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SparseMatrix-inl.h
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#ifndef SPARSEMATRIX_INL_H
#define SPARSEMATRIX_INL_H
template <typename T>
TRI_COORD<T>::TRI_COORD(unsigned row, unsigned col) : i(row), j(col) {}
template <typename T>
TRI_COORD<T>::TRI_COORD(unsigned row, unsigned col, T val, bool add_to)
: i(row), j(col), v(val), add(add_to) {}
// General flat index by value operator (by nth nonzero)
template <typename T> inline T SparseMatrix<T>::operator[](INDEX i) const
{
VICK(i); return _val[i];
}
// General flat index by reference operator (by nth nonzero)
template <typename T> inline T& SparseMatrix<T>::operator[](INDEX i)
{
VICK(i); return _val[i];
}
template<typename T>
T SparseMatrix<T>::_zero = T(0);
//-----------------------------------------------------------------------------
// triplet comparison operator returns true if x < y
//-----------------------------------------------------------------------------
template <typename T>
bool triplet_comparision(const TRI_COORD<T> &x, const TRI_COORD<T> &y)
{
const bool row_less = (x.i) < (y.i);
const bool row_equal = (x.i) == (y.i);
const bool col_less = (x.j) < (y.j);
return (row_less || (row_equal && col_less));
}
//-----------------------------------------------------------------------------
// triplet comparison operator returns true if x == y
//-----------------------------------------------------------------------------
template <typename T>
bool triplets_equal(const TRI_COORD<T> &x, const TRI_COORD<T> &y)
{
return x.i==y.i && x.j==y.j;
}
//-----------------------------------------------------------------------------
// multiply sparse matrix by a vector
//-----------------------------------------------------------------------------
template<typename T>
DenseVector<T> operator*(const SparseMatrix<T> &A, const Vector<T>& x)
{
SparseMatrix<T>::compress(A);
GCK(A, x, A.nCols()!=x.size(), "SparseMatrix * Vector")
DenseVector<T> y(A.nRows(), true);
INDEX i, j;
for (i=0; i<A._nRowsCRS; i++)
for (j=A._ia[i]; j<A._ia[i+1]; j++)
y(i) += A._val[j]*x(A._ja[j]);
return y;
}
//-----------------------------------------------------------------------------
// multiply a vector by a sparse matrix
//-----------------------------------------------------------------------------
template<typename T>
DenseVector<T> operator*(const Vector<T>& x, const SparseMatrix<T> &A)
{
return A.transMat(x);
}
//-----------------------------------------------------------------------------
// multiply sparse matrix by dense matrix
//-----------------------------------------------------------------------------
template<typename T>
DenseMatrix<T> operator*(const SparseMatrix<T> &A, const Matrix<T>& D)
{
GCK(A, D, A.nCols()!=D.nRows(),"SparseMatrix * DenseMatrix")
DenseMatrix<T> C(A.nRows(), D.nCols(), true); // initialized to zero
const INDEX J = D.nCols();
INDEX i, ik, j, k;
for (i=0; i<A._nRowsCRS; i++)
for (ik=A._ia[i]; ik<A._ia[i+1]; ik++)
for (j=0; j<J; j++)
C(i, j) += A._val[ik]*D(A._ja[ik],j); // C(i,j) = S(i,k) * D(k, j)
return C;
}
//-----------------------------------------------------------------------------
// multiply sparse matrix by a diagonal matrix - scales each column
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T> operator*(const SparseMatrix<T> &A, const DiagonalMatrix<T>& D)
{
GCK(A, D, A.nCols()!=D.nRows(),"SparseMatrix * DiagonalMatrix")
SparseMatrix<T> C(A); // C has same sparcity as A
// C(i,j) = A(i,k) * D(k, j) * j==k
INDEX i, ij, j;
for (i=0; i<A._nRowsCRS; i++)
for (ij=A._ia[i]; ij<A._ia[i+1]; ij++)
C[ij] = A._val[ij]*D(A._ja[ij],A._ja[ij]);
return C;
}
//-----------------------------------------------------------------------------
