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Diffstat (limited to 'extern/libmv/third_party/ssba/Math/v3d_optimization.cpp')
| -rw-r--r-- | extern/libmv/third_party/ssba/Math/v3d_optimization.cpp | 955 |
1 files changed, 955 insertions, 0 deletions
diff --git a/extern/libmv/third_party/ssba/Math/v3d_optimization.cpp b/extern/libmv/third_party/ssba/Math/v3d_optimization.cpp new file mode 100644 index 00000000000..234815fcd1f --- /dev/null +++ b/extern/libmv/third_party/ssba/Math/v3d_optimization.cpp @@ -0,0 +1,955 @@ +/* +Copyright (c) 2008 University of North Carolina at Chapel Hill + +This file is part of SSBA (Simple Sparse Bundle Adjustment). + +SSBA is free software: you can redistribute it and/or modify it under the +terms of the GNU Lesser General Public License as published by the Free +Software Foundation, either version 3 of the License, or (at your option) any +later version. + +SSBA is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR +A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more +details. + +You should have received a copy of the GNU Lesser General Public License along +with SSBA. If not, see <http://www.gnu.org/licenses/>. +*/ + +#include "Math/v3d_optimization.h" + +#if defined(V3DLIB_ENABLE_SUITESPARSE) +//# include "COLAMD/Include/colamd.h" +# include "colamd.h" +extern "C" +{ +//# include "LDL/Include/ldl.h" +# include "ldl.h" +} +#endif + +#include <iostream> +#include <map> + +#define USE_BLOCK_REORDERING 1 +#define USE_MULTIPLICATIVE_UPDATE 1 + +using namespace std; + +namespace +{ + + using namespace V3D; + + inline double + squaredResidual(VectorArray<double> const& e) + { + int const N = e.count(); + int const M = e.size(); + + double res = 0.0; + + for (int n = 0; n < N; ++n) + for (int m = 0; m < M; ++m) + res += e[n][m] * e[n][m]; + + return res; + } // end squaredResidual() + +} // end namespace <> + +namespace V3D +{ + + int optimizerVerbosenessLevel = 0; + +#if defined(V3DLIB_ENABLE_SUITESPARSE) + + void + SparseLevenbergOptimizer::setupSparseJtJ() + { + int const nVaryingA = _nParametersA - _nNonvaryingA; + int const nVaryingB = _nParametersB - _nNonvaryingB; + int const nVaryingC = _paramDimensionC - _nNonvaryingC; + + int const bColumnStart = nVaryingA*_paramDimensionA; + int const cColumnStart = bColumnStart + nVaryingB*_paramDimensionB; + int const nColumns = cColumnStart + nVaryingC; + + _jointNonzerosW.clear(); + _jointIndexW.resize(_nMeasurements); +#if 1 + { + map<pair<int, int>, int> jointNonzeroMap; + for (size_t k = 0; k < _nMeasurements; ++k) + { + int const i = _correspondingParamA[k] - _nNonvaryingA; + int const j = _correspondingParamB[k] - _nNonvaryingB; + if (i >= 0 && j >= 0) + { + map<pair<int, int>, int>::const_iterator p = jointNonzeroMap.find(make_pair(i, j)); + if (p == jointNonzeroMap.end()) + { + jointNonzeroMap.insert(make_pair(make_pair(i, j), _jointNonzerosW.size())); + _jointIndexW[k] = _jointNonzerosW.size(); + _jointNonzerosW.push_back(make_pair(i, j)); + } + else + { + _jointIndexW[k] = (*p).second; + } // end if + } // end if + } // end for (k) + } // end scope +#else + for (size_t k = 0; k < _nMeasurements; ++k) + { + int const i = _correspondingParamA[k] - _nNonvaryingA; + int const j = _correspondingParamB[k] - _nNonvaryingB; + if (i >= 0 && j >= 0) + { + _jointIndexW[k] = _jointNonzerosW.size(); + _jointNonzerosW.push_back(make_pair(i, j)); + } + } // end for (k) +#endif + +#if defined(USE_BLOCK_REORDERING) + int const bBlockColumnStart = nVaryingA; + int const cBlockColumnStart = bBlockColumnStart + nVaryingB; + + int const nBlockColumns = cBlockColumnStart + ((nVaryingC > 0) ? 