Group Abstract

Message Boards

WOLFRAM COMMUNITY

9.5K Views

12 Replies

4 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Astronomy Physics Mathematica Wolfram Language

[Solved] Making a function from data by interpolation

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

Attachments: Energy density.xlsx Pressure.xlsx

POSTED BY: Davood Rafiei

12 Replies

Sort By:

Rohit Namjoshi

Posted 5 years ago

Hi Davood, There are a couple of problems. The XLSX files have an empty second column, so ignore it energyDensity = Import["~/Downloads/Energy density.xlsx", {"Data", 1, All, 1}]; pressure = Import["~/Downloads/Pressure.xlsx", {"Data", 1, All, 1}]; There is one data point that is duplicated Transpose[{pressure, energyDensity}] // Counts // Select[GreaterThan@1] (* <\|{970.137, 1659.82} -> 2\|> *) It happens to be the last one, so ignore it. fromPressureToEnergy = Interpolation[Most@Transpose[{pressure, energyDensity}], InterpolationOrder -> 1]

Hi Davood,

There are a couple of problems. The XLSX files have an empty second column, so ignore it

energyDensity = Import["~/Downloads/Energy density.xlsx", {"Data", 1, All, 1}];
pressure = Import["~/Downloads/Pressure.xlsx", {"Data", 1, All, 1}];

There is one data point that is duplicated

Transpose[{pressure, energyDensity}] // Counts // Select[GreaterThan@1]
(* <|{970.137, 1659.82} -> 2|> *)

It happens to be the last one, so ignore it.

fromPressureToEnergy = 
 Interpolation[Most@Transpose[{pressure, energyDensity}], InterpolationOrder -> 1]

POSTED BY: Rohit Namjoshi

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 5 years ago

Prepare the data in form of lists and then feed them to Interpolation this way: pressure = {0.695, 0.408, 0.021, 0.458, 0.636}; energyDensity = {0.521, 0.256, 0.076, 0.356, 0.870}; fromPressureToEnergy = Interpolation[Transpose[{pressure, energyDensity}], InterpolationOrder -> 1]; fromEnergyToPressure = Interpolation[Transpose[{energyDensity, pressure}], InterpolationOrder -> 1]; fromPressureToEnergy[.3] fromEnergyToPressure[.5] For example, `fromPressureToEnergy[.3]` gives the energy corresponding to a pressure `=.3`.

Prepare the data in form of lists and then feed them to Interpolation this way:

pressure = {0.695, 0.408, 0.021, 0.458, 0.636};
energyDensity = {0.521, 0.256, 0.076, 0.356, 0.870};
fromPressureToEnergy = 
  Interpolation[Transpose[{pressure, energyDensity}], 
   InterpolationOrder -> 1];
fromEnergyToPressure = 
  Interpolation[Transpose[{energyDensity, pressure}], 
   InterpolationOrder -> 1];
fromPressureToEnergy[.3]
fromEnergyToPressure[.5]

For example, fromPressureToEnergy[.3] gives the energy corresponding to a pressure =.3.

POSTED BY: Gianluca Gorni

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 5 years ago

Assuming that your data are simple lists of numbers of the same length, here is a syntax that plots one against the other: pressure = RandomReal[{0, 1}, 5] energyDensity = RandomReal[{0, 1}, 5] f1 = Interpolation[Transpose[{pressure, energyDensity}], InterpolationOrder -> 1] f2 = Interpolation[Transpose[{energyDensity, pressure}], InterpolationOrder -> 1] Plot[f1[t], {t, 0, 1}] Plot[f2[t], {t, 0, 1}]

Assuming that your data are simple lists of numbers of the same length, here is a syntax that plots one against the other:

pressure = RandomReal[{0, 1}, 5]
energyDensity = RandomReal[{0, 1}, 5]
f1 = Interpolation[Transpose[{pressure, energyDensity}],
  InterpolationOrder -> 1]
f2 = Interpolation[Transpose[{energyDensity, pressure}],
  InterpolationOrder -> 1]
Plot[f1[t], {t, 0, 1}]
Plot[f2[t], {t, 0, 1}]

POSTED BY: Gianluca Gorni

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

I really appreciate your help, the codes works quite well.

POSTED BY: Davood Rafiei

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

Thank you very much for your attention.. the problems are solved. I really appreciate your help.

