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Features

Statistic

Pre-Analysis

As part of the fitting procedure in SpectraFit, the initial data will be first analyzed based on standard statistic. The standard statistics includes:

  • Number of points in the data array
  • The mean value of the data array
  • The standard deviation of the data array
  • The minimum value of the data array
  • The maximum value of the data array
  • The percentage based contribution of the data array

The evaluation of the standard statistics is performed via pandas-describe; see also the Command Line Interface for more information in the API-section.

Pre-Analysis
0 1
count 611.00 611.00
mean 3.48 0.06
std 2.94 0.12
min -1.60 0.00
10% -0.58 0.00
20% 0.43 0.00
30% 1.45 0.00
40% 2.47 0.01
50% 3.48 0.02
60% 4.50 0.03
70% 5.52 0.06
80% 6.53 0.10
90% 7.55 0.14
max 8.57 1.00

Fit Statistic

The fit statistic provides standard statistics of the data based on the fit report module of lmfit. So following standard insights are provided by lmfit:

  • used fitting method
  • number of evaluated function
  • number of data points
  • number of variables
  • chi-square
  • reduced chi-square
  • Akaike info criteria is an estimator of prediction error
  • Bayesian info criteria is an estimator of model validity

This information will be also saved and extended in the json-output.

Variable Analysis

In addition to Fit Statistic, the variable analysis of lmfit provides a more detail look on the fitting result of each peak's attribute. In case of a pseudovoigt distribution, the attributes consists of:

  1. Amplitude
  2. Center
  3. Full Width at Half Maximum of the gaussian distribution
  4. Full Width at Half Maximum of the lorentzian distribution

And every of these attributes has to be analyzed according to the:

  1. Best Value
  2. Initial Value
  3. Absolute Error
  4. Relative Error
Variable Analysis
variable name value absolute error relative error init value model value
pseudovoigt_amplitude_1 0.16403603 ± 0.28617283 174.46% 1 0.164036
pseudovoigt_center_1 0.03500058 ± 0.07534815 215.28% 0 0.03500058
pseudovoigt_fwhmg_1 0.06876795 ± 0.04790400 69.66% 0.02 0.06876795
pseudovoigt_fwhml_1 0.09252389 ± 0.03757126 40.61% 0.01 0.09252389
pseudovoigt_amplitude_2 0.09740402 ± 0.12049276 123.70% 1 0.09740402
pseudovoigt_center_2 -0.01805236 ± 0.02098358 116.24% 0 -0.01805236
pseudovoigt_fwhmg_2 0.04334471 ± 0.03017987 69.63% 0.02 0.04334471
pseudovoigt_fwhml_2 0.09989511 ± 0.07669355 76.77% 0.01 0.09989511
constant_amplitude_3 0.03676873 ± 0.00277773 7.55% 1 0.03676873
gaussian_amplitude_4 0.01411288 ± 0.18946470 1342.49% 1 0.01411288
gaussian_center_4 7.8507e-04 ± 0.07239645 9221.69% 0 0.0007850674
gaussian_fwhmg_4 0.04893397 ± 0.27055202 552.89% 0.02 0.04893397

Correlation Analysis

The Variable Analysis will be completed by the two kinds of correlation analysis. In the first case, the correlation analysis of lmfit is used to analyze every peak's attributes against each other. In contrast to the default values of lmfit, the threshold of the correlation analysis is set to 0.0; please check also the Performing Fits and Analyzing Outputs in lmfit

In the second case, the linear correlation analysis of pandas-module corr is used to generally analyze the fit results in the concept of the dataframes. In more detail, a linear pearson correlation will be performed between each components in the dataframe, which normally consists of:

  1. Energy (1D-array)
  2. Intensity (1D-array)
  3. Residual (1D-array)
  4. Fit (1D-array)
  5. Single components of the fit as multiple variables (1D-array)

This analysis should give insights, if the fit model can be further simplified as a result of a superposition of the components, see also the Wikipedia article about Correlation.

