This page was generated from the notebook convert_rascal.ipynb found in the Python-RAT repository. Download notebook.

Note

To get the output project and results from this example in your Python session, run:

from RATapi.examples import convert_rascal
project, results = convert_rascal()

RasCAL-1 to RAT#

RasCAL-1 (R1) project structs can be converted to RAT Project classes, and vice versa. This is done via the functions r1_to_project_class and project_class_to_r1.

Converting from R1 to a Project is very simple. We use the example R1 project in the file R1monolayerVolumeModel.mat, which is a project for analysing a monolayer of DSPC with various deuterations (tail-deuterated, head-deuterated, fully deuterated, hydrogenated)

Simply give the file path to the function r1_to_project_class, and it returns a RAT Project that you can use exactly like any other.

[1]:
from RATapi.utils.convert import r1_to_project_class

project = r1_to_project_class("R1monolayerVolumeModel.mat")
print(project)
Name: ----------------------------------------------------------------------------------------------

monolayerVolumeModel

Calculation: ---------------------------------------------------------------------------------------

normal

Model: ---------------------------------------------------------------------------------------------

custom layers

Geometry: ------------------------------------------------------------------------------------------

air/substrate

Parameters: ----------------------------------------------------------------------------------------

+-------+---------------------+------+--------------------+-------+------+
| index |         name        | min  |       value        |  max  | fit  |
+-------+---------------------+------+--------------------+-------+------+
|   0   | Substrate Roughness | 1.0  | 2.9979642781948908 |  8.0  | True |
|   1   |  Area per molecule  | 47.0 | 53.052680457664785 | 100.0 | True |
|   2   |    Head Thickness   | 7.0  | 12.276333836779942 |  20.0 | True |
|   3   |        Theta        | 0.0  | 28.870541049836262 |  50.0 | True |
+-------+---------------------+------+--------------------+-------+------+

Bulk In: -------------------------------------------------------------------------------------------

+-------+------+-----+-------+-----+-------+
| index | name | min | value | max |  fit  |
+-------+------+-----+-------+-----+-------+
|   0   | Air  | 0.0 |  0.0  | 0.0 | False |
+-------+------+-----+-------+-----+-------+

Bulk Out: ------------------------------------------------------------------------------------------

+-------+------+---------+----------+---------+-------+
| index | name |   min   |  value   |   max   |  fit  |
+-------+------+---------+----------+---------+-------+
|   0   | D2O  | 6.3e-06 | 6.35e-06 | 6.4e-06 | False |
|   1   | ACMW |  -5e-07 |   0.0    |  5e-07  | False |
+-------+------+---------+----------+---------+-------+

Scalefactors: --------------------------------------------------------------------------------------

+-------+---------------+-----+--------------------+-----+-------+
| index |      name     | min |       value        | max |  fit  |
+-------+---------------+-----+--------------------+-----+-------+
|   0   | Scalefactor 1 | 0.1 | 0.2272676786810902 | 0.4 | False |
+-------+---------------+-----+--------------------+-----+-------+

Background Parameters: -----------------------------------------------------------------------------

+-------+------------------------+-------+------------------------+-------+------+
| index |          name          |  min  |         value          |  max  | fit  |
+-------+------------------------+-------+------------------------+-------+------+
|   0   | Background parameter 1 | 1e-07 | 2.2653463958223856e-06 | 7e-06 | True |
|   1   | Background parameter 2 | 1e-07 | 5.7431759430575025e-06 | 7e-06 | True |
+-------+------------------------+-------+------------------------+-------+------+

Backgrounds: ---------------------------------------------------------------------------------------

+-------+-----------------+----------+------------------------+
| index |       name      |   type   |         source         |
+-------+-----------------+----------+------------------------+
|   0   | Background  D2O | constant | Background parameter 1 |
|   1   | Background ACMW | constant | Background parameter 2 |
+-------+-----------------+----------+------------------------+

Resolution Parameters: -----------------------------------------------------------------------------

+-------+------------------------+------+-------+------+-------+
| index |          name          | min  | value | max  |  fit  |
+-------+------------------------+------+-------+------+-------+
|   0   | Resolution parameter 1 | 0.01 |  0.03 | 0.05 | False |
+-------+------------------------+------+-------+------+-------+

