Lanczos2: Generated data
In NISTnls: Nonlinear least squares examples from NIST
Description
Format
Details
Source
Examples
Description
The Lanczos2 data frame has 24 rows and 2 columns of generated data.
Format
This data frame contains the following columns:
- y
-
A numeric vector of generated responses.
- x
-
A numeric vector of generated input values.
Details
These data are taken from an example discussed in
Lanczos (1956). The data were generated to 6-digits
of accuracy using
f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x).
Source
Lanczos, C. (1956).
Applied Analysis.
Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
Examples
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Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Lanczos2)
## plot log response to see the number of exponential terms
plot(y ~ x, data = Lanczos2, log = "y")
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm1 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE,
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm1a <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm2 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE,
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
Try(fm2a <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm3 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))),
data = Lanczos2, trace = TRUE, algorithm = "plinear",
start = c(b2 = 0.3, b4 = 5.5, b6 = 7.6)))
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm4 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))),
data = Lanczos2, trace = TRUE, algorithm = "plinear",
start = c(b2 = 0.7, b4 = 4.2, b6 = 6.3)))
## Use analytic derivatives
Lanczos <- deriv(~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
paste("b", 1:6, sep = ""),
function(x, b1, b2, b3, b4, b5, b6){})
Try(fm5 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE,
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm5a <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm6 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE,
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
Try(fm6a <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
Example output
269.7505 : 1.2 0.3 5.6 5.5 6.5 7.6
12.09318 : 0.1557447 0.3657416 -4.2718714 3.6361873 6.6294277 6.6558506
0.01606173 : 0.09636116 0.60836498 1.59521204 3.66887107 0.82180845 6.54393093
3.988663e-05 : 0.1187054 1.0189614 1.5699075 3.5934999 0.8247741 5.7094101
3.586373e-05 : 0.1203312 1.0348053 1.5128131 3.5660713 0.8802440 5.6210972
3.15019e-05 : 0.1213519 1.0470438 1.4554398 3.5361368 0.9365976 5.5418962
2.862045e-05 : 0.1222942 1.0652189 1.3422732 3.4723715 1.0488240 5.4009803
1.876212e-05 : 0.1202569 1.0797316 1.1315686 3.3340389 1.2615694 5.1848428
3.035105e-06 : 0.1131085 1.0646111 0.9876847 3.2002783 1.4126038 5.0804798
3.02715e-06 : 0.1062082 1.0434084 0.9191323 3.1097336 1.4880577 5.0371973
1.870897e-06 : 0.09702604 1.01075878 0.85997733 3.00952199 1.55639621 5.00053642
2.867039e-11 : 0.09624652 1.00572800 0.86425328 3.00781285 1.55289980 5.00287794
2.229943e-11 : 0.09625117 1.00573399 0.86424724 3.00782926 1.55290120 5.00288010
2.229943e-11 : 0.09625101 1.00573321 0.86424685 3.00782830 1.55290174 5.00287978
Nonlinear regression model
model: y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * x)
data: Lanczos2
b1 b2 b3 b4 b5 b6
0.09625 1.00573 0.86425 3.00783 1.55290 5.00288
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 13
Achieved convergence tolerance: 5.502e-06
0: 134.87524: 1.20000 0.300000 5.60000 5.50000 6.50000 7.60000
1: 37.391901: -0.0911437 0.161578 4.29176 6.72459 5.25608 9.60465
2: 0.53986128: 0.103108 0.245678 0.839264 4.06245 1.71732 9.96535
3: 0.0015421788: 0.120011 0.807061 2.15803 3.87560 0.235291 9.61764
4: 0.00031018901: 0.194294 1.40097 2.10711 4.10424 0.211953 7.60707
5: 2.7613392e-06: 0.215716 1.35716 2.09319 4.14383 0.205080 7.54005
6: 1.3703830e-06: 0.235462 1.42753 2.08152 4.18293 0.196838 7.42023
7: 1.0937083e-06: 0.260767 1.50244 2.06768 4.23051 0.185245 7.31404
8: 8.5640049e-07: 0.288994 1.57650 2.05292 4.28366 0.171647 7.19315
9: 4.2162329e-07: 0.296933 1.59444 2.02559 4.28489 0.190967 6.89846
10: 9.2786359e-08: 0.295711 1.59196 2.01392 4.27632 0.203857 6.82756
11: 8.8508463e-08: 0.293496 1.58747 2.00400 4.26602 0.215992 6.75756
12: 8.4706376e-08: 0.291256 1.58286 1.99388 4.25563 0.228353 6.69223
13: 8.0385968e-08: 0.290320 1.58066 1.99315 4.25319 0.230012 6.69199
14: 7.9765280e-08: 0.290357 1.58082 1.99198 4.25264 0.231150 6.68412
15: 7.9399375e-08: 0.290280 1.58072 1.99077 4.25183 0.232440 6.67651
16: 7.8702123e-08: 0.290251 1.58080 1.98825 4.25049 0.234980 6.66001
17: 7.8158291e-08: 0.289929 1.58016 1.98640 4.24879 0.237148 6.64920
18: 7.7174556e-08: 0.289216 1.57870 1.98276 4.24528 0.241505 6.62801
19: 7.6500261e-08: 0.288891 1.57809 1.98043 4.24333 0.244161 6.61499
20: 7.5428069e-08: 0.288203 1.57675 1.97580 4.23938 0.249474 6.58905
21: 7.4791387e-08: 0.287975 1.57634 1.97371 4.23779 0.251791 6.57808
22: 7.4238606e-08: 0.287564 1.57550 1.97158 4.23576 0.254332 6.56693
23: 7.3590335e-08: 0.285815 1.57187 1.96277 4.22728 0.264893 6.52114
24: 7.3236651e-08: 0.283193 1.56629 1.95086 4.21529 0.279428 6.46511
25: 7.0585258e-08: 0.283167 1.56630 1.95084 4.21532 0.279424 6.46511
26: 6.9418691e-08: 0.283170 1.56625 1.95083 4.21532 0.279470 6.46583
27: 6.9126008e-08: 0.283177 1.56619 1.95078 4.21529 0.279522 6.46640
28: 6.9084711e-08: 0.283170 1.56620 1.95059 4.21514 0.279716 6.46596
29: 6.8984300e-08: 0.283159 1.56621 1.95005 4.21484 0.280264 6.46344
30: 6.8737269e-08: 0.283042 1.56600 1.94882 4.21395 0.281616 6.45768
31: 6.7699014e-08: 0.281797 1.56343 1.94158 4.20748 0.290095 6.42542
32: 6.7036980e-08: 0.279708 1.55899 1.93076 4.19730 0.303003 6.38054
33: 6.3830149e-08: 0.278347 1.55601 1.92444 4.19105 0.310691 6.35742
34: 6.2602186e-08: 0.276946 1.55297 1.91759 4.18445 0.318937 6.33200
35: 6.1220200e-08: 0.275070 1.54868 1.91094 4.17688 0.327456 6.30916
36: 6.0246058e-08: 0.274508 1.54773 1.90343 4.17189 0.335537 6.28157
37: 5.8931428e-08: 0.273461 1.54551 1.89669 4.16618 0.343326 6.25891
