Matlab structures

We are using the typical structure syntax, but MATLAB also supports the set to perform the same task. 

If basic assumptions concerning the error structure are incorrect (e.g., non-Gaussian distribution) or cannot be specified, more robust estimation techniques may be necessary, e.g., Maria and Heinzle (1998). In addition to the above considerations, it is often important to introduce constraints on the estimated parameters (e.g., the parameters can only be positive). Such constraints are included in the simulation and parameter estimation package ACSL-OPTIMIZE and in the MATLAB Optimisation Toolbox. Because of numerical inaccuracy, scaling of parameters and data may be necessary if the numerical values are of greatly differing order. Plots of the residuals, difference between model and measurement value, are very useful in identifying systematic or model errors. 

These simplifications in the parameter handling are best organised by using structures and cell arrays, as provided by Matlab to supplement the matrix as a basic data type. We introduce both, beginning with structures. 

Structures are Matlab arrays with named "data containers" called fields. The fields of a structure can contain any kind of data. For example, one field might contain a text string representing a name, another might contain a scalar representing a billing amount, a third might hold a matrix of medical test results, and so on. (also see Matlab Help on structures). 

Many of the fields in the structure s now contain two entries. These are arranged as cell arrays e.g. the field s. Y contains the arrays s. Y 1 and s.Y 2, the field s. t contains the two vectors s.t l and s. t 2, etc. Naturally, more than two data sets can be arranged in this way. A new field, s. nm, contains the number of measurements nm (i.e. data sets). Recall that Matlab requires curly brackets when referring to elements of a cell array. This natural expansion of the structure requires veiy few changes in the other programs. As an example, the central fitting function nglm3. m is not affected at all. 

EFA. m is a short Matlab function that computes forward and backward EFA matrices for a given number, ne, of singular values. Its structure is essentially identical to the one discussed for Main EFA2, m. 

The solver is implemented in Fortran, using optimized treatment of diagonal-band matrices and analytical derivatives of reaction rates to minimize computation time. The software structure is modular, so that different reaction-kinetic modules for individual types of catalysts can be easily employed in the monolith channel model. The compiled converter models are then linked in the form of dynamic libraries into the common environment (ExACT) under Matlab/Simulink. Such combination enables fast and effective simulation of combined systems of catalytic monolith converters for automobile exhaust treatment. 

Due to the special structure of MATLAB, readers should be familiar with the mathematical concepts pertaining to matrices, such as systems of linear equations, Gaussian elimination, size and rank of a matrix, matrix eigenvalues, basis change in n-dimensional space, matrix transpose, etc. For those who need a refresher on these topics there is a concise Appendix on linear algebra and matrices at the end of the book. 

Organizing J in a three-dimensional array is elegant, but it does not fit well into the standard routines of MATLAB for matrix manipulation. There is no command for the calculation of the pseudoinverse J+ of such a three-dimensional array. There are several ways around this problem one of them is discussed in the following. The matrices R(k) and R(k + 5k) as well as each matrix < RIdk, are vectorized, i.e., unfolded into long column vectors r(k) and r(k + 5k). The nk vectorized partial derivatives then form the columns of the matricized Jacobian J. The structure of the resulting analogue to Equation 7.13 can be represented graphically in Equation 7.17. 

In this section we analyze processes involving the second-order A + B —> 2P reaction. Such processes have been studied, among others, by Luyben andTyreus [10]. It has been noticed [11] that certain control structures lead to state multiplicity and instability. Here, we use dimensionless models to derive general feasibility and stability conditions. The reader is encouraged to check carefully the balance equations, writing them first in the dimensional form, and then deriving the dimensionless versions. To solve these equations, software such as Maple or the symbolic toolbox of Matlab can be used. 

By default Matlab will be installed in the directory C matlabrxx on your PC, where xx relates to the edition of the package. You can choose to install elsewhere but at first it is best to stick to the standard directories, which we will assume below. You need some knowledge of DOS directory structure to use the directory commands within Matlab. According to particular combinations of versions of Windows and Matlab there is some flexibility, but keeping to the commands below is safe for the first time user. 