// multiplies two sparse matrices - assumes their output is sparse
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T> operator*(const SparseMatrix<T> &A, const SparseMatrix<T> &B)
{
SparseMatrix<T> At(A.transpose());
SparseMatrix<T>::compress(B);
GCK(A, B, A.nCols()!=B.nRows(), "SparseMatrix * SparseMatrix");
SparseMatrix<T> C(A.nRows(), B.nCols());
if (At.empty() || B.empty()) return C;
INDEX k, ki, kj;
INDEX K = std::min(At._nRowsCRS, B._nRowsCRS);
for (k=0; k<K; k++) // loop over rows of A or B (smallest)
for (ki=At._ia[k]; ki<At._ia[k+1]; ki++) // loop over row nonzeros of A
for (kj=B._ia[k]; kj<B._ia[k+1]; kj++) // loop over row nonzeros of B
C.add(At._ja[ki], B._ja[kj], At[ki]*B[kj]); // C(i,j) = At(k,i)*B(k, j)
C.compress();
return C;
}
//-----------------------------------------------------------------------------
// default constructor - creates an empty sparsematrix with specified size
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>::SparseMatrix(INDEX rows, INDEX cols)
: _val(NULL), _ia(NULL), _ja(NULL), _size(0), _nRowsCRS(0),
_nRows(rows),_nCols(cols) {}
//-----------------------------------------------------------------------------
// copy constructor
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>::SparseMatrix(const SparseMatrix<T>& C)
: _val(NULL), _ia(NULL), _ja(NULL)
{
_copy(C);
}
//-----------------------------------------------------------------------------
// copy constructor - converts from DenseMatrix
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>::SparseMatrix(const DenseMatrix<T>& C)
: _val(NULL), _ia(NULL), _ja(NULL)
{
reset(C);
}
//-----------------------------------------------------------------------------
// destructor, cleans up internal storage
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>::~SparseMatrix()
{
_delete();
}
//-----------------------------------------------------------------------------
// assigns internal storage for CRS
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::_create(INDEX size, INDEX nrows)
{
_size = size;
_nRowsCRS = nrows;
// assign memory to hold matrix
try
{
_val = (_size*nrows) ? new T [_size] : NULL;
_ia = (_size*nrows) ? new INDEX [_nRowsCRS+1] : NULL;
_ja = (_size*nrows) ? new INDEX [_size] : NULL;
}
catch (std::exception &e)
{
cout << "Could not allocate SparseMatrix of "<< _size << " nonzeros.\n";
exit(EXIT_FAILURE);
}
if (!_ia) return;
// automatically handle the ends of rowpointer
*_ia = 0; // first non-zero is the zero index
_ia[_nRowsCRS] = _size; // last row pointer is the size
}
//-----------------------------------------------------------------------------
// cleans up internal storage, but retains nRows & nCols
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::_delete()
{
vector<TRI_COORD<T> >().swap(_tri); // completely deletes _tri
delete [] _val;
delete [] _ia;
delete [] _ja;
_size = _nRowsCRS = 0;
_val = NULL;
_ia = _ja = NULL;
}
//-----------------------------------------------------------------------------
// full memory copy of C into this
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::_copy(const SparseMatrix<T> &C)
{
compress(C);
_delete();
_create(C.size(), C._nRowsCRS);
if (_size) {
std::copy(C._val, C._val+_size, _val);
std::copy(C._ja, C._ja+_size, _ja);
}
if (_nRowsCRS) {
std::copy(C._ia, C._ia+_nRowsCRS+1, _ia);
}
_nCols = C._nCols;
_nRows = C._nRows;
}
//----------------------------------------------------------------------------
// general sparse matrix assignment
//----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::_set_equal(const Matrix<T> &r)
{
this->resize(r.nRows(), r.nCols());
const Matrix<T> *ptr_r = &r;