38: 5.8294551e-08: 0.271726 1.54181 1.88559 4.15675 0.356152 6.22257
39: 5.7158102e-08: 0.269836 1.53780 1.87261 4.14606 0.371027 6.18261
40: 5.4780735e-08: 0.267983 1.53381 1.86005 4.13568 0.385437 6.14662
41: 5.3013232e-08: 0.265979 1.52943 1.84698 4.12470 0.400512 6.11119
42: 5.1130792e-08: 0.264085 1.52530 1.83400 4.11402 0.415385 6.07781
43: 4.9428425e-08: 0.262197 1.52115 1.82088 4.10328 0.430395 6.04567
44: 4.7788729e-08: 0.260343 1.51707 1.80766 4.09258 0.445466 6.01483
45: 4.6215467e-08: 0.258521 1.51304 1.79437 4.08190 0.460577 5.98523
46: 4.4708627e-08: 0.256723 1.50906 1.78103 4.07123 0.475717 5.95683
47: 4.3146688e-08: 0.255109 1.50546 1.76891 4.06158 0.489446 5.93220
48: 4.1967812e-08: 0.253435 1.50172 1.75613 4.05145 0.503896 5.90702
49: 4.0663894e-08: 0.251908 1.49829 1.74436 4.04213 0.517192 5.88480
50: 3.9616570e-08: 0.250236 1.49453 1.73127 4.03182 0.531955 5.86077
50: 3.9616570e-08: 0.250236 1.49453 1.73127 4.03182 0.531955 5.86077
Error in nls(y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * :
Convergence failure: iteration limit reached without convergence (10)
78.78867 : 0.5 0.7 3.6 4.2 4.0 6.3
0.1065203 : 0.1375763 0.7888953 1.0193691 3.7835135 1.3564416 6.0486056
0.003835761 : 0.1284285 1.0311604 1.2688251 3.2657538 1.1161394 5.5365739
0.0004866298 : 0.1180552 1.0883456 1.0576360 3.2392432 1.3377068 5.0968998
8.958668e-05 : 0.1002222 1.0283572 0.8438644 3.0314828 1.5693128 4.9854297
5.769047e-08 : 0.09622398 1.00598649 0.86433935 3.00709121 1.55283627 5.00287403
2.230791e-11 : 0.09625075 1.00573168 0.86424580 3.00782602 1.55290306 5.00287905
2.229943e-11 : 0.09625053 1.00573075 0.86424563 3.00782529 1.55290344 5.00287879
2.229943e-11 : 0.09625073 1.00573174 0.86424612 3.00782650 1.55290276 5.00287919
2.229943e-11 : 0.09625079 1.00573205 0.86424628 3.00782688 1.55290254 5.00287931
2.229943e-11 : 0.09625118 1.00573403 0.86424727 3.00782932 1.55290116 5.00288012
2.229943e-11 : 0.09625118 1.00573404 0.86424727 3.00782932 1.55290116 5.00288012
2.229943e-11 : 0.09625117 1.00573402 0.86424726 3.00782930 1.55290117 5.00288011
2.229943e-11 : 0.09625117 1.00573401 0.86424726 3.00782929 1.55290118 5.00288011
2.229943e-11 : 0.09625115 1.00573389 0.86424719 3.00782914 1.55290127 5.00288006
2.229943e-11 : 0.09625109 1.00573361 0.86424706 3.00782880 1.55290146 5.00287995
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
Error in nls(y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * :
step factor 0.000488281 reduced below 'minFactor' of 0.000976562
0: 39.394337: 0.500000 0.700000 3.60000 4.20000 4.00000 6.30000
1: 15.277204: -0.0399740 0.652183 3.11185 4.94474 3.55231 7.60208
2: 1.4367574: -0.205343 1.19508 1.80328 3.97599 2.23143 8.30711
3: 0.0059191757: 0.226211 0.981935 1.99797 4.10961 0.289200 8.10938
4: 0.00046918480: 0.195340 1.22138 1.98335 4.02779 0.334687 6.42402
5: 1.8486425e-06: 0.216938 1.38319 1.94666 4.06660 0.350065 6.50037
6: 4.2336306e-07: 0.226175 1.41248 1.94012 4.07987 0.347391 6.48883
7: 2.9602576e-07: 0.235691 1.44165 1.93506 4.09858 0.342905 6.46238
8: 1.9952336e-07: 0.245065 1.46881 1.93040 4.11763 0.338152 6.43257
9: 1.3194455e-07: 0.254416 1.49482 1.92579 4.13675 0.333365 6.40143
10: 8.9565201e-08: 0.263724 1.51972 1.92106 4.15574 0.328749 6.36869
11: 6.9611457e-08: 0.266948 1.52802 1.91367 4.15958 0.332889 6.33243
12: 6.2782729e-08: 0.269678 1.53557 1.90417 4.16112 0.339648 6.29189
13: 5.9824258e-08: 0.273262 1.54521 1.89406 4.16439 0.346139 6.24941
14: 5.8035318e-08: 0.271167 1.54061 1.88208 4.15376 0.360222 6.21147
15: 5.6104328e-08: 0.269241 1.53643 1.86993 4.14339 0.374299 6.17516
16: 5.3760490e-08: 0.268138 1.53403 1.86279 4.13737 0.382543 6.15542
17: 5.2796775e-08: 0.267095 1.53177 1.85581 4.13156 0.390569 6.13596
18: 5.2617147e-08: 0.264156 1.52508 1.84091 4.11753 0.408398 6.09639
19: 4.9933515e-08: 0.263825 1.52468 1.83264 4.11276 0.417005 6.07494
20: 4.8903899e-08: 0.262801 1.52246 1.82514 4.10675 0.425529 6.05644
21: 4.8313350e-08: 0.261023 1.51857 1.81234 4.09643 0.440103 6.02554
22: 4.6323082e-08: 0.257758 1.51068 1.80075 4.08317 0.454950 6.00173
23: 4.5420911e-08: 0.258537 1.51303 1.79524 4.08234 0.459688 5.98786
24: 4.4893675e-08: 0.258205 1.51242 1.79023 4.07917 0.465027 5.97648
25: 4.4580382e-08: 0.257896 1.51177 1.78738 4.07707 0.468184 5.97035
26: 4.4010042e-08: 0.256955 1.50960 1.78196 4.07223 0.474549 5.95915
27: 4.3615305e-08: 0.256439 1.50845 1.77825 4.06922 0.478775 5.95152
28: 4.2935983e-08: 0.255462 1.50628 1.77078 4.06332 0.487219 5.93609
29: 4.2385267e-08: 0.254809 1.50482 1.76583 4.05938 0.492824 5.92629
30: 4.1668366e-08: 0.253695 1.50242 1.75565 4.05185 0.504115 5.90581
31: 4.1052786e-08: 0.251769 1.49814 1.74024 4.03984 0.521458 5.87631
32: 3.9800037e-08: 0.249699 1.49352 1.72319 4.02666 0.540570 5.84544
33: 3.7697947e-08: 0.247340 1.48803 1.70747 4.01335 0.558652 5.81911
34: 3.6422899e-08: 0.245218 1.48313 1.69159 4.00049 0.576651 5.79310
35: 3.5130871e-08: 0.243230 1.47857 1.67562 3.98788 0.594607 5.76781
36: 3.3832966e-08: 0.241251 1.47401 1.65964 3.97522 0.612569 5.74346
37: 3.2565383e-08: 0.239450 1.46983 1.64505 3.96362 0.628957 5.72209
38: 3.1498230e-08: 0.237650 1.46564 1.63036 3.95192 0.645450 5.70115
39: 3.0333142e-08: 0.235984 1.46179 1.61558 3.94045 0.661892 5.68072
40: 2.9406448e-08: 0.233959 1.45699 1.59991 3.92761 0.679583 5.65972
41: 2.8362572e-08: 0.232028 1.45242 1.58419 3.91488 0.697233 5.63934
42: 2.7776528e-08: 0.228869 1.44493 1.55796 3.89371 0.726627 5.60607
43: 2.5727151e-08: 0.227021 1.44044 1.54326 3.88143 0.743170 5.58904
44: 2.4778057e-08: 0.224041 1.43327 1.51871 3.86121 0.770697 5.56008
45: 2.3254388e-08: 0.221514 1.42709 1.49841 3.84407 0.793528 5.53758
46: 2.2357763e-08: 0.217343 1.41686 1.46455 3.81544 0.831552 5.50057
47: 2.0467229e-08: 0.215094 1.41118 1.44751 3.80019 0.850839 5.48371
48: 1.9449849e-08: 0.211506 1.40220 1.41917 3.77533 0.882775 5.45486
49: 1.8294905e-08: 0.207586 1.39251 1.38424 3.74552 0.921618 5.42052
50: 1.6835712e-08: 0.205780 1.38768 1.37328 3.73415 0.934383 5.41114
50: 1.6835712e-08: 0.205780 1.38768 1.37328 3.73415 0.934383 5.41114