1 : 0); + + //cout << "nBlockColumns = " << nBlockColumns << endl; + + // For the column reordering we treat the columns belonging to one set + // of parameters as one (logical) column. + + // Determine non-zeros of JtJ (we forget about the non-zero diagonal for now) + // Only consider nonzeros of Ai^t * Bj induced by the measurements. + vector<pair<int, int> > nz_blockJtJ(_jointNonzerosW.size()); + for (int k = 0; k < _jointNonzerosW.size(); ++k) + { + nz_blockJtJ[k].first = _jointNonzerosW[k].second + bBlockColumnStart; + nz_blockJtJ[k].second = _jointNonzerosW[k].first; + } + + if (nVaryingC > 0) + { + // We assume, that the global unknowns are linked to every other variable. + for (int i = 0; i < nVaryingA; ++i) + nz_blockJtJ.push_back(make_pair(cBlockColumnStart, i)); + for (int j = 0; j < nVaryingB; ++j) + nz_blockJtJ.push_back(make_pair(cBlockColumnStart, j + bBlockColumnStart)); + } // end if + + int const nnzBlock = nz_blockJtJ.size(); + + vector<int> permBlockJtJ(nBlockColumns + 1); + + if (nnzBlock > 0) + { +// cout << "nnzBlock = " << nnzBlock << endl; + + CCS_Matrix<int> blockJtJ(nBlockColumns, nBlockColumns, nz_blockJtJ); + +// cout << " nz_blockJtJ: " << endl; +// for (size_t k = 0; k < nz_blockJtJ.size(); ++k) +// cout << " " << nz_blockJtJ[k].first << ":" << nz_blockJtJ[k].second << endl; +// cout << endl; + + int * colStarts = (int *)blockJtJ.getColumnStarts(); + int * rowIdxs = (int *)blockJtJ.getRowIndices(); + +// cout << "blockJtJ_colStarts = "; +// for (int k = 0; k <= nBlockColumns; ++k) cout << colStarts[k] << " "; +// cout << endl; + +// cout << "blockJtJ_rowIdxs = "; +// for (int k = 0; k < nnzBlock; ++k) cout << rowIdxs[k] << " "; +// cout << endl; + + int stats[COLAMD_STATS]; + symamd(nBlockColumns, rowIdxs, colStarts, &permBlockJtJ[0], (double *) NULL, stats, &calloc, &free); + if (optimizerVerbosenessLevel >= 2) symamd_report(stats); + } + else + { + for (int k = 0; k < permBlockJtJ.size(); ++k) permBlockJtJ[k] = k; + } // end if + +// cout << "permBlockJtJ = "; +// for (int k = 0; k < permBlockJtJ.size(); ++k) +// cout << permBlockJtJ[k] << " "; +// cout << endl; + + // From the determined symbolic permutation with logical variables, determine the actual ordering + _perm_JtJ.resize(nVaryingA*_paramDimensionA + nVaryingB*_paramDimensionB + nVaryingC + 1); + + int curDstCol = 0; + for (int k = 0; k < permBlockJtJ.size()-1; ++k) + { + int const srcCol = permBlockJtJ[k]; + if (srcCol < nVaryingA) + { + for (int n = 0; n < _paramDimensionA; ++n) + _perm_JtJ[curDstCol + n] = srcCol*_paramDimensionA + n; + curDstCol += _paramDimensionA; + } + else if (srcCol >= bBlockColumnStart && srcCol < cBlockColumnStart) + { + int const bStart = nVaryingA*_paramDimensionA; + int const j = srcCol - bBlockColumnStart; + + for (int n = 0; n < _paramDimensionB; ++n) + _perm_JtJ[curDstCol + n] = bStart + j*_paramDimensionB + n; + curDstCol += _paramDimensionB; + } + else if (srcCol == cBlockColumnStart) + { + int const cStart = nVaryingA*_paramDimensionA + nVaryingB*_paramDimensionB; + + for (int n = 0; n < nVaryingC; ++n) + _perm_JtJ[curDstCol + n] = cStart + n; + curDstCol += nVaryingC; + } + else + { + cerr << "Should not reach " << __LINE__ << ":" << __LINE__ << "!" << endl; + assert(false); + } + } +#else + vector<pair<int, int> > nz, nzL; + this->serializeNonZerosJtJ(nz); + + for (int k = 0; k < nz.size(); ++k) + { + // Swap rows and columns, since serializeNonZerosJtJ() generates the + // upper