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        • 1D Data Fitting
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Table of Contents

Getting Started

  • Installations
  • Introduction to Spin Systems
  • The Basics
  • Uncoupled Spin System: Using objects
  • Coupled Spin System: Using objects
  • Configuring Simulator object
  • mrsimulator I/O

Signal Processing

  • Signal Processing

Models

  • Czjzek distribution
  • Extended Czjzek distribution

Examples and Benchmarks

  • Simulation Examples
  • Fitting Examples (Least Squares)
    • 1D Data Fitting
    • 2D Data Fitting
  • Performance benchmark

Theory

  • How does mrsimulator work?
  • Models

API and references

  • Simulation API
  • Signal-processing API
  • Models API
  • Fitting Utility API
  • C-API References

Project details

  • Changelog
  • Authors and Credits
  • License
  • Acknowledgment

Fitting Examples (Least Squares)¶

The mrsimulator library is easily integrable with other python-based libraries. In the following examples, we illustrate the use of LMFIT non-linear least-squares minimization python package to fit a simulation object to experimental data.

1D Data Fitting¶

²⁹Si 1D MAS spinning sideband (CSA)

Figure 58 ²⁹Si 1D MAS spinning sideband (CSA)¶

³¹P MAS NMR of crystalline Na2PO4 (CSA)

Figure 59 ³¹P MAS NMR of crystalline Na2PO4 (CSA)¶

³¹P static NMR of crystalline Na2PO4 (CSA)

Figure 60 ³¹P static NMR of crystalline Na2PO4 (CSA)¶

¹³C MAS NMR of Glycine (CSA) [1940 Hz]

Figure 61 ¹³C MAS NMR of Glycine (CSA) [1940 Hz]¶

¹³C MAS NMR of Glycine (CSA) [5000 Hz]

Figure 62 ¹³C MAS NMR of Glycine (CSA) [5000 Hz]¶

¹³C MAS NMR of Glycine (CSA) [960 Hz]

Figure 63 ¹³C MAS NMR of Glycine (CSA) [960 Hz]¶

1D PASS/MAT sideband order cross-section

Figure 64 1D PASS/MAT sideband order cross-section¶

¹⁷O MAS NMR of crystalline Na₂SiO₃ (2nd order quad)

Figure 65 ¹⁷O MAS NMR of crystalline Na₂SiO₃ (2nd order quad)¶

¹¹B MAS NMR of Lithium orthoborate crystal

Figure 66 ¹¹B MAS NMR of Lithium orthoborate crystal¶

²³Na MAS NMR of Nasicon

Figure 67 ²³Na MAS NMR of Nasicon¶

²⁷Al MAS NMR of YAG (1st and 2nd order Quad)

Figure 68 ²⁷Al MAS NMR of YAG (1st and 2nd order Quad)¶

²H MAS NMR of Methionine

Figure 69 ²H MAS NMR of Methionine¶

¹¹⁹Sn MAS NMR of SnO

Figure 70 ¹¹⁹Sn MAS NMR of SnO¶

2D Data Fitting¶

¹³C 2D MAT NMR of L-Histidine

Figure 71 ¹³C 2D MAT NMR of L-Histidine¶

⁸⁷Rb 2D QMAT NMR of Rb₂SO₄

Figure 72 ⁸⁷Rb 2D QMAT NMR of Rb₂SO₄¶

¹⁷O 2D DAS NMR of Coesite

Figure 73 ¹⁷O 2D DAS NMR of Coesite¶

⁸⁷Rb 2D 3QMAS NMR of RbNO₃

Figure 74 ⁸⁷Rb 2D 3QMAS NMR of RbNO₃¶

NiCl₂.2D₂O, ²H (I=1) Shifting-d echo

Figure 75 NiCl₂.2D₂O, ²H (I=1) Shifting-d echo¶

CoCl₂.2D₂O, ²H (I=1) Shifting-d echo

Figure 76 CoCl₂.2D₂O, ²H (I=1) Shifting-d echo¶

Download all examples in Python source code: fitting_python.zip

Download all examples in Jupyter notebooks: fitting_jupyter.zip

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