const SparseMatrix<T> *s_ptr = dynamic_cast<const SparseMatrix<T>*>(ptr_r);
if (s_ptr) this->reset(*s_ptr);
else if (dynamic_cast<const DiagonalMatrix<T>*>(ptr_r))
for (INDEX i=0; i<r.size(); i++) set(i,i,r[i]);
else if (dynamic_cast<const DenseMatrix<T>*>(ptr_r)) this->reset(r);
else
{
cout <<"Error in general sparse matrix assignment\n";
exit(1);
}
}
//-----------------------------------------------------------------------------
// returns the first row number with a nonzero entry or -1 if no rows
//-----------------------------------------------------------------------------
template<typename T>
int SparseMatrix<T>::_first_nonzero_row_crs() const
{
if (!_nRowsCRS) return -1;
INDEX r;
for (r=0; r<_nRowsCRS; r++)
if (_ia[r+1]>0) return r;
return -1;
}
//-----------------------------------------------------------------------------
// converts T to CRS
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::compress(const SparseMatrix<T> &C)
{
const_cast<SparseMatrix<T>*>(&C)->compress();
}
//-----------------------------------------------------------------------------
// merges all the _tri triples with CRS storage
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::compress()
{
if (_tri.empty()) return;
// sort and find the number of unique triplets
const INDEX nUnique = CountUniqueTriplets();
// max number of rows in new CRS structure
const INDEX nRows = std::max((INDEX)_tri.back().i+1, _nRowsCRS);
// make a new CRS structure
INDEX *ia = new INDEX [nRows+1];
INDEX *ja = new INDEX [nUnique];
T *val = new T [nUnique];
ia[0] = 0;
INDEX i;
for (i=1; i<nRows; i++) ia[i]=~0; // ~0 is max(INDEX)
ia[nRows] = nUnique;
INDEX crs_pt, crs_row, tri_ct;
// get the first CRS and triplet coordinates (if they exist)
TRI_COORD<T> nextCRS, nextTRI(_tri[0]), next;
int first_row = _first_nonzero_row_crs();
if (first_row != -1) nextCRS = TRI_COORD<T>(first_row, _ja[0], _val[0]);
// merge sorted triplets into a new CRS structure
crs_pt = crs_row = tri_ct = 0; // initialize counters
for (i=0; i<nUnique; i++)
{
// is the next non-zero in the new triplet vector
if (tri_ct<_tri.size()
&& (triplet_comparision(nextTRI, nextCRS) || crs_pt>=_size)) {
next = nextTRI;
// advance the triplet counter, and skip voided TRIPLET entries
do tri_ct++;
while ( tri_ct<_tri.size() && !~_tri[tri_ct].j );
// if not at the end of the vector, set the next triplet
if (tri_ct<_tri.size()) nextTRI = _tri[tri_ct];
}
// is the next nonzero in the old CRS data
else if (crs_pt < _size) {
next = nextCRS;
// advance the CRS counter, skip if it was the last one
if (++crs_pt >= _size) continue;
crs_row += _ia[crs_row+1]==crs_pt; // did the row advance
nextCRS = TRI_COORD<T>(crs_row, _ja[crs_pt], _val[crs_pt]);
}
else cout << "SparseMatrix - Error in compressing CRS\n";
// add next to the new CRS structure
// is this a new row (is j>0 and is ja[j] == 0)?
if (ia[next.i]==~0) ia[next.i] = i;
ja[i] = next.j;
val[i] = next.v;
}
// sweep backwards through row pointers and check for skipped rows
for (i=nRows-1; i>0; i--) ia[i] = (ia[i]==~0) ? ia[i+1] : ia[i];
_delete();
_val = val;
_ia = ia;
_ja = ja;
_size = nUnique;
_nRowsCRS = nRows;
}
//-----------------------------------------------------------------------------
// Sorts the triplets, condenses duplicates, and returns the # of unique values
//-----------------------------------------------------------------------------
template<typename T>
INDEX SparseMatrix<T>::CountUniqueTriplets()
{
std::sort(_tri.begin(), _tri.end(), triplet_comparision<T>);
INDEX i, nUnique=1 + _size;
// count unique entries
for (i=_tri.size()-1; i>0; i--) { // for all new triplets
if (triplets_equal(_tri[i-1], _tri[i])) { // previous has same index?