POSTED BY: Davood Rafiei

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

Thank you very much, it is exactly what i was looking for, but i think there is a problem in my data. so I attached the data. This is the problem :Interpolation::indat Interpolation::indat: Data point {<<1>>,5.6093910^-12 1.7945910^-11 3.6057510^-11 1.4556510^-10 2.9247410^-10 5.8764910^-10 2.3723510^-9 4.766610^-9 1.9242910^-8 3.8663410^-8 1.2369410^-7 2.4853110^-7 4.9935610^-7 2.0159110^-6 4.05043*10^-6 0.0000129584 0.0000328543 0.000066012 0.000266491 0.000535443 0.00216159 0.00434314 0.0138949 0.0279181 0.0560939 0.290646 0.572372 1.04226 1.51234 1.8885 2.26473 2.54695 2.8292 3.11148 3.39381 3.67615 3.95854 4.24094 4.61753 4.90001 5.18251 5.46503 5.74759 6.21858 6.59541 6.97229 7.34921 7.82044 8.19745 8.48023 <<115>>} contains abscissa <<1>>, which is not a real number.

Thank you very much, it is exactly what i was looking for, but i think there is a problem in my data. so I attached the data.

This is the problem :Interpolation::indat

Interpolation::indat: Data point {<<1>>,5.60939*10^-12


    1.79459*10^-11


    3.60575*10^-11


    1.45565*10^-10


    2.92474*10^-10


    5.87649*10^-10


    2.37235*10^-9


    4.7666*10^-9


    1.92429*10^-8


    3.86634*10^-8


    1.23694*10^-7


    2.48531*10^-7


    4.99356*10^-7


    2.01591*10^-6


    4.05043*10^-6


    0.0000129584


    0.0000328543


    0.000066012


    0.000266491


    0.000535443


    0.00216159


    0.00434314


    0.0138949


    0.0279181


    0.0560939


    0.290646


    0.572372


    1.04226


    1.51234


    1.8885


    2.26473


    2.54695


    2.8292


    3.11148


    3.39381


    3.67615


    3.95854


    4.24094


    4.61753


    4.90001


    5.18251


    5.46503


    5.74759


    6.21858


    6.59541


    6.97229


    7.34921


    7.82044


    8.19745


    8.48023


    <<115>>} contains abscissa <<1>>, which is not a real number.

POSTED BY: Davood Rafiei

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

DataA = Import["D:\\Energy density.xlsx"]; DataB = Import["D:\\Pressure.xlsx"]; Pressure = {DataB}; EnergyDensity = {DataA}; fromPressureToEnergy = Interpolation[Transpose[{Pressure, EnergyDensity}], InterpolationOrder -> 1];

DataA = Import["D:\\Energy density.xlsx"];
DataB = Import["D:\\Pressure.xlsx"];

Pressure = {DataB};

EnergyDensity = {DataA};

fromPressureToEnergy = 
  Interpolation[Transpose[{Pressure, EnergyDensity}], 
   InterpolationOrder -> 1];

POSTED BY: Davood Rafiei

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

Please kindly find the data related to pressure and energy density. Attachments: Energy density.xlsx Pressure.xlsx

POSTED BY: Davood Rafiei

EDITORIAL BOARD

EDITORIAL BOARD, WOLFRAM

Posted 5 years ago

Welcome to Wolfram Community! Please show your code written in the Wolfram Language in order to make it easier for others to help.

POSTED BY: EDITORIAL BOARD

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 5 years ago

Yes, you can attach the file to the post.

POSTED BY: Gianluca Gorni

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

I faced this error, Interpolation::indat: Data point `1` contains abscissa `2`, which is not a real number. May be there is problem in my data. Can I send you my Data? They are as a Excel file.

POSTED BY: Davood Rafiei

Davood Rafiei

Davood Rafiei, Isfahan University of Technology

Posted 5 years ago

Thanks a lot for your attention. To clarify more, In my notebook I have a set of data for energy density which I named it DataA and another set of data for pressure named DataB that were imported. The number of elements of both of data are equal since these data are related to a plot which shows pressure in terms of energy density. Due to I do not have an explicit function for energy density in terms of pressure or pressure in terms of energy density I have to use interpolation. In fact by using Interpolation I could use these data as a function. For instance, I choose an arbitrary pressure p1 for this code written in Matlab, E=interp1(Data(:,2),Data(:,1),p1); It gives me the corresponding energy density by utilizing the interpolation For an arbitrary energy density e1 I can use this code written in Matlab, P=interp1(Data(:,1),Data(:,2),e1); and the result is the corresponding pressure. Now I want to do the calculation explained above by Mathematica.

POSTED BY: Davood Rafiei

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Feedback