triangular part but symamd wants the lower triangle. + nzL.push_back(make_pair(nz[k].second, nz[k].first)); + } + + _perm_JtJ.resize(nColumns+1); + + if (nzL.size() > 0) + { + CCS_Matrix<int> symbJtJ(nColumns, nColumns, nzL); + + int * colStarts = (int *)symbJtJ.getColumnStarts(); + int * rowIdxs = (int *)symbJtJ.getRowIndices(); + +// cout << "symbJtJ_colStarts = "; +// for (int k = 0; k <= nColumns; ++k) cout << colStarts[k] << " "; +// cout << endl; + +// cout << "symbJtJ_rowIdxs = "; +// for (int k = 0; k < nzL.size(); ++k) cout << rowIdxs[k] << " "; +// cout << endl; + + int stats[COLAMD_STATS]; + symamd(nColumns, rowIdxs, colStarts, &_perm_JtJ[0], (double *) NULL, stats, &calloc, &free); + if (optimizerVerbosenessLevel >= 2) symamd_report(stats); + } + else + { + for (int k = 0; k < _perm_JtJ.size(); ++k) _perm_JtJ[k] = k; + } //// end if +#endif + _perm_JtJ.back() = _perm_JtJ.size() - 1; + +// cout << "_perm_JtJ = "; +// for (int k = 0; k < _perm_JtJ.size(); ++k) cout << _perm_JtJ[k] << " "; +// cout << endl; + + // Finally, compute the inverse of the full permutation. + _invPerm_JtJ.resize(_perm_JtJ.size()); + for (size_t k = 0; k < _perm_JtJ.size(); ++k) + _invPerm_JtJ[_perm_JtJ[k]] = k; + + vector<pair<int, int> > nz_JtJ; + this->serializeNonZerosJtJ(nz_JtJ); + + for (int k = 0; k < nz_JtJ.size(); ++k) + { + int const i = nz_JtJ[k].first; + int const j = nz_JtJ[k].second; + + int pi = _invPerm_JtJ[i]; + int pj = _invPerm_JtJ[j]; + // Swap values if in lower triangular part + if (pi > pj) std::swap(pi, pj); + nz_JtJ[k].first = pi; + nz_JtJ[k].second = pj; + } + + int const nnz = nz_JtJ.size(); + +// cout << "nz_JtJ = "; +// for (int k = 0; k < nnz; ++k) cout << nz_JtJ[k].first << ":" << nz_JtJ[k].second << " "; +// cout << endl; + + _JtJ.create(nColumns, nColumns, nz_JtJ); + +// cout << "_colStart_JtJ = "; +// for (int k = 0; k < _JtJ.num_cols(); ++k) cout << _JtJ.getColumnStarts()[k] << " "; +// cout << endl; + +// cout << "_rowIdxs_JtJ = "; +// for (int k = 0; k < nnz; ++k) cout << _JtJ.getRowIndices()[k] << " "; +// cout << endl; + + vector<int> workFlags(nColumns); + + _JtJ_Lp.resize(nColumns+1); + _JtJ_Parent.resize(nColumns); + _JtJ_Lnz.resize(nColumns); + + ldl_symbolic(nColumns, (int *)_JtJ.getColumnStarts(), (int *)_JtJ.getRowIndices(), + &_JtJ_Lp[0], &_JtJ_Parent[0], &_JtJ_Lnz[0], + &workFlags[0], NULL, NULL); + + if (optimizerVerbosenessLevel >= 1) + cout << "SparseLevenbergOptimizer: Nonzeros in LDL decomposition: " << _JtJ_Lp[nColumns] << endl; + + } // end SparseLevenbergOptimizer::setupSparseJtJ() + + void + SparseLevenbergOptimizer::serializeNonZerosJtJ(vector<pair<int, int> >& dst) const + { + int const nVaryingA = _nParametersA - _nNonvaryingA; + int const nVaryingB = _nParametersB - _nNonvaryingB; + int const nVaryingC = _paramDimensionC - _nNonvaryingC; + + int const bColumnStart = nVaryingA*_paramDimensionA; + int const cColumnStart = bColumnStart + nVaryingB*_paramDimensionB; + + dst.clear(); + + // Add the diagonal block matrices (only the upper triangular part). + + // Ui submatrices of JtJ + for (int i = 0; i < nVaryingA; ++i) + { + int const i0 = i * _paramDimensionA; + + for (int c = 0; c < _paramDimensionA; ++c) + for (int r = 0; r <= c; ++r) + dst.push_back(make_pair(i0 + r, i0 + c)); + } + + // Vj submatrices of JtJ + for (int j = 0; j < nVaryingB; ++j) + { + int const j0 = j*_paramDimensionB + bColumnStart; + + for (int c = 0; c < _paramDimensionB; ++c) + for (int r = 0; r <= c; ++r) + dst.push_back(make_pair(j0 + r, j0 + c)); + } + + // Z submatrix