Excel Add-in Development in C/C++: Applications in ... - F9

Example Add-ins and Financial Applications 351}r2 * = TWO_PI;sample_zero = r1 * cos(r2);return r1 * sin(r2);Both the above functions perform the same task but in very different ways. The first cantake static or volatile inputs and always returns a pair of samples. The second returns asingle sample but is volatile. This gives the spreadsheet developer less control than withthe first. It would be possible to modify the second so that it took a trigger argument,which would then obviate the need for it to be declared as volatile.It is a straightforward exercise to generalise the Box-Muller functions above to, optionally,generate samples using the more efficient polar rejection method. (See Clewlow andStrickland (1998) for details.)10.3 MATRIX FUNCTIONS – EIGENVALUESAND EIGENVECTORSExcel has a number of useful matrix routines, in particular MMULT(), MINVERSE(),MDETERM(), TRANSPOSE() and SUMPRODUCT(). As well as this, the way that Excel treatsrange references in array formulae greatly extends its matrix capabilities. Nevertheless,there are a number of matrix operations which, though not as fundamental as these, arevaluable for those analysing linear systems. Perhaps the most useful is the calculation ofeigenvectors and eigenvalues. The following example function takes a square symmetric(real) N×N matrix and returns an N×(N + 1) array containing the eigenvectors andeigenvalues. The code is contained in the CD ROM and is based on the Jacobi algorithmpublished in section 11.1 of Numerical Recipes in C++. (The code for the Jacobi algorithmitself is omitted from the XllMatrix.cpp source code module in the exampleproject on the CD ROM. However, it can easily be inserted into one of the memberfunctions of the class, d_matrix. Seetheread me file on the CD ROM for details.)The intention here is not to provide a comprehensive set of functions that will attemptto find the eigenvectors and values of any matrix. As NRC explains very well, this isa complex subject. The intention of this example is to show how to bridge from Excelranges to C/C++ matrices in a safe and efficient way.Function nameDescriptioneigen_system (exported)EigenSystem (registered with Excel)Takes a square symmetrical range, or array, containing onlynumbers. Returns a square matrix whose columns are theeigenvectors of the input matrix, with an extra row at the bottomcontaining the corresponding eigenvalues. Output is sorted indescending size of eigenvalue from left to right.Prototype xloper * __stdcall eigen_system(xl_array *);Type string"RK"