https://github.com/cran/nleqslv
Tip revision: 0c2311909c856f23ea71953319994cb3a3f79567 authored by Berend Hasselman on 05 September 2009, 23:10:56 UTC
version 1.5
version 1.5
Tip revision: 0c23119
dslnex.Rout.save
R version 2.8.1 (2008-12-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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Type 'license()' or 'licence()' for distribution details.
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Type 'demo()' for some demos, 'help()' for on-line help, or
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> # Dennis Schnabel example
>
> library("nleqslv")
>
> dslnex <- function(x) {
+ y <- numeric(2)
+ y[1] <- x[1]^2 + x[2]^2 - 2
+ y[2] <- exp(x[1]-1) + x[2]^3 - 2
+ y
+ }
>
> jacdsln <- function(x) {
+ n <- length(x)
+ Df <- matrix(numeric(n*n),n,n)
+ Df[1,1] <- 2*x[1]
+ Df[1,2] <- 2*x[2]
+ Df[2,1] <- exp(x[1]-1)
+ Df[2,2] <- 3*x[2]^2
+
+ Df
+ }
>
> xstart <- c(2,0.5)
> fstart <- dslnex(xstart)
> xstart
[1] 2.0 0.5
> fstart
[1] 2.2500000 0.8432818
>
> # a solution is c(1,1)
> znleqa <- nleqslv(xstart, dslnex, global="qline",control=list(trace=1,btol=.01))
Algorithm parameters
--------------------
Method: Broyden Global strategy: quadratic linesearch
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
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 9.502885e-07
13 B(1.2e-01) 1.0000 4.514342e-13 1.404463e-17 5.299877e-09
> znleqa
$x
[1] 1 1
$fvec
[1] 5.299877e-09 2.378364e-11
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 18
$njcnt
[1] 1
>
> znleqb <- nleqslv(xstart, dslnex, global="gline",control=list(trace=1,btol=.01))
Algorithm parameters
--------------------
Method: Broyden Global strategy: geometric linesearch (reduction = 0.5)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
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 0.5000 2.886523e+00 1.211981e+04 1.533192e+02
1 0.2500 2.886668e+00 3.346737e+02 2.454656e+01
1 0.1250 2.886740e+00 1.860606e+01 4.931671e+00
1 0.0625 2.886776e+00 4.468205e+00 2.514779e+00
1 0.0312 2.886794e+00 3.097106e+00 2.281039e+00
1 0.0156 2.886803e+00 2.888770e+00 2.240182e+00
1 0.0078 2.886808e+00 2.864341e+00 2.238756e+00
2 B(1.9e-02) 1.0000 2.863768e+00 1.026894e+04 1.410555e+02
2 0.5000 2.864054e+00 3.038612e+02 2.346774e+01
2 0.2500 2.864197e+00 1.774832e+01 4.936364e+00
2 0.1250 2.864269e+00 4.259875e+00 2.397912e+00
2 0.0625 2.864305e+00 2.987137e+00 2.220967e+00
2 0.0312 2.864323e+00 2.822740e+00 2.205520e+00
3 B(5.3e-02) 1.0000 2.822176e+00 3.640971e+01 7.932621e+00
3 0.5000 2.822458e+00 4.461754e+00 2.260940e+00
3 0.2500 2.822599e+00 2.451565e+00 1.898167e+00
4 B(1.7e-01) 1.0000 2.451075e+00 4.645809e-02 3.012542e-01
5 B(1.7e-01) 1.0000 4.644880e-02 3.610709e-02 2.100750e-01
6 B(1.7e-01) 1.0000 3.609987e-02 4.937229e-04 3.114050e-02