Error in nls(y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * :
Convergence failure: iteration limit reached without convergence (10)
0.01402087 : 0.3000000 5.5000000 7.6000000 0.1314193 4.3636465 -2.0156365
0.0004941276 : 0.48072705 4.11581444 9.33298634 0.08902670 2.35995861 0.06060881
2.706757e-05 : 1.2984451 4.1317758 6.2959660 0.2080367 2.0135247 0.2905097
1.555232e-06 : 1.4801400 4.0487540 5.7561206 0.2498594 1.7240716 0.5391007
1.371698e-06 : 1.4524688 3.9459188 5.5545785 0.2369986 1.5751292 0.7009011
1.124701e-06 : 1.4209367 3.8337255 5.4078029 0.2229239 1.4281879 0.8619350
8.637405e-07 : 1.385031 3.715273 5.298382 0.207693 1.293813 1.011572
6.976286e-07 : 1.3045283 3.4754953 5.1342245 0.1768827 1.0680620 1.2681346
3.537636e-08 : 1.140080 3.106602 5.007985 0.123071 0.867044 1.523218
2.85667e-08 : 1.0054630 2.9895801 4.9985102 0.0949560 0.8548438 1.5636561
2.416014e-11 : 1.00570988 3.00768642 5.00274604 0.09624596 0.86410110 1.55305193
2.229943e-11 : 1.00573319 3.00782829 5.00287977 0.09625101 0.86424684 1.55290175
2.229943e-11 : 1.00573330 3.00782841 5.00287982 0.09625103 0.86424690 1.55290168
Nonlinear regression model
model: y ~ exp(outer(x, -c(b2, b4, b6)))
data: Lanczos2
b2 b4 b6 .lin1 .lin2 .lin3
1.00573 3.00783 5.00288 0.09625 0.86425 1.55290
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 12
Achieved convergence tolerance: 2.613e-06
0.0005380147 : 0.70000000 4.20000000 6.30000000 0.11710860 2.34808127 0.04146885
3.461023e-05 : 1.2457390 3.9820400 5.5818191 0.1911534 1.7449796 0.5754493
7.528816e-07 : 1.3971116 3.8038195 5.4242194 0.2138858 1.4273660 0.8718880
6.968601e-07 : 1.3584763 3.6758709 5.2928058 0.1982923 1.2769937 1.0378401
6.758355e-07 : 1.278888 3.437353 5.123552 0.168927 1.051030 1.293132
2.506402e-08 : 1.1272595 3.1002254 5.0105008 0.1203295 0.8706027 1.5224148
1.75412e-08 : 1.0058509 2.9933271 4.9991993 0.0952787 0.8565249 1.5616397
2.325657e-11 : 1.0057392 3.0077726 5.0028040 0.0962526 0.8641682 1.5529784
2.229943e-11 : 1.00573327 3.00782838 5.00287980 0.09625103 0.86424689 1.55290170
2.229943e-11 : 1.00573316 3.00782824 5.00287976 0.09625101 0.86424683 1.55290177
2.229943e-11 : 1.00573330 3.00782841 5.00287981 0.09625103 0.86424690 1.55290168
Nonlinear regression model
model: y ~ exp(outer(x, -c(b2, b4, b6)))
data: Lanczos2
b2 b4 b6 .lin1 .lin2 .lin3
1.00573 3.00783 5.00288 0.09625 0.86425 1.55290
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 10
Achieved convergence tolerance: 2.445e-06
269.7505 : 1.2 0.3 5.6 5.5 6.5 7.6
12.0928 : 0.1557453 0.3657420 -4.2717953 3.6362013 6.6293511 6.6558640
0.01606244 : 0.09636195 0.60836746 1.59522065 3.66888806 0.82179905 6.54394417
3.990272e-05 : 0.1187057 1.0189608 1.5699093 3.5935011 0.8247720 5.7094073
3.587714e-05 : 0.1203315 1.0348048 1.5128146 3.5660724 0.8802421 5.6210947
3.151298e-05 : 0.1213522 1.0470432 1.4554407 3.5361375 0.9365965 5.5418934
2.862798e-05 : 0.1222946 1.0652194 1.3422753 3.4723737 1.0488216 5.4009800
1.876486e-05 : 0.120257 1.079731 1.131567 3.334038 1.261571 5.184840
3.035081e-06 : 0.1131083 1.0646100 0.9876828 3.2002763 1.4126060 5.0804777
3.027316e-06 : 0.1062076 1.0434056 0.9191288 3.1097286 1.4880618 5.0371943
1.870014e-06 : 0.0970268 1.0107621 0.8599810 3.0095278 1.5563917 5.0005393
2.867012e-11 : 0.09624648 1.00572780 0.86425315 3.00781252 1.55289998 5.00287785
2.229943e-11 : 0.09625103 1.00573328 0.86424689 3.00782838 1.55290169 5.00287981
Nonlinear regression model
model: y ~ Lanczos(x, b1, b2, b3, b4, b5, b6)
data: Lanczos2
b1 b2 b3 b4 b5 b6
0.09625 1.00573 0.86425 3.00783 1.55290 5.00288
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 12
Achieved convergence tolerance: 7.23e-06
0: 134.87524: 1.20000 0.300000 5.60000 5.50000 6.50000 7.60000
1: 37.391910: -0.0911435 0.161578 4.29176 6.72459 5.25608 9.60465
2: 0.53986043: 0.103108 0.245680 0.839266 4.06246 1.71732 9.96535
3: 0.0015426445: 0.120012 0.807066 2.15803 3.87558 0.235290 9.61763
4: 0.00031015690: 0.194295 1.40097 2.10711 4.10424 0.211956 7.60703
5: 2.7618128e-06: 0.215708 1.35713 2.09320 4.14381 0.205086 7.54007
6: 1.3704546e-06: 0.235451 1.42750 2.08152 4.18291 0.196845 7.42026
7: 1.0934519e-06: 0.260751 1.50239 2.06768 4.23048 0.185255 7.31409
8: 8.5621780e-07: 0.288973 1.57644 2.05293 4.28362 0.171655 7.19327
9: 4.2102278e-07: 0.296933 1.59444 2.02560 4.28490 0.190956 6.89857
10: 9.2765074e-08: 0.295716 1.59197 2.01395 4.27635 0.203825 6.82776
11: 8.8495172e-08: 0.293506 1.58749 2.00404 4.26606 0.215941 6.75785
12: 8.4699749e-08: 0.291269 1.58289 1.99393 4.25569 0.228281 6.69261
13: 8.0406994e-08: 0.290335 1.58070 1.99321 4.25325 0.229934 6.69238
14: 7.9785141e-08: 0.290372 1.58085 1.99204 4.25271 0.231071 6.68451
15: 7.9419764e-08: 0.290295 1.58075 1.99083 4.25190 0.232358 6.67691
16: 7.8723263e-08: 0.290267 1.58083 1.98832 4.25056 0.234893 6.66043
17: 7.8178005e-08: 0.289943 1.58019 1.98647 4.24886 0.237066 6.64959
18: 7.7192423e-08: 0.289235 1.57875 1.98281 4.24535 0.241431 6.62830
19: 7.6513930e-08: 0.288906 1.57812 1.98047 4.24339 0.244102 6.61523
20: 7.5440170e-08: 0.288226 1.57680 1.97580 4.23943 0.249448 6.58903
21: 7.4800758e-08: 0.287991 1.57638 1.97374 4.23783 0.251751 6.57819
22: 7.4237078e-08: 0.287569 1.57551 1.97156 4.23576 0.254344 6.56684
23: 7.3635551e-08: 0.285777 1.57179 1.96264 4.22713 0.265064 6.52048
24: 7.3316133e-08: 0.283128 1.56615 1.95061 4.21502 0.279737 6.46401
25: 7.0732088e-08: 0.283099 1.56616 1.95060 4.21505 0.279734 6.46402
26: 6.9357701e-08: 0.283103 1.56610 1.95059 4.21505 0.279781 6.46479
27: 6.9064203e-08: 0.283109 1.56604 1.95053 4.21500 0.279840 6.46537
28: 6.9023739e-08: 0.283102 1.56605 1.95034 4.21486 0.280037 6.46487
29: 6.8944242e-08: 0.283108 1.56610 1.94989 4.21465 0.280472 6.46272
30: 6.8722284e-08: 0.283011 1.56593 1.94878 4.21386 0.281687 6.45753
31: 6.7671580e-08: 0.281911 1.56366 1.94220 4.20805 0.289366 6.42815
32: 6.6859563e-08: 0.279992 1.55960 1.93207 4.19860 0.301414 6.38580
33: 6.4096924e-08: 0.278625 1.55662 1.92575 4.19234 0.309101 6.36234
34: 6.2843590e-08: 0.277099 1.55330 1.91828 4.18514 0.318094 6.33439
