PyFluxconserving 0.0.6

Flux-conserving legacy routines in Fortran and Python

FluxConserving

A Fortran legacy package to easily compute the flux-density conservation

Obs.: A Fortran legacy Interpolation routines also furnished
email: [e-mail], [e-mail]

© Copyright ®

J.G. - Jean Gomes

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RESUME

Original Fortran 2003+ routines date back to 2003-2004. Read the LICENSE.txt file. When analyzing astronomical spectra, astronomers often bin the data to increase the signal-to-noise ratio and reduce the effects of noise in the data. Binning refers to the process of averaging the intensity of adjacent spectral channels, or pixels, to produce a new, coarser set of data.

In the process of binning, it is important to ensure that the principle of flux density conservation is maintained. This means that the total energy emitted by the object, and hence its flux density, must remain constant after binning.

To conserve flux density, the intensity of each binned pixel should be scaled by the number of pixels it represents. For example, if two adjacent pixels are binned together, the intensity of the resulting bin should be the sum of the intensities of the two original pixels, divided by two. This ensures that the total energy in the bin is conserved, and that the flux density of the object remains the same.

It's worth noting that binning can introduce errors in the spectral data, especially if the signal-to-noise ratio is low or if the binning is too coarse. In general, astronomers choose a binning size that balances the need for a high signal-to-noise ratio with the desire to maintain the spectral resolution and avoid introducing significant errors in the data.

In summary, the principle of flux density conservation is important to consider when binning astronomical spectra, and astronomers need to scale the intensity of each binned pixel to ensure that the total energy emitted by the object is conserved. SpectRes from A. Carnall is NOT part of the distribution, but used as a comparison: https://github.com/ACCarnall/SpectRes.

Accompanying there are several routines for interpolations.

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INSTALLATION

You can easily install pyfluxconserving by using pip - PyPI - The Python Package Index:

pip install pyfluxconserving

or by using a generated conda repository https://anaconda.org/neutrinomuon/pyfluxconserving:

conda install -c neutrinomuon pyfluxconserving

OBS.: Linux, OS-X and Windows pre-compilations available in conda.

You can also clone the repository and install by yourself in your machine:

git clone https://github.com/neutrinomuon/FluxConserving
python setup.py install

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METHOD & REFERENCES

Here, the method used is with the Cumulative function to produce a new flux-conserved, some options can be chosen for the interpolation:

Integer Number	Option: Interpolation Schemes	Brief Description
0)	AkimaSpline	Akima Spline interpolation. The Akima spline is a C1 differentiable function (that is, has a continuous first derivative) but, in general, will have a discontinuous second derivative at the knot points. Akima, H. (1970). A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures. Journal of the ACM, 17(4), 589-602. Association for Computing Machinery. DOI: 10.1145/321607.321609. Link: https://dl.acm.org/doi/10.1145/321607.321609 De Boor, C. (1978). A Practical Guide to Splines. Springer-Verlag. ISBN: 978-0-387-95366-3. Link: https://www.springer.com/gp/book/9780387953663 Forsythe, G.E. (1979) Computer Methods for Mathematical Computations. Prentice-Hall, Inc. DOI: 10.1002/zamm.19790590235. Link: https://onlinelibrary.wiley.com/doi/10.1002/zamm.19790590235 Bartels, R.H., Beatty, J.C., and Barsky, B.A. (1987). An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers. Link: https://www.osti.gov/biblio/5545263 Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.). Cambridge University Press. ISBN: 978-0521880688. Link: http://numerical.recipes/ Cheney, W. and Kincaid, D. (2008). Numerical Mathematics and Computing (6th ed.). Brooks/Cole. ISBN: 978-0495114758. Link: https://www.amazon.com/Numerical-Mathematics-Computing-Ward-Cheney/dp/0495114758 Burden, R. L., & Faires, J. D. (2010). Numerical Analysis (9th ed.). Brooks/Cole. ISBN: 978-0538733519. Link: https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0538733519
1)	Interpolado	Based on a linear interpolation within a table of pair values. Atkinson, K. E. (1991). An introduction to numerical analysis (2nd ed.). John Wiley & Sons. ISBN: 978-0-471-62489-9. Link: https://www.wiley.com/en-us/An+Introduction+to+Numerical+Analysis%2C+2nd+Edition-p-9780471624899 Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.). Cambridge University Press. ISBN: 978-0521880688. Link: http://numerical.recipes/ Chapra, S. C., & Canale, R. P. (2010). Numerical methods for engineers (6th ed.). McGraw-Hill. ISBN: 978-0073401065. Link: https://www.amazon.com/Numerical-Methods-Engineers-Steven-Chapra/dp/0073401064 Burden, R. L., Faires, J. D. & A.M. Burden (2015). Numerical analysis (10th ed.) (9th ed.). Cengage Learning. ISBN: 978-1305253667. Link: https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/1305253663
2)	LINdexerpol	Based on a linear interpolation within a table of pair values using indexing. The references are the same as in 1).
3)	LINinterpol	Based on a linear interpolation within a table of pair values. The references are the same as in 1).
4)	SPLINE1DArr	This is a Fortran 2003 subroutine called SPLINE1DArr that takes an array of values x to interpolate from the arrays t and y. It has ten input arguments, six output arguments, and two optional arguments. The interpolation is linear. Forsythe, G.E. (1977) Computer Methods For Mathematical Computations. Ed. Prentice-Hall, Inc. https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19790590235 De Boor, C. (1978). A Practical Guide to Splines. Springer-Verlag. ISBN: 978-0-387-95366-3. Link: https://www.springer.com/gp/book/9780387953663 Bartels, R.H., Beatty, J.C., and Barsky, B.A. (1998). An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers. ISBN: 978-1558604000. Link: https://www.amazon.com/Introduction-Computer-Graphics-Geometric-Modeling/dp/1558604006 Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.). Cambridge University Press. ISBN: 978-0521880688. Link: http://numerical.recipes/ Cheney, W. and Kincaid, D. (2007). Numerical Mathematics and Computing (6th ed.). Brooks/Cole. ISBN: 978-0495114758. Link: https://www.amazon.com/Numerical-Mathematics-Computing-Ward-Cheney/dp/0495114758
5)	SPLINE3DFor	This function evaluates the cubic spline interpolation. The same references as in 4).