7 B(1.8e-01) 1.0000 4.936242e-04 1.156794e-05 3.863626e-03
8 B(1.5e-01) 1.0000 1.156563e-05 7.281774e-08 2.923123e-04
9 B(1.5e-01) 1.0000 7.280317e-08 1.723949e-10 1.815046e-05
10 B(1.4e-01) 1.0000 1.723604e-10 2.225489e-13 6.604661e-07
11 B(1.5e-01) 1.0000 2.225044e-13 4.798220e-19 9.698051e-10
> znleqb
$x
[1] 1 1
$fvec
[1] 9.698051e-10 1.382823e-10
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 25
$njcnt
[1] 1
>
> znleqc <- nleqslv(xstart, dslnex, global="dbldog",
+ control=list(trace=1,btol=.01,delta=-1.0))
Algorithm parameters
--------------------
Method: Broyden Global strategy: double dogleg (initial trust region = -1)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
Iter Jac Lambda Gamma Eta Dlt0 Dltn Fnorm Largest |f|
0 2.886812e+00 2.250000e+00
1 N(9.6e-03) C 0.9430 0.9544 0.4671 0.9343 1.699715e-01 5.421673e-01
1 W 0.0833 0.9430 0.9544 0.9343 0.4671 1.699715e-01 5.421673e-01
2 B(1.1e-02) W 0.1154 0.3564 0.4851 0.4671 0.4671 1.277667e-01 5.043571e-01
3 B(7.3e-02) W 0.7879 0.6611 0.7289 0.4671 0.0759 5.067893e-01 7.973542e-01
3 C 0.6611 0.7289 0.0759 0.1519 5.440250e-02 2.726084e-01
4 B(8.3e-02) W 0.5307 0.1588 0.3271 0.1519 0.3037 3.576547e-02 2.657553e-01
5 B(1.8e-01) N 0.5843 0.6674 0.2191 0.4383 6.566182e-03 8.555110e-02
6 B(1.8e-01) N 0.9752 0.9801 0.0376 0.0752 4.921645e-04 3.094104e-02
7 B(1.9e-01) N 0.7476 0.7981 0.0157 0.0313 4.960629e-06 2.826064e-03
8 B(1.6e-01) N 0.2427 0.3942 0.0029 0.0058 1.545503e-08 1.757498e-04
9 B(1.5e-01) N 0.5669 0.6536 0.0001 0.0003 2.968676e-11 5.983765e-06
10 B(1.5e-01) N 0.3413 0.4730 0.0000 0.0000 4.741792e-14 2.198380e-07
11 B(1.5e-01) N 0.9734 0.9787 0.0000 0.0000 6.451792e-19 8.118586e-10
> znleqc
$x
[1] 1 1
$fvec
[1] 8.118586e-10 -7.945087e-10
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 13
$njcnt
[1] 1
>
> znleqd <- nleqslv(xstart, dslnex, global="pwldog",
+ control=list(trace=1,btol=.01,delta=-1.0))
Algorithm parameters
--------------------
Method: Broyden Global strategy: single dogleg (initial trust region = -1)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
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 1.051357e-18 1.422036e-09
> znleqd
$x
[1] 1 1
$fvec
[1] 2.837748e-10 1.422036e-09
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 14
$njcnt
[1] 1
>
> znleqe <- nleqslv(xstart, dslnex, global="dbldog",
+ control=list(trace=1,btol=.01,delta=-2.0))
Algorithm parameters
--------------------
Method: Broyden Global strategy: double dogleg (initial trust region = -2)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
Iter Jac Lambda Gamma Eta Dlt0 Dltn Fnorm Largest |f|
0 2.886812e+00 2.250000e+00
1 N(9.6e-03) N 0.9430 0.9544 10.1874 1.0187 5.787362e+05 1.070841e+03
1 W 0.0932 0.9430 0.9544 1.0187 1.0187 1.862204e+00 1.387696e+00
2 B(1.9e-01) N 0.9572 0.9658 0.6119 1.2239 1.003362e-01 4.468549e-01