if (_tri[i].add) _tri[i-1].v += _tri[i].v; // add to previous
else _tri[i-1].v = _tri[i].v; // replace previous
_tri[i].j = ~0; // void this entry's col
}
else nUnique++;
}
return nUnique;
}
//-----------------------------------------------------------------------------
// Index by copy operator - return zero if not found
//-----------------------------------------------------------------------------
template<typename T>
T SparseMatrix<T>::operator()(INDEX i, INDEX j) const
{
MICK(i,j); // Matrix Index ChecKing
compress(*this);
if (i>=_nRowsCRS || _ia[i+1]==_ia[i]) return 0.0;
unsigned f = std::lower_bound(_ja+_ia[i], _ja+_ia[i+1]-1, j) - _ja;
if (f>=_ia[i] && f<_ia[i+1] && _ja[f] == j) return _val[f];
return 0.0;
}
//-----------------------------------------------------------------------------
// Index by reference operator - add to _tri if not found
//-----------------------------------------------------------------------------
template<typename T>
T& SparseMatrix<T>::operator()(INDEX i, INDEX j)
{
compress(*this);
MICK(i,j); // Matrix Index ChecKing
if (i < _nRowsCRS && _ia[i+1]>_ia[i]) {
unsigned f = std::lower_bound(_ja+_ia[i], _ja+_ia[i+1]-1, j) - _ja;
if (f>=_ia[i] && f<_ia[i+1] && _ja[f] == j) return _val[f];
}
// NEVER use index operator as LHS to modify values not already in the
// sparcity pattern - the crude check below will only catch this on the
// second infraction.
if (_zero != T(0)) cout << "Use add or set for SparseMatrix\n";
return _zero;
}
//-----------------------------------------------------------------------------
// Sets (i,j) to value
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::set(INDEX i, INDEX j, T v)
{
MICK(i,j); // Matrix Index ChecKing
if (i < _nRowsCRS)
{
const int loc = Utility::SearchSorted(_ja, j, _ia[i], _ia[i+1]);
if (loc >=0 )
{
_val[loc] = v;
return;
}
}
_tri.push_back(TRI_COORD<T>(i,j,v,false));
}
//-----------------------------------------------------------------------------
// Adds (i,j) to value
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::add(INDEX i, INDEX j, T v)
{
MICK(i,j); // Matrix Index ChecKing
if (i < _nRowsCRS)
{
const int loc = Utility::SearchSorted(_ja, j, _ia[i], _ia[i+1]);
if (loc >=0 )
{
_val[loc] += v;
return;
}
}
_tri.push_back(TRI_COORD<T>(i,j,v,true));
}
//-----------------------------------------------------------------------------
// returns a triplet value of the ith nonzero
//-----------------------------------------------------------------------------
template<typename T>
TRIPLET<T> SparseMatrix<T>::get_triplet(INDEX i) const
{
compress(*this);
if (i >= _ia[_nRowsCRS]) {
gerror("ERROR: tried indexing triplet of sparse matrix beyond range");
}
INDEX row(std::lower_bound(_ia, _ia+_nRowsCRS, i)-_ia);
row -= _ia[row] != i;
return TRIPLET<T>(row, _ja[i], _val[i]);
}
//-----------------------------------------------------------------------------
// full reset - completely wipes out all SparseMatrix data, zero is ignored
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::reset(INDEX rows, INDEX cols, bool zero)
{
_delete();
_nRows = rows;
_nCols = cols;
}
//-----------------------------------------------------------------------------
// resize - changes the _nRows and _nCols without changing anything else
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::resize(INDEX rows, INDEX cols, bool copy)
{
GCHK(_nRowsCRS>rows, "SparseMatrix::resize CRS rows exceed specified rows");
_nRows = rows;
_nCols = cols; // a check on this would be expensive
}
//-----------------------------------------------------------------------------
// get sparsity from DenseMatrix, if TOL < 0, then only zero values are added
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::reset(const DenseMatrix<T>& D, double TOL)
{
_delete(); // clears all values
// if TOL is specified then TOL = TOL^2 * max(abs(D))^2
if (TOL > 0.0)
{
TOL *= D.maxabs();
TOL *= TOL;
}
_nRows = D.nRows();
_nCols = D.nCols();
for (INDEX i=0; i<D.nRows(); i++)
for (INDEX j=0; j<D.nCols(); j++)
if (D(i,j)*D(i,j) >= TOL) // if TOL wasn't specified then TOL < 0
set(i, j, D(i,j));
compress();
}
//-----------------------------------------------------------------------------
// copy - dangerous: ignores rows & columns
