Nothing
R/nleqslv-iterationreport.R
In nleqslv: Solve Systems of Nonlinear Equations
# DO NOT EDIT - use etc/nleqslv-iterationreport-creator.R
# Copyright (c) 2026 Rob Carnell
#' Detailed iteration report of nleqslv
#'
#' The format of the iteration report provided by nleqslv when the \code{trace}
#' component of the \code{control} argument has been set to 1.
#'
#' All iteration reports consist of a series of columns with a header
#' summarising the contents. Common column headers are \describe{
#' \item{\code{Iter}}{Iteration counter} \item{\code{Jac}}{Jacobian type. The
#' Jacobian type is indicated by \code{N} for a Newton Jacobian or \code{B} for
#' a Broyden updated matrix; optionally followed by the letter \code{s}
#' indicating a totally singular matrix or the letter \code{i} indicating an
#' ill-conditioned matrix. Unless the Jacobian is singular, the Jacobian type
#' is followed by an estimate of the inverse condition number of the Jacobian
#' in parentheses as computed by Lapack. This column will be blank when
#' backtracking is active.} \item{\code{Fnorm}}{square of the euclidean norm
#' of function values / 2} \item{\code{Largest |f|}}{infinity norm of
#' \eqn{f(x)}{f(x)} at the current point} }
#'
#' @aliases Iteration-report
#'
#' @section Report for linesearch methods: A sample iteration report for the
#' linesearch global methods (\code{cline}, \code{qline} and \code{gline}) is
#' (some intercolumn space has been removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac Lambda Ftarg Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) 1.0000 2.886235e+00 5.787362e+05 1.070841e+03
#' 1 0.1000 2.886754e+00 9.857947e+00 3.214799e+00
#' 1 0.0100 2.886806e+00 2.866321e+00 2.237878e+00
#' 2 B(2.2e-02) 1.0000 2.865748e+00 4.541965e+03 9.341610e+01
#' 2 0.1000 2.866264e+00 3.253536e+00 2.242344e+00
#' 2 0.0298 2.866304e+00 2.805872e+00 2.200544e+00
#' 3 B(5.5e-02) 1.0000 2.805311e+00 2.919089e+01 7.073082e+00
#' 3 0.1000 2.805816e+00 2.437606e+00 2.027297e+00
#' 4 B(1.0e-01) 1.0000 2.437118e+00 9.839802e-01 1.142529e+00
#' 5 B(1.9e-01) 1.0000 9.837834e-01 7.263320e-02 3.785249e-01
#' 6 B(2.2e-01) 1.0000 7.261868e-02 1.581364e-02 1.774419e-01
#' 7 B(1.5e-01) 1.0000 1.581047e-02 9.328284e-03 1.213052e-01
#' 8 B(1.7e-01) 1.0000 9.326419e-03 1.003283e-04 1.400491e-02
#' 9 B(1.9e-01) 1.0000 1.003082e-04 3.072159e-06 2.206943e-03
#' 10 B(1.5e-01) 1.0000 3.071544e-06 1.143217e-07 4.757203e-04
#' 11 B(1.3e-01) 1.0000 1.142989e-07 1.144686e-09 4.783197e-05
#' 12 B(1.2e-01) 1.0000 1.144457e-09 4.515245e-13 9.502884e-07
#' 13 B(1.2e-01) 1.0000 4.514342e-13 1.404463e-17 5.299876e-09
#' }
#'
#' The column headed
#' by \code{Lambda} shows the value of the line search parameter. The column
#' headed by \code{Ftarg} follows from a sufficient decrease requirement and is
#' the value below which \code{Fnorm} must drop if the current step is to be
#' accepted.
#'
#' The value of \code{Lambda} may not be lower than a threshold determined by
#' the setting of control parameter \code{xtol} to avoid reporting false
#' convergence. When no acceptable \code{Lambda} is possible and the Broyden
#' method is being used, a new Jacobian will be computed.
#' @section Report for the pure method: The iteration report for the global
#' method \code{none} is almost the same as the above report, except that the
#' column labelled \code{Ftarg} is omitted. The column \code{Lambda} gives the
#' ratio of the maximum stepsize and the length of the full Newton step. It is
#' either exactly 1.0, indicating that the Newton step is smaller than the
#' maximum stepsize and therefore used unmodified, or smaller than 1.0,
#' indicating that the Newton step is larger than the maximum stepsize and
#' therefore truncated.