Resolutions: ---------------------------------------------------------------------------------------

+-------+--------------+----------+------------------------+
| index |     name     |   type   |         source         |
+-------+--------------+----------+------------------------+
|   0   | Resolution 1 | constant | Resolution parameter 1 |
+-------+--------------+----------+------------------------+

Custom Files: --------------------------------------------------------------------------------------

+-------+-----------+-------------+---------------+----------+------+
| index |    name   |   filename  | function name | language | path |
+-------+-----------+-------------+---------------+----------+------+
|   0   | Model_IIb | Model_IIb.m |   Model_IIb   |  matlab  |  .   |
+-------+-----------+-------------+---------------+----------+------+

Data: ----------------------------------------------------------------------------------------------

+-------+------------+----------------------+---------------------+---------------------+
| index |    name    |         data         |      data range     |   simulation range  |
+-------+------------+----------------------+---------------------+---------------------+
|   0   | Simulation |          []          |          []         |     [0.005, 0.7]    |
|   1   | d70acmw20  | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
|   2   |  d70d2o20  | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
|   3   | d13acmw20  | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
|   4   |  d13d2o20  | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
|   5   | d83acmw20  | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
|   6   |  d83d2o20  | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
|   7   |   hd2o20   | Data array: [51 x 3] | [0.051793, 0.58877] | [0.051793, 0.58877] |
+-------+------------+----------------------+---------------------+---------------------+

Contrasts: -----------------------------------------------------------------------------------------

+-------+--------------+-----------+-----------------+-------------------+---------+----------+---------------+--------------+----------+-----------+
| index |     name     |    data   |    background   | background action | bulk in | bulk out |  scalefactor  |  resolution  | resample |   model   |
+-------+--------------+-----------+-----------------+-------------------+---------+----------+---------------+--------------+----------+-----------+
|   0   |  d70, acmw   | d70acmw20 | Background ACMW |        add        |   Air   |   ACMW   | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
|   1   |   d70 d2o    |  d70d2o20 | Background  D2O |        add        |   Air   |   D2O    | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
|   2   |   d13 acmw   | d13acmw20 | Background ACMW |        add        |   Air   |   ACMW   | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
|   3   |   d13 d2o    |  d13d2o20 | Background  D2O |        add        |   Air   |   D2O    | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
|   4   |   d83 acmw   | d83acmw20 | Background ACMW |        add        |   Air   |   ACMW   | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
|   5   |   d83 d2o    |  d83d2o20 | Background  D2O |        add        |   Air   |   D2O    | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
|   6   | fully h, D2O |   hd2o20  | Background  D2O |        add        |   Air   |   D2O    | Scalefactor 1 | Resolution 1 |  False   | Model_IIb |
+-------+--------------+-----------+-----------------+-------------------+---------+----------+---------------+--------------+----------+-----------+


Note that there are various features of RAT which do not feature in RasCAL-1, such as prior_type, mu and sigma for parameters. These are given sensible default values (again e.g. for parameters, prior_type = uniform, mu = 0.0, sigma=inf), but you may change these if you would like to use these new features:

[2]:
project.parameters["Head Thickness"].prior_type = 'gaussian'
project.parameters["Theta"].mu = 2.0
project.parameters["Area per molecule"].sigma = 50.0
# etc...
print(project.parameters)
+-------+---------------------+------+--------------------+-------+------+
| index |         name        | min  |       value        |  max  | fit  |
+-------+---------------------+------+--------------------+-------+------+
|   0   | Substrate Roughness | 1.0  | 2.9979642781948908 |  8.0  | True |
|   1   |  Area per molecule  | 47.0 | 53.052680457664785 | 100.0 | True |
|   2   |    Head Thickness   | 7.0  | 12.276333836779942 |  20.0 | True |
|   3   |        Theta        | 0.0  | 28.870541049836262 |  50.0 | True |
+-------+---------------------+------+--------------------+-------+------+