35: 6.1482476e-08: 0.274667 1.54767 1.91126 4.17610 0.327547 6.31082
36: 6.0754224e-08: 0.272351 1.54230 1.90410 4.16728 0.337017 6.28714
37: 5.9822702e-08: 0.269818 1.53633 1.89709 4.15797 0.346566 6.26658
38: 5.9504943e-08: 0.267594 1.53112 1.88987 4.14927 0.356019 6.24458
39: 5.8630688e-08: 0.266155 1.52786 1.88208 4.14212 0.365246 6.22043
40: 5.8440334e-08: 0.264631 1.52465 1.86872 4.13208 0.380123 6.17850
41: 5.3577459e-08: 0.267484 1.53253 1.86068 4.13481 0.385304 6.14995
42: 5.2546072e-08: 0.266842 1.53123 1.85388 4.13005 0.392746 6.13061
43: 5.1698125e-08: 0.265354 1.52803 1.84326 4.12145 0.404853 6.10184
44: 5.0209730e-08: 0.264347 1.52587 1.83561 4.11541 0.413509 6.08240
45: 4.9240203e-08: 0.263178 1.52331 1.82759 4.10881 0.422699 6.06243
46: 4.8287709e-08: 0.262116 1.52101 1.81944 4.10241 0.431907 6.04254
47: 4.7307388e-08: 0.260882 1.51825 1.81140 4.09564 0.441181 6.02386
48: 4.6374294e-08: 0.259575 1.51538 1.80183 4.08797 0.452057 6.00198
49: 4.5308257e-08: 0.258275 1.51251 1.79225 4.08030 0.462937 5.98090
50: 4.5100527e-08: 0.256195 1.50791 1.77651 4.06782 0.480761 5.94711
50: 4.5100527e-08: 0.256195 1.50791 1.77651 4.06782 0.480761 5.94711
Error in nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), data = Lanczos2, :
Convergence failure: iteration limit reached without convergence (10)
78.78867 : 0.5 0.7 3.6 4.2 4.0 6.3
0.1065354 : 0.1375743 0.7888927 1.0193084 3.7834947 1.3565043 6.0485875
0.00383655 : 0.1284274 1.0311586 1.2688219 3.2657285 1.1161437 5.5365848
0.0004866829 : 0.1180555 1.0883470 1.0576426 3.2392443 1.3376998 5.0969078
8.95785e-05 : 0.1002228 1.0283597 0.8438680 3.0314885 1.5693086 4.9854309
5.768697e-08 : 0.09622409 1.00598716 0.86433951 3.00709171 1.55283600 5.00287427
2.230792e-11 : 0.09625103 1.00573310 0.86424651 3.00782776 1.55290207 5.00287963
2.229943e-11 : 0.09625103 1.00573328 0.86424689 3.00782839 1.55290169 5.00287981
Nonlinear regression model
model: y ~ Lanczos(x, b1, b2, b3, b4, b5, b6)
data: Lanczos2
b1 b2 b3 b4 b5 b6
0.09625 1.00573 0.86425 3.00783 1.55290 5.00288
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 7
Achieved convergence tolerance: 2.954e-08
0: 39.394337: 0.500000 0.700000 3.60000 4.20000 4.00000 6.30000
1: 15.277361: -0.0399692 0.652193 3.11185 4.94473 3.55232 7.60208
2: 1.4368269: -0.205347 1.19502 1.80330 3.97600 2.23144 8.30711
3: 0.0059207020: 0.226202 0.981855 1.99797 4.10959 0.289207 8.10937
4: 0.00046930351: 0.195329 1.22132 1.98335 4.02777 0.334699 6.42399
5: 1.8485379e-06: 0.216923 1.38314 1.94666 4.06657 0.350080 6.50038
6: 4.2361415e-07: 0.226155 1.41242 1.94012 4.07983 0.347409 6.48886
7: 2.9628231e-07: 0.235665 1.44158 1.93507 4.09852 0.342925 6.46243
8: 1.9975829e-07: 0.245033 1.46872 1.93041 4.11756 0.338176 6.43265
9: 1.3213052e-07: 0.254378 1.49471 1.92580 4.13667 0.333391 6.40152
10: 8.9681729e-08: 0.263681 1.51961 1.92107 4.15565 0.328776 6.36882
11: 6.9815130e-08: 0.266850 1.52777 1.91374 4.15939 0.332914 6.33285
12: 6.2911299e-08: 0.269551 1.53523 1.90439 4.16094 0.339555 6.29292
13: 5.9187834e-08: 0.272489 1.54322 1.89493 4.16305 0.346057 6.25398
14: 5.8532295e-08: 0.272114 1.54223 1.89466 4.16212 0.346710 6.25440
15: 5.8099501e-08: 0.271335 1.54091 1.88395 4.15504 0.358187 6.21765
16: 5.6978892e-08: 0.270532 1.53877 1.88361 4.15317 0.359323 6.21806
17: 5.5839160e-08: 0.270308 1.53871 1.87711 4.14934 0.366057 6.19727
18: 5.4840385e-08: 0.269351 1.53669 1.87023 4.14379 0.373892 6.17666
19: 5.3644369e-08: 0.266495 1.53015 1.85695 4.13076 0.390020 6.13945
20: 5.2029341e-08: 0.266267 1.53000 1.84954 4.12661 0.397666 6.11873
21: 5.1037316e-08: 0.265278 1.52788 1.84226 4.12080 0.405926 6.09945
22: 5.0242419e-08: 0.263615 1.52426 1.83083 4.11140 0.419021 6.07005
23: 4.8777105e-08: 0.262024 1.52078 1.81933 4.10214 0.432117 6.04204
24: 4.7468955e-08: 0.257247 1.50926 1.80327 4.08317 0.452941 6.00812
25: 4.6250931e-08: 0.254963 1.50366 1.79447 4.07345 0.464036 5.99124
26: 4.4962173e-08: 0.256704 1.50890 1.78327 4.07222 0.473493 5.96218
27: 4.3395222e-08: 0.255798 1.50702 1.77347 4.06541 0.484192 5.94145
28: 4.2333832e-08: 0.254316 1.50369 1.76284 4.05677 0.496310 5.92025
29: 4.1309200e-08: 0.252944 1.50063 1.75210 4.04834 0.508417 5.89940
30: 4.0278360e-08: 0.251525 1.49743 1.74138 4.03978 0.520554 5.87934
31: 3.9297183e-08: 0.250090 1.49420 1.73013 4.03091 0.533239 5.85885
32: 3.8306123e-08: 0.248784 1.49125 1.71976 4.02276 0.544915 5.84060
33: 3.7509602e-08: 0.246969 1.48715 1.70507 4.01128 0.561419 5.81524
34: 3.6204745e-08: 0.245150 1.48301 1.69038 3.99974 0.577933 5.79110
35: 3.5537654e-08: 0.244861 1.48234 1.68800 3.99786 0.580597 5.78774
36: 3.5301290e-08: 0.244399 1.48124 1.68508 3.99530 0.583986 5.78319
37: 3.4570759e-08: 0.242970 1.47799 1.67303 3.98596 0.597460 5.76394
38: 3.3814785e-08: 0.241962 1.47563 1.66548 3.97979 0.606014 5.75266
39: 3.3252630e-08: 0.241019 1.47345 1.65790 3.97377 0.614542 5.74125
40: 3.2903074e-08: 0.240459 1.47215 1.65342 3.97019 0.619579 5.73469
41: 3.2286819e-08: 0.239287 1.46940 1.64449 3.96292 0.629682 5.72161
42: 3.1937631e-08: 0.238807 1.46831 1.64003 3.95953 0.634624 5.71521
43: 3.1353493e-08: 0.237761 1.46589 1.63129 3.95264 0.644404 5.70269
44: 3.0933407e-08: 0.237061 1.46425 1.62564 3.94810 0.650758 5.69487
45: 3.0240919e-08: 0.235721 1.46112 1.61450 3.93926 0.663236 5.67941
46: 2.9872200e-08: 0.235156 1.45978 1.61005 3.93562 0.668247 5.67358
47: 2.9575334e-08: 0.234566 1.45837 1.60562 3.93194 0.673270 5.66769
48: 2.9432579e-08: 0.232954 1.45495 1.58522 3.91779 0.695281 5.63952
49: 2.8871788e-08: 0.229386 1.44658 1.55445 3.89334 0.729617 5.60056
50: 2.5391079e-08: 0.226734 1.44011 1.53444 3.87626 0.752274 5.57772
50: 2.5391079e-08: 0.226734 1.44011 1.53444 3.87626 0.752274 5.57772
Error in nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), data = Lanczos2, :
Convergence failure: iteration limit reached without convergence (10)
NISTnls documentation built on May 2, 2019, 2:37 a.m.
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Description Format Details Source Examples
Description
The Lanczos2 data frame has 24 rows and 2 columns of generated data.