#'
#' @section Report for the double dogleg global method: A sample iteration
#' report for the global method \code{dbldog} is (some intercolumn space has
#' been removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac Lambda Eta Dlt0 Dltn Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) C 0.9544 0.4671 0.9343* 1.699715e-01 5.421673e-01
#' 1 W 0.0833 0.9544 0.9343 0.4671 1.699715e-01 5.421673e-01
#' 2 B(1.1e-02) W 0.1154 0.4851 0.4671 0.4671 1.277667e-01 5.043571e-01
#' 3 B(7.3e-02) W 0.7879 0.7289 0.4671 0.0759 5.067893e-01 7.973542e-01
#' 3 C 0.7289 0.0759 0.1519 5.440250e-02 2.726084e-01
#' 4 B(8.3e-02) W 0.5307 0.3271 0.1519 0.3037 3.576547e-02 2.657553e-01
#' 5 B(1.8e-01) N 0.6674 0.2191 0.4383 6.566182e-03 8.555110e-02
#' 6 B(1.8e-01) N 0.9801 0.0376 0.0752 4.921645e-04 3.094104e-02
#' 7 B(1.9e-01) N 0.7981 0.0157 0.0313 4.960629e-06 2.826064e-03
#' 8 B(1.6e-01) N 0.3942 0.0029 0.0058 1.545503e-08 1.757498e-04
#' 9 B(1.5e-01) N 0.6536 0.0001 0.0003 2.968676e-11 5.983765e-06
#' 10 B(1.5e-01) N 0.4730 0.0000 0.0000 4.741792e-14 2.198380e-07
#' 11 B(1.5e-01) N 0.9787 0.0000 0.0000 6.451792e-19 8.118586e-10
#' }
#'
#' After the column for the Jacobian the letters indicate the following
#' \describe{ \item{\code{C}}{a fraction (\eqn{\le1.0}{<=1.0}) of the Cauchy
#' or steepest descent step is taken where the fraction is the ratio of the
#' trust region radius and the Cauchy steplength.} \item{\code{W}}{a convex
#' combination of the Cauchy and \code{eta}*(Newton step) is taken. The number
#' in the column headed by \code{Lambda} is the weight of the partial Newton
#' step.} \item{\code{P}}{a fraction (\eqn{\ge1.0}{>=1.0}) of the partial
#' Newton step, equal to \code{eta}*(Newton step), is taken where the fraction
#' is the ratio of the trust region radius and the partial Newton steplength.}
#' \item{\code{N}}{a normal full Newton step is taken.} } The number in the
#' column headed by \code{Eta} is calculated from an upper limit on the ratio
#' of the length of the steepest descent direction and the length of the Newton
#' step. See Dennis and Schnabel (1996) pp.139ff for the details. The column
#' headed by \code{Dlt0} gives the trust region size at the start of the
#' current iteration. The column headed by \code{Dltn} gives the trust region
#' size when the current step has been accepted by the dogleg algorithm.
#'
#' The trust region size is decreased when the actual reduction of the function
#' value norm does not agree well with the predicted reduction from the linear
#' approximation of the function or does not exhibit sufficient decrease. And
#' increased when the actual and predicted reduction are sufficiently close.
#' The trust region size is not allowed to decrease beyond a threshold
#' determined by the setting of control parameter \code{xtol}; when that
#' happens the backtracking is regarded as a failure and is terminated. In that
#' case a new Jacobian will be calculated if the Broyden method is being used.
#'
#' The current trust region step is continued with a doubled trust region size
#' when the actual and predicted reduction agree extremely well. This is
#' indicated by \code{*} immediately following the value in the column headed
#' by \code{Dltn}. This could save gradient calculations. However, a trial step
#' is never taken if the current step is a Newton step. If the trial step does
#' not succeed then the previous trust region size is restored by halving the
#' trial size. The exception is when a trial step takes a Newton step. In that
#' case the trust region size is immediately set to the size of the Newton step
#' which implies that a halving of the new size leads to a smaller size for the
#' trust region than before.
#'
#' Normally the initial trust region radius is the same as the final trust
#' region radius of the previous iteration but the trust region size is
#' restricted by the size of the current Newton step. So when full Newton steps
#' are being taken, the trust region radius at the start of an iteration may be
#' less than the final value of the previous iteration. The double dogleg
#' method and the trust region updating procedure are fully explained in
#' sections 6.4.2 and 6.4.3 of Dennis and Schnabel (1996).