Also note that any custom files must be available to RAT. By default, RAT will assume these files are in the same directory that you are running RAT from, but if they are elsewhere you may change the relevant file location:

[3]:
# e.g. if our model is in the directory `my_models/`
project.custom_files[0].filename = "my_models/Model_IIb.m"

As well as MATLAB functions, RAT can also run custom files provided in Python or C++ format. This may be beneficial if you do not have access to MATLAB, do not have access to the custom files from your old RasCAL project, or find it more convenient to use Python. This is done similarly to changing the file path: if we have a function defined in the Python custom file Model_IIb.py:

[4]:
project.custom_files[0].filename = "Model_IIb.py"
project.custom_files[0].language = 'python'

RAT to RasCAL-1#

To demonstrate the other way around, we will use the DSPC lipid bilayer model project from another tutorial.

[5]:
from RATapi.examples import DSPC_standard_layers
lipid_bilayer_project = DSPC_standard_layers()[0]
print(lipid_bilayer_project)
Starting RAT ───────────────────────────────────────────────────────────────────────────────────────────────────────────

Elapsed time is 0.002 seconds

Finished RAT ───────────────────────────────────────────────────────────────────────────────────────────────────────────

Name: ----------------------------------------------------------------------------------------------

original_dspc_bilayer

Calculation: ---------------------------------------------------------------------------------------

normal

Model: ---------------------------------------------------------------------------------------------

standard layers

Geometry: ------------------------------------------------------------------------------------------

substrate/liquid

Parameters: ----------------------------------------------------------------------------------------

+-------+-------------------------+----------+-----------+----------+-------+
| index |           name          |   min    |   value   |   max    |  fit  |
+-------+-------------------------+----------+-----------+----------+-------+
|   0   |   Substrate Roughness   |   1.0    |    3.0    |   10.0   |  True |
|   1   |     Oxide Thickness     |   5.0    |   19.54   |   60.0   |  True |
|   2   |        Oxide SLD        | 3.39e-06 |  3.39e-06 | 3.41e-06 | False |
|   3   |   SAM Tails Thickness   |   15.0   |   22.66   |   35.0   |  True |
|   4   |      SAM Tails SLD      |  -5e-07  | -4.01e-07 |  -3e-07  | False |
|   5   |   SAM Tails Hydration   |   1.0    |   5.252   |   50.0   |  True |
|   6   |      SAM Roughness      |   1.0    |    5.64   |   15.0   |  True |
|   7   |       CW Thickness      |   10.0   |   17.12   |   28.0   |  True |
|   8   |          CW SLD         |   0.0    |    0.0    |  1e-09   | False |
|   9   |   SAM Heads Thickness   |   5.0    |    8.56   |   17.0   |  True |
|   10  |      SAM Heads SLD      |  1e-07   |  1.75e-06 |  2e-06   | False |
|   11  |   SAM Heads Hydration   |   10.0   |   45.45   |   50.0   |  True |
|   12  | Bilayer Heads Thickness |   7.0    |    10.7   |   17.0   |  True |
|   13  |    Bilayer Heads SLD    |  5e-07   |  1.47e-06 | 1.5e-06  | False |
|   14  |    Bilayer Roughness    |   2.0    |   6.014   |   15.0   |  True |
|   15  | Bilayer Tails Thickness |   14.0   |   17.82   |   22.0   |  True |
|   16  |    Bilayer Tails SLD    |  -5e-07  | -4.61e-07 |   0.0    | False |
|   17  | Bilayer Tails Hydration |   10.0   |   17.64   |   50.0   |  True |
|   18  | Bilayer Heads Hydration |   10.0   |   36.15   |   50.0   |  True |
|   19  |       CW Hydration      |   99.9   |   100.0   |  100.0   | False |
|   20  |     Oxide Hydration     |   0.0    |   23.61   |   60.0   |  True |
+-------+-------------------------+----------+-----------+----------+-------+

Bulk In: -------------------------------------------------------------------------------------------

+-------+---------+-------+-----------+---------+-------+
| index |   name  |  min  |   value   |   max   |  fit  |
+-------+---------+-------+-----------+---------+-------+
|   0   | Silicon | 2e-06 | 2.073e-06 | 2.1e-06 | False |
+-------+---------+-------+-----------+---------+-------+

