diff options
Diffstat (limited to 'Eigen/src/SVD/BDCSVD.h')
-rw-r--r-- | Eigen/src/SVD/BDCSVD.h | 131 |
1 files changed, 102 insertions, 29 deletions
diff --git a/Eigen/src/SVD/BDCSVD.h b/Eigen/src/SVD/BDCSVD.h index effa643fd..b440901d6 100644 --- a/Eigen/src/SVD/BDCSVD.h +++ b/Eigen/src/SVD/BDCSVD.h @@ -22,6 +22,11 @@ // #define EIGEN_BDCSVD_DEBUG_VERBOSE // #define EIGEN_BDCSVD_SANITY_CHECKS +#ifdef EIGEN_BDCSVD_SANITY_CHECKS +#undef eigen_internal_assert +#define eigen_internal_assert(X) assert(X); +#endif + namespace Eigen { #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE @@ -591,7 +596,7 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec // but others are interleaved and we must ignore them at this stage. // To this end, let's compute a permutation skipping them: Index actual_n = n; - while(actual_n>1 && diag(actual_n-1)==Literal(0)) --actual_n; + while(actual_n>1 && diag(actual_n-1)==Literal(0)) {--actual_n; eigen_internal_assert(col0(actual_n)==Literal(0)); } Index m = 0; // size of the deflated problem for(Index k=0;k<actual_n;++k) if(abs(col0(k))>considerZero) @@ -618,13 +623,11 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec std::cout << " shift: " << shifts.transpose() << "\n"; { - Index actual_n = n; - while(actual_n>1 && abs(col0(actual_n-1))<considerZero) --actual_n; std::cout << "\n\n mus: " << mus.head(actual_n).transpose() << "\n\n"; std::cout << " check1 (expect0) : " << ((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n).transpose() << "\n\n"; + assert((((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n) >= 0).all()); std::cout << " check2 (>0) : " << ((singVals.array()-diag) / singVals.array()).head(actual_n).transpose() << "\n\n"; - std::cout << " check3 (>0) : " << ((diag.segment(1,actual_n-1)-singVals.head(actual_n-1).array()) / singVals.head(actual_n-1).array()).transpose() << "\n\n\n"; - std::cout << " check4 (>0) : " << ((singVals.segment(1,actual_n-1)-singVals.head(actual_n-1))).transpose() << "\n\n\n"; + assert((((singVals.array()-diag) / singVals.array()).head(actual_n) >= 0).all()); } #endif @@ -652,13 +655,13 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec #endif #ifdef EIGEN_BDCSVD_SANITY_CHECKS - assert(U.allFinite()); - assert(V.allFinite()); - assert((U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() < 1e-14 * n); - assert((V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() < 1e-14 * n); assert(m_naiveU.allFinite()); assert(m_naiveV.allFinite()); assert(m_computed.allFinite()); + assert(U.allFinite()); + assert(V.allFinite()); +// assert((U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() < 100*NumTraits<RealScalar>::epsilon() * n); +// assert((V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() < 100*NumTraits<RealScalar>::epsilon() * n); #endif // Because of deflation, the singular values might not be completely sorted. @@ -673,6 +676,15 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec if(m_compV) V.col(i).swap(V.col(i+1)); } } + +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + { + bool singular_values_sorted = (((singVals.segment(1,actual_n-1)-singVals.head(actual_n-1))).array() >= 0).all(); + if(!singular_values_sorted) + std::cout << "Singular values are not sorted: " << singVals.segment(1,actual_n).transpose() << "\n"; + assert(singular_values_sorted); + } +#endif // Reverse order so that singular values in increased order // Because of deflation, the zeros singular-values are already at the end @@ -749,19 +761,22 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d RealScalar mid = left + (right-left) / Literal(2); RealScalar fMid = secularEq(mid, col0, diag, perm, diag, Literal(0)); #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE - std::cout << right-left << "\n"; - std::cout << "fMid = " << fMid << " " << secularEq(mid-left, col0, diag, perm, diag-left, left) << " " << secularEq(mid-right, col0, diag, perm, diag-right, right) << "\n"; - std::cout << " = " << secularEq(0.1*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.2*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.3*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.4*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.49*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.5*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.51*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.6*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.7*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.8*(left+right), col0, diag, perm, diag, 