#'
#' @section Report for the single (Powell) dogleg global method: A sample
#' iteration report for the global method \code{pwldog} is (some intercolumn
#' space has been removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac Lambda Dlt0 Dltn Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) C 0.4671 0.9343* 1.699715e-01 5.421673e-01
#' 1 W 0.0794 0.9343 0.4671 1.699715e-01 5.421673e-01
#' 2 B(1.1e-02) W 0.0559 0.4671 0.4671 1.205661e-01 4.890487e-01
#' 3 B(7.3e-02) W 0.5662 0.4671 0.0960 4.119560e-01 7.254441e-01
#' 3 W 0.0237 0.0960 0.1921 4.426507e-02 2.139252e-01
#' 4 B(8.8e-02) W 0.2306 0.1921 0.3842* 2.303135e-02 2.143943e-01
#' 4 W 0.4769 0.3842 0.1921 2.303135e-02 2.143943e-01
#' 5 B(1.9e-01) N 0.1375 0.2750 8.014508e-04 3.681498e-02
#' 6 B(1.7e-01) N 0.0162 0.0325 1.355741e-05 5.084627e-03
#' 7 B(1.3e-01) N 0.0070 0.0035 1.282776e-05 4.920962e-03
#' 8 B(1.8e-01) N 0.0028 0.0056 3.678140e-08 2.643592e-04
#' 9 B(1.9e-01) N 0.0001 0.0003 1.689182e-12 1.747622e-06
#' 10 B(1.9e-01) N 0.0000 0.0000 9.568768e-16 4.288618e-08
#' 11 B(1.9e-01) N 0.0000 0.0000 1.051356e-18 1.422035e-09
#' }
#'
#' This is much simpler
#' than the double dogleg report, since the single dogleg takes either a
#' steepest descent step, a convex combination of the steepest descent and
#' Newton steps or a full Newton step. The number in the column \code{Lambda}
#' is the weight of the Newton step. The single dogleg method is a special case
#' of the double dogleg method with \code{eta} equal to 1. It uses the same
#' method of updating the trust region size as the double dogleg method.
#'
#' @section Report for the hook step global method: A sample iteration report
#' for the global method \code{hook} is (some intercolumn space has been
#' removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac mu dnorm Dlt0 Dltn Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) H 0.1968 0.4909 0.4671 0.9343* 1.806293e-01 5.749418e-01
#' 1 H 0.0366 0.9381 0.9343 0.4671 1.806293e-01 5.749418e-01
#' 2 B(2.5e-02) H 0.1101 0.4745 0.4671 0.2336 1.797759e-01 5.635028e-01
#' 3 B(1.4e-01) H 0.0264 0.2341 0.2336 0.4671 3.768809e-02 2.063234e-01
#' 4 B(1.6e-01) N 0.0819 0.0819 0.1637 3.002274e-03 7.736213e-02
#' 5 B(1.8e-01) N 0.0513 0.0513 0.1025 5.355533e-05 1.018879e-02
#' 6 B(1.5e-01) N 0.0090 0.0090 0.0179 1.357039e-06 1.224357e-03
#' 7 B(1.5e-01) N 0.0004 0.0004 0.0008 1.846111e-09 6.070166e-05
#' 8 B(1.4e-01) N 0.0000 0.0000 0.0001 3.292896e-12 2.555851e-06
#' 9 B(1.5e-01) N 0.0000 0.0000 0.0000 7.281583e-18 3.800552e-09
#' }
#'
#' The column headed by \code{mu} shows the
#' Levenberg-Marquardt parameter when the Newton step is larger than the trust
#' region radius. The column headed by \code{dnorm} gives the Euclidean norm of
#' the step (adjustment of the current \code{x}) taken by the algorithm. The
#' absolute value of the difference with \code{Dlt0} is less than 0.1 times the
#' trust region radius.
#'
#' After the column for the Jacobian the letters indicate the following
#' \describe{ \item{\code{H}}{a Levenberg-Marquardt restricted step is taken.}
#' \item{\code{N}}{a normal full Newton step is taken.} } The meaning of the
#' columns headed by \code{Dlt0} and \code{Dltn} is identical to that of the
#' same columns for the double dogleg method. The method of updating the trust
#' region size is the same as in the double dogleg method.
