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Fix overflow issues in BDCSVD

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This commit is contained in:
Gael Guennebaud 2017-11-08 10:24:28 +01:00
parent 3949615176
commit e8468ea91b
1 changed files with 24 additions and 9 deletions
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29
Eigen/src/SVD/BDCSVD.h
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@ -11,7 +11,7 @@
// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr> // Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr> // Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
// Copyright (C) 2013 Jitse Niesen <jitse@maths.leeds.ac.uk> // Copyright (C) 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
// Copyright (C) 2014-2016 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2014-2017 Gael Guennebaud <gael.guennebaud@inria.fr>
// //
// Source Code Form is subject to the terms of the Mozilla // Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed // Public License v. 2.0. If a copy of the MPL was not distributed
@ -696,7 +696,9 @@ typename BDCSVD<MatrixType>::RealScalar BDCSVD<MatrixType>::secularEq(RealScalar
for(Index i=0; i<m; ++i) for(Index i=0; i<m; ++i)
{ {
Index j = perm(i); Index j = perm(i);
res += numext::abs2(col0(j)) / ((diagShifted(j) - mu) * (diag(j) + shift + mu)); // The following expression could be rewritten to involve only a single division,
// but this would make the expression more sensitive to overflow.
res += (col0(j) / (diagShifted(j) - mu)) * (col0(j) / (diag(j) + shift + mu));
} }
return res; return res;
@ -708,9 +710,12 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
{ {
using std::abs; using std::abs;
using std::swap; using std::swap;
using std::sqrt;
Index n = col0.size(); Index n = col0.size();
Index actual_n = n; Index actual_n = n;
// Note that here actual_n is computed based on col0(i)==0 instead of diag(i)==0 as above
// because 1) we have diag(i)==0 => col0(i)==0 and 2) if col0(i)==0, then diag(i) is already a singular value.
while(actual_n>1 && col0(actual_n-1)==Literal(0)) --actual_n; while(actual_n>1 && col0(actual_n-1)==Literal(0)) --actual_n;
for (Index k = 0; k < n; ++k) for (Index k = 0; k < n; ++k)
@ -732,7 +737,9 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
right = (diag(actual_n-1) + col0.matrix().norm()); right = (diag(actual_n-1) + col0.matrix().norm());
else else
{ {
// Skip deflated singular values // Skip deflated singular values,
// recall that at this stage we assume that z[j]!=0 and all entries for which z[j]==0 have been put aside.
// This should be equivalent to using perm[]
Index l = k+1; Index l = k+1;
while(col0(l)==Literal(0)) { ++l; eigen_internal_assert(l<actual_n); } while(col0(l)==Literal(0)) { ++l; eigen_internal_assert(l<actual_n); }
right = diag(l); right = diag(l);
@ -818,14 +825,22 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
RealScalar leftShifted, rightShifted; RealScalar leftShifted, rightShifted;
if (shift == left) if (shift == left)
{ {
leftShifted = (std::numeric_limits<RealScalar>::min)(); // to avoid overflow, we must have mu > max(real_min, |z(k)|/sqrt(real_max)),
// the factor 2 is to be more conservative
leftShifted = numext::maxi( (std::numeric_limits<RealScalar>::min)(), Literal(2) * abs(col0(k)) / sqrt((std::numeric_limits<RealScalar>::max)()) );
// check that we did it right:
eigen_internal_assert( (std::isfinite)( (col0(k)/leftShifted)*(col0(k)/(diag(k)+shift+leftShifted)) ) );
// I don't understand why the case k==0 would be special there: // I don't understand why the case k==0 would be special there:
// if (k == 0) rightShifted = right - left; else // if (k == 0) rightShifted = right - left; else
rightShifted = (k==actual_n-1) ? right : ((right - left) * RealScalar(0.6)); // theoretically we can take 0.5, but let's be safe rightShifted = (k==actual_n-1) ? right : ((right - left) * RealScalar(0.51)); // theoretically we can take 0.5, but let's be safe
} }
else else
{ {
leftShifted = -(right - left) * RealScalar(0.6); leftShifted = -(right - left) * RealScalar(0.51);
if(k+1<n)
rightShifted = -numext::maxi( (std::numeric_limits<RealScalar>::min)(), abs(col0(k+1)) / sqrt((std::numeric_limits<RealScalar>::max)()) );
else
rightShifted = -(std::numeric_limits<RealScalar>::min)(); rightShifted = -(std::numeric_limits<RealScalar>::min)();
} }
@ -980,7 +995,7 @@ void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index
Index start = firstCol + shift; Index start = firstCol + shift;
RealScalar c = m_computed(start, start); RealScalar c = m_computed(start, start);
RealScalar s = m_computed(start+i, start); RealScalar s = m_computed(start+i, start);
RealScalar r = sqrt(numext::abs2(c) + numext::abs2(s)); RealScalar r = numext::hypot(c,s);
if (r == Literal(0)) if (r == Literal(0))
{ {
m_computed(start+i, start+i) = Literal(0); m_computed(start+i, start+i) = Literal(0);