Bulk Out: ------------------------------------------------------------------------------------------

+-------+------+---------+----------+----------+------+
| index | name |   min   |  value   |   max    | fit  |
+-------+------+---------+----------+----------+------+
|   0   | D2O  | 5.5e-06 | 5.98e-06 | 6.4e-06  | True |
|   1   | SMW  |  1e-06  | 2.21e-06 | 4.99e-06 | True |
+-------+------+---------+----------+----------+------+

Scalefactors: --------------------------------------------------------------------------------------

+-------+---------------+------+-------+-----+-------+
| index |      name     | min  | value | max |  fit  |
+-------+---------------+------+-------+-----+-------+
|   0   | Scalefactor 1 | 0.05 |  0.1  | 0.2 | False |
|   1   | Scalefactor 2 | 0.05 |  0.15 | 0.2 | False |
+-------+---------------+------+-------+-----+-------+

Background Parameters: -----------------------------------------------------------------------------

+-------+--------------------------+-------+----------+----------+------+
| index |           name           |  min  |  value   |   max    | fit  |
+-------+--------------------------+-------+----------+----------+------+
|   0   | Background parameter D2O | 5e-10 | 2.23e-06 |  7e-06   | True |
|   1   | Background parameter SMW | 1e-10 | 3.38e-06 | 4.99e-06 | True |
+-------+--------------------------+-------+----------+----------+------+

Backgrounds: ---------------------------------------------------------------------------------------

+-------+----------------+----------+--------------------------+
| index |      name      |   type   |          source          |
+-------+----------------+----------+--------------------------+
|   0   | D2O Background | constant | Background parameter D2O |
|   1   | SMW Background | constant | Background parameter SMW |
+-------+----------------+----------+--------------------------+

Resolution Parameters: -----------------------------------------------------------------------------

+-------+--------------------+------+-------+------+-------+
| index |        name        | min  | value | max  |  fit  |
+-------+--------------------+------+-------+------+-------+
|   0   | Resolution Param 1 | 0.01 |  0.03 | 0.05 | False |
+-------+--------------------+------+-------+------+-------+

Resolutions: ---------------------------------------------------------------------------------------

+-------+--------------+----------+--------------------+
| index |     name     |   type   |       source       |
+-------+--------------+----------+--------------------+
|   0   | Resolution 1 | constant | Resolution Param 1 |
+-------+--------------+----------+--------------------+

Data: ----------------------------------------------------------------------------------------------

+-------+--------------+----------------------+---------------------+---------------------+
| index |     name     |         data         |      data range     |   simulation range  |
+-------+--------------+----------------------+---------------------+---------------------+
|   0   |  Simulation  |          []          |          []         |     [0.005, 0.7]    |
|   1   | dspc_bil_D2O | Data array: [82 x 3] | [0.011403, 0.59342] | [0.011403, 0.59342] |
|   2   | dspc_bil_smw | Data array: [82 x 3] | [0.011403, 0.59342] | [0.011403, 0.59342] |
+-------+--------------+----------------------+---------------------+---------------------+

Layers: --------------------------------------------------------------------------------------------

+-------+---------------+-------------------------+-------------------+---------------------+-------------------------+--------------+
| index |      name     |        thickness        |        SLD        |      roughness      |        hydration        | hydrate with |
+-------+---------------+-------------------------+-------------------+---------------------+-------------------------+--------------+
|   0   |     Oxide     |     Oxide Thickness     |     Oxide SLD     | Substrate Roughness |     Oxide Hydration     |   bulk out   |
|   1   |   SAM Tails   |   SAM Tails Thickness   |   SAM Tails SLD   |    SAM Roughness    |   SAM Tails Hydration   |   bulk out   |
|   2   |   SAM Heads   |   SAM Heads Thickness   |   SAM Heads SLD   |    SAM Roughness    |   SAM Heads Hydration   |   bulk out   |
|   3   | Central Water |       CW Thickness      |       CW SLD      |  Bilayer Roughness  |       CW Hydration      |   bulk out   |
|   4   | Bilayer Heads | Bilayer Heads Thickness | Bilayer Heads SLD |  Bilayer Roughness  | Bilayer Heads Hydration |   bulk out   |
|   5   | Bilayer Tails | Bilayer Tails Thickness | Bilayer Tails SLD |  Bilayer Roughness  | Bilayer Tails Hydration |   bulk out   |
+-------+---------------+-------------------------+-------------------+---------------------+-------------------------+--------------+

