Matrix computations, MATLAB examples

For your information, relative gain array can be computed as the so-called Hadamard product, Ay = KjjKrH, which is the element-by-element product of the gain matrix K and the transpose of its inverse. You can confirm this by repeating the examples with MATLAB calculations. 

This function is called numerous times from the Matlab ODE solver. In the example it is the ode45 which is the standard Runge-Kutta algorithm. ode45 requires as parameters the file name of the inner function, ode autocat. m, the vector of initial concentrations, cO, the rate constants, k, and the total amount of time for which the reaction should be modelled (20 time units in the example). The solver returns the vector t at which the concentrations were calculated and the concentrations themselves, the matrix C. Note that due to the adaptive step size control, the concentrations are computed at times t which are not predefined. 

The SVD is generally accepted to be the most numerically accurate and stable technique for calculating the principal components of a data matrix. MATLAB has an implementation of the SVD that gives the singular values and the row and column eigenvectors sorted in order from largest to smallest. Its use is shown in Example 4.3. We will use the SVD from now on whenever we need to compute a principal component model of a data set. 

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