Update the docs and make interpolation optional (#10)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

## Release Notes

- **New Features**
  - Added optional curve interpolation with configurable sample points.
  - Introduced a new data file for magnetic field strength measurements.
- Enhanced datasets with new entries and updated formatting for existing
data files.

- **Documentation**
- Updated README with detailed usage instructions for the Jiles-Atherton
system identification tool.
- Added clarifications on interpolation and parameter specifications,
including an output symbol legend.

- **Bug Fixes**
  - Improved handling of reference curve data with repeated values.

- **Chores**
- Updated GitHub Actions workflow timeout duration from 120 to 180
minutes.
  - Modified test configurations.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

.github/workflows/test.yml

@@ -5,7 +5,7 @@ on:
 
 jobs:
   nox:
-    timeout-minutes: 120
+    timeout-minutes: 180
     runs-on: ubuntu-latest
     if: >
       github.event_name == 'pull_request' ||

README.md

@@ -45,12 +45,16 @@ so it may be a good idea to create a dedicated directory for this purpose.
 
 ```shell
 # Fit the example curve from Altair Flux:
-jafit model=venk ref="data/Altair_Flux_HystereticExample.csv"
+jafit model=venk ref="data/B(H).Altair_Flux.Example.csv" interpolate=300
 
 # Find coefficients for isotropic AlNiCo 5:
-jafit model=venk ref="data/B(H).AlNiCo_5.tab"
+jafit model=venk ref="data/B(H).Jesenik.AlNiCo.tab"
 ```
 
+Output symbol legend per function evaluation:
+💚 -- best match so far; ❌ -- no solution (convergence failure); 🔵 -- solution exists but is not the best.
+Use `quiet=1` to reduce the verbosity.
+
 The input reference curve file must contain two columns: H \[A/m\] and B \[T\], either tab- or comma-separated.
 The first row may or may not be the header row.
 
@@ -59,10 +63,27 @@ e.g., only a part of the descending branch.
 If a full loop is provided, then that loop doesn't need to be the major loop;
 the tool will simply use the H amplitude seen in the reference loop for solving the JA equation.
 
+Option `interpolate=N`, where N is a positive integer, can be used to interpolate the reference curve
+with N equidistant sample points distributed along its length. Note that this is not the same as sampling the curve
+on a regular H-axis grid; the difference is that the used method ensures consistent Euclidean distances between
+the sample points. This is useful with irregularly sampled curves, but may cause adverse effects if the reference
+curves contain large gaps, as the interpolation error within the gaps may be large.
+
+If interpolation is not used (it is not by default), then the optimizer will naturally assign higher importance
+to the regions of the curve with higher density of sample points. This may be leveraged to great advantage
+if the reference curve is pre-processed to leave out the regions that are less important for the fitting.
+
 If the reference curve is only a part of the hysteresis loop,
 then the tool will use simple heuristics to guess the reasonable H amplitude for solving the JA equation,
 assuming that the loop is the major loop (i.e., it reaches saturation).
-In this case, it is recommended to specify `H_amp_min`/`H_amp_max` explicitly instead of relying on heuristics.
+In this case, it is recommended to specify `H_amp_min` and/or `H_amp_max` explicitly instead of relying on heuristics.
+
+`H_amp_min` specifies the minimum H magnitude that must be reached before switching the H sweep direction,
+and `H_amp_max` is the maximum H magnitude that the solver is allowed to use; the solver will flip the H sweep
+direction somewhere between these two values as soon as the material reaches saturation ($\chi^\prime$ becomes small).
+
+If the loop is known to be the major loop, then it is occasionally useful to manually extend `H_amp_max` a little
+to ensure that the material reaches deep saturation, so that the optimizer converges to a good $M_s$ value faster.
 
 Optionally, you can provide the initial guess for (some of) the coefficients: `c_r`, `M_s`, `a`, `k_p`, `alpha`.
 
@@ -123,6 +144,14 @@ jafit model=venk H_amp_max=65e3 c_r=0.1 M_s=1.6e6 a=560 k_p=1200 alpha=0.0007
 
 <img src="validation/jafit-comsol-default-material.png" alt="" height="200px"><img src="validation/hysteresis-comsol-default-material.png" alt="" height="200px">
 
+#### Specimen B: LNGT72 approximation
+
+```shell
+jafit model=venk c_r=0.00000098783341818 M_s=0931849.980906066 a=025958.529588940 k_p=147381.227474120 alpha=0.17527880356890363 H_amp_min=1e6
+```
+
+<img src="validation/jafit hysteresis model=venk c_r=0.00000098783341818 M_s=0931849.980906066 a=025958.529588940 k_p=147381.227474120 alpha=0.17527880356890363.png" alt="" height="200px"><img src="validation/hysteresis model=venk c_r=0.00000098783341818 M_s=0931849.980906066 a=025958.529588940 k_p=147381.227474120 alpha=0.17527880356890363.png" alt="" height="200px">
+
 ### Against Altair Flux
 