Overall Correlation Analysis
energy intensity residual fit pseudovoigt_1 pseudovoigt_2 constant_3 gaussian_4
energy 1.00 -0.31 0.12 -0.23 -0.21 -0.25 nan -0.10
intensity -0.31 1.00 0.05 0.90 0.88 0.85 nan 0.61
residual 0.12 0.05 1.00 0.47 0.47 0.39 nan 0.39
fit -0.23 0.90 0.47 1.00 0.98 0.92 nan 0.71
pseudovoigt_1 -0.21 0.88 0.47 0.98 1.00 0.85 nan 0.65
pseudovoigt_2 -0.25 0.85 0.39 0.92 0.85 1.00 nan 0.56
constant_3 nan nan nan nan nan nan nan nan
gaussian_4 -0.10 0.61 0.39 0.71 0.65 0.56 nan 1.00

Confidence Intervals

SpectraFinder provides the possibility to calculate the confidence intervals. This is an optional feature in SpectraFinder provided by the lmfit package to further investigated the statistical legality of the fit.

Confidence Intervals
99.73% 95.45% 68.27% BEST 68.27% 95.45% 99.73%
pseudovoigt_amplitude_1 -inf -inf -inf 0.16404 +inf +inf +inf
pseudovoigt_center_1 -inf -inf -inf 0.03500 +inf +inf +inf
pseudovoigt_fwhmg_1 -inf -inf -inf 0.06877 +inf +inf +inf
pseudovoigt_fwhml_1 -inf -inf -inf 0.09252 +inf +inf +inf
pseudovoigt_amplitude_2 -inf -inf -inf 0.09740 +inf +inf +inf
pseudovoigt_center_2 -inf -inf -inf -0.01805 +inf +inf +inf
pseudovoigt_fwhmg_2 -inf -inf -inf 0.04334 +inf +inf +inf
pseudovoigt_fwhml_2 -inf -inf -inf 0.09990 +inf +inf +inf
constant_amplitude_3 -inf -inf -inf 0.03677 +inf +inf +inf
gaussian_amplitude_4 -inf -inf -inf 0.01411 +inf +inf +inf
gaussian_center_4 -inf -inf -inf 0.00079 +inf +inf +inf
gaussian_fwhmg_4 -inf -inf -inf 0.04893 +inf +inf +inf

About the trace in confidence intervals

The trace in the confidence intervals is the sum of the weights of the diagonal elements of the confidence matrix. lmfit allows calculating the trace of the confidence matrix. The export is a nested dictionary in a dictionary, where the arrays are saved as array objects and not as a list. The problem is that these arrays are not pickable, so they cannot be saved in a json-file. So please never use trace!=True in the input file.

Plotting

For the plotting of the results, the SpectraFinder provides the possibility to plot both the fit results and the residuals. A detail description of the plotting options is available in the API-section.

Saving the Results as CSV- and JSON-files

SpectraFinder automatically saves the fit results and the statistics in file format. By default, the results starts with fit_results_*.*, but can be individually labeled via -o command or in the input file. Furthermore, four different types of output files will be generated

  1. Fit results as *_fit.csv file, which combines the original data with the fit, residuals, and the single contribution.
  2. Fit errors as *_errors.csv file, which contains the value and fit errors for each parameter. The saved report is identically to printed report of Variable Analysis.
  3. Fit correlation as *_correlation.csv file, which contains the correlation analysis of the dataframe. The saved report is identically to printed report of Correlation Analysis.

  4. Fit summary as *_summary.json file, which contains all results of the fit project including the meta-data. The overall goal is to save the results in a NoSQL-format, so that every fit becomes an unique fitting-project.

    A closer look on the output file format

    The fitting-project consists of the following parts:

    1. The input parameter including the file-name of the original data.
      JSON
      "infile": "reference_data.txt",
"outfile": "fit_results",
"input": "spectrafit/test/test_input_2.json",
"oversampling": false,
"energy_start": 0,
"energy_stop": 8,
"smooth": 0,
"shift": 0,
"column": [
    0,
    1
],
"separator": "\t",
"decimal": ".",
"header": null,
"noplot": true,