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::copy(const T * ptr, INDEX rows, INDEX cols)
{
cout << "SparseMatrix<T>::copy() has no effect.\n";
}
//-----------------------------------------------------------------------------
// dense_copy - copy to dense matrix
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::dense_copy(DenseMatrix <T> & D ) const
{
SparseMatrix<T>::compress(*this);
D.reset(nRows(),nCols());
for (INDEX i=0; i<_nRowsCRS; i++)
for (INDEX j=_ia[i]; j<_ia[i+1]; j++)
D(i, _ja[j]) = _val[j];
}
template<typename T>
DenseMatrix <T> SparseMatrix<T>::dense_copy(void) const
{
DenseMatrix<T> D;
dense_copy(D);
return D;
}
//-----------------------------------------------------------------------------
// returns true if the matrix has no non-zero elements
//-----------------------------------------------------------------------------
template<typename T>
bool SparseMatrix<T>::empty() const
{
return _size==0 && _tri.empty();
}
//-----------------------------------------------------------------------------
// returns the number of rows specified by the user
//-----------------------------------------------------------------------------
template<typename T>
inline INDEX SparseMatrix<T>::nRows() const
{
return _nRows;
}
//-----------------------------------------------------------------------------
// returns the number of columns specified by the user
//-----------------------------------------------------------------------------
template<typename T>
inline INDEX SparseMatrix<T>::nCols() const
{
return _nCols;
}
//-----------------------------------------------------------------------------
// returns the number of non-zeros in the matrix
//-----------------------------------------------------------------------------
template<typename T>
INDEX SparseMatrix<T>::size() const
{
compress(*this);
return _size;
}
//-----------------------------------------------------------------------------
// returns the number of nonzero elements in a row
//-----------------------------------------------------------------------------
template<typename T>
INDEX SparseMatrix<T>::RowSize(INDEX r) const
{
compress(*this);
GCHK(r>=_nRows, "Rowsize: invalid row");
if (r >= _nRowsCRS) return 0;
return _ia[r+1]-_ia[r];
}
//-----------------------------------------------------------------------------
// returns a pointer to the data, causes a compress
//-----------------------------------------------------------------------------
template<typename T>
T* SparseMatrix<T>::get_ptr() const
{
compress(*this);
return _val;
}
//-----------------------------------------------------------------------------
// returns true if (i,j) falls in the user specified range
//-----------------------------------------------------------------------------
template<typename T>
bool SparseMatrix<T>::in_range(INDEX i, INDEX j) const
{
return i < nRows() && j < nCols();
}
//-----------------------------------------------------------------------------
// assigns this sparsematrix from another one - full memory copy
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>& SparseMatrix<T>::operator=(const SparseMatrix<T> &C)
{
_delete();
_copy(C);
return *this;
}
//-----------------------------------------------------------------------------
// assigns this sparsematrix from another one - full memory copy
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>& SparseMatrix<T>::operator=(const T v)
{
// set_all_elements only changes _data, so we need a compress
compress(*this);
return set_all_elements_to(v);
}
//-----------------------------------------------------------------------------
// scales this sparse matrix by a constant
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>& SparseMatrix<T>::operator*=(const T &a)
{
compress(*this);
for (INDEX i=0; i<size(); i++) _val[i] *= a;
return *this;
}
//-----------------------------------------------------------------------------
// Multiplies this Sparsematrix tranposed times a vector
//-----------------------------------------------------------------------------
template<typename T>
DenseVector<T> SparseMatrix<T>::transMat(const Vector<T> &x) const
{
DenseVector<T> y(nCols(), true);
GCK(*this, x, nRows()!=x.size(),"operator *: Sparse matrix incompatible with Vector.")