 The following invocation results in a curve matching the example material from Altair Flux.

data/B(H).Ansys.AlNiCo_5-7.tab

@@ -0,0 +1,17 @@
+"H (A_per_meter)" 	"B (tesla)"
+-59300 	0
+-58914 	0.13
+-58147 	0.32400000000000001
+-57258 	0.52100000000000002
+-56490 	0.72099999999999997
+-55237 	0.92200000000000004
+-53889 	0.99099999999999999
+-51934 	1.0609999999999999
+-49618 	1.1200000000000001
+-46577 	1.167
+-39653 	1.2190000000000001
+-31522 	1.2490000000000001
+-23392 	1.272
+-15503 	1.3009999999999999
+-7616 	1.321
+0 	1.3320000000000001

data/B(H).Ansys.LNG52.tab

@@ -0,0 +1,21 @@
+"H (A_per_meter)" 	"B (tesla)"
+-56000 	0
+-55874 	0.10717400000000001
+-55722.400000000001 	0.21434800000000001
+-55536.300000000003 	0.321521
+-55302.800000000003 	0.42869499999999999
+-55000.699999999997 	0.53586900000000004
+-54594.900000000001 	0.64304300000000003
+-54020.800000000003 	0.75021599999999999
+-53146.400000000001 	0.85738999999999999
+-51652.5 	0.96456399999999998
+-48519.300000000003 	1.0717399999999999
+-43128.300000000003 	1.1457200000000001
+-37737.300000000003 	1.17906
+-32346.200000000001 	1.19834
+-26955.200000000001 	1.2152799999999999
+-21564.200000000001 	1.23221
+-16173.1 	1.24915
+-10782.1 	1.2660899999999999
+-5391.04 	1.28302
+0 	1.3

data/B(H).Campbell.AlNiCo_5.tab

@@ -0,0 +1,47 @@
+H	B
+172437.400000	1.547170
+150113.800000	1.518142
+124145.800000	1.494920
+100227.800000	1.457184
+76082.000000	1.416546
+50113.800000	1.375908
+25968.200000	1.335268
+3872.400000	1.300436
+0.000000	1.291728
+-19817.800000	1.236574
+-31890.600000	1.184326
+-43052.400000	1.100146
+-49886.200000	0.998548
+-54669.800000	0.830188
+-55808.600000	0.560232
+-56036.400000	0.301886
+-56492.000000	0.133526
+-56719.800000	0.000000
+-56947.600000	-0.136430
+-66287.000000	-1.149492
+-90660.600000	-1.341074
+-151025.000000	-1.526850
+-181549.000000	-1.576198
+-151252.800000	-1.526850
+-124829.200000	-1.492018
+-100911.200000	-1.448476
+-76082.000000	-1.407838
+-50569.400000	-1.367198
+-27107.000000	-1.320754
+-3872.400000	-1.277214
+455.600000	-1.259796
+17539.800000	-1.216256
+26195.800000	-1.181422
+38268.800000	-1.111756
+47836.000000	-1.004354
+52619.600000	-0.870828
+55808.600000	-0.502178
+56492.000000	-0.287374
+56719.800000	-0.075472
+56720.000000	-0.002902
+57175.400000	0.098694
+60820.000000	0.981132
+70615.000000	1.222060
+99088.800000	1.390420
+149886.200000	1.521044
+172665.200000	1.547170

data/B(H).Ibrayeva.LNGT40.tab

@@ -0,0 +1,136 @@
+H	B
+400000.000000	1.641026
+379906.000000	1.605770
+358555.600000	1.576924
+334066.000000	1.544872
+316483.600000	1.506410
+299529.200000	1.483974
+279434.800000	1.458334
+259340.800000	1.423076
+239246.400000	1.403846
+219780.400000	1.368590
+203453.600000	1.336538
+178336.000000	1.307692
+149450.400000	1.253206
+128728.400000	1.227564
+111146.000000	1.185898
+96075.200000	1.153846
+81004.800000	1.131410
+62166.400000	1.102564
+47095.600000	1.060898
+34536.800000	1.044872
+25745.600000	1.016026
+13186.800000	1.000000
+6279.600000	0.974358
+-3767.600000	0.948718
+-10047.200000	0.926282
+-20722.000000	0.903846
+-30141.200000	0.868590
+-37048.800000	0.849358
+-47723.600000	0.820512
+-58398.800000	0.778846
+-67818.000000	0.743590
+-74097.200000	0.708334
+-81632.800000	0.685898
+-87912.000000	0.650642
+-94191.600000	0.615384
+-100470.800000	0.576924
+-106122.400000	0.538462
+-111774.000000	0.490384
+-114285.600000	0.432692
+-120565.200000	0.403846
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+-124332.800000	0.304488
+-126216.800000	0.269230
+-127472.400000	0.214744
+-129984.400000	0.157052
+-130612.400000	0.121794
+-131240.000000	0.086538
+-132496.000000	0.048076
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