.resize(A.rows(),1);
boost::connected_components(bA,C.data());
}
IGL_INLINE void igl::sum(
const Eigen::SparseMatrix<T>& X,
const int dim,
Eigen::SparseVector<T>& S)
{
// dim must be 2 or 1
assert(dim == 1 || dim == 2);
// Get size of input
int m = X.rows();
int n = X.cols();
// resize output
if(dim==1)
{
S = Eigen::SparseVector<T>(n);
}else
{
S = Eigen::SparseVector<T>(m);
}
// Iterate over outside
for(int k=0; k<X.outerSize(); ++k)
{
// Iterate over inside
for(typename Eigen::SparseMatrix<T>::InnerIterator it (X,k); it; ++it)
{
if(dim == 1)
{
S.coeffRef(it.col()) += it.value();
}else
{
S.coeffRef(it.row()) += it.value();
}
}
}
}
IGL_INLINE void igl::slice(
const Eigen::SparseMatrix<TX>& X,
const Eigen::Matrix<int,Eigen::Dynamic,1> & R,
const Eigen::Matrix<int,Eigen::Dynamic,1> & C,
Eigen::SparseMatrix<TY>& Y)
{
#if 1
int xm = X.rows();
int xn = X.cols();
int ym = R.size();
int yn = C.size();
// special case when R or C is empty
if(ym == 0 || yn == 0)
{
Y.resize(ym,yn);
return;
}
assert(R.minCoeff() >= 0);
assert(R.maxCoeff() < xm);
assert(C.minCoeff() >= 0);
assert(C.maxCoeff() < xn);
// Build reindexing maps for columns and rows, -1 means not in map
std::vector<std::vector<int> > RI;
RI.resize(xm);
for(int i = 0;i<ym;i++)
{
RI[R(i)].push_back(i);
}
std::vector<std::vector<int> > CI;
CI.resize(xn);
// initialize to -1
for(int i = 0;i<yn;i++)
{
CI[C(i)].push_back(i);
}
// Resize output
Eigen::DynamicSparseMatrix<TY, Eigen::RowMajor> dyn_Y(ym,yn);
// Take a guess at the number of nonzeros (this assumes uniform distribution
// not banded or heavily diagonal)
dyn_Y.reserve((X.nonZeros()/(X.rows()*X.cols())) * (ym*yn));
// Iterate over outside
for(int k=0; k<X.outerSize(); ++k)
{
// Iterate over inside
for(typename Eigen::SparseMatrix<TX>::InnerIterator it (X,k); it; ++it)
{
std::vector<int>::iterator rit, cit;
for(rit = RI[it.row()].begin();rit != RI[it.row()].end(); rit++)
{
for(cit = CI[it.col()].begin();cit != CI[it.col()].end(); cit++)
{
dyn_Y.coeffRef(*rit,*cit) = it.value();
}
}
}
}
Y = Eigen::SparseMatrix<TY>(dyn_Y);
#else
// Alec: This is _not_ valid for arbitrary R,C since they don't necessary
// representation a strict permutation of the rows and columns: rows or
// columns could be removed or replicated. The removal of rows seems to be
// handled here (although it's not clear if there is a performance gain when
// the #removals >> #remains). If this is sufficiently faster than the
// correct code above, one could test whether all entries in R and C are
// unique and apply the permutation version if appropriate.