3 B(2.1e-01) N 0.5588 0.6470 0.2521 0.5042 1.763418e-02 1.819978e-01
4 B(1.3e-01) N 0.1857 0.3486 0.2617 0.0598 5.952083e-02 3.020657e-01
4 W 0.6248 0.1857 0.3486 0.0598 0.1196 6.625459e-03 8.319100e-02
5 B(1.5e-01) N 0.2765 0.4212 0.1186 0.1186 3.368227e-03 5.868436e-02
6 B(1.4e-01) N 0.9944 0.9955 0.0177 0.0354 9.352918e-05 1.350724e-02
7 B(1.8e-01) N 0.6950 0.7560 0.0073 0.0146 9.330438e-06 3.933436e-03
8 B(1.5e-01) N 0.8498 0.8799 0.0020 0.0041 1.458619e-09 3.825434e-05
9 B(1.5e-01) N 0.9961 0.9969 0.0000 0.0000 1.640555e-13 4.501888e-07
10 B(1.5e-01) N 0.9974 0.9979 0.0000 0.0000 3.239034e-18 2.056389e-09
> znleqe
$x
[1] 1 1
$fvec
[1] 1.499778e-09 2.056389e-09
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 12
$njcnt
[1] 1
>
> znleqf <- nleqslv(xstart, dslnex, global="pwldog",
+ control=list(trace=1,btol=.01,delta=-2.0))
Algorithm parameters
--------------------
Method: Broyden Global strategy: single dogleg (initial trust region = -2)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
Iter Jac Lambda Dlt0 Dltn Fnorm Largest |f|
0 2.886812e+00 2.250000e+00
1 N(9.6e-03) N 10.1874 1.0187 5.787362e+05 1.070841e+03
1 W 0.0888 1.0187 1.0187 1.838308e+00 1.378307e+00
2 B(1.9e-01) N 0.6096 1.2192 1.003319e-01 4.467900e-01
3 B(2.1e-01) N 0.2521 0.5041 1.741527e-02 1.807484e-01
4 B(1.3e-01) N 0.2596 0.0597 5.827737e-02 2.987481e-01
4 W 0.2042 0.0597 0.1195 7.171322e-03 9.908693e-02
5 B(1.5e-01) N 0.1177 0.1177 4.991568e-03 7.167276e-02
6 B(1.4e-01) N 0.0206 0.0412 1.473080e-04 1.672712e-02
7 B(1.8e-01) N 0.0092 0.0183 8.799389e-06 3.660344e-03
8 B(1.5e-01) N 0.0017 0.0035 1.377573e-10 1.596674e-05
9 B(1.6e-01) N 0.0000 0.0000 9.117172e-14 4.240867e-07
10 B(1.5e-01) N 0.0000 0.0000 6.229751e-18 3.480300e-09
> znleqf
$x
[1] 1 1
$fvec
[1] 3.480300e-09 -5.890812e-10
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 12
$njcnt
[1] 1
>
> znlejc <- nleqslv(xstart, dslnex, jacdsln, global="dbldog",
+ control=list(trace=1,btol=.01,delta=-1.0))
Algorithm parameters
--------------------
Method: Broyden Global strategy: double dogleg (initial trust region = -1)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
Iter Jac Lambda Gamma Eta Dlt0 Dltn Fnorm Largest |f|
0 2.886812e+00 2.250000e+00
1 N(9.6e-03) C 0.9430 0.9544 0.4671 0.9343 1.699714e-01 5.421673e-01
1 W 0.0833 0.9430 0.9544 0.9343 0.4671 1.699714e-01 5.421673e-01
2 B(1.1e-02) W 0.1154 0.3564 0.4851 0.4671 0.4671 1.277668e-01 5.043571e-01
3 B(7.3e-02) W 0.7879 0.6611 0.7289 0.4671 0.0759 5.067894e-01 7.973543e-01
3 C 0.6611 0.7289 0.0759 0.1519 5.440250e-02 2.726085e-01
4 B(8.3e-02) W 0.5307 0.1588 0.3271 0.1519 0.3037 3.576547e-02 2.657553e-01
5 B(1.8e-01) N 0.5843 0.6674 0.2191 0.4383 6.566179e-03 8.555108e-02
6 B(1.8e-01) N 0.9752 0.9801 0.0376 0.0752 4.921642e-04 3.094104e-02
7 B(1.9e-01) N 0.7476 0.7981 0.0157 0.0313 4.960623e-06 2.826062e-03
