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Werner Wothke

The Simple C++ Numerical Toolkit (SCPPNT) consists of a set of classes and functions that implement simple dense matrix and vector classes and some associated algorithms. SCPPNT is a modified version of the Template Numerical Toolkit (TNT) by Brad Hanson (2001). The major changes that were made to TNT are:

- Row, column, and diagonal iterators were added to the matrix class, and are used in algorithms involving matrices. Some tests I have done indicate that using iterators in algorithms involving matrices can result in increased performance relative to using matrix subscripting.
- Assignment operators (+=, -=, *=, /=) were added to matrix and vector classes. The use of assignment operators can help eliminate the creation of temporary matrix and vector objects in computations.
- Errors result in an exception being thrown rather than the program being aborted. This allows programs to more gracefully deal with errors that occur in SCPPNT functions.

The matrix and vector classes in SCPPNT have an interface that is mostly compatible with TNT. The algorithms in SCPPNT involving matrices that were modified from TNT use matrix iterators rather than matrix subscripting and cannot be used with the TNT Matrix class. There are some elements of TNT that have not been implemented in SCPPNT. For example, a matrix class where the data are stored internally in column-major order (TNT class Fortran_Matrix).

The current release of SCPPNT is a beta version. SCPPNT has not been extensively tested, and the public interface to classes and functions may change.

Please contact me if you have any questions or comments about this software

Download SCPPNT - Zip archive containing SCPPNT source files and documentation. The files are stored with DOS line breaks (they are DOS text files).

The documentation for SCPPNT consists of this file as well as comments in the source files. The source file comments were written to be compatible with the doxygen documentation system. The on-line source code documentation contains descriptions of each file, class, and function that are part of SCPPNT. This documentation is also contained in the doc directory of the SCPPNT distribution.

The examples directory in the SCPPNT distribution contains several SCPPNT example programs. Most of these are modified versions of TNT example programs. One of the example programs (scppnt_test.cpp) showing some basic features of SCPPNT is given below.

// scppnt_test.cpp // Example program illustrating some basic features of // the Simple C++ Numerical Toolkit (SCPPNT). // // SCPPNT is available from // http://www.smallwaters.com/programs/cpp/scppnt.html //#define BOOST_MSVC //#define SCPPNT_NO_IO #include <algorithm> #include <iostream> #include <iterator> #include <vector> // Make matrix region functions available in Matrix class #define SCPPNT_USE_REGIONS //#define SCPPNT_NO_DIR_PREFIX // Unless SCPPNT_NO_DIR_PREFIX is defined the // directory prefix scppnt/ is used for SCPPNT // header file includes. Alternatively, the header // file directory may be specified in the compilers // search path. #ifdef SCPPNT_NO_DIR_PREFIX // Include files are in same directory as main code

// or in include search path #include "vec.h" #include "cmat.h" #include "matop.h" #include "transv.h" #include "region2d.h" #else // Include files are in scppnt subfolder #include "scppnt/vec.h" #include "scppnt/cmat.h" #include "scppnt/matop.h" #include "scppnt/transv.h" #include "scppnt/region2d.h" #endif using namespace SCPPNT; int main() { // Construct matrix. Elements are not initialized. // To initialize all elements to zero use // Matrix<double> a(2, 2, 0.0). Matrix<double> a(2, 2); // Assign elements to first row using // Fortran-style one-based indexing. a(1,1) = 0.5; a(1,2) = 1.0; // Assign elements to second row using // C-style zero-based indexing. a[1][0] = 1.5; a[1][1] = 2.0; // Multiply all elements of a by 2. // Analogous +=, -=, and /= operators are also available // for both matrices and vectors. a *= 2.0; // Construct 2X3 matrix with initial elements given // in row-major order by an iterator. double belem[6] = {0.1, 0.2, 0.3, 0.3, 0.2, 0.1}; Matrix<double> b(belem,2,3); // Construct vector. Elements are not initialized. // To initialize all elements to zero use // Vector<double> v(2, 0.0). Vector<double> v(2); // Assign first element using // Fortran-style one-based indexing v(1) = 2.0; // Assign second element using // C-style zero-based indexing. v[1] = 3.0; // Write a, b, and v std::cout << "a: " << a << std::endl; std::cout << "b: " << b << std::endl; std::cout << "v: " << v << std::endl; // Create new matrix that is the // product of a and b. // Analogous + and - operators are also // available for both matrices and vectors. Matrix<double> c = a * b; std::cout << "c = a * b: " << c << std::endl; // Matrix product b' * a, without forming the transpose of b Matrix<double> e = Transpose_View< Matrix<double> >(b) * a; std::cout << "b' * a: " << e << std::endl; // Matrix times vector b' * v, without forming the transpose of b Vector<double> u = Transpose_View<Matrix<double> >(b) * v; std::cout << "b' * v: " << u << std::endl; // Create new matrix that is the transpose of c Matrix<double> d = transpose(c); // Upper 2X2 region of d Index1D J(1, 2); // Index range of 1 through 2 Region2D< Matrix<double> > dregion = d(J,J); std::cout << "d: " << dregion << std::endl; // Multiply upper 2X2 region of d by a and store result in dregion. // Analogous += and -= operators are also // available for both matrices and vectors. dregion *= a; // Print product of upper 2X2 submatrix of d and v std::cout << "d * a: " << dregion << std::endl; return 0; }