#'
#' @seealso \code{\link{nleqslv}}
#' @name nleqslv-iterationreport
#'
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# DO NOT EDIT - use etc/nleqslv-iterationreport-creator.R
# Copyright (c) 2026 Rob Carnell
#' Detailed iteration report of nleqslv
#'
#' The format of the iteration report provided by nleqslv when the \code{trace}
#' component of the \code{control} argument has been set to 1.
#'
#' All iteration reports consist of a series of columns with a header
#' summarising the contents. Common column headers are \describe{
#' \item{\code{Iter}}{Iteration counter} \item{\code{Jac}}{Jacobian type. The
#' Jacobian type is indicated by \code{N} for a Newton Jacobian or \code{B} for
#' a Broyden updated matrix; optionally followed by the letter \code{s}
#' indicating a totally singular matrix or the letter \code{i} indicating an
#' ill-conditioned matrix. Unless the Jacobian is singular, the Jacobian type
#' is followed by an estimate of the inverse condition number of the Jacobian
#' in parentheses as computed by Lapack. This column will be blank when
#' backtracking is active.} \item{\code{Fnorm}}{square of the euclidean norm
#' of function values / 2} \item{\code{Largest |f|}}{infinity norm of
#' \eqn{f(x)}{f(x)} at the current point} }
#'
#' @aliases Iteration-report
#'
#' @section Report for linesearch methods: A sample iteration report for the
#' linesearch global methods (\code{cline}, \code{qline} and \code{gline}) is
#' (some intercolumn space has been removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac Lambda Ftarg Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) 1.0000 2.886235e+00 5.787362e+05 1.070841e+03
#' 1 0.1000 2.886754e+00 9.857947e+00 3.214799e+00
#' 1 0.0100 2.886806e+00 2.866321e+00 2.237878e+00
#' 2 B(2.2e-02) 1.0000 2.865748e+00 4.541965e+03 9.341610e+01
#' 2 0.1000 2.866264e+00 3.253536e+00 2.242344e+00
#' 2 0.0298 2.866304e+00 2.805872e+00 2.200544e+00
#' 3 B(5.5e-02) 1.0000 2.805311e+00 2.919089e+01 7.073082e+00
#' 3 0.1000 2.805816e+00 2.437606e+00 2.027297e+00
#' 4 B(1.0e-01) 1.0000 2.437118e+00 9.839802e-01 1.142529e+00
#' 5 B(1.9e-01) 1.0000 9.837834e-01 7.263320e-02 3.785249e-01
#' 6 B(2.2e-01) 1.0000 7.261868e-02 1.581364e-02 1.774419e-01
#' 7 B(1.5e-01) 1.0000 1.581047e-02 9.328284e-03 1.213052e-01
#' 8 B(1.7e-01) 1.0000 9.326419e-03 1.003283e-04 1.400491e-02
#' 9 B(1.9e-01) 1.0000 1.003082e-04 3.072159e-06 2.206943e-03
#' 10 B(1.5e-01) 1.0000 3.071544e-06 1.143217e-07 4.757203e-04
#' 11 B(1.3e-01) 1.0000 1.142989e-07 1.144686e-09 4.783197e-05
#' 12 B(1.2e-01) 1.0000 1.144457e-09 4.515245e-13 9.502884e-07
#' 13 B(1.2e-01) 1.0000 4.514342e-13 1.404463e-17 5.299876e-09
#' }
#'
#' The column headed
#' by \code{Lambda} shows the value of the line search parameter. The column
#' headed by \code{Ftarg} follows from a sufficient decrease requirement and is
#' the value below which \code{Fnorm} must drop if the current step is to be
#' accepted.
#'
#' The value of \code{Lambda} may not be lower than a threshold determined by
#' the setting of control parameter \code{xtol} to avoid reporting false
#' convergence. When no acceptable \code{Lambda} is possible and the Broyden
#' method is being used, a new Jacobian will be computed.
#' @section Report for the pure method: The iteration report for the global
#' method \code{none} is almost the same as the above report, except that the
#' column labelled \code{Ftarg} is omitted. The column \code{Lambda} gives the
#' ratio of the maximum stepsize and the length of the full Newton step. It is
#' either exactly 1.0, indicating that the Newton step is smaller than the
#' maximum stepsize and therefore used unmodified, or smaller than 1.0,
#' indicating that the Newton step is larger than the maximum stepsize and
#' therefore truncated.