"verbose": 1,
    2. The project-specific meta-data.
      JSON
        "description": {
  "project_name": "Template",
  "project_details": "Template for testing",
  "keywords": [
      "2D-Spectra",
      "fitting",
      "curve-fitting",
      "peak-fitting",
      "spectrum"
  ]
},
      The meta-data will be automatically extended by timestamp, name of the user (username), name of system of the user (system), and unique ID. For getting the username and the name of the used system, the built-in function getpass.getuser() and socket.gethostname() are used.
      JSON
      {
"timestamp": "2021-08-22 12:33:26",
"ID": "89b1a4ef-320a-4ac0-80da-e8d946b00e13",
"host_info": "e74490816920d147adc2315b45c4c6ce05e99ae9e09e34d2a263e2e9da861ffd",
"used_version": "0.3.0",
}
    3. The lmfit-settings.
      JSON
        "minimizer": {
        "nan_policy": "propagate",
        "calc_covar": true
    },
  "optimizer": {
        "max_nfev": 1,
        "method": "leastsq"
    },
  "report": {
        "min_correl": 0.0
    },
    4. The initial peak definitions.
    5. The results are saved as dictionary-list and can be imported by pandas.DataFrame.from_dict. For example:
      JSON
          "data_statistic": {
    "0": {
        "count": 611.0,
        "mean": 3.483333333333315,
        "std": 2.942079763251376,
        "min": -1.6,
        "10%": -0.5833333333333369,
        "20%": 0.433333333333326,
        "30%": 1.4499999999999895,
        "40%": 2.466666666666652,
        "50%": 3.483333333333315,
        "60%": 4.499999999999979,
        "70%": 5.516666666666641,
        "80%": 6.533333333333305,
        "90%": 7.549999999999968,
        "max": 8.566666666666633
    },
    "1": {
        "count": 611.0,
        "mean": 0.0603440425183391,
        "std": 0.12314108298811662,
        "min": 0.0,
        "10%": 0.00015819900201364986,
        "20%": 0.0015617780277680387,
        "30%": 0.0045243182103807894,
        "40%": 0.010958904109588984,
        "50%": 0.016245522651620947,
        "60%": 0.02770646393851211,
        "70%": 0.059617904082309055,
        "80%": 0.10112180177353332,
        "90%": 0.13932494130255624,
        "max": 1.0
    }
},
      becomes again the result of pre-analysis:
    0 1
    count 611.00 611.00
    mean 3.48 0.06
    std 2.94 0.12
    min -1.60 0.00
    10% -0.58 0.00
    20% 0.43 0.00
    30% 1.45 0.00
    40% 2.47 0.01
    50% 3.48 0.02
    60% 4.50 0.03
    70% 5.52 0.06
    80% 6.53 0.10
    90% 7.55 0.14
    max 8.57 1.00

    This is the one of the universal concepts of SpectraFit to to keep the results of the fit in a universal format, so that it can be switch between dictionary representation and dataframe representation.

Fit summary in JSON format

This is an extended example of the fit summary in JSON format to highlight the complexity of the fitting procedure.

JSON
{
  "infile": "spectrafit/test/rixs_fecl4.txt",
  "outfile": "fit_results",
  "input": "spectrafit/test/fitting_input.json",
  "oversampling": false,
  "energy_start": 0,
  "energy_stop": 8,
  "smooth": 0,
  "shift": 0,
  "column": [0, 1],
  "separator": "\t",
  "decimal": ".",
  "header": null,
  "noplot": true,

