| |
| template<typename Functor, typename Scalar> |
| int ei_lmstr( |
| Matrix< Scalar, Dynamic, 1 > &x, |
| Matrix< Scalar, Dynamic, 1 > &fvec, |
| int &nfev, |
| int &njev, |
| Matrix< Scalar, Dynamic, Dynamic > &fjac, |
| VectorXi &ipvt, |
| Matrix< Scalar, Dynamic, 1 > &diag, |
| int mode=1, |
| Scalar factor = 100., |
| int maxfev = 400, |
| Scalar ftol = ei_sqrt(epsilon<Scalar>()), |
| Scalar xtol = ei_sqrt(epsilon<Scalar>()), |
| Scalar gtol = Scalar(0.), |
| int nprint=0 |
| ) |
| { |
| const int m = fvec.size(), n = x.size(); |
| Matrix< Scalar, Dynamic, 1 > |
| qtf(n), |
| wa1(n), wa2(n), wa3(n), |
| wa4(m); |
| int ldfjac = m; |
| |
| ipvt.resize(n); |
| fjac.resize(ldfjac, n); |
| diag.resize(n); |
| |
| /* Local variables */ |
| int i, j, l; |
| Scalar par, sum; |
| int sing; |
| int iter; |
| Scalar temp, temp1, temp2; |
| int iflag; |
| Scalar delta; |
| Scalar ratio; |
| Scalar fnorm, gnorm, pnorm, xnorm, fnorm1, actred, dirder, prered; |
| int info; |
| |
| /* Function Body */ |
| info = 0; |
| iflag = 0; |
| nfev = 0; |
| njev = 0; |
| |
| /* check the input parameters for errors. */ |
| |
| if (n <= 0 || m < n || ldfjac < n || ftol < 0. || xtol < 0. || |
| gtol < 0. || maxfev <= 0 || factor <= 0.) { |
| goto L340; |
| } |
| if (mode != 2) { |
| goto L20; |
| } |
| for (j = 0; j < n; ++j) { |
| if (diag[j] <= 0.) { |
| goto L340; |
| } |
| /* L10: */ |
| } |
| L20: |
| |
| /* evaluate the function at the starting point */ |
| /* and calculate its norm. */ |
| |
| iflag = Functor::f(x, fvec); |
| nfev = 1; |
| if (iflag < 0) { |
| goto L340; |
| } |
| fnorm = fvec.stableNorm();; |
| |
| /* initialize levenberg-marquardt parameter and iteration counter. */ |
| |
| par = 0.; |
| iter = 1; |
| |
| /* beginning of the outer loop. */ |
| |
| L30: |
| |
| /* if requested, call Functor::f to enable printing of iterates. */ |
| |
| if (nprint <= 0) { |
| goto L40; |
| } |
| iflag = 0; |
| if ((iter - 1) % nprint == 0) { |
| iflag = Functor::debug(x, fvec, wa3); |
| } |
| if (iflag < 0) { |
| goto L340; |
| } |
| L40: |
| |
| /* compute the qr factorization of the jacobian matrix */ |
| /* calculated one row at a time, while simultaneously */ |
| /* forming (q transpose)*fvec and storing the first */ |
| /* n components in qtf. */ |
| |
| for (j = 0; j < n; ++j) { |
| qtf[j] = 0.; |
| for (i = 0; i < n; ++i) { |
| fjac(i,j) = 0.; |
| /* L50: */ |
| } |
| /* L60: */ |
| } |
| iflag = 2; |
| for (i = 0; i < m; ++i) { |
| if (Functor::df(x, wa3, iflag) < 0) { |
| goto L340; |
| } |
| temp = fvec[i]; |
| ei_rwupdt<Scalar>(n, fjac.data(), ldfjac, wa3.data(), qtf.data(), &temp, wa1.data(), wa2.data()); |
| ++iflag; |
| /* L70: */ |
| } |
| ++njev; |
| |
| /* if the jacobian is rank deficient, call qrfac to */ |
| /* reorder its columns and update the components of qtf. */ |
| |
| sing = false; |
| for (j = 0; j < n; ++j) { |
| if (fjac(j,j) == 0.) { |
| sing = true; |
| } |
| ipvt[j] = j; |
| wa2[j] = fjac.col(j).start(j).stableNorm(); |
| // wa2[j] = ei_enorm<Scalar>(j, &fjac[j * ldfjac + 1]); |
| // sum += fjac[i + j * ldfjac] * (qtf[i] / fnorm); |
| /* L80: */ |
| } |
| if (! sing) { |
| goto L130; |
| } |
| ipvt.cwise()+=1; |
| ei_qrfac<Scalar>(n, n, fjac.data(), ldfjac, true, ipvt.data(), n, wa1.data(), wa2.data(), wa3.data()); |
| ipvt.cwise()-=1; // qrfac() creates ipvt with fortran convetion (1->n), convert it to c (0->n-1) |
| for (j = 0; j < n; ++j) { |
| if (fjac(j,j) == 0.) { |
| goto L110; |
| } |
| sum = 0.; |
| for (i = j; i < n; ++i) { |
| sum += fjac(i,j) * qtf[i]; |
| /* L90: */ |
| } |
| temp = -sum / fjac(j,j); |
| for (i = j; i < n; ++i) { |
| qtf[i] += fjac(i,j) * temp; |
| /* L100: */ |
| } |
| L110: |
| fjac(j,j) = wa1[j]; |
| /* L120: */ |
| } |
| L130: |
| |
| /* on the first iteration and if mode is 1, scale according */ |
| /* to the norms of the columns of the initial jacobian. */ |
| |
| if (iter != 1) { |
| goto L170; |
| } |
| if (mode == 2) { |
| goto L150; |
| } |
| for (j = 0; j < n; ++j) { |
| diag[j] = wa2[j]; |
| if (wa2[j] == 0.) { |
| diag[j] = 1.; |