Format
This data frame contains the following columns:
- y
-
A numeric vector of generated responses.
- x
-
A numeric vector of generated input values.
Details
These data are taken from an example discussed in
Lanczos (1956). The data were generated to 6-digits
of accuracy using
f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x).
Source
Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Lanczos2)
## plot log response to see the number of exponential terms
plot(y ~ x, data = Lanczos2, log = "y")
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm1 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE,
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm1a <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm2 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE,
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
Try(fm2a <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm3 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))),
data = Lanczos2, trace = TRUE, algorithm = "plinear",
start = c(b2 = 0.3, b4 = 5.5, b6 = 7.6)))
## Numerical derivatives do not produce sufficient accuracy to converge
Try(fm4 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))),
data = Lanczos2, trace = TRUE, algorithm = "plinear",
start = c(b2 = 0.7, b4 = 4.2, b6 = 6.3)))
## Use analytic derivatives
Lanczos <- deriv(~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
paste("b", 1:6, sep = ""),
function(x, b1, b2, b3, b4, b5, b6){})
Try(fm5 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE,
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm5a <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm6 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE,
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
Try(fm6a <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6),
data = Lanczos2, trace = TRUE, alg = "port",
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
|
Example output
269.7505 : 1.2 0.3 5.6 5.5 6.5 7.6
12.09318 : 0.1557447 0.3657416 -4.2718714 3.6361873 6.6294277 6.6558506
0.01606173 : 0.09636116 0.60836498 1.59521204 3.66887107 0.82180845 6.54393093
3.988663e-05 : 0.1187054 1.0189614 1.5699075 3.5934999 0.8247741 5.7094101
3.586373e-05 : 0.1203312 1.0348053 1.5128131 3.5660713 0.8802440 5.6210972
3.15019e-05 : 0.1213519 1.0470438 1.4554398 3.5361368 0.9365976 5.5418962
2.862045e-05 : 0.1222942 1.0652189 1.3422732 3.4723715 1.0488240 5.4009803
1.876212e-05 : 0.1202569 1.0797316 1.1315686 3.3340389 1.2615694 5.1848428
3.035105e-06 : 0.1131085 1.0646111 0.9876847 3.2002783 1.4126038 5.0804798
3.02715e-06 : 0.1062082 1.0434084 0.9191323 3.1097336 1.4880577 5.0371973
1.870897e-06 : 0.09702604 1.01075878 0.85997733 3.00952199 1.55639621 5.00053642
2.867039e-11 : 0.09624652 1.00572800 0.86425328 3.00781285 1.55289980 5.00287794
2.229943e-11 : 0.09625117 1.00573399 0.86424724 3.00782926 1.55290120 5.00288010
2.229943e-11 : 0.09625101 1.00573321 0.86424685 3.00782830 1.55290174 5.00287978
Nonlinear regression model
model: y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * x)
data: Lanczos2
b1 b2 b3 b4 b5 b6
0.09625 1.00573 0.86425 3.00783 1.55290 5.00288
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 13
Achieved convergence tolerance: 5.502e-06
0: 134.87524: 1.20000 0.300000 5.60000 5.50000 6.50000 7.60000
1: 37.391901: -0.0911437 0.161578 4.29176 6.72459 5.25608 9.60465
2: 0.53986128: 0.103108 0.245678 0.839264 4.06245 1.71732 9.96535
3: 0.0015421788: 0.120011 0.807061 2.15803 3.87560 0.235291 9.61764
4: 0.00031018901: 0.194294 1.40097 2.10711 4.10424 0.211953 7.60707
5: 2.7613392e-06: 0.215716 1.35716 2.09319 4.14383 0.205080 7.54005
6: 1.3703830e-06: 0.235462 1.42753 2.08152 4.18293 0.196838 7.42023
7: 1.0937083e-06: 0.260767 1.50244 2.06768 4.23051 0.185245 7.31404
8: 8.5640049e-07: 0.288994 1.57650 2.05292 4.28366 0.171647 7.19315
9: 4.2162329e-07: 0.296933 1.59444 2.02559 4.28489 0.190967 6.89846
10: 9.2786359e-08: 0.295711 1.59196 2.01392 4.27632 0.203857 6.82756
11: 8.8508463e-08: 0.293496 1.58747 2.00400 4.26602 0.215992 6.75756
12: 8.4706376e-08: 0.291256 1.58286 1.99388 4.25563 0.228353 6.69223
13: 8.0385968e-08: 0.290320 1.58066 1.99315 4.25319 0.230012 6.69199
14: 7.9765280e-08: 0.290357 1.58082 1.99198 4.25264 0.231150 6.68412
15: 7.9399375e-08: 0.290280 1.58072 1.99077 4.25183 0.232440 6.67651
16: 7.8702123e-08: 0.290251 1.58080 1.98825 4.25049 0.234980 6.66001
17: 7.8158291e-08: 0.289929 1.58016 1.98640 4.24879 0.237148 6.64920
18: 7.7174556e-08: 0.289216 1.57870 1.98276 4.24528 0.241505 6.62801
19: 7.6500261e-08: 0.288891 1.57809 1.98043 4.24333 0.244161 6.61499
20: 7.5428069e-08: 0.288203 1.57675 1.97580 4.23938 0.249474 6.58905
21: 7.4791387e-08: 0.287975 1.57634 1.97371 4.23779 0.251791 6.57808
22: 7.4238606e-08: 0.287564 1.57550 1.97158 4.23576 0.254332 6.56693
23: 7.3590335e-08: 0.285815 1.57187 1.96277 4.22728 0.264893 6.52114
24: 7.3236651e-08: 0.283193 1.56629 1.95086 4.21529 0.279428 6.46511
25: 7.0585258e-08: 0.283167 1.56630 1.95084 4.21532 0.279424 6.46511
26: 6.9418691e-08: 0.283170 1.56625 1.95083 4.21532 0.279470 6.46583
27: 6.9126008e-08: 0.283177 1.56619 1.95078 4.21529 0.279522 6.46640
28: 6.9084711e-08: 0.283170 1.56620 1.95059 4.21514 0.279716 6.46596
29: 6.8984300e-08: 0.283159 1.56621 1.95005 4.21484 0.280264 6.46344
30: 6.8737269e-08: 0.283042 1.56600 1.94882 4.21395 0.281616 6.45768
31: 6.7699014e-08: 0.281797 1.56343 1.94158 4.20748 0.290095 6.42542
32: 6.7036980e-08: 0.279708 1.55899 1.93076 4.19730 0.303003 6.38054
33: 6.3830149e-08: 0.278347 1.55601 1.92444 4.19105 0.310691 6.35742
34: 6.2602186e-08: 0.276946 1.55297 1.91759 4.18445 0.318937 6.33200
35: 6.1220200e-08: 0.275070 1.54868 1.91094 4.17688 0.327456 6.30916
36: 6.0246058e-08: 0.274508 1.54773 1.90343 4.17189 0.335537 6.28157
37: 5.8931428e-08: 0.273461 1.54551 1.89669 4.16618 0.343326 6.25891
38: 5.8294551e-08: 0.271726 1.54181 1.88559 4.15675 0.356152 6.22257
39: 5.7158102e-08: 0.269836 1.53780 1.87261 4.14606 0.371027 6.18261