8 B(1.6e-01) N 0.2427 0.3942 0.0029 0.0058 1.545502e-08 1.757497e-04
9 B(1.5e-01) N 0.5669 0.6536 0.0001 0.0003 2.968669e-11 5.983760e-06
10 B(1.5e-01) N 0.3413 0.4730 0.0000 0.0000 4.741776e-14 2.198378e-07
11 B(1.5e-01) N 0.9734 0.9787 0.0000 0.0000 6.451765e-19 8.118572e-10
> znlejc
$x
[1] 1 1
$fvec
[1] 8.118572e-10 -7.945067e-10
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 13
$njcnt
[1] 1
>
> znlejd <- nleqslv(xstart, dslnex, jacdsln, global="dbldog",
+ method="Newton", control=list(trace=1,btol=.01,delta=-1.0))
Algorithm parameters
--------------------
Method: Newton Global strategy: double dogleg (initial trust region = -1)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
Iter Jac Lambda Gamma Eta Dlt0 Dltn Fnorm Largest |f|
0 2.886812e+00 2.250000e+00
1 N(9.6e-03) C 0.9430 0.9544 0.4671 0.9343 1.699714e-01 5.421673e-01
1 W 0.0833 0.9430 0.9544 0.9343 0.4671 1.699714e-01 5.421673e-01
2 N(2.7e-03) W 0.0229 0.3992 0.5194 0.4671 0.9343 9.974170e-02 4.398408e-01
2 W 0.0466 0.3992 0.5194 0.9343 0.4671 9.974170e-02 4.398408e-01
3 N(1.7e-01) N 0.5096 0.6077 0.4366 0.4366 5.854330e-02 2.841666e-01
4 N(1.5e-01) N 0.9950 0.9960 0.0780 0.1561 1.989417e-04 1.899518e-02
5 N(1.5e-01) N 0.8605 0.8884 0.0092 0.0184 2.284798e-08 1.962281e-04
6 N(1.5e-01) N 0.9142 0.9313 0.0001 0.0002 1.933627e-16 1.833717e-08
7 N(1.5e-01) N 0.8930 0.9144 0.0000 0.0000 0.000000e+00 0.000000e+00
> znlejd
$x
[1] 1 1
$fvec
[1] 0 0
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 9
$njcnt
[1] 7
>
> # singular function with a singular start
>
> sngsrt <- function(x) {
+ y <- numeric(length(x))
+ y[1] <- x[1]^2/2 + x[2]
+ y[2] <- x[1] + x[2]^2/2
+
+ y
+ }
>
> sngsrtjac <- function(x) {
+ n <- length(x)
+ Df <- matrix(numeric(n*n),n,n)
+ Df[1,1] <- x[1]
+ Df[1,2] <- 1
+ Df[2,1] <- 1
+ Df[2,2] <- x[2]
+
+ Df
+ }
> xstart <- c(1,1)
> nleqslv(xstart, sngsrt, sngsrtjac, global="dbldog",control=list(trace=1,btol=.01,delta=-1.0))
Algorithm parameters
--------------------
Method: Broyden Global strategy: double dogleg (initial trust region = -1)
Maximum stepsize = 1000
Scaling: fixed
ftol = 1e-08 xtol = 1e-08 btol = 0.01
Iteration report
----------------
Iter Jac Lambda Gamma Eta Dlt0 Dltn Fnorm Largest |f|
0 2.250000e+00 1.500000e+00
1 Ns(4.2e-07) N 1.0000 1.0000 1.0607 2.1213 7.910156e-02 2.812500e-01
2 Bi(3.4e-07) N 1.0000 1.0000 0.2448 0.4895 6.381079e-03 7.988166e-02
3 Bi(2.5e-07) N 1.0000 1.0000 0.0971 0.1942 6.886699e-05 8.298613e-03
4 Bi(2.2e-07) N 1.0000 1.0000 0.0113 0.0225 9.297897e-08 3.049245e-04
5 Bi(2.1e-07) N 1.0000 1.0000 0.0004 0.0009 1.573651e-12 1.254453e-06
6 Bi(2.1e-07) N 1.0000 1.0000 0.0000 0.0000 3.655673e-20 1.911984e-10
$x
[1] 1.911979e-10 1.911984e-10
$fvec
[1] 1.911984e-10 1.911979e-10
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 6
$njcnt
[1] 1
>
