================================== Eigenvalues (Non-Symmetric Matrix) [TOC] ================================== In this example we compute the eigenvalues $w \in \mathbb{C}$, left eigenvectors $V_L$ and right eigenvectors $V_R$ of a non-symmetric Matrix $A$. We use __lapack::ev__ which is the FLENS port of LAPACK's __dgeev__. :links: __lapack::ev__ -> file:flens/lapack/ge/ev.h __dgeev__ -> file:cxxlapack/netlib/lapack/dgeev.f Example Code ============ :import: flens/examples/lapack-geev.cc [stripped, downloadable] Comments on Example Code ======================== :import: flens/examples/lapack-geev.cc [brief] Compile ======= *--[SHELL]----------------------------------------------------------------* | | | cd flens/examples | | g++ -std=c++11 -Wall -I../.. -o lapack-geev lapack-geev.cc | | | *-------------------------------------------------------------------------* Run === *--[SHELL]----------------------------------------------------------------* | | | cd flens/examples | | ./lapack-geev | | | *-------------------------------------------------------------------------* Using QD (Double-Double and Quad-Double Package) ================================================ The following description is taken from the __QD Library__ page: *--[BOX]------------------------------------------------------------------* | | | The __QD Library__ supports both a double-double datatype (approx. 32 | | decimal digits) and a quad-double datatype (approx. 64 decimal digits). | | The computational library is written in C++. Both C++ and Fortran-90 | | high-level language interfaces are provided to permit one to use convert| | an existing C++ or Fortran-90 program to use the library with only minor| | changes to the source code. In most cases only a few type statements and| | (for Fortran-90 programs) read/write statements need to be changed. PSLQ| | and numerical quadrature programs are included. | | | *-------------------------------------------------------------------------* :links: __QD Library__ -> http://crd-legacy.lbl.gov/~dhbailey/mpdist/ Modified Example Code --------------------- :import: flens/examples/qd-lapack-geev.cc [stripped, downloadable] Comments on Modifications ------------------------- Only a few modifications were made which will be pointed out in the following: :import: flens/examples/qd-lapack-geev.cc [brief] Compile and Run --------------- *--[SHELL]-----------------------------------------------------------------* | | | cd flens/examples | | g++ -Wall -std=c++11 -I../.. -I/opt/local/include/ -c qd-lapack-geev.cc | | g++ -o qd-lapack-geev qd-lapack-geev.o /opt/local/lib/libqd.a | | ./qd-lapack-geev | | | *--------------------------------------------------------------------------* Using mpfr::real (C++ Interface for mpfr) ========================================= The following description is taken from the __mpfr::real__ page: *--[BOX]------------------------------------------------------------------* | | | The class __mpfr::real__ is a high-level C++ wrapper for the | | __GNU MPFR library__, _a C library for multiple-precision floating-point| | computations with correct rounding_. | | | | The objects of mpfr::real can (almost) be used like doubles or other | | fundamental floating-point types, thus avoiding the use of C functions | | to manipulate MPFR's low-level data type directly. In addition to | | all arithmetic and comparison operators available for fundamental | | floating-point types, mpfr::real also supports the set of | | mathematical functions for double from math.h/cmath. Finally, | | std::istream operator >> and std::ostream operator << are | | implemented for mpfr::reals. This allows to substitute double with | | mpfr::real with no further modifications of the code in many cases. | | | *-------------------------------------------------------------------------* :links: __mpfr::real__ -> http://chschneider.eu/programming/mpfr_real/ __GNU MPFR library__ -> http://www.mpfr.org/ Modified Example Code --------------------- :import: flens/examples/mpfr-real-lapack-geev.cc [stripped, downloadable] Comments on Modifications ------------------------- :import: flens/examples/mpfr-real-lapack-geev.cc [brief] Compile and Run --------------- *--[SHELL]----------------------------------------------------------------* | | | cd flens/examples | | g++ -Wall -std=c++11 -I../.. -I/opt/local/include +++| | -o mpfr-real-lapack-geev mpfr-real-lapack-geev.cc +++| | -L /opt/local/lib -lmpfr -lgmp | | ./mpfr-real-lapack-geev | | | *-------------------------------------------------------------------------* :navigate: __up__ -> doc:flens/examples/tutorial __back__ -> doc:flens/examples/tut04-page03