40: 5.4780735e-08: 0.267983 1.53381 1.86005 4.13568 0.385437 6.14662
41: 5.3013232e-08: 0.265979 1.52943 1.84698 4.12470 0.400512 6.11119
42: 5.1130792e-08: 0.264085 1.52530 1.83400 4.11402 0.415385 6.07781
43: 4.9428425e-08: 0.262197 1.52115 1.82088 4.10328 0.430395 6.04567
44: 4.7788729e-08: 0.260343 1.51707 1.80766 4.09258 0.445466 6.01483
45: 4.6215467e-08: 0.258521 1.51304 1.79437 4.08190 0.460577 5.98523
46: 4.4708627e-08: 0.256723 1.50906 1.78103 4.07123 0.475717 5.95683
47: 4.3146688e-08: 0.255109 1.50546 1.76891 4.06158 0.489446 5.93220
48: 4.1967812e-08: 0.253435 1.50172 1.75613 4.05145 0.503896 5.90702
49: 4.0663894e-08: 0.251908 1.49829 1.74436 4.04213 0.517192 5.88480
50: 3.9616570e-08: 0.250236 1.49453 1.73127 4.03182 0.531955 5.86077
50: 3.9616570e-08: 0.250236 1.49453 1.73127 4.03182 0.531955 5.86077
Error in nls(y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * :
Convergence failure: iteration limit reached without convergence (10)
78.78867 : 0.5 0.7 3.6 4.2 4.0 6.3
0.1065203 : 0.1375763 0.7888953 1.0193691 3.7835135 1.3564416 6.0486056
0.003835761 : 0.1284285 1.0311604 1.2688251 3.2657538 1.1161394 5.5365739
0.0004866298 : 0.1180552 1.0883456 1.0576360 3.2392432 1.3377068 5.0968998
8.958668e-05 : 0.1002222 1.0283572 0.8438644 3.0314828 1.5693128 4.9854297
5.769047e-08 : 0.09622398 1.00598649 0.86433935 3.00709121 1.55283627 5.00287403
2.230791e-11 : 0.09625075 1.00573168 0.86424580 3.00782602 1.55290306 5.00287905
2.229943e-11 : 0.09625053 1.00573075 0.86424563 3.00782529 1.55290344 5.00287879
2.229943e-11 : 0.09625073 1.00573174 0.86424612 3.00782650 1.55290276 5.00287919
2.229943e-11 : 0.09625079 1.00573205 0.86424628 3.00782688 1.55290254 5.00287931
2.229943e-11 : 0.09625118 1.00573403 0.86424727 3.00782932 1.55290116 5.00288012
2.229943e-11 : 0.09625118 1.00573404 0.86424727 3.00782932 1.55290116 5.00288012
2.229943e-11 : 0.09625117 1.00573402 0.86424726 3.00782930 1.55290117 5.00288011
2.229943e-11 : 0.09625117 1.00573401 0.86424726 3.00782929 1.55290118 5.00288011
2.229943e-11 : 0.09625115 1.00573389 0.86424719 3.00782914 1.55290127 5.00288006
2.229943e-11 : 0.09625109 1.00573361 0.86424706 3.00782880 1.55290146 5.00287995
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
2.229943e-11 : 0.0962511 1.0057336 0.8642471 3.0078288 1.5529014 5.0028800
Error in nls(y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * :
step factor 0.000488281 reduced below 'minFactor' of 0.000976562
0: 39.394337: 0.500000 0.700000 3.60000 4.20000 4.00000 6.30000
1: 15.277204: -0.0399740 0.652183 3.11185 4.94474 3.55231 7.60208
2: 1.4367574: -0.205343 1.19508 1.80328 3.97599 2.23143 8.30711
3: 0.0059191757: 0.226211 0.981935 1.99797 4.10961 0.289200 8.10938
4: 0.00046918480: 0.195340 1.22138 1.98335 4.02779 0.334687 6.42402
5: 1.8486425e-06: 0.216938 1.38319 1.94666 4.06660 0.350065 6.50037
6: 4.2336306e-07: 0.226175 1.41248 1.94012 4.07987 0.347391 6.48883
7: 2.9602576e-07: 0.235691 1.44165 1.93506 4.09858 0.342905 6.46238
8: 1.9952336e-07: 0.245065 1.46881 1.93040 4.11763 0.338152 6.43257
9: 1.3194455e-07: 0.254416 1.49482 1.92579 4.13675 0.333365 6.40143
10: 8.9565201e-08: 0.263724 1.51972 1.92106 4.15574 0.328749 6.36869
11: 6.9611457e-08: 0.266948 1.52802 1.91367 4.15958 0.332889 6.33243
12: 6.2782729e-08: 0.269678 1.53557 1.90417 4.16112 0.339648 6.29189
13: 5.9824258e-08: 0.273262 1.54521 1.89406 4.16439 0.346139 6.24941
14: 5.8035318e-08: 0.271167 1.54061 1.88208 4.15376 0.360222 6.21147
15: 5.6104328e-08: 0.269241 1.53643 1.86993 4.14339 0.374299 6.17516
16: 5.3760490e-08: 0.268138 1.53403 1.86279 4.13737 0.382543 6.15542
17: 5.2796775e-08: 0.267095 1.53177 1.85581 4.13156 0.390569 6.13596
18: 5.2617147e-08: 0.264156 1.52508 1.84091 4.11753 0.408398 6.09639
19: 4.9933515e-08: 0.263825 1.52468 1.83264 4.11276 0.417005 6.07494
20: 4.8903899e-08: 0.262801 1.52246 1.82514 4.10675 0.425529 6.05644
21: 4.8313350e-08: 0.261023 1.51857 1.81234 4.09643 0.440103 6.02554
22: 4.6323082e-08: 0.257758 1.51068 1.80075 4.08317 0.454950 6.00173
23: 4.5420911e-08: 0.258537 1.51303 1.79524 4.08234 0.459688 5.98786
24: 4.4893675e-08: 0.258205 1.51242 1.79023 4.07917 0.465027 5.97648
25: 4.4580382e-08: 0.257896 1.51177 1.78738 4.07707 0.468184 5.97035
26: 4.4010042e-08: 0.256955 1.50960 1.78196 4.07223 0.474549 5.95915
27: 4.3615305e-08: 0.256439 1.50845 1.77825 4.06922 0.478775 5.95152
28: 4.2935983e-08: 0.255462 1.50628 1.77078 4.06332 0.487219 5.93609
29: 4.2385267e-08: 0.254809 1.50482 1.76583 4.05938 0.492824 5.92629
30: 4.1668366e-08: 0.253695 1.50242 1.75565 4.05185 0.504115 5.90581
31: 4.1052786e-08: 0.251769 1.49814 1.74024 4.03984 0.521458 5.87631
32: 3.9800037e-08: 0.249699 1.49352 1.72319 4.02666 0.540570 5.84544
33: 3.7697947e-08: 0.247340 1.48803 1.70747 4.01335 0.558652 5.81911
34: 3.6422899e-08: 0.245218 1.48313 1.69159 4.00049 0.576651 5.79310
35: 3.5130871e-08: 0.243230 1.47857 1.67562 3.98788 0.594607 5.76781
36: 3.3832966e-08: 0.241251 1.47401 1.65964 3.97522 0.612569 5.74346
37: 3.2565383e-08: 0.239450 1.46983 1.64505 3.96362 0.628957 5.72209
38: 3.1498230e-08: 0.237650 1.46564 1.63036 3.95192 0.645450 5.70115
39: 3.0333142e-08: 0.235984 1.46179 1.61558 3.94045 0.661892 5.68072
40: 2.9406448e-08: 0.233959 1.45699 1.59991 3.92761 0.679583 5.65972
41: 2.8362572e-08: 0.232028 1.45242 1.58419 3.91488 0.697233 5.63934
42: 2.7776528e-08: 0.228869 1.44493 1.55796 3.89371 0.726627 5.60607
43: 2.5727151e-08: 0.227021 1.44044 1.54326 3.88143 0.743170 5.58904
44: 2.4778057e-08: 0.224041 1.43327 1.51871 3.86121 0.770697 5.56008
45: 2.3254388e-08: 0.221514 1.42709 1.49841 3.84407 0.793528 5.53758
46: 2.2357763e-08: 0.217343 1.41686 1.46455 3.81544 0.831552 5.50057
47: 2.0467229e-08: 0.215094 1.41118 1.44751 3.80019 0.850839 5.48371
48: 1.9449849e-08: 0.211506 1.40220 1.41917 3.77533 0.882775 5.45486
49: 1.8294905e-08: 0.207586 1.39251 1.38424 3.74552 0.921618 5.42052
50: 1.6835712e-08: 0.205780 1.38768 1.37328 3.73415 0.934383 5.41114
50: 1.6835712e-08: 0.205780 1.38768 1.37328 3.73415 0.934383 5.41114