  "verbose": 1,
  "description": {
    "project_name": "Template",
    "project_details": "Template for testing",
    "keywords": [
      "2D-Spectra",
      "fitting",
      "curve-fitting",
      "peak-fitting",
      "spectrum"
    ]
  },
  "minimizer": {
    "nan_policy": "propagate",
    "calc_covar": true
  },
  "optimizer": {
    "max_nfev": 1000,
    "method": "leastsq"
  },
  "report": {
    "min_correl": 0.0
  },
  "conf_interval": {
    "p_names": null,
    "sigmas": null,
    "trace": false,
    "maxiter": 200,
    "verbose": 1,
    "prob_func": null
  },
  "peaks": {
    "1": {
      "pseudovoigt": {
        "amplitude": {
          "max": 2,
          "min": 0,
          "vary": true,
          "value": 1
        },
        "center": {
          "max": 2,
          "min": -2,
          "vary": true,
          "value": 0
        },
        "fwhmg": {
          "max": 0.1,
          "min": 0.02,
          "vary": true,
          "value": 0.01
        },
        "fwhml": {
          "max": 0.1,
          "min": 0.01,
          "vary": true,
          "value": 0.01
        }
      }
    },
    "2": {
      "pseudovoigt": {
        "amplitude": {
          "max": 2,
          "min": 0,
          "vary": true,
          "value": 1
        },
        "center": {
          "max": 2,
          "min": -2,
          "vary": true,
          "value": 0
        },
        "fwhmg": {
          "max": 0.1,
          "min": 0.02,
          "vary": true,
          "value": 0.01
        },
        "fwhml": {
          "max": 0.1,
          "min": 0.01,
          "vary": true,
          "value": 0.01
        }
      }
    },
    "3": {
      "constant": {
        "amplitude": {
          "max": 2,
          "min": 0.01,
          "vary": true,
          "value": 1
        }
      }
    },
    "4": {
      "gaussian": {
        "amplitude": {
          "max": 2,
          "min": 0,
          "vary": true,
          "value": 1
        },
        "center": {
          "max": 2,
          "min": -2,
          "vary": true,
          "value": 0
        },
        "fwhmg": {
          "max": 0.1,
          "min": 0.02,
          "vary": true,
          "value": 0.01
        }
      }
    }
  },
  "timestamp": "2021-08-19 21:08:57",
  "ID": "ce43d306-43e4-4350-9f09-fd1b13064f39",
  "host_info": "username",
  "host_info": "e74490816920d147adc2315b45c4c6ce05e99ae9e09e34d2a263e2e9da861ffd",
  "used_version": "0.2.0",
  "data_statistic": {
    "0": {
      "count": 611.0,
      "mean": 3.483333333333315,
      "std": 2.942079763251376,
      "min": -1.6,
      "10%": -0.5833333333333369,
      "20%": 0.433333333333326,
      "30%": 1.4499999999999895,
      "40%": 2.466666666666652,
      "50%": 3.483333333333315,
      "60%": 4.499999999999979,
      "70%": 5.516666666666641,
      "80%": 6.533333333333305,
      "90%": 7.549999999999968,
      "max": 8.566666666666633
    },
    "1": {
      "count": 611.0,
      "mean": 0.0603440425183391,
      "std": 0.12314108298811662,
      "min": 0.0,
      "10%": 0.00015819900201364986,
      "20%": 0.0015617780277680387,
      "30%": 0.0045243182103807894,
      "40%": 0.010958904109588984,
      "50%": 0.016245522651620947,
      "60%": 0.02770646393851211,
      "70%": 0.059617904082309055,
      "80%": 0.10112180177353332,
      "90%": 0.13932494130255624,
      "max": 1.0
    }
  },
  "fit_insights": {
    "configurations": {
      "fitting_method": "leastsq",
      "function_evals": 92,
      "data_points": 577,
      "variable_names": [
        "pseudovoigt_amplitude_1",
        "pseudovoigt_center_1",
        "pseudovoigt_fwhmg_1",
        "pseudovoigt_fwhml_1",
        "pseudovoigt_amplitude_2",
        "pseudovoigt_center_2",
        "pseudovoigt_fwhmg_2",
        "pseudovoigt_fwhml_2",
        "constant_amplitude_3",
        "gaussian_amplitude_4",
        "gaussian_center_4",
        "gaussian_fwhmg_4"
      ],
      "variable_numbers": 12,
      "degree_of_freedom": 565
    },
    "statistics": {
      "chi_square": 2.149830777028136,
      "reduced_chi_square": 0.0038050102248285596,
      "akaike_information": -3202.8454593711404,
      "bayesian_information": -3150.551352173043
    },
    "variables": {
      "pseudovoigt_amplitude_1": {
        "init_value": 1,
        "model_value": 0.16403602584115073,
        "best_value": 0.16403602584115073,
        "error_relative": 0.28617283308359887,
        "error_absolute": 174.45730693373602