0) - << " " << secularEq(0.9*(left+right), col0, diag, perm, diag, 0) << "\n"; + std::cout << "right-left = " << right-left << "\n"; +// std::cout << "fMid = " << fMid << " " << secularEq(mid-left, col0, diag, perm, ArrayXr(diag-left), left) +// << " " << secularEq(mid-right, col0, diag, perm, ArrayXr(diag-right), right) << "\n"; + std::cout << " = " << secularEq(left+RealScalar(0.000001)*(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.1) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.2) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.3) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.4) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.49) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.5) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.51) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.6) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.7) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.8) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.9) *(right-left), col0, diag, perm, diag, 0) + << " " << secularEq(left+RealScalar(0.999999)*(right-left), col0, diag, perm, diag, 0) << "\n"; #endif RealScalar shift = (k == actual_n-1 || fMid > Literal(0)) ? left : right; @@ -804,13 +819,16 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d // And find mu such that f(mu)==0: RealScalar muZero = -a/b; RealScalar fZero = secularEq(muZero, col0, diag, perm, diagShifted, shift); + +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + assert((std::isfinite)(fZero)); +#endif muPrev = muCur; fPrev = fCur; muCur = muZero; fCur = fZero; - if (shift == left && (muCur < Literal(0) || muCur > right - left)) useBisection = true; if (shift == right && (muCur < -(right - left) || muCur > Literal(0))) useBisection = true; if (abs(fCur)>abs(fPrev)) useBisection = true; @@ -843,18 +861,30 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d else rightShifted = -(std::numeric_limits<RealScalar>::min)(); } - + RealScalar fLeft = secularEq(leftShifted, col0, diag, perm, diagShifted, shift); -#if defined EIGEN_INTERNAL_DEBUGGING || defined EIGEN_BDCSVD_DEBUG_VERBOSE +#if defined EIGEN_INTERNAL_DEBUGGING || defined EIGEN_BDCSVD_SANITY_CHECKS RealScalar fRight = secularEq(rightShifted, col0, diag, perm, diagShifted, shift); #endif +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + if(!(std::isfinite)(fLeft)) + std::cout << "f(" << leftShifted << ") =" << fLeft << " ; " << left << " " << shift << " " << right << "\n"; + assert((std::isfinite)(fLeft)); + + if(!(std::isfinite)(fRight)) + std::cout << "f(" << rightShifted << ") =" << fRight << " ; " << left << " " << shift << " " << right << "\n"; +// assert((std::isfinite)(fRight)); +#endif + #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE if(!(fLeft * fRight<0)) { - std::cout << "fLeft: " << leftShifted << " - " << diagShifted.head(10).transpose() << "\n ; " << bool(left==shift) << " " << (left-shift) << "\n"; - std::cout << k << " : " << fLeft << " * " << fRight << " == " << fLeft * fRight << " ; " << left << " - " << right << " -> " << leftShifted << " " << rightShifted << " shift=" << shift << "\n"; + std::cout << "f(leftShifted) using leftShifted=" << leftShifted << " ; diagShifted(1:10):" << diagShifted.head(10).transpose() << "\n ; " + << "left==shift=" << bool(left==shift) << " ; left-shift = " << (left-shift) << "\n"; + std::cout << "k=" << k << ", " << fLeft << " * " << fRight << " == " << fLeft * fRight << " ; " + << "[" << left << " .. " << right << "] -> [" << leftShifted << " " << rightShifted << "], shift=" << shift << " , f(right)=" << secularEq(0, col0, diag, perm, diagShifted, shift) << " == " << secularEq(right, col0, diag, perm, diag, 0) << "\n"; } #endif eigen_internal_assert(fLeft * fRight < Literal(0)); @@ -863,6 +893,8 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d { RealScalar midShifted = (leftShifted + rightShifted) / Literal(2); fMid = secularEq(midShifted, col0, diag, perm, diagShifted, shift); + eigen_internal_assert((numext::isfinite)(fMid)); + if (fLeft * fMid < Literal(0)) { rightShifted = midShifted; @@ -881,6 +913,15 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d shifts[k] = shift; mus[k] = muCur; +#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE + if(k+1<n) + std::cout << "found " << singVals[k] << " == " << shift << " + " << muCur << " from " << diag(k) << " .. " << diag(k+1) << "\n"; +#endif +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + assert(k==0 || singVals[k]>=singVals[k-1]); + assert(singVals[k]>=diag(k)); +#endif + // perturb singular value slightly if it equals diagonal entry to avoid division by zero later // (deflation is supposed to avoid this from happening) // - this does no seem to be necessary anymore - @@ -915,14 +956,42 @@ void BDCSVD<MatrixType>::perturbCol0 // see equation (3.6) RealScalar dk = diag(k); RealScalar prod = (singVals(last) + dk) * (mus(last) + (shifts(last) - dk)); +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + if(prod<0) { + std::cout << "k = " << k << " ; z(k)=" << col0(k) << ", diag(k)=" << dk << "\n"; + std::cout << "prod = " << "(" << singVals(last) << " + " << dk << ") * (" << mus(last) << " + (" << shifts(last) << " - " << dk << "))" << "\n"; + std::cout << " = " << singVals(last) + dk << " * " << mus(last) + (shifts(last) - dk) << "\n"; + } + assert(prod>=0); +#endif for(Index l = 0; l<m; ++l) { Index i = perm(l); if(i!=k) { +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + if(i>=k && (l==0 || l-1>=m)) + { + std::cout << "Error in perturbCol0\n"; + std::cout << " " << k << "/" << n << " " << l << "/" << m << " " << i << "/" << n << " ; " << col0(k) << " " << diag(k) << " " << "\n"; + std::cout << " " <<diag(i) << "\n"; + Index j = (i<k /*|| l==0*/) ? i : perm(l-1); + std::cout << " " << "j=" << j << "\n"; + } +#endif Index j = i<k ? i : perm(l-1); +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + if(!(dk!=Literal(0) || diag(i)!=Literal(0))) + { + std::cout << "k=" << k << ", i=" << i << ", l=" << l << ", perm.size()=" << perm.size() << "\n"; + } + assert(dk!=Literal(0) || diag(i)!=Literal(0)); +#endif prod *= ((singVals(j)+dk) / ((diag(i)+dk))) * ((mus(j)+(shifts(j)-dk)) / ((diag(i)-dk))); +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + assert(prod>=0); +#endif #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE if(i!=k && std::abs(((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) - 1) > 0.9 ) std::cout << " " << ((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) << " == (" << (singVals(j)+dk) << " * " << (mus(j)+(shifts(j)-dk)) @@ -934,6 +1003,9 @@ void BDCSVD<MatrixType>::perturbCol0 std::cout << "zhat(" << k << ") = sqrt( " << prod << ") ; " << (singVals(last) + dk) << " * " << mus(last) + shifts(last) << " - " << dk << "\n"; #endif RealScalar tmp = sqrt(prod); +#ifdef EIGEN_BDCSVD_SANITY_CHECKS + assert((std::isfinite)(tmp)); +#endif zhat(k) = col0(k) > Literal(0) ? tmp : -tmp; } } @@ -1043,7 +1115,7 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi } c/=r; s/=r; - m_computed(firstColm + i, firstColm) = r; + m_computed(firstColm + i, firstColm) = r; m_computed(firstColm + j, firstColm + j) = m_computed(firstColm + i, firstColm + i); m_computed(firstColm + j, firstColm) = Literal(0); @@ -1117,6 +1189,7 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index #endif #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE std::cout << "to be sorted: " << diag.transpose() << "\n\n"; + std::cout << " : " << col0.transpose() << "\n\n"; #endif { // Check for total deflation @@ -1207,7 +1280,7 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index if( (diag(i) - diag(i-1)) < NumTraits<RealScalar>::epsilon()*maxDiag ) { #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE - std::cout << "deflation 4.4 with i = " << i << " because " << (diag(i) - diag(i-1)) << " < " << NumTraits<RealScalar>::epsilon()*diag(i) << "\n"; + std::cout << "deflation 4.4 with i = " << i << " because " << diag(i) << " - " << diag(i-1) << " == " << (diag(i) - diag(i-1)) << " < " << NumTraits<RealScalar>::epsilon()*/*diag(i)*/maxDiag << "\n"; #endif eigen_internal_assert(abs(diag(i) - diag(i-1))<epsilon_coarse && " diagonal entries are not properly sorted"); deflation44(firstCol, firstCol + shift, firstRowW, firstColW, i-1, i, length); |