remove some duplicated code LevenbergMarquardt::minimizeNumericalDiff*() by

using the generic Eigen NumericalDiff recently introduced.

LevenbergMarquardt::lmdif1(), which is provided as a convenience method for
people porting code from (c)minpack, is now a static function

unsupported/Eigen/NonLinear

@@ -26,6 +26,7 @@
 #define EIGEN_NONLINEAR_MODULE_H
 
 #include <Eigen/Core>
+#include <unsupported/Eigen/NumericalDiff>
 
 namespace Eigen {
 

unsupported/Eigen/src/NonLinear/LevenbergMarquardt.h

@@ -54,24 +54,13 @@ public:
             const int mode=1
             );
 
-    Status lmdif1(
+    static Status lmdif1(
+            FunctorType &_functor,
             Matrix< Scalar, Dynamic, 1 >  &x,
+            int *nfev,
             const Scalar tol = ei_sqrt(epsilon<Scalar>())
             );
 
-    Status minimizeNumericalDiff(
-            Matrix< Scalar, Dynamic, 1 >  &x,
-            const int mode=1
-            );
-    Status minimizeNumericalDiffInit(
-            Matrix< Scalar, Dynamic, 1 >  &x,
-            const int mode=1
-            );
-    Status minimizeNumericalDiffOneStep(
-            Matrix< Scalar, Dynamic, 1 >  &x,
-            const int mode=1
-            );
-
     Status lmstr1(
             Matrix< Scalar, Dynamic, 1 >  &x,
             const Scalar tol = ei_sqrt(epsilon<Scalar>())
@@ -392,283 +381,6 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(
     return Running;
 }
 
-template<typename FunctorType, typename Scalar>
-typename LevenbergMarquardt<FunctorType,Scalar>::Status
-LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
-        Matrix< Scalar, Dynamic, 1 >  &x,
-        const Scalar tol
-        )
-{
-    n = x.size();
-    m = functor.values();
-
-    /* check the input parameters for errors. */
-    if (n <= 0 || m < n || tol < 0.)
-        return ImproperInputParameters;
-
-    resetParameters();
-    parameters.ftol = tol;
-    parameters.xtol = tol;
-    parameters.maxfev = 200*(n+1);
-
-    return minimizeNumericalDiff(x);
-}
-
-template<typename FunctorType, typename Scalar>
-typename LevenbergMarquardt<FunctorType,Scalar>::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiffInit(
-        Matrix< Scalar, Dynamic, 1 >  &x,
-        const int mode
-        )
-{
-    n = x.size();
-    m = functor.values();
-
-    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);
-    assert( (mode!=2 || diag.size()==n) || "When using mode==2, the caller must provide a valid 'diag'");
-    qtf.resize(n);
-
-    /* Function Body */
-    nfev = 0;
-    njev = 0;
-
-    /*     check the input parameters for errors. */
-
-    if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
-        return ImproperInputParameters;
-    if (mode == 2)
-        for (int j = 0; j < n; ++j)
-            if (diag[j] <= 0.)
-                return ImproperInputParameters;
-
-    /*     evaluate the function at the starting point */
-    /*     and calculate its norm. */
-
-    nfev = 1;
-    if ( functor(x, fvec) < 0)
-        return UserAsked;
-    fnorm = fvec.stableNorm();
-
-    /*     initialize levenberg-marquardt parameter and iteration counter. */
-
-    par = 0.;
-    iter = 1;
-
-    return Running;
-}
-
-template<typename FunctorType, typename Scalar>
-typename LevenbergMarquardt<FunctorType,Scalar>::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiffOneStep(
-        Matrix< Scalar, Dynamic, 1 >  &x,
-        const int mode
-        )
-{
-    int i, j, l;
-
-    /* calculate the jacobian matrix. */
-
-    if ( ei_fdjac2(functor, x, fvec, fjac, parameters.epsfcn) < 0)
-        return UserAsked;
-    nfev += n;
-
-    /* compute the qr factorization of the jacobian. */
-
-    ei_qrfac<Scalar>(m, n, fjac.data(), fjac.rows(), true, ipvt.data(), wa1.data(), wa2.data());
-    ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1)
-
-    /* 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.;
-            }
-
-        /* on the first iteration, calculate the norm of the scaled x */
-        /* and initialize the step bound delta. */
-
-        wa3 = diag.cwise() * x;
-        xnorm = wa3.stableNorm();
-        delta = parameters.factor * xnorm;
-        if (delta == 0.)
-            delta = parameters.factor;
-    }
-
-    /* form (q transpose)*fvec and store the first n components in */
-    /* qtf. */
-
-    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];
-    }
-
-    /* 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]));
-            }
-        }
-
-    /* test for convergence of the gradient norm. */
-
-    if (gnorm <= parameters.gtol)
-        return CosinusTooSmall;
-
-    /* rescale if necessary. */
-
-    if (mode != 2) /* Computing MAX */
-        diag = diag.cwise().max(wa2);
-
-    /* beginning of the inner loop. */
-    do {
-
-        /* determine the levenberg-marquardt parameter. */
-
-        ei_lmpar<Scalar>(fjac, ipvt, diag, qtf, delta, par, wa1, wa2);
-
-        /* store the direction p and x + p. calculate the norm of p. */
-
-        wa1 = -wa1;
-        wa2 = x + wa1;
-        wa3 = diag.cwise() * wa1;
-        pnorm = wa3.stableNorm();
-
-        /* on the first iteration, adjust the initial step bound. */
-
-        if (iter == 1)
-            delta = std::min(delta,pnorm);
-
-        /* evaluate the function at x + p and calculate its norm. */
-
-        if ( functor(wa2, wa4) < 0)
-            return UserAsked;
-        ++nfev;
-        fnorm1 = wa4.stableNorm();
-
-        /* compute the scaled actual reduction. */
-
-        actred = -1.;
-        if (Scalar(.1) * fnorm1 < fnorm) /* Computing 2nd power */
-            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;
-        }
-        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);
-
-        /* compute the ratio of the actual to the predicted */
-        /* reduction. */
-
-        ratio = 0.;
-        if (prered != 0.)
-            ratio = actred / prered;
-
-        /* update the step bound. */
-
-        if (ratio <= Scalar(.25)) {
-            if (actred >= 0.)
-                temp = Scalar(.5);
-            if (actred < 0.)
-                temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
-            if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
-                temp = Scalar(.1);
-            /* Computing MIN */
-            delta = temp * std::min(delta, pnorm / Scalar(.1));
-            par /= temp;
-        } else if (!(par != 0. && ratio < Scalar(.75))) {
-            delta = pnorm / Scalar(.5);
-            par = Scalar(.5) * par;
-        }
-
-        /* test for successful iteration. */
-
-        if (ratio >= Scalar(1e-4)) {
-            /* successful iteration. update x, fvec, and their norms. */
-            x = wa2;
-            wa2 = diag.cwise() * x;
-            fvec = wa4;
-            xnorm = wa2.stableNorm();
-            fnorm = fnorm1;
-            ++iter;
-        }
-
-        /* tests for convergence. */
-
-        if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
-            return RelativeErrorAndReductionTooSmall;
-        if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
-            return RelativeReductionTooSmall;
-        if (delta <= parameters.xtol * xnorm)
-            return RelativeErrorTooSmall;
-
-        /* tests for termination and stringent tolerances. */
-
-        if (nfev >= parameters.maxfev)
-            return TooManyFunctionEvaluation;
-        if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.)
-            return FtolTooSmall;
-        if (delta <= epsilon<Scalar>() * xnorm)
-            return XtolTooSmall;
-        if (gnorm <= epsilon<Scalar>())
-            return GtolTooSmall;
-        /* end of the inner loop. repeat if iteration unsuccessful. */
-    } while (ratio < Scalar(1e-4));
-    /* end of the outer loop. */
-    return Running;
-}
-
-template<typename FunctorType, typename Scalar>
-typename LevenbergMarquardt<FunctorType,Scalar>::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeNumericalDiff(
-        Matrix< Scalar, Dynamic, 1 >  &x,
-        const int mode
-        )
-{
-    Status status = minimizeNumericalDiffInit(x, mode);
-    while (status==Running)
-        status = minimizeNumericalDiffOneStep(x, mode);
-    return status;
-}
-
-
 template<typename FunctorType, typename Scalar>
 typename LevenbergMarquardt<FunctorType,Scalar>::Status
 LevenbergMarquardt<FunctorType,Scalar>::lmstr1(
@@ -966,4 +678,36 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(
     return status;
 }
 
