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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> # Broyden banded function
> 
> library("nleqslv")
> 
> brdban <- function(x) {
+ 	ml <- 5
+ 	mu <- 1
+ 	n <- length(x)
+     y <- numeric(n)
+ 
+ 	for( k in 1:n ) {
+ 
+ 		k1 <- max(1, k - ml)
+ 		k2 <- min(n, k + mu)
+ 
+ 		temp = 0.0
+ 		for(j in k1:k2) {
+ 		  	if ( j != k ) {
+ 		    	temp <- temp + x[j] * (1.0 + x[j])
+ 		    }
+ 		}
+ 
+ 		y[k] <- x[k] * (2.0 + 5.0 * x[k]**2) + 1.0 - temp
+ 
+ 	}
+ 	y
+ }
> 
> n <- 10
> xstart <- -rep(1,n)
> 
> xsol <- c( -0.42830,  -0.47660,  -0.51965,  -0.55810,  -0.59251,
+            -0.62450,  -0.62324,  -0.62139,  -0.62045,  -0.58647  )
> 
> fsol <- brdban(xsol)
> 
> znlq <- nleqslv(xstart, brdban, global="dbldog",
+                   control=list(trace=1,ftol=1e-8,xtol=1e-8,btol=1e-2,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                                                             1.800000e+02  6.000000e+00
     1  N(5.6e-01) C            0.9939   0.9952   0.8783   1.7567  1.095254e+01  2.052478e+00
     1             N            0.9939   0.9952   0.8880   1.7760  1.022871e+01  1.589807e+00
     2  B(5.9e-01) N            0.9808   0.9846   0.2793   0.5586  1.439892e+00  6.815532e-01
     3  B(2.5e-01) N            0.8983   0.9186   0.1683   0.3365  7.485024e-02  2.163321e-01
     4  B(1.7e-01) N            0.5093   0.6074   0.0464   0.0928  7.964714e-03  8.281790e-02
     5  B(1.5e-01) N            0.7803   0.8242   0.0119   0.0119  2.364606e-03  4.189804e-02
     6  B(1.5e-01) N            0.8663   0.8931   0.0069   0.0138  4.306996e-04  1.854601e-02
     7  B(7.4e-02) N            0.7998   0.8398   0.0047   0.0094  5.034267e-06  2.447328e-03
     8  B(5.2e-02) N            0.8719   0.8975   0.0004   0.0009  1.159785e-06  7.808025e-04
     9  B(4.5e-02) N            0.9817   0.9854   0.0001   0.0001  4.326464e-07  5.795349e-04
    10  B(4.8e-02) W   0.5515   0.5765   0.6612   0.0001   0.0002  7.420325e-08  3.148056e-04
    10             N            0.5765   0.6612   0.0002   0.0003  2.202833e-08  1.251008e-04
    11  B(5.3e-02) N            0.8557   0.8846   0.0000   0.0000  5.492722e-09  6.574238e-05
    12  B(5.6e-02) N            0.9578   0.9662   0.0000   0.0000  1.322667e-09  2.887975e-05
    13  B(6.9e-02) N            0.8883   0.9106   0.0000   0.0000  8.694772e-11  7.360340e-06
    14  B(1.2e-01) N            0.6186   0.6949   0.0000   0.0000  3.517077e-12  1.544708e-06
    15  B(1.1e-01) N            0.9176   0.9341   0.0000   0.0000  1.198874e-12  1.064222e-06
    16  B(1.0e-01) N            0.9841   0.9873   0.0000   0.0000  3.388443e-13  5.645454e-07
    17  B(6.8e-02) P            0.7798   0.8239   0.0000   0.0000  5.690742e-15  6.905413e-08
    17             N            0.7798   0.8239   0.0000   0.0000  1.182053e-15  2.821496e-08
    18  B(7.3e-02) N            0.9936   0.9949   0.0000   0.0000  3.519352e-16  1.471924e-08
> znlq
$x
 [1] -0.4283029 -0.4765964 -0.5196525 -0.5580993 -0.5925062 -0.6245037
 [7] -0.6232395 -0.6213938 -0.6204536 -0.5864693