of JtJ + for (int c = 0; c < nVaryingC; ++c) + for (int r = 0; r <= c; ++r) + dst.push_back(make_pair(cColumnStart + r, cColumnStart + c)); + + // Add the elements i and j linked by an observation k + // W submatrix of JtJ + for (size_t n = 0; n < _jointNonzerosW.size(); ++n) + { + int const i0 = _jointNonzerosW[n].first; + int const j0 = _jointNonzerosW[n].second; + int const r0 = i0*_paramDimensionA; + int const c0 = j0*_paramDimensionB + bColumnStart; + + for (int r = 0; r < _paramDimensionA; ++r) + for (int c = 0; c < _paramDimensionB; ++c) + dst.push_back(make_pair(r0 + r, c0 + c)); + } // end for (n) + + if (nVaryingC > 0) + { + // Finally, add the dense columns linking i (resp. j) with the global parameters. + // X submatrix of JtJ + for (int i = 0; i < nVaryingA; ++i) + { + int const i0 = i*_paramDimensionA; + + for (int r = 0; r < _paramDimensionA; ++r) + for (int c = 0; c < nVaryingC; ++c) + dst.push_back(make_pair(i0 + r, cColumnStart + c)); + } + + // Y submatrix of JtJ + for (int j = 0; j < nVaryingB; ++j) + { + int const j0 = j*_paramDimensionB + bColumnStart; + + for (int r = 0; r < _paramDimensionB; ++r) + for (int c = 0; c < nVaryingC; ++c) + dst.push_back(make_pair(j0 + r, cColumnStart + c)); + } + } // end if + } // end SparseLevenbergOptimizer::serializeNonZerosJtJ() + + void + SparseLevenbergOptimizer::fillSparseJtJ(MatrixArray<double> const& Ui, + MatrixArray<double> const& Vj, + MatrixArray<double> const& Wn, + Matrix<double> const& Z, + Matrix<double> const& X, + Matrix<double> const& Y) + { + int const nVaryingA = _nParametersA - _nNonvaryingA; + int const nVaryingB = _nParametersB - _nNonvaryingB; + int const nVaryingC = _paramDimensionC - _nNonvaryingC; + + int const bColumnStart = nVaryingA*_paramDimensionA; + int const cColumnStart = bColumnStart + nVaryingB*_paramDimensionB; + + int const nCols = _JtJ.num_cols(); + int const nnz = _JtJ.getNonzeroCount(); + + // The following has to replicate the procedure as in serializeNonZerosJtJ() + + int serial = 0; + + double * values = _JtJ.getValues(); + int const * destIdxs = _JtJ.getDestIndices(); + + // Add the diagonal block matrices (only the upper triangular part). + + // Ui submatrices of JtJ + for (int i = 0; i < nVaryingA; ++i) + { + int const i0 = i * _paramDimensionA; + + for (int c = 0; c < _paramDimensionA; ++c) + for (int r = 0; r <= c; ++r, ++serial) + values[destIdxs[serial]] = Ui[i][r][c]; + } + + // Vj submatrices of JtJ + for (int j = 0; j < nVaryingB; ++j) + { + int const j0 = j*_paramDimensionB + bColumnStart; + + for (int c = 0; c < _paramDimensionB; ++c) + for (int r = 0; r <= c; ++r, ++serial) + values[destIdxs[serial]] = Vj[j][r][c]; + } + + // Z submatrix of JtJ + for (int c = 0; c < nVaryingC; ++c) + for (int r = 0; r <= c; ++r, ++serial) + values[destIdxs[serial]] = Z[r][c]; + + // Add the elements i and j linked by an observation k + // W submatrix of JtJ + for (size_t n = 0; n < _jointNonzerosW.size(); ++n) + { + for (int r = 0; r < _paramDimensionA; ++r) + for (int c = 0; c < _paramDimensionB; ++c, ++serial) + values[destIdxs[serial]] = Wn[n][r][c]; + } // end for (k) + + if (nVaryingC > 0) + { + // Finally, add the dense columns linking i (resp. j) with the global parameters. + // X submatrix of JtJ + for (int i = 0; i < nVaryingA; ++i) + { + int const r0 = i * _paramDimensionA; + for (int r = 0; r < _paramDimensionA; ++r) + for (int c = 0; c < nVaryingC; ++c, ++serial) + values[destIdxs[serial]] = X[r0+r][c]; + } + + // Y submatrix of JtJ + for (int j = 0; j < nVaryingB; ++j) + { + int