+template<typename FunctorType, typename Scalar>
+typename LevenbergMarquardt<FunctorType,Scalar>::Status
+LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
+        FunctorType &functor,
+        Matrix< Scalar, Dynamic, 1 >  &x,
+        int *nfev,
+        const Scalar tol
+        )
+{
+    int n = x.size();
+    int m = functor.values();
+
+    /* check the input parameters for errors. */
+    if (n <= 0 || m < n || tol < 0.)
+        return ImproperInputParameters;
+
+    NumericalDiff<FunctorType> numDiff(functor);
+    // embedded LevenbergMarquardt
+    LevenbergMarquardt<NumericalDiff<FunctorType> > lm(numDiff);
+    lm.parameters.ftol = tol;
+    lm.parameters.xtol = tol;
+    lm.parameters.maxfev = 200*(n+1);
+
+    Status info = Status(lm.minimize(x));
+
+    if (nfev)
+        * nfev = lm.nfev;
+
+    return info;
+}
+
+
 

unsupported/test/NonLinear.cpp

@@ -524,8 +524,6 @@ struct lmdif_functor : Functor<double>
     lmdif_functor(void) : Functor<double>(3,15) {}
     int operator()(const VectorXd &x, VectorXd &fvec) const
     {
-        /* function fcn for lmdif1 example */
-
         int i;
         double tmp1,tmp2,tmp3;
         double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,
@@ -551,22 +549,23 @@ void testLmdif1()
   const int n=3;
   int info;
 
-  VectorXd x(n);
+  VectorXd x(n), fvec(15);
 
   /* the following starting values provide a rough fit. */
   x.setConstant(n, 1.);
 
   // do the computation
   lmdif_functor functor;
-  LevenbergMarquardt<lmdif_functor> lm(functor);
+  int nfev;
-  info = lm.lmdif1(x);
+  info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);
 
   // check return value
   VERIFY( 1 == info);
-  VERIFY(lm.nfev==21);
+  VERIFY(nfev==21);
 
   // check norm
-  VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
+  functor(x, fvec);
+  VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);
 
   // check x
   VectorXd x_ref(n);
@@ -587,8 +586,9 @@ void testLmdif()
 
   // do the computation
   lmdif_functor functor;
-  LevenbergMarquardt<lmdif_functor> lm(functor);
+  NumericalDiff<lmdif_functor> numDiff(functor);
-  info = lm.minimizeNumericalDiff(x);
+  LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);
+  info = lm.minimize(x);
 
   // check return values
   VERIFY( 1 == info);