INDEX i, ij;
for(i=0; i<_nRowsCRS; i++)
for(ij=_ia[i]; ij<_ia[i+1]; ij++)
y(_ja[ij]) += _val[ij]*x(i);
return y;
}
//-----------------------------------------------------------------------------
// Return matrix transpose
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T> SparseMatrix<T>::transpose() const
{
compress(*this);
SparseMatrix<T> At(nCols(), nRows());
for (INDEX i=0; i<_nRowsCRS; i++)
for (INDEX ij=_ia[i]; ij<_ia[i+1]; ij++)
At.set(_ja[ij], i, _val[ij]);
compress(At);
return At;
}
//-----------------------------------------------------------------------------
// Matrix Transpose/DenseMatrix multiply
//-----------------------------------------------------------------------------
template<typename T>
DenseMatrix<T> SparseMatrix<T>::transMat(const DenseMatrix<T> &D) const
{
compress(*this);
GCK(*this, D, nRows()!=D.nRows(),"transMat: Sparse matrix incompatible with DenseMatrix.")
DenseMatrix<T> C(nCols(), D.nCols(), true); // initialized to zero
INDEX j, k, ki;
for (k=0; k<_nRowsCRS; k++)
for (ki=_ia[k]; ki<_ia[k+1]; ki++)
for (j=0; j<D.nCols(); j++)
C(_ja[ki], j) += _val[ki]*D(k,j); // C(i,j) = S(k,i) * D(k, j)
return C;
}
//-----------------------------------------------------------------------------
// Matrix Transpose/SparseMatrix multiply - IS THIS REALLY NEEDED??
//-----------------------------------------------------------------------------
template<typename T>
DenseMatrix<T> SparseMatrix<T>::transMat(const SparseMatrix<T> &D) const
{
compress(*this);
GCK(*this, D, nRows()!=D.nRows(),"transMat: Sparse matrix incompatible with DenseMatrix.")
DenseMatrix<T> C(nCols(), D.nCols(), true); // initialized to zero
INDEX k, ki, kj;
for (k=0; k<_nRowsCRS; k++)
for (kj=D._ia[k]; kj<D._ia[k+1]; kj++)
for (ki=_ia[k]; ki<_ia[k+1]; ki++)
C(_ja[ki], D._ja[kj]) += _val[ki]*D._val[kj]; // C(i,j) = S(k,i)*D(k,j)
return C;
}
//-----------------------------------------------------------------------------
// multiplies each row by the corresponding element in Vector scale
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>& SparseMatrix<T>::row_scale(const Vector<T> &v)
{
compress(*this);
INDEX i,ij;
GCK(*this, v, v.size()!=nRows(), "Incompatible Vector length in row_scale.");
for(i=0; i<_nRowsCRS; i++)
for(ij=_ia[i]; ij<_ia[i+1]; ij++) _val[ij] *= v[i];
return *this;
}
//-----------------------------------------------------------------------------
// multiples each column by the corresponding element in Vector scale
//-----------------------------------------------------------------------------
template<typename T>
SparseMatrix<T>& SparseMatrix<T>::col_scale(const Vector<T> &v)
{
compress(*this);
INDEX i,ij;
GCK(*this, v, v.size()!=nCols(), "Incompatible Vector length in col_scale.");
for(i=0; i<_nRowsCRS; i++)
for(ij=_ia[i]; ij<_ia[i+1]; ij++) _val[ij] *= v[_ja[ij]];
return *this;
}
//-----------------------------------------------------------------------------
// Returns a vector of the sums of each column
//-----------------------------------------------------------------------------
template<typename T>
DenseVector<T> SparseMatrix<T>::col_sum() const
{
compress(*this);
INDEX i,ij;
GCHK(!nRows(), "SparseMatrix::Matrix not initialized in col_sum.")