#'
#' @section Report for the double dogleg global method: A sample iteration
#' report for the global method \code{dbldog} is (some intercolumn space has
#' been removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac Lambda Eta Dlt0 Dltn Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) C 0.9544 0.4671 0.9343* 1.699715e-01 5.421673e-01
#' 1 W 0.0833 0.9544 0.9343 0.4671 1.699715e-01 5.421673e-01
#' 2 B(1.1e-02) W 0.1154 0.4851 0.4671 0.4671 1.277667e-01 5.043571e-01
#' 3 B(7.3e-02) W 0.7879 0.7289 0.4671 0.0759 5.067893e-01 7.973542e-01
#' 3 C 0.7289 0.0759 0.1519 5.440250e-02 2.726084e-01
#' 4 B(8.3e-02) W 0.5307 0.3271 0.1519 0.3037 3.576547e-02 2.657553e-01
#' 5 B(1.8e-01) N 0.6674 0.2191 0.4383 6.566182e-03 8.555110e-02
#' 6 B(1.8e-01) N 0.9801 0.0376 0.0752 4.921645e-04 3.094104e-02
#' 7 B(1.9e-01) N 0.7981 0.0157 0.0313 4.960629e-06 2.826064e-03
#' 8 B(1.6e-01) N 0.3942 0.0029 0.0058 1.545503e-08 1.757498e-04
#' 9 B(1.5e-01) N 0.6536 0.0001 0.0003 2.968676e-11 5.983765e-06
#' 10 B(1.5e-01) N 0.4730 0.0000 0.0000 4.741792e-14 2.198380e-07
#' 11 B(1.5e-01) N 0.9787 0.0000 0.0000 6.451792e-19 8.118586e-10
#' }
#'
#' After the column for the Jacobian the letters indicate the following
#' \describe{ \item{\code{C}}{a fraction (\eqn{\le1.0}{<=1.0}) of the Cauchy
#' or steepest descent step is taken where the fraction is the ratio of the
#' trust region radius and the Cauchy steplength.} \item{\code{W}}{a convex
#' combination of the Cauchy and \code{eta}*(Newton step) is taken. The number
#' in the column headed by \code{Lambda} is the weight of the partial Newton
#' step.} \item{\code{P}}{a fraction (\eqn{\ge1.0}{>=1.0}) of the partial
#' Newton step, equal to \code{eta}*(Newton step), is taken where the fraction
#' is the ratio of the trust region radius and the partial Newton steplength.}
#' \item{\code{N}}{a normal full Newton step is taken.} } The number in the
#' column headed by \code{Eta} is calculated from an upper limit on the ratio
#' of the length of the steepest descent direction and the length of the Newton
#' step. See Dennis and Schnabel (1996) pp.139ff for the details. The column
#' headed by \code{Dlt0} gives the trust region size at the start of the
#' current iteration. The column headed by \code{Dltn} gives the trust region
#' size when the current step has been accepted by the dogleg algorithm.
#'
#' The trust region size is decreased when the actual reduction of the function
#' value norm does not agree well with the predicted reduction from the linear
#' approximation of the function or does not exhibit sufficient decrease. And
#' increased when the actual and predicted reduction are sufficiently close.
#' The trust region size is not allowed to decrease beyond a threshold
#' determined by the setting of control parameter \code{xtol}; when that
#' happens the backtracking is regarded as a failure and is terminated. In that
#' case a new Jacobian will be calculated if the Broyden method is being used.
#'
#' The current trust region step is continued with a doubled trust region size
#' when the actual and predicted reduction agree extremely well. This is
#' indicated by \code{*} immediately following the value in the column headed
#' by \code{Dltn}. This could save gradient calculations. However, a trial step
#' is never taken if the current step is a Newton step. If the trial step does
#' not succeed then the previous trust region size is restored by halving the
#' trial size. The exception is when a trial step takes a Newton step. In that
#' case the trust region size is immediately set to the size of the Newton step
#' which implies that a halving of the new size leads to a smaller size for the
#' trust region than before.
#'
#' Normally the initial trust region radius is the same as the final trust
#' region radius of the previous iteration but the trust region size is
#' restricted by the size of the current Newton step. So when full Newton steps
#' are being taken, the trust region radius at the start of an iteration may be
#' less than the final value of the previous iteration. The double dogleg
#' method and the trust region updating procedure are fully explained in
#' sections 6.4.2 and 6.4.3 of Dennis and Schnabel (1996).
