# SLE

### From OpenOpt

**System of linear equations (SLE)****FuncDesigner SLE examples:**- Simplest (3 unknowns)
- Unknowns are 1 variable and 2 arrays (size n and 2n), with "for" cycle and matrix multiplication
- Sparse SLE of size 45000
- Rendering FuncDesigner SLE into ordinary SLE Ax=b
- Eigenvalue analysis for obtained SLE

- Attention

- for dense SLE numpy.linalg.solve (LAPACK routine dgesv) is used
- for sparse SLE scipy.sparse.linalg.spsolve is used. If you have SciPy installed without UMFPACK (license: GPL), then SuperLU will be used (license: BSD, is included into latest SciPy versions code). However, most of times UMFPACK yields speed of many times greater. Installation of SciPy from Linux soft channels has UMFPACK as optional dependence (thus is installed as well), as for presence in scientific Python distributions - check by yourself (probably via google search), maybe information placed here will be obsolete the time you're read it
- solving SLE by FuncDesigner requires OpenOpt installed, maybe in future the dependence will be ceased
- using FuncDesigner ooSystem can
**automatically determine is your system of equations linear or nonlinear, subjected to given set of free/fixed variables**. For more details see the doc entry.

See also:

- EIG (eigenvalue analysis for OpenOpt and FuncDesigner)
- SNLE (system of nonlinear equations)
- LLSP (overdetermined system of linear equations, solving by linear least squares approach)