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Remove dense nested loops in IncompleteCholesky

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This commit is contained in:
Gael Guennebaud 2015-08-04 18:01:38 +02:00
parent e31fc50280
commit 7e0d7a76b8
1 changed files with 54 additions and 33 deletions
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87
unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
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@ -72,7 +72,7 @@ class IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,_Up
/**
* \brief Set the initial shift parameter
*/
void setShift( Scalar shift) { m_initialShift = shift; }
void setInitialShift(RealScalar shift) { m_initialShift = shift; }
/**
* \brief Computes the fill reducing permutation vector.
@ -114,9 +114,9 @@ class IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,_Up
}
protected:
FactorType m_L; // The lower part stored in CSC
FactorType m_L; // The lower part stored in CSC
VectorRx m_scale; // The vector for scaling the matrix
Scalar m_initialShift; // The initial shift parameter
RealScalar m_initialShift; // The initial shift parameter
bool m_analysisIsOk;
bool m_factorizationIsOk;
ComputationInfo m_info;
@ -157,8 +157,11 @@ void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType
Map<VectorIx> colPtr( m_L.outerIndexPtr(), n+1); // Pointer to the beginning of each row
VectorIx firstElt(n-1); // for each j, points to the next entry in vals that will be used in the factorization
VectorList listCol(n); // listCol(j) is a linked list of columns to update column j
VectorSx curCol(n); // Store a nonzero values in each column
VectorIx irow(n); // Row indices of nonzero elements in each column
VectorSx col_vals(n); // Store a nonzero values in each column
VectorIx col_irow(n); // Row indices of nonzero elements in each column
VectorIx col_pattern(n);
col_pattern.fill(-1);
StorageIndex col_nnz;
// Computes the scaling factors
@ -196,59 +199,77 @@ void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType
for (Index j=0; j < n; ++j)
{
// Left-looking factorization of the j-th column
// First, load the j-th column into curCol
// First, load the j-th column into col_vals
Scalar diag = vals[colPtr[j]]; // It is assumed that only the lower part is stored
curCol.setZero();
irow.setLinSpaced(n,0,internal::convert_index<StorageIndex,Index>(n-1));
col_nnz = 0;
for (Index i = colPtr[j] + 1; i < colPtr[j+1]; i++)
{
curCol(rowIdx[i]) = vals[i];
irow(rowIdx[i]) = rowIdx[i];
StorageIndex l = rowIdx[i];
col_vals(col_nnz) = vals[i];
col_irow(col_nnz) = l;
col_pattern(l) = col_nnz;
col_nnz++;
}
typename std::list<StorageIndex>::iterator k;
// Browse all previous columns that will update column j
for(k = listCol[j].begin(); k != listCol[j].end(); k++)
{
Index jk = firstElt(*k); // First element to use in the column
eigen_internal_assert(rowIdx[jk]==j);
Scalar v_j_jk = numext::conj(vals[jk]);
jk += 1;
for (Index i = jk; i < colPtr[*k+1]; i++)
curCol(rowIdx[i]) -= vals[i] * v_j_jk;
updateList(colPtr,rowIdx,vals, *k, jk, firstElt, listCol);
typename std::list<StorageIndex>::iterator k;
// Browse all previous columns that will update column j
for(k = listCol[j].begin(); k != listCol[j].end(); k++)
{
Index jk = firstElt(*k); // First element to use in the column
eigen_internal_assert(rowIdx[jk]==j);
Scalar v_j_jk = numext::conj(vals[jk]);
jk += 1;
for (Index i = jk; i < colPtr[*k+1]; i++)
{
StorageIndex l = rowIdx[i];
if(col_pattern[l]<0)
{
col_vals(col_nnz) = vals[i] * v_j_jk;
col_irow[col_nnz] = l;
col_pattern(l) = col_nnz;
col_nnz++;
}
else
col_vals(col_pattern[l]) -= vals[i] * v_j_jk;
}
updateList(colPtr,rowIdx,vals, *k, jk, firstElt, listCol);
}
}
// Scale the current column
if(numext::real(diag) <= 0)
{
//std::cerr << "\nNegative diagonal during Incomplete factorization at position " << j << " (value = " << diag << ")\n";
std::cerr << "\nNegative diagonal during Incomplete factorization at position " << j << " (value = " << diag << ")\n";
m_info = NumericalIssue;
return;
}
RealScalar rdiag = sqrt(numext::real(diag));
vals[colPtr[j]] = rdiag;
// TODO, the following should iterate on the structurally non-zeros only
for (Index i = j+1; i < n; i++)
for (Index k = 0; k<col_nnz; ++k)
{
//Scale
curCol(i) /= rdiag;
//Update the remaining diagonals with curCol
vals[colPtr[i]] -= numext::abs2(curCol(i));
Index i = col_irow[k];
//Scale
col_vals(k) /= rdiag;
//Update the remaining diagonals with col_vals
vals[colPtr[i]] -= numext::abs2(col_vals(k));
}
// Select the largest p elements
// p is the original number of elements in the column (without the diagonal)
// TODO, QuickSplit should operate on the structurally non zeros only.
Index p = colPtr[j+1] - colPtr[j] - 1 ;
internal::QuickSplit(curCol, irow, p);
Ref<VectorSx> cvals = col_vals.head(col_nnz);
Ref<VectorIx> cirow = col_irow.head(col_nnz);
internal::QuickSplit(cvals,cirow, p);
// Insert the largest p elements in the matrix
Index cpt = 0;
for (Index i = colPtr[j]+1; i < colPtr[j+1]; i++)
{
vals[i] = curCol(cpt);
rowIdx[i] = irow(cpt);
cpt ++;
vals[i] = col_vals(cpt);
rowIdx[i] = col_irow(cpt);
// restore col_pattern:
col_pattern(col_irow(cpt)) = -1;
cpt++;
}
// Get the first smallest row index and put it after the diagonal element
Index jk = colPtr(j)+1;