DenseVector<T> csum(nCols());
for(i=0; i<_nRowsCRS; i++)
for(ij=_ia[i]; ij<_ia[i+1]; ij++) csum(_ja[ij]) += _val[ij];
return(csum);
}
//-----------------------------------------------------------------------------
// Returns a vector with the number of nonzeros in each column
//-----------------------------------------------------------------------------
template<typename T>
DenseVector<INDEX> SparseMatrix<T>::column_count() const
{
compress(*this);
INDEX i,j;
DenseVector<INDEX> counts(nCols());
for (i=0; i<_nRowsCRS; i++)
for(j=_ia[i]; j<_ia[i+1]; j++) counts(_ja[j])++;
return(counts);
}
//-----------------------------------------------------------------------------
// Writes a the nonzeros of a row to a vector
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::get_row(INDEX i, DenseVector<T>& row, DenseVector<INDEX>& indx) const
{
GCHK(i>=nRows(), "get_row() - invalid row number");
row.resize(RowSize(i));
indx.resize(row.size());
INDEX idx=0, ij;
for(ij=_ia[i]; ij<_ia[i+1]; ij++)
{
row(idx) = _val[ij];
indx(idx++) = _ja[ij];
}
}
//-----------------------------------------------------------------------------
// Computes the product of N'DN
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::
WeightedLeastSquares(const SparseMatrix<T> &N, const DiagonalMatrix<T> &D)
{
compress(N);
GCK(N,D,N.nRows()!=D.nRows(),"SparseMatrix::WeightedLeastSquares()");
INDEX k, ki, kj;
resize(N.nCols(), N.nCols()); // set size of this matrix
for (k=0; k<_size; k++) _val[k] = 0.0;
// compute R(i,j) = N(k,i) D(k,q) N(i,j) = N(k,i)*D(k,k)*N(k,j) (sum on k)
for (k=0; k<N._nRowsCRS; k++)
for (ki=N._ia[k]; ki<N._ia[k+1]; ki++)
for (kj=N._ia[k]; kj<N._ia[k+1]; kj++)
add(N._ja[ki],N._ja[kj], D[k]*N[kj]*N[ki]);
compress();
}
//-----------------------------------------------------------------------------
// Return a diagonal matrix containing the diagonal entries of this matrix
//-----------------------------------------------------------------------------
template<typename T>
DiagonalMatrix<T> SparseMatrix<T>::get_diag() const
{
compress(*this);
DiagonalMatrix<T> D(nRows(), true); // initialized to zero
INDEX i, ij;
for (i=0; i<_nRowsCRS; i++)
{
for(ij=_ia[i]; ij<_ia[i+1]; ij++)
{
if (_ja[ij]>=i) // have we reached or passed the diagonal?
{
if (_ja[ij]==i) D[i]=_val[ij]; // this this the diagonal?
break; // D[i] is already zero if there is no diagonal
}
}
}
return D;
}
//-----------------------------------------------------------------------------
// output function - builds a string with each nonzero triplet value
//-----------------------------------------------------------------------------
template<typename T>
string SparseMatrix<T>::tostring() const
{
compress(*this);
string out;
INDEX i, ij;
for(i=0; i<_nRowsCRS; i++)
{
for(ij=_ia[i]; ij<_ia[i+1]; ij++)
{
if (ij) out += "\n"; // append newline if not first nonzero
out += "(" + ATC_STRING::tostring(i) + ", "; // append "(i,"
out += ATC_STRING::tostring(_ja[ij]) + ") = "; // append "j) = "
out += ATC_STRING::tostring(_val[ij]); // append "value"
}
}
return out; // return the completed string
}
//-----------------------------------------------------------------------------
// returns the maximum value in the row
//-----------------------------------------------------------------------------
template<typename T>
T SparseMatrix<T>::get_row_max(INDEX row) const
{
compress(*this);
if (!RowSize(row)) return (T)0; // if there are no nonzeros in the row
INDEX ij;
T max = _val[_ia[row]];
for(ij=_ia[row]+1; ij<_ia[row+1]; ij++) max = std::max(max,_val[ij]);
return max;
}
//-----------------------------------------------------------------------------
// returns the minimum value in the row
//-----------------------------------------------------------------------------
template<typename T>
T SparseMatrix<T>::get_row_min(INDEX row) const
{
compress(*this);
if (!RowSize(row)) return (T)0; // if there are no nonzeros in the row
INDEX ij;
T min = _val[_ia[row]];