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STRUCTURE

The main structure of the directories and files are:

FluxConserving
├── dist
│   └── pyfluxconserving-0.0.1.tar.gz
├── README.md
├── LICENSE.txt
├── setup.py
├── tutorials
│   ├── fluxconserving.png
│   └── Flux-Conserving Example.ipynb
├── pyfluxconserving.egg-info
│   ├── PKG-INFO
│   ├── dependency_links.txt
│   ├── SOURCES.txt
│   ├── top_level.txt
│   └── requires.txt
├── src
│   ├── python
│   │   ├── PyFluxConSpec.py
│   │   ├── califa_cmap_alternative.py
│   │   ├── PyLinear__int.py
│   │   ├── PyLINinterpol.py
│   │   ├── PySPLINECubic.py
│   │   ├── fluxconserve.py
│   │   ├── __init__.py
│   │   ├── PySPLINE1DArr.py
│   │   ├── PySPLINE3DFor.py
│   │   ├── fluxconserving.png
│   │   ├── PyAkimaSpline.py
│   │   ├── PySPLINE3DAlt.py
│   │   ├── PyInterpolado.py
│   │   └── PyLINdexerpol.py
│   └── fortran
│       ├── LINdexerpol.f90
│       ├── SPLINE3DFor.cpython-39-x86_64-linux-gnu.so
│       ├── SPLINE1DFlt.cpython-39-x86_64-linux-gnu.so
│       ├── SPLINE3DFor.compile
│       ├── FluxConSpec.compile
│       ├── SPLINE1DArr.compile
│       ├── Interpolado.cpython-39-x86_64-linux-gnu.so
│       ├── Interpolado.cpython-38-x86_64-linux-gnu.so
│       ├── SPLINE1DFlt.f90
│       ├── AkimaSpline.f90
│       ├── SPLINE1DArr.f90
│       ├── SPLINE1DFlt.cpython-38-x86_64-linux-gnu.so
│       ├── SPLINE3DFor.cpython-38-x86_64-linux-gnu.so
│       ├── AkimaSpline.compile
│       ├── DataTypes.f90
│       ├── LINdexerpol.compile
│       ├── SPLINE3DFor.f90
│       ├── SPLINE1DFlt.compile
│       ├── Interpolado.f90
│       ├── SPLINE1DFlt.cpython-310-x86_64-linux-gnu.so
│       ├── FluxConSpec.f90
│       ├── Interpolado.cpython-310-x86_64-linux-gnu.so
│       ├── LINdexerpol.cpython-310-x86_64-linux-gnu.so
│       ├── README.txt
│       ├── Interpolado.compile
│       ├── SPLINE3DFor.cpython-310-x86_64-linux-gnu.so
│       ├── LINinterpol.f90
│       ├── LINdexerpol.cpython-39-x86_64-linux-gnu.so
│       └── LINdexerpol.cpython-38-x86_64-linux-gnu.so
├── version.txt
└── build
    ├── lib.linux-x86_64-3.9
    │   └── pyfluxconserving
    ├── src.linux-x86_64-3.9
    │   ├── pyfluxconserving
    │   ├── build
    │   └── numpy
    └── temp.linux-x86_64-3.9
        ├── pyfluxconserving
        ├── ccompiler_opt_cache_ext.py
        ├── src
        ├── .libs
        └── build

18 directories, 56 files

PyFluxConSPec.py is a python wrapper to the library in fortran called pyfluxconserving.flib. The fortran directory can be compiled separately for each individual subroutine.

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LICENSE

This software is provided "AS IS" (see DISCLAIMER below). Permission to use, for non-commercial purposes is granted. Permission to modify for personal or internal use is granted, provided this copyright and disclaimer are included in ALL copies of the software. All other rights are reserved. In particular, redistribution of the code is not allowed without explicit permission by the author.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.