(C-style i >= 0). (There is also a const version of this function.)</i></tt></li><li><tt><a href="#numeric_vectorO11">operator[]</a> -</tt></li><li><tt><a href="#numeric_vectorO12">operator()</a> - - <i>Returns the i-thelement in the numeric_vector (Fortran style i >= 1). (There is also aconst version of this function).</i></tt></li><li><tt><a href="#numeric_vectorO13">operator()</a> -</tt></li><li><tt><a href="#numeric_vectorO14">size</a> - - <i>Returns the number ofelements in the numeric_vector.</i></tt></li><li><tt><a href="#numeric_vectorO15">dim</a> - - <i>This function is addedto give compatibility with TNT.</i></tt></li><li><tt><a href="#numeric_vectorO16">operator=</a> - - <i>Vector assignment.</i></tt></li><li><tt><a href="#numeric_vectorO17">operator+</a> - - <i>Vector addition.</i></tt></li><li><tt><a href="#numeric_vectorO18">operator+=</a> - - <i>Vector additionand assignment.</i></tt></li><li><tt><a href="#numeric_vectorO19">operator-</a> - - <i>Vector subtraction.</i></tt></li><li><tt><a href="#numeric_vectorO20">operator-</a> - - <i>Vector negation (unaryminus operator).</i></tt></li><li><tt><a href="#numeric_vectorO21">operator-=</a> - - <i>Vector subtractionand assignment.</i></tt></li><li><tt><a href="#numeric_vectorO22">operator+</a> - - <i>Add a scalar to eachelement in the numeric_vector.</i></tt></li><li><tt><a href="#numeric_vectorO23">operator+=</a> - - <i>Add and assign ascalar to each element in the numeric_vector.</i></tt></li><li><tt><a href="#numeric_vectorO24">operator-</a> - - <i>Subtract a scalarfrom each element in the numeric_vector.</i></tt></li><li><tt><a href="#numeric_vectorO25">operator-=</a> - - <i>Subtract and assigna scalar from each element in the numeric_vector.</i></tt></li><li><tt><a href="#numeric_vectorO26">operator*</a> - - <i>Vector scalar/dotproduct.</i></tt></li><li><tt><a href="#numeric_vectorO27">operator%</a> - - <i>Vector cross product.</i></tt></li><li><tt><a href="#numeric_vectorO28">operator*</a> - - <i>Vector multiplicationby a scalar.</i></tt></li><li><tt><a href="#numeric_vectorO29">operator*=</a> - - <i>Vector multiplicationby a scalar and assignment.</i></tt></li><li><tt><a href="#numeric_vectorO30">operator/</a> - - <i>Vector division bya scalar.</i></tt></li><li><tt><a href="#numeric_vectorO31">operator/=</a> - - <i>Vector divisionby a scalar and assignment.</i></tt></li><li><tt><a href="#numeric_vectorO32">operator==</a> - - <i>Equality operator</i></tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="scalar_product"></a><h2>scalar_product</h2><p><br>Scalar/dot product of two vectors.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#scalar_productO0">scalar_product</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="direct_product"></a><h2>direct_product</h2><p><br>Direct product of two matrices or vectors .<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#direct_productO0">direct_product</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="triple_vector_product"></a><h2>triple_vector_product</h2><p><br>Vector product of three triples.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#triple_vector_productO0">triple_vector_product</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="triple_scalar_product"></a><h2>triple_scalar_product</h2><p><br>Scalar product of three triples.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#triple_scalar_productO0">triple_scalar_product</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="separation_squared"></a><h2>separation_squared</h2><p><br>Calculate the squared distance between the points represented bytwo vectors.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#separation_squaredO0">separation_squared</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="separation"></a><h2>separation</h2><p><br>Calculate the distance between the points represented by two vectors.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#separationO0">separation</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="sum"></a><h2>sum</h2><p><br>Returns the sum of the vector elements.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#sumO0">sum</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="sum_precise"></a><h2>sum_precise</h2><p><br>Returns the sum of the vector elements, but accumulates the elementsin order of ascending value in order to minimise rounding errors.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#sum_preciseO0">sum_precise</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="sum_of_squares"></a><h2>sum_of_squares</h2><p><br>Returns the sum of the squares of the vector elements.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#sum_of_squaresO0">sum_of_squares</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="sum_of_squares_precise"></a><h2>sum_of_squares_precise</h2><p><br>Returns the sum of the squares of the vector elements, but accumulatesthe elements in order of ascending value in order to minimise roundingerrors.