Contrasts: -----------------------------------------------------------------------------------------

+-------+------+--------------+----------------+-------------------+---------+----------+---------------+--------------+----------+---------------+
| index | name |     data     |   background   | background action | bulk in | bulk out |  scalefactor  |  resolution  | resample |     model     |
+-------+------+--------------+----------------+-------------------+---------+----------+---------------+--------------+----------+---------------+
|   0   | D2O  | dspc_bil_D2O | D2O Background |        add        | Silicon |   D2O    | Scalefactor 1 | Resolution 1 |  False   |     Oxide     |
|       |      |              |                |                   |         |          |               |              |          |   SAM Tails   |
|       |      |              |                |                   |         |          |               |              |          |   SAM Heads   |
|       |      |              |                |                   |         |          |               |              |          | Central Water |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Heads |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Tails |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Tails |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Heads |
|   1   | SMW  | dspc_bil_smw | SMW Background |        add        | Silicon |   SMW    | Scalefactor 2 | Resolution 1 |  False   |     Oxide     |
|       |      |              |                |                   |         |          |               |              |          |   SAM Tails   |
|       |      |              |                |                   |         |          |               |              |          |   SAM Heads   |
|       |      |              |                |                   |         |          |               |              |          | Central Water |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Heads |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Tails |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Tails |
|       |      |              |                |                   |         |          |               |              |          | Bilayer Heads |
+-------+------+--------------+----------------+-------------------+---------+----------+---------------+--------------+----------+---------------+


project_class_to_r1 takes parameters project and filename, which are the Project object and filename for the produced .mat file respectively. This .mat file can then be loaded into RasCAL-1.

Alternatively, if one sets return_struct=True, the struct is returned as a Python dictionary instead of being saved.

Note that a MATLAB engine is used to save the project to a .mat file, so the Python library matlabengine must be installed.

[6]:
from RATapi.utils.convert import project_class_to_r1
from pprint import pp  # for printing the struct