      },
      "pseudovoigt_center_1": {
        "init_value": 0,
        "model_value": 0.03500058482452051,
        "best_value": 0.03500058482452051,
        "error_relative": 0.07534814694716585,
        "error_absolute": 215.27682273005587
      },
      "pseudovoigt_fwhmg_1": {
        "init_value": 0.02,
        "model_value": 0.0687679507938458,
        "best_value": 0.0687679507938458,
        "error_relative": 0.04790400069682786,
        "error_absolute": 69.66035797756372
      },
      "pseudovoigt_fwhml_1": {
        "init_value": 0.01,
        "model_value": 0.09252389394106236,
        "best_value": 0.09252389394106236,
        "error_relative": 0.037571255043319145,
        "error_absolute": 40.607083687217056
      },
      "pseudovoigt_amplitude_2": {
        "init_value": 1,
        "model_value": 0.09740402120893221,
        "best_value": 0.09740402120893221,
        "error_relative": 0.12049275689025189,
        "error_absolute": 123.7040887991618
      },
      "pseudovoigt_center_2": {
        "init_value": 0,
        "model_value": -0.018052359245206206,
        "best_value": -0.018052359245206206,
        "error_relative": 0.02098357900187265,
        "error_absolute": 116.23732231810547
      },
      "pseudovoigt_fwhmg_2": {
        "init_value": 0.02,
        "model_value": 0.043344705776687614,
        "best_value": 0.043344705776687614,
        "error_relative": 0.030179868797834665,
        "error_absolute": 69.62757794071015
      },
      "pseudovoigt_fwhml_2": {
        "init_value": 0.01,
        "model_value": 0.09989511131863486,
        "best_value": 0.09989511131863486,
        "error_relative": 0.0766935496518902,
        "error_absolute": 76.77407696885308
      },
      "constant_amplitude_3": {
        "init_value": 1,
        "model_value": 0.03676872733249155,
        "best_value": 0.03676872733249155,
        "error_relative": 0.0027777331216664375,
        "error_absolute": 7.554607741921567
      },
      "gaussian_amplitude_4": {
        "init_value": 1,
        "model_value": 0.014112879601465012,
        "best_value": 0.014112879601465012,
        "error_relative": 0.18946469610443273,
        "error_absolute": 1342.494951099597
      },
      "gaussian_center_4": {
        "init_value": 0,
        "model_value": 0.000785067433615172,
        "best_value": 0.000785067433615172,
        "error_relative": 0.0723964536938497,
        "error_absolute": 9221.686009884514
      },
      "gaussian_fwhmg_4": {
        "init_value": 0.02,
        "model_value": 0.0489339673857355,
        "best_value": 0.0489339673857355,
        "error_relative": 0.27055202071590273,
        "error_absolute": 552.8920608116684
      }
    },
    "errorbars": {},
    "correlations": {
      "pseudovoigt_amplitude_1": {
        "pseudovoigt_center_1": -0.9862283106649913,
        "pseudovoigt_fwhmg_1": 0.08087768591070482,
        "pseudovoigt_fwhml_1": 0.026422859895268734,
        "pseudovoigt_amplitude_2": -0.8508056947473775,
        "pseudovoigt_center_2": 0.443720894718587,
        "pseudovoigt_fwhmg_2": 0.46503877490597423,
        "pseudovoigt_fwhml_2": -0.7971320712781913,
        "constant_amplitude_3": -0.19256163835611795,
        "gaussian_amplitude_4": -0.9391516417433717,
        "gaussian_center_4": 0.4275708026546227
      },
      "pseudovoigt_center_1": {
        "pseudovoigt_fwhmg_1": 0.016337719047078703,
        "pseudovoigt_fwhml_1": 0.09199213704177446,
        "pseudovoigt_amplitude_2": 0.7845675730452338,
        "pseudovoigt_center_2": -0.5671057830051938,
        "pseudovoigt_fwhmg_2": -0.543356574051609,
        "pseudovoigt_fwhml_2": 0.7838468315613173,
        "constant_amplitude_3": 0.1908234141503389,
        "gaussian_amplitude_4": 0.9606615151849531,
        "gaussian_center_4": -0.45981680639412886
      },
      "pseudovoigt_fwhmg_1": {
        "pseudovoigt_fwhml_1": 0.9707589530283234,
        "pseudovoigt_amplitude_2": -0.12947342434289133,
        "pseudovoigt_center_2": -0.22593963910738113,
        "pseudovoigt_fwhmg_2": -0.041441070112167695,
        "pseudovoigt_fwhml_2": -0.22029948420194614,
        "constant_amplitude_3": -0.08828608501696038,
        "gaussian_amplitude_4": -0.02662835781007091,
        "gaussian_center_4": 0.11186439414852514
      },
      "pseudovoigt_fwhml_1": {
        "pseudovoigt_amplitude_2": -0.13806698462988234,
        "pseudovoigt_center_2": -0.3754173331238591,