$fvec
 [1] -5.236529e-10  1.430344e-09 -6.745516e-09  9.923324e-09 -1.301495e-08
 [6]  1.471924e-08  6.127840e-10 -1.214721e-08  4.770360e-09  9.189667e-10

$termcd
[1] 2

$message
[1] "x-values within tolerance `xtol'"

$scalex
 [1] 1 1 1 1 1 1 1 1 1 1

$nfcnt
[1] 21

$njcnt
[1] 1

> 
> xstart <- -2*rep(1,n)
> znlq <- nleqslv(xstart, brdban, global="dbldog",
+                   control=list(trace=1,ftol=1e-8,xtol=1e-8,btol=1e-2,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                                                             1.347700e+04  5.500000e+01
     1  N(6.1e-01) C            0.9970   0.9976   2.1667   4.3334  1.107526e+03  1.734646e+01
     1             N            0.9970   0.9976   2.1781   4.3562  1.081593e+03  1.539037e+01
     2  B(5.1e-01) N            0.9886   0.9909   0.8616   1.7233  2.352076e+02  7.052426e+00
     3  B(1.5e-01) N            0.8884   0.9107   0.7539   1.5077  3.033773e+01  2.624047e+00
     4  B(4.9e-02) N            0.5217   0.6174   0.4222   0.8445  3.726499e+00  1.172257e+00
     5  B(2.7e-02) N            0.1237   0.2989   0.2216   0.4432  3.920544e-01  5.632242e-01
     6  B(1.9e-02) N            0.4300   0.5440   0.0761   0.0761  1.430604e-01  3.553678e-01
     7  B(1.5e-02) N            0.9480   0.9584   0.0177   0.0177  1.077089e-01  2.901659e-01
     8  B(1.3e-02) N            0.9826   0.9861   0.0119   0.0119  7.660051e-02  2.445633e-01
     9  B(5.2e-03) W   0.2073   0.9508   0.9606   0.0119   0.0119  5.132645e-02  2.161259e-01
    10  B(7.3e-03) W   0.2172   0.8361   0.8689   0.0119   0.0119  7.362918e-02  2.620698e-01
    11  N(6.1e-01) C            0.8690   0.8952   0.0447   0.0893  7.711139e-03  8.514345e-02
    11             N            0.8690   0.8952   0.0543   0.1086  1.209667e-04  1.195480e-02
    12  B(5.8e-01) N            0.8575   0.8860   0.0029   0.0057  5.138149e-07  8.390791e-04
    13  B(5.5e-01) N            0.9155   0.9324   0.0002   0.0004  5.140388e-11  5.725924e-06
    14  B(5.5e-01) N            0.8667   0.8934   0.0000   0.0000  1.214646e-13  3.399846e-07
    15  B(5.3e-01) N            0.8236   0.8589   0.0000   0.0000  1.596621e-16  1.233130e-08
    16  B(5.1e-01) N            0.8465   0.8772   0.0000   0.0000  1.991123e-20  1.448182e-10
> znlq
$x
 [1] -0.4283029 -0.4765964 -0.5196525 -0.5580993 -0.5925062 -0.6245037
 [7] -0.6232395 -0.6213938 -0.6204536 -0.5864693

$fvec
 [1] -1.902917e-11 -1.612172e-11 -6.240031e-11 -5.284440e-12 -1.104761e-11
 [6] -1.505085e-11  2.676104e-11  1.062976e-10  1.448182e-10  4.407386e-11

$termcd
[1] 1

$message
[1] "Function criterion near zero"

$scalex
 [1] 1 1 1 1 1 1 1 1 1 1

$nfcnt
[1] 18

$njcnt
[1] 2

>