The matrix classes in SCPPNT provide row, column, and diagonal iterators. The
`Matrix<T>::begin_row(i)`

member function returns in iterator
of type `Matrix<T>::row_iterator`

to the first element of row
`i`

of a matrix. The `Matrix<T>::begin_rows()`

member
function returns an iterator of type `Matrix<T>::rows_iterator`

which is an iterator over row iterators (of type `Matrix<T>::row_iterator`

)
pointing to the row iterator for the first row. The analogous functions and
data types for columns are: `Matrix<T>::begin_columns()`

which
returns an iterator of type `Matrix<T>::columns_iterator`

pointing
initially to the iterator over elements in the first column, and `Matrix<T>::begin_column(i)`

which returns an iterator of type `Matrix<T>::column_iterator`

which points initially to the first element of column i.

The example below illustrates the use of row and column iterators. See the
function `matmult`

in matop.h for a further example of the use of
row and column iterators in matrix algorithms.

#include "cmat.h" using namespace SCPPNT; // 2X2 matrix with all elements initialized to 1 Matrix<double> B(2, 2, 1.0); // m.row(i) returns an iterator of type row_iterator that can // be used to iterate over the elements in the i-th row of the matrix. // The iterator initially points to the first element of the i-th row. // The following adds 1 to every element of the first row of matrix B. Matrix<double>::row_iterator ib = B.begin_row(1); for(int i = B.num_columns(); i--; ++ib) *ib += 1.0; // 3X3 matrix with all elements initialized to 5 Matrix<double> A(3, 3, 5.0); // Multiply every element of a matrix A by 2 (same as A *= 2.0). // icols is an iterator over column iterators of matrix A. Matrix<double>::columns_iterator icols = A.begin_columns(); for (int i = A.num_columns(); i--; ++icols) { // icol is an interator over elements in a column of A Matrix<double>::column_iterator icol = *icols; for (int j = A.num_rows(); j--; ++icol) *icol *= 2.0; }

Release notes for all releases are given in the file release_notes.txt in the SCPPNT distribution.

Release 071218 (December 18, 2007)

This version received some general housekeeping/clean-up to ensure compilation under gcc 3.4.4 and cygwin 1.5.24-2 and correct execution of all test problems. These changes required adding "typename" keywords where needed, correcting a mistyped variable name (in cmat.h), adding "std::" namespace keyword to several instances of "endl", commenting out non-functional code sections (in region2d.h), and refactoring most "...col..." matrix variables and iterators to a "...column..." convention. In addition, the use of the SCPPNT_NO_DIR_PREFIX preprossesor macro was standardized, and the code was reformatted for readability.

Release 0.010619 (June 19, 2001)

Replace instances of rowit_iterator with rows_iterator, and instances of columnit_iterator with columns_iterator in matalg.h. [matalg.h]

Brad successfully compiled programs using SCPPNT with the CodeWarrior 6.0 compiler on Mac OS and Windows NT, the gcc 2.95.2 compiler on Linux, and the free Borland 5.5 compiler on Windows 95/NT. There may be some problems in using SCPPNT with compilers that are less compliant with the C++ standard.

Release 0.010516 (May 16, 2001)

Corrected initialize method of Region2D and const_Region2D classes so that an exception is not thrown when SCPPNT_BOUNDS_CHECK is defined. [region2d.h] Make private member function diagonal_size() constant in matrix classes. [cmat.h, region2d.h]

Release 0.010515 (May 15, 2001)

Renamed the rows(), columns(), row(), column(), and diagonal() member functions of the matrix classes to begin_rows(), begin_columns(), begin_row(), begin_column() and begin_diagonal(), respectively. Added member functions end_rows(), end_columns(), end_row(), end_column(), and end_diagonal() to return an iterator to one past the last element of the sequences for which the associated begin function return an iterator to the first element. [cmat.h, region2d.h, transv.h, trisolve.h, matalg.h, cholesky.h, qr.h, lu.h, matop.h, rowcolfunc.h] The begin_diagonal() member functions of the matrix classes now take two arguments: the row and column corresponding to the first element of the diagonal the iterator points to. [cmat.h, transv.h, region2d.h, qr.h, lu.h, cholesky.h, trisolve.h] Symbol BOOST_MSVC can be define when using Microsoft Visual C++ 6. Defining this symbol will NOT allow all elements of SCPPNT to be compiled with Microsoft Visual C++, but the basic matrix and vector operations defined in vec.h and cmat.h should compile. Currently, BOOST_MSVC is only used in vec.h. [vec.h, scppnt.h]

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Last updated: November 18, 2014