#'
#' @section Report for the single (Powell) dogleg global method: A sample
#' iteration report for the global method \code{pwldog} is (some intercolumn
#' space has been removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac Lambda Dlt0 Dltn Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) C 0.4671 0.9343* 1.699715e-01 5.421673e-01
#' 1 W 0.0794 0.9343 0.4671 1.699715e-01 5.421673e-01
#' 2 B(1.1e-02) W 0.0559 0.4671 0.4671 1.205661e-01 4.890487e-01
#' 3 B(7.3e-02) W 0.5662 0.4671 0.0960 4.119560e-01 7.254441e-01
#' 3 W 0.0237 0.0960 0.1921 4.426507e-02 2.139252e-01
#' 4 B(8.8e-02) W 0.2306 0.1921 0.3842* 2.303135e-02 2.143943e-01
#' 4 W 0.4769 0.3842 0.1921 2.303135e-02 2.143943e-01
#' 5 B(1.9e-01) N 0.1375 0.2750 8.014508e-04 3.681498e-02
#' 6 B(1.7e-01) N 0.0162 0.0325 1.355741e-05 5.084627e-03
#' 7 B(1.3e-01) N 0.0070 0.0035 1.282776e-05 4.920962e-03
#' 8 B(1.8e-01) N 0.0028 0.0056 3.678140e-08 2.643592e-04
#' 9 B(1.9e-01) N 0.0001 0.0003 1.689182e-12 1.747622e-06
#' 10 B(1.9e-01) N 0.0000 0.0000 9.568768e-16 4.288618e-08
#' 11 B(1.9e-01) N 0.0000 0.0000 1.051356e-18 1.422035e-09
#' }
#'
#' This is much simpler
#' than the double dogleg report, since the single dogleg takes either a
#' steepest descent step, a convex combination of the steepest descent and
#' Newton steps or a full Newton step. The number in the column \code{Lambda}
#' is the weight of the Newton step. The single dogleg method is a special case
#' of the double dogleg method with \code{eta} equal to 1. It uses the same
#' method of updating the trust region size as the double dogleg method.
#'
#' @section Report for the hook step global method: A sample iteration report
#' for the global method \code{hook} is (some intercolumn space has been
#' removed to make the table fit)
#'
#' \preformatted{
#' Iter Jac mu dnorm Dlt0 Dltn Fnorm Largest |f|
#' 0 2.886812e+00 2.250000e+00
#' 1 N(9.6e-03) H 0.1968 0.4909 0.4671 0.9343* 1.806293e-01 5.749418e-01
#' 1 H 0.0366 0.9381 0.9343 0.4671 1.806293e-01 5.749418e-01
#' 2 B(2.5e-02) H 0.1101 0.4745 0.4671 0.2336 1.797759e-01 5.635028e-01
#' 3 B(1.4e-01) H 0.0264 0.2341 0.2336 0.4671 3.768809e-02 2.063234e-01
#' 4 B(1.6e-01) N 0.0819 0.0819 0.1637 3.002274e-03 7.736213e-02
#' 5 B(1.8e-01) N 0.0513 0.0513 0.1025 5.355533e-05 1.018879e-02
#' 6 B(1.5e-01) N 0.0090 0.0090 0.0179 1.357039e-06 1.224357e-03
#' 7 B(1.5e-01) N 0.0004 0.0004 0.0008 1.846111e-09 6.070166e-05
#' 8 B(1.4e-01) N 0.0000 0.0000 0.0001 3.292896e-12 2.555851e-06
#' 9 B(1.5e-01) N 0.0000 0.0000 0.0000 7.281583e-18 3.800552e-09
#' }
#'
#' The column headed by \code{mu} shows the
#' Levenberg-Marquardt parameter when the Newton step is larger than the trust
#' region radius. The column headed by \code{dnorm} gives the Euclidean norm of
#' the step (adjustment of the current \code{x}) taken by the algorithm. The
#' absolute value of the difference with \code{Dlt0} is less than 0.1 times the
#' trust region radius.
#'
#' After the column for the Jacobian the letters indicate the following
#' \describe{ \item{\code{H}}{a Levenberg-Marquardt restricted step is taken.}
#' \item{\code{N}}{a normal full Newton step is taken.} } The meaning of the
#' columns headed by \code{Dlt0} and \code{Dltn} is identical to that of the
#' same columns for the double dogleg method. The method of updating the trust
#' region size is the same as in the double dogleg method.
#'
#' @seealso \code{\link{nleqslv}}
#' @name nleqslv-iterationreport
#'
NULL
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