LA: linear algebra C++ interface library

    Copyright (C) 2008- Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
    complex versions written by Roman Curik <roman.curik@jh-inst.cas.cz>
    cuda interface contributed by Miroslav Sulc <miroslav.sulc@jh-inst.cas.cz>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
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This software provides a C++ vector and matrix class with an interface
to BLAS and ATLAS linear algebra libraries and a few additional features.
Templates are employed in order to achieve generic applicability of the algorithms.
In particular, iterative methods suitable for sparse matrices (Davidson diagonalization, linear solvers, matrix exponential)
can be applied to your custom matrix class, which does not need to contain any explicit
storage of the matrix (only matrix times vector operation has to be provided).
(In quantum chemistry, a particular application of this technique is called direct-CI.)
The library implements reference counting to avoid overhead when copying matrices and passing them by value;
on the other hand it does NOT optimize matrix expressions, you should yourself call gemv, axpy etc. instead of using operator* etc. where appropriate.

vec.h, vec.cc : vector class
mat.h, mat.cc : general matrix class
smat.h, smat.cc: symmetric matrix class
vecmat3.h, vecmat3.cc : simplified class for 3-dimensional entities
quaternion.h, quaternion.cc : quaternions and 3-dim rotations
sparsemat.h sparsemat.cc: sparse matrix class
sparsesmat.h sparsesmat.cc: sparse symmetric matrix class
csrmat.h, csrmat.cc: unfinished work on compressed row format sparse matrices
nonclass.h nonclass.cc: some methods not belonging to a class - linear solver, diagonalization
conjgrad.h: conjugate gradient sparse linear solver
gmres.h: generalized minimal residual sparse linear solver
matexp.h: matrix exponential (suitable both for dense and sparse matrices - cf. exptimes routine)
qsort.h: generic quick-sort template
bitvector.h: bit vector class
bisection.h: generic bisection search
diis.h: DIIS convergence acceleration
davidson.h: Davidson (modified Lanczos) sparse matrix diagonalization
fourindex.h, fourindex.cc: class for four-index quantities, in particular two-electron integrals in quantum chemistry, allows transparent access to externally stored integrals
auxstorage.h: class facilitating simple file IO for the vectors and matrices
permutation.h, qsort.h : permutations and sorting


INSTALLATION:
0. autoreconf --install if ./configure does not exist
1. ./configure with DEBUG, OPTIMIZE and MATPTR options, export CXXFLAGS=-I<path> and export LDFLAGS=-L<path> (and possibly added -latlas -lcblas) 
   pointing to your preferred BLAS/LAPACK, your preferred --prefix and --enable/--disable options for optimization and debugging
2. make
3. make check (to see that the programs t and test compile and link without errors)
4. make install

USING:
1. #include "la.h"
2. using namespace LA;
3. look at test.cc and t.cc for examples of use
4. remember to always call .copyonwrite() before you start writing to individual matrix elements explicitly
   (when modifying a matrix via provided methods or operators other than () and [], copy on write is performed transparently)
5. Note that the library does not attempt to do any optimizations of the evaluation of matrix expressions (by template metaprogramming and postponed evaluation techniques), so instead of inefficient "z=A*2*x + y*1.5 " call gemv and axpy methods. On the other hand it makes shallow copies, so you can pass matrix by value to a subroutine and you are allowed to write x=A*x, as a temporary will be created.
6. you may compile it with DEBUG defined to perform index range and other checks

NOTE: 
We named the classes NRMat, NRVec etc. since we started to use them together with the Numerical Recipes library. They can be used with Numerical Recipes in C++, however, they are completely independent of this library.

This is a beta release. The library has already been in use, but not every function/method has been tested.
There is no documentation except the source itself, since I originaly did not intend to distribute it.
I will appreciate your bugfixes, exhancements, suggestions etc.

Jiri Pittner