diff options
| -rw-r--r-- | matlab_usage_source/fitted_data.png | bin | 0 -> 3575 bytes | |||
| -rw-r--r-- | matlab_usage_source/index.t2t | 126 |
2 files changed, 120 insertions, 6 deletions
diff --git a/matlab_usage_source/fitted_data.png b/matlab_usage_source/fitted_data.png Binary files differnew file mode 100644 index 0000000..5b37fdc --- /dev/null +++ b/matlab_usage_source/fitted_data.png diff --git a/matlab_usage_source/index.t2t b/matlab_usage_source/index.t2t index d09131e..4bc5b32 100644 --- a/matlab_usage_source/index.t2t +++ b/matlab_usage_source/index.t2t @@ -135,8 +135,8 @@ Yet again we need proper labeling ``` title('Dependence of voltage on current') -xlabel('Voltage (V)') -ylabel('Current (A)') +xlabel('Current (A)') +ylabel('Voltage (V)') ``` [errorbar_plot.png] @@ -154,28 +154,142 @@ set(gca,'FontSize',fontSize ); errorbar(I,V,dV) title('Dependence of voltage on current') -xlabel('Voltage (V)') -ylabel('Current (A)') +xlabel('Current (A)') +ylabel('Voltage (V)') ``` [errorbar_with_large_font_plot.png] += Fitting and data reduction = + +Modern experiments generate a lot of data, while humans can keep in their +mind only about 7 things. So there is no way to intelligently work with +large data set. We need to extract essential information out of our +data i.e. do data reduction. Often we have some idea for analytical +representation/model of the experimental data but we are not sure about +the model parameters values. The process of extracting them is called +**fitting**. + +So let's look at above Voltage vs Current dependence. According to the +Ohm's law such dependence must be linear i.e **``V = R*I``**. Where +**``R``** is constant coefficient called resistance. + +So first we need to define the model for Matlab. We **must** specify an +independent variable name unless it is called **``x``**, which is not our +choice here. Also, notice that **``fittype``** function wants to know +independent variable //name// thus **``I``** is surrounded by **``' '``** + +``` +f=fittype( @(R,I) R*I, 'independent', 'I' ) +%______________^ independent variable must be last in the function arguments +%____________^ even though R is supposed to be fixed it is still a variable +% from fitting point of view +``` + +Now our job is simple, we need to specify a guessed value of the R as starting point +for the fit function. + +``` param_guessed = [ 4 ] + +You might have a model with multiple parameters than it is a bit more +evolved. Please, do read help file about fitting. + +Finally, we fit. +``` +[fitobject, goodness_of_fit] = fit (I, V, f, 'StartPoint', param_guessed) +``` + +You will see the following +``` +fitobject = + + General model: + fitobject(I) = R*I + Coefficients (with 95% confidence bounds): + R = 1.291 (0.8872, 1.695) + +goodness_of_fit = + + sse: 2.6340 + rsquare: 0.7050 + dfe: 4 + adjrsquare: 0.7050 + rmse: 0.8115 +``` + +The most interesting part is **``R = 1.291 (0.8872, 1.695)``**, +where 1.291 is the mean for the extracted parameter ``**R**`` +and **``(0.8872, 1.695)``** is the interval within one standard deviation. +So we get our error bars as well: +one sigma is equal ``1.695 - 1.291 = 0.4040`` + +So our conclusion is that **``R = 1.3 +/- 0.4``**. + +== Checking the fitting result == + +We should not trust computed fit parameters blindly. For our simple case it +is probably OK, but for more evolved nonlinear fitting functions result +might go way off if we specify starting point significantly far from +optimal. + +One way to see check fit quality is to look at Root Mean Squared error +(**``rmse``**) parameter from above output. It reflect what is the typical +deviation of the model/fit from experimental points. It should be about the +size of your experimental error bars. If it is much smaller then most +likely you are over fitting (you model has to many free parameters). If it is +much bigger your fit model is not good enough. + + +Another way to check consistency of the fit it to look at plotted data and the fit +simultaneously. Let's open yet one more window and plot our data first +``` +figure(3) +fontSize=24; +set(gca,'FontSize',fontSize ); + +errorbar(I,V,dV, 'x') + +hold on +``` + +notice **``hold on``** statement, now next plotting command will draw over presented plot i.e. graphics window //holds on// to already present content. + +Now we the plot corresponding to our model/fit. There are multiple way to do it, +the simplest is +``` +plot( fitobject ) + +title('Dependence of voltage on current') +xlabel('Current (A)') +ylabel('Voltage (V)') +``` + +[fitted_data.png] + + = Saving you Matlab plots = Well it nice to have Matlab plots. But as soon as you close Matlab they will go away. How to save them for a future use? Actually, quite easy with **``print``** command. Unlike the name suggest it does not make a carbon copy but actually an electronic one. For figure saved in png format do -``` print('V_vs_I.png') +``` print('-dpng', 'V_vs_I.png') + +If you find that you figures are to large specify resolution in dots per inch +with **``-r``** option. For example +``` print('-dpng', '-r50', 'V_vs_I.png') or if you need a pdf (Matlab usually make very bad pdfs without a lot of tweaking) -``` print('V_vs_I.pdf') +``` print('-dpdf', 'V_vs_I.pdf') + +The **``-d``** stands for output driver option, i.e png or pdf in above examples. Make sure that you read documentation for **``print``** command there are some useful parameters. + = Where to learn more = At W&M Physics 256 class teaches how scientists use computers. Matlab was a language of |