Error in nls(y ~ b1 * exp(-b2 * x) + b3 * exp(-b4 * x) + b5 * exp(-b6 * :
Convergence failure: iteration limit reached without convergence (10)
0.01402087 : 0.3000000 5.5000000 7.6000000 0.1314193 4.3636465 -2.0156365
0.0004941276 : 0.48072705 4.11581444 9.33298634 0.08902670 2.35995861 0.06060881
2.706757e-05 : 1.2984451 4.1317758 6.2959660 0.2080367 2.0135247 0.2905097
1.555232e-06 : 1.4801400 4.0487540 5.7561206 0.2498594 1.7240716 0.5391007
1.371698e-06 : 1.4524688 3.9459188 5.5545785 0.2369986 1.5751292 0.7009011
1.124701e-06 : 1.4209367 3.8337255 5.4078029 0.2229239 1.4281879 0.8619350
8.637405e-07 : 1.385031 3.715273 5.298382 0.207693 1.293813 1.011572
6.976286e-07 : 1.3045283 3.4754953 5.1342245 0.1768827 1.0680620 1.2681346
3.537636e-08 : 1.140080 3.106602 5.007985 0.123071 0.867044 1.523218
2.85667e-08 : 1.0054630 2.9895801 4.9985102 0.0949560 0.8548438 1.5636561
2.416014e-11 : 1.00570988 3.00768642 5.00274604 0.09624596 0.86410110 1.55305193
2.229943e-11 : 1.00573319 3.00782829 5.00287977 0.09625101 0.86424684 1.55290175
2.229943e-11 : 1.00573330 3.00782841 5.00287982 0.09625103 0.86424690 1.55290168
Nonlinear regression model
model: y ~ exp(outer(x, -c(b2, b4, b6)))
data: Lanczos2
b2 b4 b6 .lin1 .lin2 .lin3
1.00573 3.00783 5.00288 0.09625 0.86425 1.55290
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 12
Achieved convergence tolerance: 2.613e-06
0.0005380147 : 0.70000000 4.20000000 6.30000000 0.11710860 2.34808127 0.04146885
3.461023e-05 : 1.2457390 3.9820400 5.5818191 0.1911534 1.7449796 0.5754493
7.528816e-07 : 1.3971116 3.8038195 5.4242194 0.2138858 1.4273660 0.8718880
6.968601e-07 : 1.3584763 3.6758709 5.2928058 0.1982923 1.2769937 1.0378401
6.758355e-07 : 1.278888 3.437353 5.123552 0.168927 1.051030 1.293132
2.506402e-08 : 1.1272595 3.1002254 5.0105008 0.1203295 0.8706027 1.5224148
1.75412e-08 : 1.0058509 2.9933271 4.9991993 0.0952787 0.8565249 1.5616397
2.325657e-11 : 1.0057392 3.0077726 5.0028040 0.0962526 0.8641682 1.5529784
2.229943e-11 : 1.00573327 3.00782838 5.00287980 0.09625103 0.86424689 1.55290170
2.229943e-11 : 1.00573316 3.00782824 5.00287976 0.09625101 0.86424683 1.55290177
2.229943e-11 : 1.00573330 3.00782841 5.00287981 0.09625103 0.86424690 1.55290168
Nonlinear regression model
model: y ~ exp(outer(x, -c(b2, b4, b6)))
data: Lanczos2
b2 b4 b6 .lin1 .lin2 .lin3
1.00573 3.00783 5.00288 0.09625 0.86425 1.55290
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 10
Achieved convergence tolerance: 2.445e-06
269.7505 : 1.2 0.3 5.6 5.5 6.5 7.6
12.0928 : 0.1557453 0.3657420 -4.2717953 3.6362013 6.6293511 6.6558640
0.01606244 : 0.09636195 0.60836746 1.59522065 3.66888806 0.82179905 6.54394417
3.990272e-05 : 0.1187057 1.0189608 1.5699093 3.5935011 0.8247720 5.7094073
3.587714e-05 : 0.1203315 1.0348048 1.5128146 3.5660724 0.8802421 5.6210947
3.151298e-05 : 0.1213522 1.0470432 1.4554407 3.5361375 0.9365965 5.5418934
2.862798e-05 : 0.1222946 1.0652194 1.3422753 3.4723737 1.0488216 5.4009800
1.876486e-05 : 0.120257 1.079731 1.131567 3.334038 1.261571 5.184840
3.035081e-06 : 0.1131083 1.0646100 0.9876828 3.2002763 1.4126060 5.0804777
3.027316e-06 : 0.1062076 1.0434056 0.9191288 3.1097286 1.4880618 5.0371943
1.870014e-06 : 0.0970268 1.0107621 0.8599810 3.0095278 1.5563917 5.0005393
2.867012e-11 : 0.09624648 1.00572780 0.86425315 3.00781252 1.55289998 5.00287785
2.229943e-11 : 0.09625103 1.00573328 0.86424689 3.00782838 1.55290169 5.00287981
Nonlinear regression model
model: y ~ Lanczos(x, b1, b2, b3, b4, b5, b6)
data: Lanczos2
b1 b2 b3 b4 b5 b6
0.09625 1.00573 0.86425 3.00783 1.55290 5.00288
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 12
Achieved convergence tolerance: 7.23e-06
0: 134.87524: 1.20000 0.300000 5.60000 5.50000 6.50000 7.60000
1: 37.391910: -0.0911435 0.161578 4.29176 6.72459 5.25608 9.60465
2: 0.53986043: 0.103108 0.245680 0.839266 4.06246 1.71732 9.96535
3: 0.0015426445: 0.120012 0.807066 2.15803 3.87558 0.235290 9.61763
4: 0.00031015690: 0.194295 1.40097 2.10711 4.10424 0.211956 7.60703
5: 2.7618128e-06: 0.215708 1.35713 2.09320 4.14381 0.205086 7.54007
6: 1.3704546e-06: 0.235451 1.42750 2.08152 4.18291 0.196845 7.42026
7: 1.0934519e-06: 0.260751 1.50239 2.06768 4.23048 0.185255 7.31409
8: 8.5621780e-07: 0.288973 1.57644 2.05293 4.28362 0.171655 7.19327
9: 4.2102278e-07: 0.296933 1.59444 2.02560 4.28490 0.190956 6.89857
10: 9.2765074e-08: 0.295716 1.59197 2.01395 4.27635 0.203825 6.82776
11: 8.8495172e-08: 0.293506 1.58749 2.00404 4.26606 0.215941 6.75785
12: 8.4699749e-08: 0.291269 1.58289 1.99393 4.25569 0.228281 6.69261
13: 8.0406994e-08: 0.290335 1.58070 1.99321 4.25325 0.229934 6.69238
14: 7.9785141e-08: 0.290372 1.58085 1.99204 4.25271 0.231071 6.68451
15: 7.9419764e-08: 0.290295 1.58075 1.99083 4.25190 0.232358 6.67691
16: 7.8723263e-08: 0.290267 1.58083 1.98832 4.25056 0.234893 6.66043
17: 7.8178005e-08: 0.289943 1.58019 1.98647 4.24886 0.237066 6.64959
18: 7.7192423e-08: 0.289235 1.57875 1.98281 4.24535 0.241431 6.62830
19: 7.6513930e-08: 0.288906 1.57812 1.98047 4.24339 0.244102 6.61523
20: 7.5440170e-08: 0.288226 1.57680 1.97580 4.23943 0.249448 6.58903
21: 7.4800758e-08: 0.287991 1.57638 1.97374 4.23783 0.251751 6.57819
22: 7.4237078e-08: 0.287569 1.57551 1.97156 4.23576 0.254344 6.56684
23: 7.3635551e-08: 0.285777 1.57179 1.96264 4.22713 0.265064 6.52048
24: 7.3316133e-08: 0.283128 1.56615 1.95061 4.21502 0.279737 6.46401
25: 7.0732088e-08: 0.283099 1.56616 1.95060 4.21505 0.279734 6.46402
26: 6.9357701e-08: 0.283103 1.56610 1.95059 4.21505 0.279781 6.46479
27: 6.9064203e-08: 0.283109 1.56604 1.95053 4.21500 0.279840 6.46537
28: 6.9023739e-08: 0.283102 1.56605 1.95034 4.21486 0.280037 6.46487
29: 6.8944242e-08: 0.283108 1.56610 1.94989 4.21465 0.280472 6.46272
30: 6.8722284e-08: 0.283011 1.56593 1.94878 4.21386 0.281687 6.45753
31: 6.7671580e-08: 0.281911 1.56366 1.94220 4.20805 0.289366 6.42815
32: 6.6859563e-08: 0.279992 1.55960 1.93207 4.19860 0.301414 6.38580
33: 6.4096924e-08: 0.278625 1.55662 1.92575 4.19234 0.309101 6.36234
