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<html>
<head>
<title>
SOLVE - Linear Solver for Double Dimensioned Arrays
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SOLVE <br> Linear Solver for Double Dimensioned Arrays
</h1>
<hr>
<p>
<b>SOLVE</b>
is a C++ library which
implements a linear solver which makes it easy to create
doubly-dimensioned arrays and solve associated linear systems.
</p>
<p>
The purpose of the library is to allow the user to declare a square
matrix A of any size, access matrix entries using the usual double
indexing formula <b>A[i][j]=value;</b>, and call a linear solver
to solve A*x=b using a call like:
<pre>
x = solve ( n, A, b );
</pre>
</p>
<p>
In C and C++, it can be awkward to set up matrices in a way that makes it
easy to access them with the usual two index form, and to pass these
matrices back and forth to other functions. This is because, when
using the simplest interface to another function, it is necessary
that the second dimension, that is, the number of columns, be declared
as a fixed integer, not a variable. Such an interface is impossible
to use with a general purpose linear solver.
</p>
<p>
These problems can be overcome by using a data structure known as
a pointer to a pointer. However, creating and deleting such objects
can be unfamiliar to the average user. This library hides the details
behind an object called an R8RMAT, that is, a double precision real (R8)
row-major (R) matrix (MAT). A set of functions, with the "r8rmat_"
label, are provided to make it easy to create and delete such objects,
and more importantly, to solve an associated linear system.
</p>
<p>
The SOLVE library makes it possible to set up and solve linear systems
in a natural way, as long as the user does the following:
<ul>
<li>
declare the matrix as a "double **" quantity;
</li>
<li>
call <b>r8rmat_new()</b> or <b>r8rmat_zero()</b> to create,
or create and zero out, the matrix.
</li>
<li>
call <b>r8rmat_fs_new()</b> to solve the linear system.
</li>
<li>
call <b>r8rmat_delete()</b> to free the matrix memory when
no longer needed.
</li>
</ul>
</p>
<p>
The library can also be useful because:
<ul>
<li>
it shows the steps involved in a simple Gauss-elimination procedure;
</li>
<li>
it can be used to count the number of operations in Gauss-elimination;
</li>
<li>
it can be used as a guide for writing a corresponding program
in another language;
</li>
<li>
its performance can be compared to corresponding versions in
Fortran or Matlab;
</li>
<li>
it can be used as a starting point for exploring band storage,
sparse storage, iterative solutions and other topics in linear
algebra.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SOLVE</b> is available in
<a href = "../../c_src/solve/solve.html">a C version</a> and
<a href = "../../cpp_src/solve/solve.html">a C++ version</a> and
<a href = "../../f77_src/solve/solve.html">a FORTRAN77 version</a> and
<a href = "../../f_src/solve/solve.html">a FORTRAN90 version</a> and
<a href = "../../m_src/solve/solve.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/allocatable_array/allocatable_array.html">
ALLOCATABLE_ARRAY</a>,
a C++ program which
demonstrates how a C++ function can declare a pointer to an array,
call a function, which can then allocate it and fill it with data,
and then return the allocated and initialized array to the
calling function through the argument list.
</p>
<p>
<a href = "../../cpp_src/cpp_arrays/cpp_arrays.html">
CPP_ARRAYS</a>,
C++ programs which
illustrate the use of vectors, matrices and tensors.
</p>
<p>
<a href = "../../cpp_src/linpack/linpack.html">
LINPACK</a>,
a C++ library which
solves linear systems for a variety of matrix storage schemes,
real or complex arithmetic, and single or double precision.
It includes a routine for computing the singular value decomposition (SVD)
of a rectangular matrix.
The original version of this library is
by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
</p>
<p>
<a href = "../../cpp_src/linplus/linplus.html">
LINPLUS</a>,
a C++ library which
carries out operations such as matrix-vector products,
matrix factorization, direct and iterative linear solvers
for matrices in a variety of formats, including banded, border-banded,
circulant, lower triangular, pentadiagonal, sparse, symmetric,
toeplitz, tridiagonal, upper triangular and vandermonde formats.
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines
using double precision real (R8) arithmetic.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "solve.cpp">solve.cpp</a>, the source code.
</li>
<li>
<a href = "solve.hpp">solve.hpp</a>, the include file.
</li>
<li>
<a href = "solve.sh">solve.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "solve_prb.cpp">solve_prb.cpp</a>
a sample calling program.
</li>
<li>
<a href = "solve_prb.sh">solve_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "solve_prb_output.txt">solve_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>R8RMAT_COPY_NEW</b> makes a new copy of an R8RMAT .
</li>
<li>
<b>R8RMAT_DELETE</b> frees the memory set aside by R8RMAT_NEW.
</li>
<li>
<b>R8RMAT_FS_NEW</b> factors and solves an R8RMAT system with one right hand side.
</li>
<li>
<b>R8RMAT_NEW</b> sets up an R8RMAT of the desired dimensions.
</li>
<li>
<b>R8RMAT_ZERO</b> sets up and zeros an R8RMAT of the desired dimensions.
</li>
<li>
<b>R8VEC_COPY_NEW</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 27 May 2014.
</i>
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