        "pseudovoigt_fwhmg_2": -0.14152665304317025,
        "pseudovoigt_fwhml_2": -0.16783283765319543,
        "constant_amplitude_3": -0.07658241281626063,
        "gaussian_amplitude_4": 0.05913347928634629,
        "gaussian_center_4": 0.06599377246402101
      },
      "pseudovoigt_amplitude_2": {
        "pseudovoigt_center_2": 0.01906524917689979,
        "pseudovoigt_fwhmg_2": 0.06033478892009533,
        "pseudovoigt_fwhml_2": 0.44749434233368474,
        "constant_amplitude_3": 0.18484185277297382,
        "gaussian_amplitude_4": 0.6203122316031827,
        "gaussian_center_4": 0.0556317158685396
      },
      "pseudovoigt_center_2": {
        "pseudovoigt_fwhmg_2": 0.8392271456101567,
        "pseudovoigt_fwhml_2": -0.5198485790152048,
        "constant_amplitude_3": -0.09631860290887163,
        "gaussian_amplitude_4": -0.6669343985978409,
        "gaussian_center_4": 0.6369311212860583
      },
      "pseudovoigt_fwhmg_2": {
        "pseudovoigt_fwhml_2": -0.7677038773609103,
        "constant_amplitude_3": -0.04615140867123564,
        "gaussian_amplitude_4": -0.7331418848699987,
        "gaussian_center_4": 0.9347248046811267
      },
      "pseudovoigt_fwhml_2": {
        "constant_amplitude_3": 0.07011958877932851,
        "gaussian_amplitude_4": 0.9079454516212739,
        "gaussian_center_4": -0.8457904795491098
      },
      "constant_amplitude_3": {
        "gaussian_amplitude_4": 0.15153400546405374,
        "gaussian_center_4": 0.000926625676270801
      },
      "gaussian_amplitude_4": {
        "gaussian_center_4": -0.680824994264301
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      "gaussian_center_4": {},
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      6.863236326161793e-5, 6.821591894229805e-5, 6.78032533747231e-5,
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      4.685386084614401e-5, 4.66187724703072e-5, 4.638544896011623e-5,
      4.615387269430442e-5, 4.592402627097728e-5, 4.569589250434352e-5,
      4.5469454421502686e-5, 4.524469525928835e-5, 4.5021598461166e-5,
      4.48001476741839e-5, 4.458032674597668e-5, 4.436211972182013e-5,
      4.414551084173634e-5, 4.393048453764809e-5, 4.371702543058175e-5,
      4.350511832791763e-5, 4.329474822068677e-5, 4.3085900280913395e-5,
      4.28785598590022e-5, 4.2672712481169414e-5, 4.2468343846917126e-5,
      4.226543982654949e-5, 4.206398645873065e-5, 4.186396994808343e-5,
      4.1665376662827354e-5, 4.146819313245634e-5, 4.127240604545447e-5,
      4.1078002247049506e-5, 4.088496873700335e-5, 4.069329266743872e-5,
      4.050296134070135e-5, 4.031396220725737e-5, 4.012628286362455e-5,
      3.99399110503375e-5, 3.97548346499456e-5, 3.957104168504358e-5,
      3.9388520316333784e-5, 3.9207258840719535e-5, 3.902724568942921e-5,
      3.8848469426170554e-5, 3.867091874531438e-5, 3.849458247010693e-5,
      3.831944955091137e-5, 3.814550906347674e-5, 3.7972750207234464e-5,
      3.780116230362176e-5, 3.7630734794431556e-5, 3.7461457240188474e-5,
      3.729331931855013e-5, 3.7126310822733576e-5, 3.696042165996636e-5,
      3.679564184996181e-5, 3.6631961523418004e-5, 3.646937092053987e-5,
      3.630786038958455e-5, 3.6147420385429095e-5, 3.598804146816008e-5,
      3.582971430168522e-5, 3.567242965236617e-5, 3.551617838767226e-5,
      3.536095147485507e-5, 3.520673997964266e-5, 3.505353506495445e-5,
      3.490132798963498e-5, 3.475011010720733e-5, 3.459987286464499e-5,
      3.445060780116261e-5, 3.4302306547024884e-5, 3.4154960822373234e-5,
      3.4008562436070106e-5, 3.386310328456072e-5, 3.371857535075167e-5,
      3.357497070290638e-5, 3.343228149355674e-5, 3.3290499958431115e-5,
      3.314961841539827e-5, 3.300962926342669e-5, 3.287052498155941e-5,
      3.273229812790386e-5, 3.25949413386366e-5, 3.245844732702256e-5,
      3.232280888244874e-5, 3.218801886947186e-5, 3.205407022688011e-5,
      3.1920955966768215e-5
    ],
    "constant_3": [
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}

Jupyter Notebook Interface

SpectraFit provides also an interface to Jupyter Notebook as an package import. This interface is useful for interactive fitting and plotting of the results. For interactive working the following tools are implemented:

  1. Plotly for interactive plotting of the results
  2. Dtale for interactive data exploration (external)
  3. itables for interactive data exploration (internal)

For more information, please check the Jupyter Notebook Interface section.