MATLAB® advantages

The advantage of a seript file is that it only needs to be ereated onee and saves the labour of eontinually typing lists of eommands at the MATLAB prompt. 

The function NewtonRaphson. m is written in a very compact manner, taking full advantage of Matlab s vectorised commands. Sometimes this makes the lines difficult to read — a few additional remarks are appropriate. 

While most of the Matlab listing in Main EFAl, m is close to self explanatory, a few statements might need clarification. The singular values are stored in the matrix EFA f which has ns rows and ne columns. It is advantageous to plot the logarithms of the singular values their values span several orders of magnitude and cannot be represented in a normal plot. 

We shall subsequently use the MATLAB ODE solvers as black boxes, sometimes varying between the individual ones only for higher speed or better accuracy when warranted. Our students should experiment freely with using either of the above seven ODE solvers to learn which is more advantageous where. It only takes a different call of MATLAB to find out. 

A significant advantage of Matlab is that there are several further veiy useful matrix operations. Most are in the form of functions the arguments are enclosed in brackets. Three that are important in chemometrics are as follows ... 

We see that we have j coupled ordinary differential equations that must be solved simultaneously with either a numerical package or by writing an ODE solver. In fact, this procedure has been developed to take advantage of the vast number of computation techniques now available on mainframe (e.g., Sifflusolv) and personal computers (POLYMATH athematica, MATLAB). 

Programs such as Excel and MATLAB allow us to easily solve for the specific volumes. However, one advantage of process simulators like Aspen Plus is that the physical properties of many components are saved in a database that users can access. In fact, users do not need to look up the numbers because Aspen Plus will do that when it needs them. The next section illustrates how to use each of these programs to solve equations of state. 

You can also use the process simulator Aspen Plus to solve chemical reaction equil-brium problems. It has a huge advantage over Excel and MATLAB Aspen Plus contains the Gibbs free energies of many chemicals, and it can calculate them as a function of temperature. Thus, the data-gathering aspect of the problem is handled for you. Your job is to compare the results and the predicted A -values with experimental information. 

FEMLAB is treated in detail in Chapters 9-11 and Appendix D, but it can also be used to solve reactor problems. The advantage of FEMLAB is that you program with a GUI, so computer errors are less likely. It is still necessary to check your work, though. While the applications in this chapter are all one-dimensional (to compare with MATLAB solutions), it is easy to solve two-dimensional problems, as described in more detail in later chapters. We show here how to solve the same three problems already solved using MATLAB the simple exponential, Eq. (8.16) the isothermal flow reactor, Eqs. (8.21)—(8.22) and the nonisothermal reactor, Eqs. (8.24)-(8.26). 

To conclude this section on tensor-product QMOM, it is important to highlight that, although it is not necessary, the formulation of the problem in terms of translated (i.e. centered on the mean) and rotated (i.e. with diagonal covariance matrix) internal coordinates can be advantageous. In fact, if a change of variables is implemented so that the distribution is rewritten with respect to its principal coordinates, the calculations for the derivation of the quadrature approximation are simplified. These concepts will be illustrated in Exercise 3.8. A Matlab script implementing a tensor-product QMOM can be found in Section A.3.2 of Appendix A. 

In addition to commercial software products we also took advantage of custom designed software (MicrobeMS Lasch 2015) for the evaluation of our microbial mass spectra. MicrobeMS is Matlab-based and involves a specifically optimized peak detection routine. One of the key features of peak detection in MicrobeMS is a sigmoid intensity threshold function which was introduced to model the m/z dependence of the analytical sensitivity of MALDI-TOF MS. This threshold function defines intensity thresholds at each m/z value. In the MicrobeMS implementation, an intensity threshold at low m/z values is larger than at high m/z values. Another feature of the MicrobeMS peak detection routine allows to precisely define the number of resulting peaks per spectrum. This particular feature makes peak detection partially independent from the SNR which turned out to be extremely useful for subsequent classification analysis. 

The authors used five algorithms based on the above mentioned techniques. They developed MatLab and Fortran versions of the above formulae and they compared the accuracy and computational efficiency. They used in both cases fixed step size procedure for equality of conditions of all implementations. They applied these methodologies on real problems of sciences and engineering and they expressed the advantages of the proposed algorithms, especially when they are integrating stiff problems. 

This chapter is intended for advanced users (i.e., developers) to demonstrate the advantage of using the MATLAB built-in Graphical User Interface Design Environment (GUIDE) as a tool to create a code working behind a friendly Graphic User Interface (GUI). 

A spreadsheet such as Excel is a program that let you analyze moderately large amounts of data by placing each data point in a cell and then perform the same operation on groups of cells at once. One of the advantages of spreadsheets is that data input and manipulation are relatively intuitive and hence easier than doing the same tasks in MATLAB (Towler and Sinnott, 2013). 

Note that the controller parameters for the expanded form are three gains, Kc, Kj, and Kjy, rather than the standard parameters, Kc, t/, and td. The expanded form of PID control is used in MATLAB. This form might appear to be well suited for controller tuning, because each gain independently adjust the influences only one control mode. But the well-established controller tuning relations presented in Chapters 12 and 14 were developed for the series and parallel forms. Thus, there is httle advantage in using the expanded form in Eq. 8-16. 

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