| } |
| /* L140: */ |
| } |
| L150: |
| |
| /* on the first iteration, calculate the norm of the scaled x */ |
| /* and initialize the step bound delta. */ |
| |
| for (j = 0; j < n; ++j) { |
| wa3[j] = diag[j] * x[j]; |
| /* L160: */ |
| } |
| xnorm = wa3.stableNorm(); |
| delta = factor * xnorm; |
| if (delta == 0.) { |
| delta = factor; |
| } |
| L170: |
| |
| /* compute the norm of the scaled gradient. */ |
| |
| gnorm = 0.; |
| if (fnorm == 0.) { |
| goto L210; |
| } |
| for (j = 0; j < n; ++j) { |
| l = ipvt[j]; |
| if (wa2[l] == 0.) { |
| goto L190; |
| } |
| sum = 0.; |
| for (i = 0; i < j; ++i) { |
| sum += fjac(i,j) * (qtf[i] / fnorm); |
| /* L180: */ |
| } |
| /* Computing MAX */ |
| gnorm = std::max(gnorm, ei_abs(sum/wa2[l])); |
| L190: |
| /* L200: */ |
| ; |
| } |
| L210: |
| |
| /* test for convergence of the gradient norm. */ |
| |
| if (gnorm <= gtol) { |
| info = 4; |
| } |
| if (info != 0) { |
| goto L340; |
| } |
| |
| /* rescale if necessary. */ |
| |
| if (mode == 2) { |
| goto L230; |
| } |
| for (j = 0; j < n; ++j) /* Computing MAX */ |
| diag[j] = std::max(diag[j], wa2[j]); |
| L230: |
| |
| /* beginning of the inner loop. */ |
| |
| L240: |
| |
| /* determine the levenberg-marquardt parameter. */ |
| |
| ipvt.cwise()+=1; // lmpar() expects the fortran convention (as qrfac provides) |
| ei_lmpar<Scalar>(n, fjac.data(), ldfjac, ipvt.data(), diag.data(), qtf.data(), delta, par, |
| wa1.data(), wa2.data(), wa3.data(), wa4.data()); |
| ipvt.cwise()-=1; |
| |
| /* store the direction p and x + p. calculate the norm of p. */ |
| |
| for (j = 0; j < n; ++j) { |
| wa1[j] = -wa1[j]; |
| wa2[j] = x[j] + wa1[j]; |
| wa3[j] = diag[j] * wa1[j]; |
| /* L250: */ |
| } |
| 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. */ |
| |
| iflag = Functor::f(wa2, wa4); |
| ++nfev; |
| if (iflag < 0) { |
| goto L340; |
| } |
| 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. */ |
| |
| for (j = 0; j < n; ++j) { |
| wa3[j] = 0.; |
| l = ipvt[j]; |
| temp = wa1[l]; |
| for (i = 0; i <= j; ++i) { |
| wa3[i] += fjac(i,j) * temp; |
| /* L260: */ |
| } |
| /* L270: */ |
| } |
| 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)) { |
| goto L280; |
| } |
| 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; |
| goto L300; |
| L280: |
| if (par != 0. && ratio < Scalar(.75)) { |
| goto L290; |
| } |
| delta = pnorm / Scalar(.5); |
| par = Scalar(.5) * par; |
| L290: |
| L300: |
| |
| /* test for successful iteration. */ |
| |
| if (ratio < Scalar(1e-4)) { |
| goto L330; |
| } |
| |
| /* successful iteration. update x, fvec, and their norms. */ |
| |
| for (j = 0; j < n; ++j) { |
| x[j] = wa2[j]; |
| wa2[j] = diag[j] * x[j]; |
| /* L310: */ |
| } |
| for (i = 0; i < m; ++i) { |
| fvec[i] = wa4[i]; |
| /* L320: */ |
| } |
| xnorm = wa2.stableNorm(); |
| fnorm = fnorm1; |
| ++iter; |
| L330: |
| |
| /* tests for convergence. */ |
| |
| if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1.) { |
| info = 1; |
| } |
| if (delta <= xtol * xnorm) { |
| info = 2; |
| } |
| if (ei_abs(actred) <= ftol && prered <= ftol && Scalar(.5) * ratio <= 1. && info |
| == 2) { |
| info = 3; |
| } |
| if (info != 0) { |
| goto L340; |
| } |
| |
| /* tests for termination and stringent tolerances. */ |
| |
| if (nfev >= maxfev) { |
| info = 5; |
| } |
| if (ei_abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && Scalar(.5) * ratio <= 1.) { |
| info = 6; |
| } |
| if (delta <= epsilon<Scalar>() * xnorm) { |
| info = 7; |
| } |
| if (gnorm <= epsilon<Scalar>()) { |
| info = 8; |
| } |
| if (info != 0) { |
| goto L340; |
| } |
| |
| /* end of the inner loop. repeat if iteration unsuccessful. */ |
| |
| if (ratio < Scalar(1e-4)) { |
| goto L240; |
| } |
| |
| /* end of the outer loop. */ |
| |
| goto L30; |
| L340: |
| |
| /* termination, either normal or user imposed. */ |
| |
| if (iflag < 0) { |
| info = iflag; |
| } |
| iflag = 0; |
| if (nprint > 0) { |
| iflag = Functor::debug(x, fvec, wa3); |
| } |
| return info; |
| |
| /* last card of subroutine lmstr. */ |
| |
| } /* lmstr_ */ |
| |