const r0 = j * _paramDimensionB; + for (int r = 0; r < _paramDimensionB; ++r) + for (int c = 0; c < nVaryingC; ++c, ++serial) + values[destIdxs[serial]] = Y[r0+r][c]; + } + } // end if + } // end SparseLevenbergOptimizer::fillSparseJtJ() + + void + SparseLevenbergOptimizer::minimize() + { + status = LEVENBERG_OPTIMIZER_TIMEOUT; + bool computeDerivatives = true; + + int const nVaryingA = _nParametersA - _nNonvaryingA; + int const nVaryingB = _nParametersB - _nNonvaryingB; + int const nVaryingC = _paramDimensionC - _nNonvaryingC; + + if (nVaryingA == 0 && nVaryingB == 0 && nVaryingC == 0) + { + // No degrees of freedom, nothing to optimize. + status = LEVENBERG_OPTIMIZER_CONVERGED; + return; + } + + this->setupSparseJtJ(); + + Vector<double> weights(_nMeasurements); + + MatrixArray<double> Ak(_nMeasurements, _measurementDimension, _paramDimensionA); + MatrixArray<double> Bk(_nMeasurements, _measurementDimension, _paramDimensionB); + MatrixArray<double> Ck(_nMeasurements, _measurementDimension, _paramDimensionC); + + MatrixArray<double> Ui(nVaryingA, _paramDimensionA, _paramDimensionA); + MatrixArray<double> Vj(nVaryingB, _paramDimensionB, _paramDimensionB); + + // Wn = Ak^t*Bk + MatrixArray<double> Wn(_jointNonzerosW.size(), _paramDimensionA, _paramDimensionB); + + Matrix<double> Z(nVaryingC, nVaryingC); + + // X = A^t*C + Matrix<double> X(nVaryingA*_paramDimensionA, nVaryingC); + // Y = B^t*C + Matrix<double> Y(nVaryingB*_paramDimensionB, nVaryingC); + + VectorArray<double> residuals(_nMeasurements, _measurementDimension); + VectorArray<double> residuals2(_nMeasurements, _measurementDimension); + + VectorArray<double> diagUi(nVaryingA, _paramDimensionA); + VectorArray<double> diagVj(nVaryingB, _paramDimensionB); + Vector<double> diagZ(nVaryingC); + + VectorArray<double> At_e(nVaryingA, _paramDimensionA); + VectorArray<double> Bt_e(nVaryingB, _paramDimensionB); + Vector<double> Ct_e(nVaryingC); + + Vector<double> Jt_e(nVaryingA*_paramDimensionA + nVaryingB*_paramDimensionB + nVaryingC); + + Vector<double> delta(nVaryingA*_paramDimensionA + nVaryingB*_paramDimensionB + nVaryingC); + Vector<double> deltaPerm(nVaryingA*_paramDimensionA + nVaryingB*_paramDimensionB + nVaryingC); + + VectorArray<double> deltaAi(_nParametersA, _paramDimensionA); + VectorArray<double> deltaBj(_nParametersB, _paramDimensionB); + Vector<double> deltaC(_paramDimensionC); + + double err = 0.0; + + for (currentIteration = 0; currentIteration < maxIterations; ++currentIteration) + { + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: currentIteration: " << currentIteration << endl; + if (computeDerivatives) + { + this->evalResidual(residuals); + this->fillWeights(residuals, weights); + for (int k = 0; k < _nMeasurements; ++k) + scaleVectorIP(weights[k], residuals[k]); + + err = squaredResidual(residuals); + + if (optimizerVerbosenessLevel >= 1) cout << "SparseLevenbergOptimizer: |residual|^2 = " << err << endl; + if (optimizerVerbosenessLevel >= 2) cout << "SparseLevenbergOptimizer: lambda = " << lambda << endl; + + for (int k = 0; k < residuals.count(); ++k) scaleVectorIP(-1.0, residuals[k]); + + this->setupJacobianGathering(); + this->fillAllJacobians(weights, Ak, Bk, Ck); + + // Compute the different parts of J^t*e + if (nVaryingA > 0) + { + for (int i = 0; i < nVaryingA; ++i) makeZeroVector(At_e[i]); + + Vector<double> tmp(_paramDimensionA); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const i = _correspondingParamA[k] - _nNonvaryingA; + if (i < 0) continue; + multiply_At_v(Ak[k], residuals[k], tmp); + addVectors(tmp, At_e[i], At_e[i]); + } // end