Usually complex structures with more than 15 layers are employed, called the multilayer perceptron (MLP). Some of the commercial programs which have been used to fit tableting parameters are INForm (Intelligensys, Billingham Teesside), CAD/Chem (AI Ware, Cleveland, OH), which is no longer commercially available, and the Neural Network Toolbox of MATLAB (MathWorks, Natick, MA). 

Imaging spectroscopy is particularly useful toward understanding the structure and functional relationships of materials and biological samples. Spatial images of chemical structure demonstrate physical or chemical phenomena related to a particular structural anatomy. Software packages such as MATLAB and many others provide easily learned methods for image display and mathematical manipulation for matrices of data [1]. 

This chapter serves three purposes (a) to provide a brief overview of PBPK modeling, (b) to present a tutorial on the issues and steps involved in the development of a PBPK model, and (c) to present an application and discuss relevant issues associated with model refinement, evaluation, parameter estimation, and sensitiv-ity/uncertainty analysis. First, some basic background information is provided, and references to important resources are presented. Then the process of developing a PBPK model is discussed, and a step-by-step description of a PBPK modeling example is provided, along with a brief discussion on relevant complementary issues such as model parameter estimation and sensitivity/uncertainty analysis. The example is presented in a manner that a novice PBPK modeler can follow the model structure, mathematical equations, and the code. Relevant cross-references between the equations, parameter tables, and the actual code is presented. Though the example is implemented in Matlab (5), it does not require substantial Matlab... 

The model has been implemented in Matlab 7.0 and utilizes features for defining flexible structures (objects) in Matlab in order to improve both the model readability and extensibility. All the parameters that are needed to specify the model are included in a model configuration object, which is specified as part of the model configuration section. 

Below a minimal Matlab script for the determination of the CQMOM approximation (Yuan Fox, 2011) for a bivariate case is reported. The script requires the specification of the number of nodes desired for the first (Nl) and second (N2) internal coordinate. The moments used in the calculation must be provided in matrix form. The matrix containing the moments m is defined by two indices the first one indicates the order of the moments with respect to the first internal coordinate (index 1 for moment 0, index 2 for moment order 1, etc.), whereas the second one is for the order of the moments with respect to the second internal coordinate. The structure of the data resembles that of Tables 3.9-3.11. The script calculates the N = N1N2 weights and nodes and stores them in the vector w and in the matrix xi, which have the same structure as in the previous script. The procedure is based on the calculation of the moments with respect to the second internal coordinate, conditioned on the value of the first internal coordinate. The calculation of the quadrature constructed on moments conditioned on the second internal coordinate can be simply carried out by providing the script with the transpose of the moment matrix. 

Column-wise augmentation, in which matrices of various runs are joined one below the others in a structure that keeps common wavelengths (or m/q ratios) in the same column. According to MATLAB nomenclature, these matrices can be written as [Run l Run 2 Run 3 ... Run j]. 

MATLAB Image Processing Toolbox [13]. The block size of the Wiener filter was tuned to find the least MSE reconstruction. Since quantification requires true images for comparative reasons, the evaluation was carried out on the basis of a simulated image (Fig. 6), which has simple features, such as rectangular bumps with increasing widths, resembling structures in some real... 

The structure evolving, damage-allowable thermoviscoplastic constitutive model was computed in MATLAB . The corresponding model parameters were mainly obtained by curvefitting various thermal and mechanical testing results, as summarized in Table 4.4. 

System is made of 8 elements with series-parallel structure Fig. 1. Simulation experiment was made for 10000 simulations. During simulation cycle, maximum event was chosen from parallel structure. This event was used in series structure and minimal event was chosen for system failure. Elements are described with time to failure distributions according to computer language MATLAB (HOLUB, R. VINTR, Z.). 

With classical structure, the proposed GA is implemented in Matlab to search the optimal/good solutions for the problem. This study considers the problem associated with soft precedence constraints, which will incur a penalty if violated rather rendering the sequence and schedule infeasible. A penalty implies that the respective chromosome is less likely to pass in the next generation, but still may have very valuable characteristics to pass on through the evolution process. 

The co-simulation cooling network model made of Amesim and Matlab is used to analyze the relationship of pipeline diameter and the cooling effect of motor. The thermal model of cooling system is modeled in Amesim (introduced in the Cooling Effect of Jacket Structures Section)... 

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