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more eigenization, dropped 'ipvt' in lm

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This commit is contained in:
Thomas Capricelli
2010-01-26 12:09:52 +01:00
parent 8a690299c6
commit 69f11c08a1
3 changed files with 42 additions and 102 deletions
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112
unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
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@@ -125,7 +125,7 @@ public:
Parameters parameters;
FVectorType fvec, qtf, diag;
JacobianType fjac;
VectorXi ipvt;
PermutationMatrix<Dynamic,Dynamic> permutation;
int nfev;
int njev;
int iter;
@@ -195,7 +195,6 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(
wa1.resize(n); wa2.resize(n); wa3.resize(n);
wa4.resize(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
if (mode != 2)
diag.resize(n);
@@ -236,7 +235,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
const int mode
)
{
int i, j, l;
int j;
/* calculate the jacobian matrix. */
int df_ret = functor.df(x, fjac);
@@ -251,21 +250,14 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
wa2 = fjac.colwise().blueNorm();
ColPivHouseholderQR<JacobianType> qrfac(fjac);
fjac = qrfac.matrixQR();
wa1 = fjac.diagonal();
fjac.diagonal() = qrfac.hCoeffs();
ipvt = qrfac.colsPermutation().indices();
// TODO : avoid this:
for(int i=0; i< fjac.cols(); i++) fjac.col(i).segment(i+1, fjac.rows()-i-1) *= fjac(i,i); // rescale vectors
permutation = qrfac.colsPermutation();
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
for (j = 0; j < n; ++j)
diag[j] = (wa2[j]==0.)? 1. : wa2[j];
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
@@ -278,48 +270,23 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
/* form (q transpose)*fvec and store the first n components in */
/* qtf. */
#if 0
// find a way to only compute the first n items, we have m>>n here.
wa4 = fvec;
wa4.applyOnTheLeft(qrfac.householderQ().adjoint());
wa4 = wa4.head(n);
fjac.diagonal() = wa1;
#else
wa4 = fvec;
for (j = 0; j < n; ++j) {
if (fjac(j,j) != 0.) {
sum = 0.;
for (i = j; i < m; ++i)
sum += fjac(i,j) * wa4[i];
temp = -sum / fjac(j,j);
for (i = j; i < m; ++i)
wa4[i] += fjac(i,j) * temp;
}
fjac(j,j) = wa1[j];
qtf[j] = wa4[j];
}
#endif
qtf = wa4.head(n);
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm != 0.)
for (j = 0; j < n; ++j) {
l = ipvt[j];
if (wa2[l] != 0.) {
sum = 0.;
for (i = 0; i <= j; ++i)
sum += fjac(i,j) * (qtf[i] / fnorm);
/* Computing MAX */
gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
}
}
for (j = 0; j < n; ++j)
if (wa2[permutation.indices()[j]] != 0.)
gnorm = std::max(gnorm, ei_abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (gnorm <= parameters.gtol)
return CosinusTooSmall;
/* rescale if necessary. */
if (mode != 2) /* Computing MAX */
if (mode != 2)
diag = diag.cwiseMax(wa2);
/* beginning of the inner loop. */
@@ -346,21 +313,14 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
if (Scalar(.1) * fnorm1 < fnorm)
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
wa3.fill(0.);
for (j = 0; j < n; ++j) {
l = ipvt[j];
temp = wa1[l];
for (i = 0; i <= j; ++i)
wa3[i] += fjac(i,j) * temp;
}
wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
temp1 = ei_abs2(wa3.stableNorm() / fnorm);
temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
/* Computing 2nd power */
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
@@ -455,7 +415,6 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(
wa1.resize(n); wa2.resize(n); wa3.resize(n);
wa4.resize(m);
fvec.resize(m);
ipvt.resize(n);
fjac.resize(m, n);
if (mode != 2)
diag.resize(n);
@@ -497,7 +456,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(
const int mode
)
{
int i, j, l;
int i, j;
bool sing;
/* compute the qr factorization of the jacobian matrix */
@@ -519,20 +478,20 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(
/* reorder its columns and update the components of qtf. */
sing = false;
for (j = 0; j < n; ++j) {
if (fjac(j,j) == 0.) {
if (fjac(j,j) == 0.)
sing = true;
}
ipvt[j] = j;
wa2[j] = fjac.col(j).head(j).stableNorm();
}
permutation.setIdentity(n);
if (sing) {
wa2 = fjac.colwise().blueNorm();
// TODO We have no unit test covering this branch.. untested
// TODO We have no unit test covering this code path, do not modify
// before it is carefully tested
ColPivHouseholderQR<JacobianType> qrfac(fjac);
fjac = qrfac.matrixQR();
wa1 = fjac.diagonal();
fjac.diagonal() = qrfac.hCoeffs();
ipvt = qrfac.colsPermutation().indices();
permutation = qrfac.colsPermutation();
// TODO : avoid this:
for(int ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
@@ -553,11 +512,8 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(
/* to the norms of the columns of the initial jacobian. */
if (iter == 1) {
if (mode != 2)
for (j = 0; j < n; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.)
diag[j] = 1.;
}
for (j = 0; j < n; ++j)
diag[j] = (wa2[j]==0.)? 1. : wa2[j];
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
@@ -571,30 +527,23 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm != 0.)
for (j = 0; j < n; ++j) {
l = ipvt[j];
if (wa2[l] != 0.) {
sum = 0.;
for (i = 0; i <= j; ++i)
sum += fjac(i,j) * (qtf[i] / fnorm);
/* Computing MAX */
gnorm = std::max(gnorm, ei_abs(sum / wa2[l]));
}
}
for (j = 0; j < n; ++j)
if (wa2[permutation.indices()[j]] != 0.)
gnorm = std::max(gnorm, ei_abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (gnorm <= parameters.gtol)
return CosinusTooSmall;
/* rescale if necessary. */
if (mode != 2) /* Computing MAX */
if (mode != 2)
diag = diag.cwiseMax(wa2);
/* beginning of the inner loop. */
do {
/* determine the levenberg-marquardt parameter. */
ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1);
ei_lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);
/* store the direction p and x + p. calculate the norm of p. */
wa1 = -wa1;
@@ -614,21 +563,14 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
if (Scalar(.1) * fnorm1 < fnorm)
actred = 1. - ei_abs2(fnorm1 / fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
wa3.fill(0.);
for (j = 0; j < n; ++j) {
l = ipvt[j];
temp = wa1[l];
for (i = 0; i <= j; ++i)
wa3[i] += fjac(i,j) * temp;
}
wa3 = fjac.corner(TopLeft,n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
temp1 = ei_abs2(wa3.stableNorm() / fnorm);
temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
/* Computing 2nd power */
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);

1
unsupported/Eigen/src/NonLinearOptimization/lmpar.h
View File

@@ -178,7 +178,6 @@ void ei_lmpar2(
const int n = qr.matrixQR().cols();
assert(n==diag.size());
assert(n==qtb.size());
assert(n==x.size());
Matrix< Scalar, Dynamic, 1 > wa1, wa2;