MATLAB Function Arguments

All functions have this standard function syntax  

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Shown next is a Command Line session that sets the first two arguments (actual argument names x and y) and then calls the testfunction. The output arguments (actual arguments f and g) are printed using the fprint command. 

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Many other matlab functions, for example, impulse (), isim (), etc., take both transfer function and state space arguments (what you can call polymorphic). There is very little reason to do the conversion back to transfer function once you can live in state space with peace. 

MATLAB has its own built-in function fzero for root finding. The statement fzero file nam jc, ) finds the root of the function/(x) introduced in the user-defined MATLAB function The second argument jt , is a starting guess. Starting with... 

Linear interpolation method (U.m) This function consists of the same parts as the XGX.m function. The number of input arguments is one more than that of XGX.m, because the linear interpolation method needs two starting points. Special care should be taken to introduce two starting values in which the function have opposite signs. Eq. (1.5) is used without change as the function the root of which is to be located. This function is contained in a MATLAB function called Colebrook.m. 

Program Description The MATLAB function Causs. m consists of three main sections. At the beginning, it checks the sizes of input arguments (coefficient matrix and vector of constants) to see if they are consistent. It also checks the coefficient matrix for singularity. 

Program Description The MATLAB function LinearODE.m solves a set of linear ordinary differential equations. The first part of the function checks the number of inputs and their sizes, or values. The next section of the function performs the solution of the set of ordinary differential equations, which can be done by either the matrix exponential method [Eq. (5.40)] or the eigenvector method [Eq. (5.53)]. The method of. solution may be introduced to the function through the fifth input argument. The default method of solution is the matrix exponential method. 

Program Description Five general MATLAB functions are written for the solution of a set of simultaneous nonlinear ordinary differential equations. They are Euler.m, MEuler.m, RK.m, Adarrts.m, and AdamsMoulton.m. All these functions consist of two main sections. Tiie first part is initialization, in which specific input arguments are checked, and some vectors to be used in the second part are initiated. The next section of the function is solution of the set of nonlinear ordinary differential equations according to the specified method, which is done simultaneously in vector form, Brief descriptions of the method of. solution of these five functions are given below ... 

The first input argument to all the above method functions is the name of the MATLAB function containing the set of differential equations. Note that the first input argument to this function has to be the independent variable, even if it is not used explicitly in the equations. It is important that this function returns the values of the derivatives (f as a column vector. The other inputs to the method functions are initial and final values of the independent... 

The function Ex5 5 func.m evaluates the values of the set of Eqs. (1), (2), and (4) at a given point. It is important to note that the first input argument to ExSJJunc is the independcnl variable, though it does not appear in the differential equations in this case. This function also calls the MATLAB function/zero to calculate Ihe temperature from Eq. (8), which is introduced in the function Ex5 5 theta.m. 

Program Description The MATLAB function paraboliclD.m is written for solution of the parabolic partial differential equation in an unsteady-state two-dimensional problem. The boundary conditions are passed to the function in the same format as that of Example 6.1, Initial condition, is a matrix of the values of the dependent variable for all x and y at time / = 0. If the problem at hand is nonhomogeneous, the name of the MATLAB function containing the function/should be given as the 10th input argument. 

MATLAB is object-oriented. Linear time-invariant (LTI) models are handled as objects. Functions use these objects as arguments. In classical control, LTI objects include transfer functions in polynomial form or in pole-zero form. The LTI-oriented syntax allows us to better organize our problem solving we no longer have to work with individual polynomials that we can only identify as numerators and denominators. 

Note that this kind of normalisation, via the norm function, can only be performed column- (or row-) wise via a loop as seen in the Matlab box above. Calling norm with one matrix argument determines a different kind of normalisation coefficients. We refer to the Matlab help and function references for more detail. 

The function in Example 4.4 can be used to autoscale a data matrix. The function determines the size of the argument, its mean vector, and its standard deviation vector. On the last fine, a MATLAB programming trick is used to extend the mean vector and standard deviation vector into matrices having the same number of rows as the original argument prior to subtraction and division. The expression ones < r, i) creates an r x 1 column vector of ones. When used as an index in the statement mn (ones(r,1), ), it instructs MATLAB to replicate the mean vector r times to give a matrix having the dimensions r x c. 

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 ... 

Needless to say that within MATLAB we have all the algebraic, statistical functions predefined along with plotting capabilities. Before briefly commenting on the basics, it is interesting to point out the use of help within the command window. We use the help function followed by any built-in function and MATLAB returns a small tutorial on the use of that function, the arguments, and the options (i.e., try help ode45 ). 

The identity matrix can be defined in MATLAB with the help of the eye function with an argument representing the size of the matrix ... 

A function file is a user-defined function using MATLAB. We use function files for repetitive tasks. The first line of a function file must contain the word function, followed by the output argument, the equal sign (=), function name, and the input argument enclosed in parentheses. The function name and file name must be the same, but the file name must have the extension. m. For example, the function file consisting of the following two lines... 

NOTE Here we used. / and instead of / and respectively, to tell MATLAB that the y vector is a function of the x vector mapping each point of x by the corresponding point of y. This kind of dot division, dot multiplication, and dot exponentiation should be applied for matrix (or vector as a subset of matrix) arguments. 

Note that the Matlab ODE solver is given three arguments the function evaluating the right-hand side of the differential eqnation, the time interval to integrate over, and the initial conditions. The first line of code (opts) sets the relative error tolerance to le-4 (default is le-3). This line is followed by a command which calls the ode45 solver, and specifies that the differential equation is specified in the m-file. Fmther, the command also specifies that the ODE should be solved in the interval 0-1 and at the initial condition yo = 1 - The third line is just used to plot the solution in a graph. 

MATLAB has several functions for interpolation. The function = interpl(x, y, x) takes the values of the independent variable x and the dependent variable y (base points) and does the one-dimensional interpolation based on x, to find yj. The default method of interpolation is linear. However, the user can choose the method of interpolation in the fourth input argument from nearest (nearest neighbor interpolation), linear (linear interpolation), spline (cubic spline interpolation), and cubic (cubic inteipolation). If the vector of independent variable is not equally spaced, the function interplq may be used instead. It is faster than interpl because it does not check the input arguments. MATLAB also has the function sp/ine to perform one-dimensional interpolation by cubic. splines, using nat-a- not method, ft can also return coefficients of piecewise poiynomiais, if required. The functions interp2, inte.rp3, and interpn perform two-, three-, and n-dimensional interpolation, respectively. 

To use any of the methods or functions from within another MATLAB script, invoke the method by its specific name and provide the necessary arguments for that method or function. To get a brief description of any program, type help followed by the name of the program ... 

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