LAPACK¶

HighFM also supports more advanced mathematical operations, such as QR factorization, eigen decomposition, solving least-square problems, etc. In many cases, these routines may return more than one object at the same time. Take for example the eigen decomposition \(\mathbf{A} = \mathbf{VDV}^{-1}\), where \(\mathbf{V}\) contains the eigenvectors of A and \(\mathbf{D}\) is a diagonal matrix containing the corresponding eigenvalues.

Matrix<double> A(n, n);
Vector<std::complex<double>> D(n);
Matrix<double> V(n, n);           // Matrix with the eigenvectors
Matrix<double> Vinv(n, n);
D = eigen(A);                     // Calculates only the eigenvalues.
tie(D, V) = eigen(A);             // Calculates the eigenvalues and V.
tie(D, V, Vinv) = eigen(A);       // Calculates the eigenvalues, V and Vinv.

Notice that you need to use tie() to assign the result of the eigen decomposition to multiple objects(D, V and Vinv). Moreover, depending on the number of objects, the eigen routine will behave differently.

There are some exceptions, though. For instance, both QR and LQ factorizations are stored in a compact form, and thus, qr(A) and lq(A) will return an abstract object instead of the corresponding matrices.

Available operations: