nleqslv-iterationreport {nleqslv} | R Documentation |
The format of the iteration report
provided by nleqslv when the trace
component of the control parameter
has been set to 1.
All iteration reports consist of a series of columns with a header summarising the contents. Common column headers are
Iter
Jac
N
for a Newton jacobian
or B
for a Broyden updated matrix; optionally followed by the letter s
indicating a totally singular matrix or the letter i
indicating an ill-conditioned matrix.
This is followed by a number in parentheses, indicating the inverse condition number of the matrix or
the correction factor mu applied to make J'J+mu S'S
not singular, where S is the
diagonal scaling matrix consisting of the scaling factor for the x
-values.
This column will be blank when backtracking is active.Fnorm
Largest |f|
A sample iteration report for qline
is
(some intercolumn space has been removed to make the table fit)
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+01The column headed by
Lambda
shows the value of the linesearch parameter.
The column headed by Ftarg
follows from a sufficient decrease requirement and
is the value below which Fnorm
must drop if the current step is to be accepted.
A sample iteration report for dbldog
is
(some intercolumn space and the final column with header Largest |f|
have been removed to make the table fit)
Iter Jac Lambda Gamma Eta Dlt0 Dltn Fnorm 0 2.886812e+00 1 N(9.6e-03) C 0.9430 0.9544 0.4671 0.9343 1.699715e-01 1 W 0.0833 0.9430 0.9544 0.9343 0.4671 1.699715e-01 2 B(1.1e-02) W 0.1154 0.3564 0.4851 0.4671 0.4671 1.277667e-01 3 B(7.3e-02) W 0.7879 0.6611 0.7289 0.4671 0.0759 5.067893e-01 3 C 0.6611 0.7289 0.0759 0.1519 5.440250e-02 4 B(8.3e-02) W 0.5307 0.1588 0.3271 0.1519 0.3037 3.576547e-02 5 B(1.8e-01) N 0.5843 0.6674 0.2191 0.4383 6.566182e-03
After the column for the jacobian the letters indicate the following
C
W
eta
*Newton step is taken.
The number in the column headed by Lambda
is the weight of the partial
Newton step.P
Eta
is the fraction and is calculated as 0.8*gamma+0.2
.N
The number in the column headed by Gamma
is an upper limit on the ratio
of the length 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 Dlt0
gives the size of the trust region at the start of the current
iteration.
The column headed by Dltn
gives the size of the trust region when the current
step has been accepted by the dogleg algorithm.
The size of the trust region 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.
And increased when the actual and predicted reduction are sufficiently close.
Normally the initial trust region size is the same as the final trust region size of the previous iteration but the size of the trust region is restricted by the size of the current Newton step. So when full Newton steps are being taken, the trust region size at the start of an iteration may be less than the the final value of the previous iteration.
A sample iteration report for pwldog
is
(some intercolumn space has been removed to make the table fit)
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-02This 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 directions or a full Newton step. The number in the column
Lambda
is the weight of the Newton step.
It is a special case of the double dogleg method with eta
equal to 1.