for(ij=_ia[row]+1; ij<_ia[row+1]; ij++) min = std::min(min,_val[ij]);
return min;
}
//-----------------------------------------------------------------------------
// prints a histogram of the values of a row to the screen
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::print_row_histogram(const string &name, INDEX nbins) const
{
compress(*this);
cout << "Begin histogram " << name << "\n";
cout << "# rows: " << _nRows << " columns: " << _nCols
<< " size: " << _size << "\n";
for(INDEX i=0; i<_nRows; i++)
{
print_row_histogram(i, nbins);
cout << "\n";
}
cout << "End histogram " << name << "\n";
}
//-----------------------------------------------------------------------------
// prints a histogram of the values of a row to the screen
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::print_row_histogram(INDEX row, INDEX nbins) const
{
compress(*this);
if (!nbins) nbins++;
vector<INDEX> counts(nbins, 0);
const T min = get_row_min(row);
const T max = get_row_max(row);
const T range = max-min;
const double bin_size = range/double(nbins);
if (range<=0.0) counts[nbins-1]=RowSize(row);
else
{
for(INDEX ij=_ia[row]; ij<_ia[row+1]; ij++)
{
INDEX bin = INDEX((_val[ij]-min)/bin_size);
counts[bin-(bin==nbins)]++;
}
}
cout<<showbase<<scientific;
cout<<"# Histogram: row "<<row<<" min "<<min<<" max "<<max<<" cnt " <<RowSize(row)<<"\n";
T bin_start = min;
for(INDEX i=0; i<nbins; i++)
{
cout << "(" << bin_start << ",";
bin_start += bin_size;
cout << bin_start << ") " << counts[i] << "\n";
}
}
//-----------------------------------------------------------------------------
// Outputs a string to a sparse Matlab type
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::matlab(ostream &o, const string &s) const
{
compress(*this);
INDEX i, ij;
o << s <<" = sparse(" << nRows() << "," << nCols() << ");\n";
o << showbase << scientific;
for(i=0; i<_nRowsCRS; i++)
for(ij=_ia[i]; ij<_ia[i+1]; ij++)
o<<s<<"("<<i+1<<","<<_ja[ij]+1<<")="<<_val[ij]<<";\n";
}
//-----------------------------------------------------------------------------
// Writes the matrix to a binary file (after a compress).
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::binary_write(std::fstream& f) const
{
compress(*this);
f.write((char*)&_size, sizeof(INDEX)); // writes number of nonzeros
f.write((char*)&_nRowsCRS, sizeof(INDEX)); // writes number of rows in crs
f.write((char*)&_nRows, sizeof(INDEX)); // write matrix rows
f.write((char*)&_nCols, sizeof(INDEX)); // write number of columns
if (!_size) return;
f.write((char*)_val, sizeof(T) *_size);
f.write((char*)_ja, sizeof(INDEX)*_size);
f.write((char*)_ia, sizeof(INDEX)*(_nRowsCRS+1));
}
//-----------------------------------------------------------------------------
// Reads a SparseMatrix from a binary file. (wipes out any original data)
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::binary_read(std::fstream& f)
{
_delete();
f.read((char*)&_size, sizeof(INDEX));
f.read((char*)&_nRowsCRS, sizeof(INDEX));
f.read((char*)&_nRows, sizeof(INDEX));
f.read((char*)&_nCols, sizeof(INDEX));
if (!_size) return;
_create(_size,_nRowsCRS);
f.read((char*)_val, sizeof(T)*_size);
f.read((char*)_ja, sizeof(INDEX)*_size);
f.read((char*)_ia, sizeof(INDEX)*(_nRowsCRS+1));
}
//-----------------------------------------------------------------------------
// Writes the sparse matrix to a file in a binary format
//-----------------------------------------------------------------------------
template<typename T>
void SparseMatrix<T>::write_restart(FILE *f) const
{
compress(*this);
fwrite(&_size, sizeof(INDEX), 1 ,f); // write number of nonzeros
fwrite(&_nRowsCRS, sizeof(INDEX), 1 ,f); // write number of rows
fwrite(&_nRows, sizeof(INDEX), 1 ,f); // write number of columns
fwrite(&_nCols, sizeof(INDEX), 1 ,f); // write number of columns
if (!_size) return;
fwrite(_val, sizeof(T), _size ,f);
fwrite(_ja, sizeof(T), _size ,f);
fwrite(_ia, sizeof(INDEX), _nRowsCRS+1 ,f);
}
#endif

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