Chapter 4
The LAPACK Interface (cvxopt.lapack)

The module cvxopt.lapack includes functions for solving dense sets of linear equations, for the corresponding matrix factorizations (LU, Cholesky, LDLT), for solving least-squares and least-norm problems, for QR factorization, for symmetric eigenvalue problems, singular value decomposition, and Schur factorization.

In this chapter we briefly describe the Python calling sequences. For further details on the underlying LAPACK functions we refer to the LAPACK Users’ Guide and manual pages.

The BLAS conventional storage scheme of section 3.1 is used. As in the previous chapter, we omit from the function definitions less important arguments that are useful for selecting submatrices. The complete definitions are documented in the docstrings in the source code.

See also: LAPACK Users’ Guide, Third Edition, SIAM, 1999.

 4.1 General Linear Equations
 4.2 Positive Definite Linear Equations
 4.3 Symmetric and Hermitian Linear Equations
 4.4 Triangular Linear Equations
 4.5 Least-Squares and Least-Norm Problems
 4.6 Symmetric and Hermitian Eigenvalue Decomposition
 4.7 Generalized Symmetric Definite Eigenproblems
 4.8 Singular Value Decomposition
 4.9 Schur and Generalized Schur Factorization
 4.10 Example: Analytic Centering