34: 6.2843590e-08: 0.277099 1.55330 1.91828 4.18514 0.318094 6.33439
35: 6.1482476e-08: 0.274667 1.54767 1.91126 4.17610 0.327547 6.31082
36: 6.0754224e-08: 0.272351 1.54230 1.90410 4.16728 0.337017 6.28714
37: 5.9822702e-08: 0.269818 1.53633 1.89709 4.15797 0.346566 6.26658
38: 5.9504943e-08: 0.267594 1.53112 1.88987 4.14927 0.356019 6.24458
39: 5.8630688e-08: 0.266155 1.52786 1.88208 4.14212 0.365246 6.22043
40: 5.8440334e-08: 0.264631 1.52465 1.86872 4.13208 0.380123 6.17850
41: 5.3577459e-08: 0.267484 1.53253 1.86068 4.13481 0.385304 6.14995
42: 5.2546072e-08: 0.266842 1.53123 1.85388 4.13005 0.392746 6.13061
43: 5.1698125e-08: 0.265354 1.52803 1.84326 4.12145 0.404853 6.10184
44: 5.0209730e-08: 0.264347 1.52587 1.83561 4.11541 0.413509 6.08240
45: 4.9240203e-08: 0.263178 1.52331 1.82759 4.10881 0.422699 6.06243
46: 4.8287709e-08: 0.262116 1.52101 1.81944 4.10241 0.431907 6.04254
47: 4.7307388e-08: 0.260882 1.51825 1.81140 4.09564 0.441181 6.02386
48: 4.6374294e-08: 0.259575 1.51538 1.80183 4.08797 0.452057 6.00198
49: 4.5308257e-08: 0.258275 1.51251 1.79225 4.08030 0.462937 5.98090
50: 4.5100527e-08: 0.256195 1.50791 1.77651 4.06782 0.480761 5.94711
50: 4.5100527e-08: 0.256195 1.50791 1.77651 4.06782 0.480761 5.94711
Error in nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), data = Lanczos2, :
Convergence failure: iteration limit reached without convergence (10)
78.78867 : 0.5 0.7 3.6 4.2 4.0 6.3
0.1065354 : 0.1375743 0.7888927 1.0193084 3.7834947 1.3565043 6.0485875
0.00383655 : 0.1284274 1.0311586 1.2688219 3.2657285 1.1161437 5.5365848
0.0004866829 : 0.1180555 1.0883470 1.0576426 3.2392443 1.3376998 5.0969078
8.95785e-05 : 0.1002228 1.0283597 0.8438680 3.0314885 1.5693086 4.9854309
5.768697e-08 : 0.09622409 1.00598716 0.86433951 3.00709171 1.55283600 5.00287427
2.230792e-11 : 0.09625103 1.00573310 0.86424651 3.00782776 1.55290207 5.00287963
2.229943e-11 : 0.09625103 1.00573328 0.86424689 3.00782839 1.55290169 5.00287981
Nonlinear regression model
model: y ~ Lanczos(x, b1, b2, b3, b4, b5, b6)
data: Lanczos2
b1 b2 b3 b4 b5 b6
0.09625 1.00573 0.86425 3.00783 1.55290 5.00288
residual sum-of-squares: 2.23e-11
Number of iterations to convergence: 7
Achieved convergence tolerance: 2.954e-08
0: 39.394337: 0.500000 0.700000 3.60000 4.20000 4.00000 6.30000
1: 15.277361: -0.0399692 0.652193 3.11185 4.94473 3.55232 7.60208
2: 1.4368269: -0.205347 1.19502 1.80330 3.97600 2.23144 8.30711
3: 0.0059207020: 0.226202 0.981855 1.99797 4.10959 0.289207 8.10937
4: 0.00046930351: 0.195329 1.22132 1.98335 4.02777 0.334699 6.42399
5: 1.8485379e-06: 0.216923 1.38314 1.94666 4.06657 0.350080 6.50038
6: 4.2361415e-07: 0.226155 1.41242 1.94012 4.07983 0.347409 6.48886
7: 2.9628231e-07: 0.235665 1.44158 1.93507 4.09852 0.342925 6.46243
8: 1.9975829e-07: 0.245033 1.46872 1.93041 4.11756 0.338176 6.43265
9: 1.3213052e-07: 0.254378 1.49471 1.92580 4.13667 0.333391 6.40152
10: 8.9681729e-08: 0.263681 1.51961 1.92107 4.15565 0.328776 6.36882
11: 6.9815130e-08: 0.266850 1.52777 1.91374 4.15939 0.332914 6.33285
12: 6.2911299e-08: 0.269551 1.53523 1.90439 4.16094 0.339555 6.29292
13: 5.9187834e-08: 0.272489 1.54322 1.89493 4.16305 0.346057 6.25398
14: 5.8532295e-08: 0.272114 1.54223 1.89466 4.16212 0.346710 6.25440
15: 5.8099501e-08: 0.271335 1.54091 1.88395 4.15504 0.358187 6.21765
16: 5.6978892e-08: 0.270532 1.53877 1.88361 4.15317 0.359323 6.21806
17: 5.5839160e-08: 0.270308 1.53871 1.87711 4.14934 0.366057 6.19727
18: 5.4840385e-08: 0.269351 1.53669 1.87023 4.14379 0.373892 6.17666
19: 5.3644369e-08: 0.266495 1.53015 1.85695 4.13076 0.390020 6.13945
20: 5.2029341e-08: 0.266267 1.53000 1.84954 4.12661 0.397666 6.11873
21: 5.1037316e-08: 0.265278 1.52788 1.84226 4.12080 0.405926 6.09945
22: 5.0242419e-08: 0.263615 1.52426 1.83083 4.11140 0.419021 6.07005
23: 4.8777105e-08: 0.262024 1.52078 1.81933 4.10214 0.432117 6.04204
24: 4.7468955e-08: 0.257247 1.50926 1.80327 4.08317 0.452941 6.00812
25: 4.6250931e-08: 0.254963 1.50366 1.79447 4.07345 0.464036 5.99124
26: 4.4962173e-08: 0.256704 1.50890 1.78327 4.07222 0.473493 5.96218
27: 4.3395222e-08: 0.255798 1.50702 1.77347 4.06541 0.484192 5.94145
28: 4.2333832e-08: 0.254316 1.50369 1.76284 4.05677 0.496310 5.92025
29: 4.1309200e-08: 0.252944 1.50063 1.75210 4.04834 0.508417 5.89940
30: 4.0278360e-08: 0.251525 1.49743 1.74138 4.03978 0.520554 5.87934
31: 3.9297183e-08: 0.250090 1.49420 1.73013 4.03091 0.533239 5.85885
32: 3.8306123e-08: 0.248784 1.49125 1.71976 4.02276 0.544915 5.84060
33: 3.7509602e-08: 0.246969 1.48715 1.70507 4.01128 0.561419 5.81524
34: 3.6204745e-08: 0.245150 1.48301 1.69038 3.99974 0.577933 5.79110
35: 3.5537654e-08: 0.244861 1.48234 1.68800 3.99786 0.580597 5.78774
36: 3.5301290e-08: 0.244399 1.48124 1.68508 3.99530 0.583986 5.78319
37: 3.4570759e-08: 0.242970 1.47799 1.67303 3.98596 0.597460 5.76394
38: 3.3814785e-08: 0.241962 1.47563 1.66548 3.97979 0.606014 5.75266
39: 3.3252630e-08: 0.241019 1.47345 1.65790 3.97377 0.614542 5.74125
40: 3.2903074e-08: 0.240459 1.47215 1.65342 3.97019 0.619579 5.73469
41: 3.2286819e-08: 0.239287 1.46940 1.64449 3.96292 0.629682 5.72161
42: 3.1937631e-08: 0.238807 1.46831 1.64003 3.95953 0.634624 5.71521
43: 3.1353493e-08: 0.237761 1.46589 1.63129 3.95264 0.644404 5.70269
44: 3.0933407e-08: 0.237061 1.46425 1.62564 3.94810 0.650758 5.69487
45: 3.0240919e-08: 0.235721 1.46112 1.61450 3.93926 0.663236 5.67941
46: 2.9872200e-08: 0.235156 1.45978 1.61005 3.93562 0.668247 5.67358
47: 2.9575334e-08: 0.234566 1.45837 1.60562 3.93194 0.673270 5.66769
48: 2.9432579e-08: 0.232954 1.45495 1.58522 3.91779 0.695281 5.63952
49: 2.8871788e-08: 0.229386 1.44658 1.55445 3.89334 0.729617 5.60056
50: 2.5391079e-08: 0.226734 1.44011 1.53444 3.87626 0.752274 5.57772
50: 2.5391079e-08: 0.226734 1.44011 1.53444 3.87626 0.752274 5.57772
Error in nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), data = Lanczos2, :
Convergence failure: iteration limit reached without convergence (10)
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