//
int xm = X.rows();
int xn = X.cols();
int ym = R.size();
int yn = C.size();
// special case when R or C is empty
if(ym == 0 || yn == 0)
{
Y.resize(ym,yn);
return;
}
assert(R.minCoeff() >= 0);
assert(R.maxCoeff() < xm);
assert(C.minCoeff() >= 0);
assert(C.maxCoeff() < xn);
// initialize row and col permutation vectors
Eigen::VectorXi rowIndexVec = Eigen::VectorXi::LinSpaced(xm,0,xm-1);
Eigen::VectorXi rowPermVec = Eigen::VectorXi::LinSpaced(xm,0,xm-1);
for(int i=0;i<ym;i++)
{
int pos = rowIndexVec.coeffRef(R(i));
if(pos != i)
{
int& val = rowPermVec.coeffRef(i);
std::swap(rowIndexVec.coeffRef(val),rowIndexVec.coeffRef(R(i)));
std::swap(rowPermVec.coeffRef(i),rowPermVec.coeffRef(pos));
}
}
Eigen::PermutationMatrix<Eigen::Dynamic,Eigen::Dynamic,int> rowPerm(rowIndexVec);
Eigen::VectorXi colIndexVec = Eigen::VectorXi::LinSpaced(xn,0,xn-1);
Eigen::VectorXi colPermVec = Eigen::VectorXi::LinSpaced(xn,0,xn-1);
for(int i=0;i<yn;i++)
{
int pos = colIndexVec.coeffRef(C(i));
if(pos != i)
{
int& val = colPermVec.coeffRef(i);
std::swap(colIndexVec.coeffRef(val),colIndexVec.coeffRef(C(i)));
std::swap(colPermVec.coeffRef(i),colPermVec.coeffRef(pos));
}
}
Eigen::PermutationMatrix<Eigen::Dynamic,Eigen::Dynamic,int> colPerm(colPermVec);
Eigen::SparseMatrix<T> M = (rowPerm * X);
Y = (M * colPerm).block(0,0,ym,yn);
#endif
}
void Poisson_LIMSolver2D::prepareProblemData(std::vector<int>& hessRowIdx, std::vector<int>& hessColIdx)
{
const int numNodes = mesh->InitalVertices->rows();
// create sparse gradient operator matrix
Eigen::SparseMatrix<double> tempG;
Eigen::VectorXd dAreas,dAreasTemp;
Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic> vertices(*mesh->DeformedVertices);
Eigen::Matrix<int,Eigen::Dynamic,Eigen::Dynamic> faces(*mesh->Triangles);
igl::grad(vertices,faces,tempG);
// Only get x and y derivatives of elements as z is zero
int newRowSize = 2.0/3.0*tempG.rows();
std::vector<Eigen::Triplet<double> > triplets;
for (int k=0;k<tempG.outerSize();++k)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(tempG,k);it;++it)
{
int row = it.row();
int col = it.col();
if(row < newRowSize)
{
triplets.push_back(Eigen::Triplet<double>(row,col,it.value()));
}
}
}
tempG.setZero();
tempG.resize(newRowSize,tempG.cols());
tempG.setFromTriplets(triplets.begin(), triplets.end());
// Extend gradient operator matrix for x and y scalar function
triplets.clear();
G.resize(newRowSize*2,tempG.cols()*2);
for (int k=0;k<tempG.outerSize();++k)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(tempG,k);it;++it)
{
int row = it.row()*2;
int col = it.col()*2;
triplets.push_back(Eigen::Triplet<double>(row,col,it.value()));
triplets.push_back(Eigen::Triplet<double>(row+1,col+1,it.value()));
}
}
G.setFromTriplets(triplets.begin(), triplets.end());
// Compute area weights
Eigen::SparseMatrix<double> M;
igl::doublearea(vertices,faces,dAreas);
triplets.clear();
M.resize(dAreas.rows()*4,dAreas.rows()*4);
for(int r=0;r<dAreas.rows();r++)
{
int id = 4*r;
triplets.push_back(Eigen::Triplet<double>(id,id,dAreas(r)));
triplets.push_back(Eigen::Triplet<double>(id+1,id+1,dAreas(r)));
triplets.push_back(Eigen::Triplet<double>(id+2,id+2,dAreas(r)));
triplets.push_back(Eigen::Triplet<double>(id+3,id+3,dAreas(r)));
}
M.setFromTriplets(triplets.begin(),triplets.end());
// Compute laplacian
L = 0.5*G.transpose()*M*G;
for (int k=0;k<L.outerSize();++k)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(L,k);it;++it)
{
int row = it.row();
int col = it.col();
// std::sort for upper triangule matrix
if(row <= col)
{
hessRowIdx.push_back(row);
hessColIdx.push_back(col);
}
}
}
GTb = 0.5*G.transpose()*M*b;
constantEnergyPart = b.transpose()*b;
}
inline vcl_size_t size2(Eigen::SparseMatrix<T, options> & m) { return m.cols(); }