for (k) + } // end if + + if (nVaryingB > 0) + { + for (int j = 0; j < nVaryingB; ++j) makeZeroVector(Bt_e[j]); + + Vector<double> tmp(_paramDimensionB); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const j = _correspondingParamB[k] - _nNonvaryingB; + if (j < 0) continue; + multiply_At_v(Bk[k], residuals[k], tmp); + addVectors(tmp, Bt_e[j], Bt_e[j]); + } // end for (k) + } // end if + + if (nVaryingC > 0) + { + makeZeroVector(Ct_e); + + Vector<double> tmp(_paramDimensionC); + + for (int k = 0; k < _nMeasurements; ++k) + { + multiply_At_v(Ck[k], residuals[k], tmp); + for (int l = 0; l < nVaryingC; ++l) Ct_e[l] += tmp[_nNonvaryingC + l]; + } + } // end if + + int pos = 0; + for (int i = 0; i < nVaryingA; ++i) + for (int l = 0; l < _paramDimensionA; ++l, ++pos) + Jt_e[pos] = At_e[i][l]; + for (int j = 0; j < nVaryingB; ++j) + for (int l = 0; l < _paramDimensionB; ++l, ++pos) + Jt_e[pos] = Bt_e[j][l]; + for (int l = 0; l < nVaryingC; ++l, ++pos) + Jt_e[pos] = Ct_e[l]; + +// cout << "Jt_e = "; +// for (int k = 0; k < Jt_e.size(); ++k) cout << Jt_e[k] << " "; +// cout << endl; + + if (this->applyGradientStoppingCriteria(norm_Linf(Jt_e))) + { + status = LEVENBERG_OPTIMIZER_CONVERGED; + goto end; + } + + // The lhs J^t*J consists of several parts: + // [ U W X ] + // J^t*J = [ W^t V Y ] + // [ X^t Y^t Z ], + // where U, V and W are block-sparse matrices (due to the sparsity of A and B). + // X, Y and Z contain only a few columns (the number of global parameters). + + if (nVaryingA > 0) + { + // Compute Ui + Matrix<double> U(_paramDimensionA, _paramDimensionA); + + for (int i = 0; i < nVaryingA; ++i) makeZeroMatrix(Ui[i]); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const i = _correspondingParamA[k] - _nNonvaryingA; + if (i < 0) continue; + multiply_At_A(Ak[k], U); + addMatricesIP(U, Ui[i]); + } // end for (k) + } // end if + + if (nVaryingB > 0) + { + // Compute Vj + Matrix<double> V(_paramDimensionB, _paramDimensionB); + + for (int j = 0; j < nVaryingB; ++j) makeZeroMatrix(Vj[j]); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const j = _correspondingParamB[k] - _nNonvaryingB; + if (j < 0) continue; + multiply_At_A(Bk[k], V); + addMatricesIP(V, Vj[j]); + } // end for (k) + } // end if + + if (nVaryingC > 0) + { + Matrix<double> ZZ(_paramDimensionC, _paramDimensionC); + Matrix<double> Zsum(_paramDimensionC, _paramDimensionC); + + makeZeroMatrix(Zsum); + + for (int k = 0; k < _nMeasurements; ++k) + { + multiply_At_A(Ck[k], ZZ); + addMatricesIP(ZZ, Zsum); + } // end for (k) + + // Ignore the non-varying parameters + for (int i = 0; i < nVaryingC; ++i) + for (int j = 0; j < nVaryingC; ++j) + Z[i][j] = Zsum[i+_nNonvaryingC][j+_nNonvaryingC]; + } // end if + + if (nVaryingA > 0 && nVaryingB > 0) + { + for (int n = 0; n < Wn.count(); ++n) makeZeroMatrix(Wn[n]); + + Matrix<double> W(_paramDimensionA, _paramDimensionB); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const n = _jointIndexW[k]; + if (n >= 0) + { + int const i0 = _jointNonzerosW[n].first; + int const j0 = _jointNonzerosW[n].second; + + multiply_At_B(Ak[k], Bk[k], W); + addMatricesIP(W, Wn[n]); + } // end if + } // end for (k) + } // end if + + if (nVaryingA > 0 && nVaryingC > 0) + { + Matrix<double> XX(_paramDimensionA, _paramDimensionC); + + makeZeroMatrix(X); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const i = _correspondingParamA[k] - _nNonvaryingA; + // Ignore the non-varying parameters + if (i < 0) continue; + + multiply_At_B(Ak[k], Ck[k], XX); + + for (int r = 0; r < _paramDimensionA; ++r) + for (int c = 0; c < nVaryingC; ++c) + X[r+i*_paramDimensionA][c] += XX[r][c+_nNonvaryingC]; + } // end for (k) + } // end if + + if (nVaryingB > 0 && nVaryingC > 0) + { + Matrix<double> YY(_paramDimensionB, _paramDimensionC); + + makeZeroMatrix(Y); + + for (int k = 0; k < _nMeasurements; ++k) + { + int const j = _correspondingParamB[k] - _nNonvaryingB; + // Ignore the non-varying parameters + if (j < 0) continue; + + multiply_At_B(Bk[k], Ck[k], YY); + + for (int r = 0; r < _paramDimensionB; ++r) + for (int c = 0; c < nVaryingC; ++c) + Y[r+j*_paramDimensionB][c] += YY[r][c+_nNonvaryingC]; + } // end for (k) + } // end if + + if (currentIteration == 0) + { + // Initialize lambda as tau*max(JtJ[i][i]) + double maxEl = -1e30; + if (nVaryingA > 0) + { + for (int i = 0; i < nVaryingA; ++i) + for (int l = 0; l < _paramDimensionA; ++l) + maxEl = std::max(maxEl, Ui[i][l][l]); + } + if (nVaryingB > 0) + { + for (int j = 0; j < nVaryingB; ++j) + for (int l = 0; l < _paramDimensionB; ++l) + maxEl = std::max(maxEl, Vj[j][l][l]); + } + if (nVaryingC > 0) + { + for (int l = 0; l < nVaryingC; ++l) + maxEl = std::max(maxEl, Z[l][l]); + } + + lambda = tau * maxEl; + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: initial lambda = " << lambda << endl; + } // end if (currentIteration == 0) + } // end if (computeDerivatives) + + for (int i = 0; i < nVaryingA; ++i) + { + for (int l = 0; l < _paramDimensionA; ++l) diagUi[i][l] = Ui[i][l][l]; + } // end for (i) + + for (int j = 0; j < nVaryingB; ++j) + { + for (int l = 0; l < _paramDimensionB; ++l) diagVj[j][l] = Vj[j][l][l]; + } // end for (j) + + for (int l = 0; l < nVaryingC; ++l) diagZ[l] = Z[l][l]; + + // Augment the diagonals with lambda (either by the standard additive update or by multiplication). +#if !defined(USE_MULTIPLICATIVE_UPDATE) + for (int i = 0; i < nVaryingA; ++i) + for (unsigned l = 0; l < _paramDimensionA; ++l) + Ui[i][l][l] += lambda; + + for (int j = 0; j < nVaryingB; ++j) + for (unsigned l = 0; l < _paramDimensionB; ++l) + Vj[j][l][l] += lambda; + + for (unsigned l = 0; l < nVaryingC; ++l) + Z[l][l] += lambda; +#else + for (int i = 0; i < nVaryingA; ++i) + for (unsigned l = 0; l < _paramDimensionA; ++l) + Ui[i][l][l] = std::max(Ui[i][l][l] * (1.0 + lambda), 1e-15); + + for (int j = 0; j < nVaryingB; ++j) + for (unsigned l = 0; l < _paramDimensionB; ++l) + Vj[j][l][l] = std::max(Vj[j][l][l] * (1.0 + lambda), 1e-15); + + for (unsigned l = 0; l < nVaryingC; ++l) + Z[l][l] = std::max(Z[l][l] * (1.0 + lambda), 1e-15); +#endif + + this->fillSparseJtJ(Ui, Vj, Wn, Z, X, Y); + + bool success = true; + double rho = 0.0; + { + int const nCols = _JtJ_Parent.size(); + int const nnz = _JtJ.getNonzeroCount(); + int const lnz = _JtJ_Lp.back(); + + vector<int> Li(lnz); + vector<double> Lx(lnz); + vector<double> D(nCols), Y(nCols); + vector<int> workPattern(nCols), workFlag(nCols); + + int * colStarts = (int *)_JtJ.getColumnStarts(); + int * rowIdxs = (int *)_JtJ.getRowIndices(); + double * values = _JtJ.getValues(); + + int const d = ldl_numeric(nCols, colStarts, rowIdxs, values, + &_JtJ_Lp[0], &_JtJ_Parent[0], &_JtJ_Lnz[0], + &Li[0], &Lx[0], &D[0], + &Y[0], &workPattern[0], &workFlag[0], + NULL, NULL); + + if (d == nCols) + { + ldl_perm(nCols, &deltaPerm[0], &Jt_e[0], &_perm_JtJ[0]); + ldl_lsolve(nCols, &deltaPerm[0], &_JtJ_Lp[0], &Li[0], &Lx[0]); + ldl_dsolve(nCols, &deltaPerm[0], &D[0]); + ldl_ltsolve(nCols, &deltaPerm[0], &_JtJ_Lp[0], &Li[0], &Lx[0]); + ldl_permt(nCols, &delta[0], &deltaPerm[0], &_perm_JtJ[0]); + } + else + { + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: LDL decomposition failed. Increasing lambda." << endl; + success = false; + } + } + + if (success) + { + double const deltaSqrLength = sqrNorm_L2(delta); + + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: ||delta||^2 = " << deltaSqrLength << endl; + + double const paramLength = this->getParameterLength(); + if (this->applyUpdateStoppingCriteria(paramLength, sqrt(deltaSqrLength))) + { + status = LEVENBERG_OPTIMIZER_SMALL_UPDATE; + goto end; + } + + // Copy the updates from delta to the respective arrays + int pos = 0; + + for (int i = 0; i < _nNonvaryingA; ++i) makeZeroVector(deltaAi[i]); + for (int i = _nNonvaryingA; i < _nParametersA; ++i) + for (int l = 0; l < _paramDimensionA; ++l, ++pos) + deltaAi[i][l] = delta[pos]; + + for (int j = 0; j < _nNonvaryingB; ++j) makeZeroVector(deltaBj[j]); + for (int j = _nNonvaryingB; j < _nParametersB; ++j) + for (int l = 0; l < _paramDimensionB; ++l, ++pos) + deltaBj[j][l] = delta[pos]; + + makeZeroVector(deltaC); + for (int l = _nNonvaryingC; l < _paramDimensionC; ++l, ++pos) + deltaC[l] = delta[pos]; + + saveAllParameters(); + if (nVaryingA > 0) updateParametersA(deltaAi); + if (nVaryingB > 0) updateParametersB(deltaBj); + if (nVaryingC > 0) updateParametersC(deltaC); + + this->evalResidual(residuals2); + for (int k = 0; k < _nMeasurements; ++k) + scaleVectorIP(weights[k], residuals2[k]); + + double const newErr = squaredResidual(residuals2); + rho = err - newErr; + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: |new residual|^2 = " << newErr << endl; + +#if !defined(USE_MULTIPLICATIVE_UPDATE) + double const denom1 = lambda * deltaSqrLength; +#else + double denom1 = 0.0f; + for (int i = _nNonvaryingA; i < _nParametersA; ++i) + for (int l = 0; l < _paramDimensionA; ++l) + denom1 += deltaAi[i][l] * deltaAi[i][l] * diagUi[i-_nNonvaryingA][l]; + + for (int j = _nNonvaryingB; j < _nParametersB; ++j) + for (int l = 0; l < _paramDimensionB; ++l) + denom1 += deltaBj[j][l] * deltaBj[j][l] * diagVj[j-_nNonvaryingB][l]; + + for (int l = _nNonvaryingC; l < _paramDimensionC; ++l) + denom1 += deltaC[l] * deltaC[l] * diagZ[l-_nNonvaryingC]; + + denom1 *= lambda; +#endif + double const denom2 = innerProduct(delta, Jt_e); + rho = rho / (denom1 + denom2); + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: rho = " << rho + << " denom1 = " << denom1 << " denom2 = " << denom2 << endl; + } // end if (success) + + if (success && rho > 0) + { + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: Improved solution - decreasing lambda." << endl; + // Improvement in the new solution + decreaseLambda(rho); + computeDerivatives = true; + } + else + { + if (optimizerVerbosenessLevel >= 2) + cout << "SparseLevenbergOptimizer: Inferior solution - increasing lambda." << endl; + restoreAllParameters(); + increaseLambda(); + computeDerivatives = false; + + // Restore diagonal elements in Ui, Vj and Z. + for (int i = 0; i < nVaryingA; ++i) + { + for (int l = 0; l < _paramDimensionA; ++l) Ui[i][l][l] = diagUi[i][l]; + } // end for (i) + + for (int j = 0; j < nVaryingB; ++j) + { + for (int l = 0; l < _paramDimensionB; ++l) Vj[j][l][l] = diagVj[j][l]; + } // end for (j) + + for (int l = 0; l < nVaryingC; ++l) Z[l][l] = diagZ[l]; + } // end if + } // end for + + end:; + if (optimizerVerbosenessLevel >= 2) + cout << "Leaving SparseLevenbergOptimizer::minimize()." << endl; + } // end SparseLevenbergOptimizer::minimize() + +#endif // defined(V3DLIB_ENABLE_SUITESPARSE) + +} // end namespace V3D |