# save to a file called lipid_bilayer.mat
project_class_to_r1(lipid_bilayer_project, filename="lipid_bilayer.mat")

# return as a Python dictionary
struct = project_class_to_r1(lipid_bilayer_project, return_struct=True)
pp(struct)
{'name': 'original_dspc_bilayer',
 'module': {'type': 'standard layers',
            'experiment_type': 'Solid / Liquid',
            'name': ''},
 'paramnames': ['Substrate Roughness',
                'Oxide Thickness',
                'Oxide SLD',
                'SAM Tails Thickness',
                'SAM Tails SLD',
                'SAM Tails Hydration',
                'SAM Roughness',
                'CW Thickness',
                'CW SLD',
                'SAM Heads Thickness',
                'SAM Heads SLD',
                'SAM Heads Hydration',
                'Bilayer Heads Thickness',
                'Bilayer Heads SLD',
                'Bilayer Roughness',
                'Bilayer Tails Thickness',
                'Bilayer Tails SLD',
                'Bilayer Tails Hydration',
                'Bilayer Heads Hydration',
                'CW Hydration',
                'Oxide Hydration'],
 'params': [3.0,
            19.54,
            3.39e-06,
            22.66,
            -4.01e-07,
            5.252,
            5.64,
            17.12,
            0.0,
            8.56,
            1.75e-06,
            45.45,
            10.7,
            1.47e-06,
            6.014,
            17.82,
            -4.61e-07,
            17.64,
            36.15,
            100.0,
            23.61],
 'constr': [[1.0, 10.0],
            [5.0, 60.0],
            [3.39e-06, 3.41e-06],
            [15.0, 35.0],
            [-5e-07, -3e-07],
            [1.0, 50.0],
            [1.0, 15.0],
            [10.0, 28.0],
            [0.0, 1e-09],
            [5.0, 17.0],
            [1e-07, 2e-06],
            [10.0, 50.0],
            [7.0, 17.0],
            [5e-07, 1.5e-06],
            [2.0, 15.0],
            [14.0, 22.0],
            [-5e-07, 0.0],
            [10.0, 50.0],
            [10.0, 50.0],
            [99.9, 100.0],
            [0.0, 60.0]],
 'fityesno': [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1],
 'scalesNames': ['Scalefactor 1', 'Scalefactor 2'],
 'scalefac': [0.1, 0.15],
 'scale_constr': [[0.05, 0.2], [0.05, 0.2]],
 'scalefac_fityesno': [0, 0],
 'numberOfScales': 2,
 'nbaNames': 'Silicon',
 'nba': 2.073e-06,
 'nbairs_constr': [2e-06, 2.1e-06],
 'nbairs_fityesno': 0,
 'numberOfNbas': 1,
 'nbsNames': ['D2O', 'SMW'],
 'nbs': [5.98e-06, 2.21e-06],
 'nbsubs_constr': [[5.5e-06, 6.4e-06], [1e-06, 4.99e-06]],
 'nbsubs_fityesno': [1, 1],
 'numberOfNbss': 2,
 'numberOfShifts': 1,
 'shiftsNames': 'Shift 1',
 'shifts_horisontal': 0,
 'shifts_fityesno': 0,
 'shifts_constr': [-0.0001, 0.0001],
 'resolNames': 'Resolution 1',
 'resolution': 0.03,
 'resolution_constr': [0.01, 0.05],
 'resolution_fityesno': 0,
 'numberOfResolutions': 1,
 'backsNames': ['D2O Background', 'SMW Background'],
 'backs': [2.23e-06, 3.38e-06],
 'backs_constr': [[5e-10, 7e-06], [1e-10, 4.99e-06]],
 'backgrounds_fityesno': [1, 1],
 'numberOfBacks': 2,
 'numberOfLayers': 6,
 'layersDetails': [[2, 3, 1, 21, 'Oxide', 'bulk out'],
                   [4, 5, 7, 6, 'SAM Tails', 'bulk out'],
                   [10, 11, 7, 12, 'SAM Heads', 'bulk out'],
                   [8, 9, 15, 20, 'Central Water', 'bulk out'],
                   [13, 14, 15, 19, 'Bilayer Heads', 'bulk out'],
                   [16, 17, 15, 18, 'Bilayer Tails', 'bulk out']],
 'contrastNames': ['D2O', 'SMW'],
 'contrastNbas': [1, 1],
 'contrastNbss': [1, 2],
 'contrastScales': [1, 2],
 'data': [array([[1.1403e-02, 1.0063e-01, 1.9003e-03],
       [1.1973e-02, 1.1082e-01, 1.8830e-03],
       [1.2572e-02, 1.0766e-01, 1.6413e-03],
       [1.3201e-02, 1.0652e-01, 1.4669e-03],
       [1.3861e-02, 9.0118e-02, 1.1774e-03],
       [1.4554e-02, 3.4255e-02, 4.8888e-04],
       [1.5281e-02, 1.7209e-02, 2.6267e-04],
       [1.6045e-02, 1.0465e-02, 1.7551e-04],
       [1.6848e-02, 7.0455e-03, 1.3083e-04],
       [1.7690e-02, 4.5958e-03, 9.7193e-05],
       [1.8575e-02, 3.4925e-03, 8.0937e-05],
       [1.9503e-02, 2.4510e-03, 6.4505e-05],
       [2.0479e-02, 1.7544e-03, 5.1254e-05],
       [2.1502e-02, 1.3384e-03, 4.2675e-05],
       [2.2578e-02, 1.0447e-03, 3.5865e-05],
       [2.3706e-02, 7.6523e-04, 2.9299e-05],
       [2.4892e-02, 6.4257e-04, 2.6236e-05],
       [2.6136e-02, 5.0024e-04, 1.3657e-05],
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