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#sum_of_squares_preciseO0">sum_of_squares_precise</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="magnitude"></a><h2>magnitude</h2><p><br>Returns the length of a vector.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#magnitudeO0">magnitude</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="magnitude_precise"></a><h2>magnitude_precise</h2><p><br>Returns the precise length of a vector.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#magnitude_preciseO0">magnitude_precise</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="rotate"></a><h2>rotate</h2><p><br>Rotates each triple in a container about a given axis and originby a given number of radians.<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#rotateO0">rotate</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="translate"></a><h2>translate</h2><p><br>Translates a each triple in a container by a given vector<p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#translateO0">translate</a> -</tt></li></ul><a href="#Classes"><img SRC="leftb.gif" ALT="back" BORDER=0 ></a><hr><p><a NAME="matrix"></a><h2>matrix</h2><p><br>This template class represents a numerical matrix of any dimension.Matrices of dimension 1 are more efficiently modelled using the numeric_vector.<p>&nbsp;There are two types associated with this class:<p>&nbsp;<tt>value_type</tt> : this type is the same as the numeric_vector::value_typeand defines the type of the elements of the matrix.<p>&nbsp;<tt>size_type</tt> : this type is the same as the numeric_vector::size_typeand defines the type of the matrix indexes. It should always be an unsignedinteger type.<p><b>Authors:</b> D.S.Moss, W.R.Pitt, I.Tickle, M.A.Williams.<br><b>Files:</b> <a href="btl/btl_matrix.h">btl_matrix.h</a><br><b>Friends:</b> Friend equivalents to some functions are availableand are documented with these functions. Also available is: friend ostream&amp;operator&lt;&lt;(ostream &amp;os, const matrix<T> &amp;m);<br><b>Dependencies:</b> <a href="#numeric_vector">btl_numeric_vector.h</a>,<a href="#vector_algorithms">btl_vector_algorithms.h</a>,<a href="#NumericLimits">NumericLimits.h</a><p><b>Operations</b><br>&nbsp;<br>&nbsp;<ul><li><tt><a href="#matrixO0">matrix</a> - - <i>Constructor for default 3x3 matrixand initialise elements to zero.</i></tt></li><li><tt><a href="#matrixO1">matrix</a> - - <i>Constructs an identity matrixof size p*p.</i></tt></li><li><tt><a href="#matrixO2">matrix</a> - - <i>Constructs a matrix with p rowsand q columns. Initialises each element to a value v. The default valueis zero</i></tt></li><li><tt><a href="#matrixO3">matrix</a> - - <i>Constructs a matrix with p rowsand q columns. Elements are initialised to those in given array. This isobsolete and will be deleted in future releases</i></tt></li><li><tt><a href="#matrixO4">matrix</a> - - <i>Constructor for a 3x3 Matrixwith initialisation</i></tt></li><li><tt><a href="#matrixO5">matrix</a> - - <i>Copy constructor</i></tt></li><li><tt><a href="#matrixO6">~matrix</a> - - <i>Destructor</i></tt></li><li><tt><a href="#matrixO7">begin</a> - - <i>Returns an iterator that pointsto the first element in the Matrix. (There is also a const version of thisfunction.)</i></tt></li><li><tt><a href="#matrixO8">begin</a> -</tt></li><li><tt><a href="#matrixO9">end</a> - - <i>Returns an iterator that can beused in a comparison for ending a traversal through this Matrix. (Thereis also a const version of this function.)</i></tt></li><li><tt><a href="#matrixO10">end</a> -</tt></li><li><tt><a href="#matrixO11">size</a> - - <i>Size of Matrix (the number ofrows times the number of columns)</i></tt></li><li><tt><a href="#matrixO12">lbound</a> - - <i>This function is added to givecompatibility with TNT.</i></tt></li><li><tt><a href="#matrixO13">num_rows</a> - - <i>Read number of rows (for compatabilitywith TNT).</i></tt></li><li><tt><a href="#matrixO14">num_cols</a> - - <i>Read number of columns (forcompatability with TNT).</i></tt></li><li><tt><a href="#matrixO15">rows</a> - - <i>Read number of rows.</i></tt></li><li><tt><a href="#matrixO16">cols</a> - - <i>Set number of columns.</i></tt></li><li><tt><a href="#matrixO17">rows</a> - - <i>Set number of rows.</i></tt></li><li><tt><a href="#matrixO18">cols</a> - - <i>Read number of columns.</i></tt></li><li><tt><a href="#matrixO19">dim</a> - - <i>This function is added to givecompatibility with TNT.</i></tt></li><li><tt><a href="#matrixO20">operator()</a> - - <i>Returns a matrix elementgiven its indices e.g. x(i,j) i = row, j = col N.B. (i,j >= 1). (Thereis also a const (read only) version of this function.)</i></tt></li><li><tt><a href="#matrixO21">operator()</a> -</tt></li><li><tt><a href="#matrixO22">operator[]</a> - - <i>Returns an iterator thatpoints to the first element of a given row. N.B. ( 0 &lt;= i &lt; nrows). (There is also a const (read only) version of this function.)</i></tt></li><li><tt><a href="#matrixO23">operator[]</a> -</tt></li><li><tt><a href="#matrixO24">operator=</a> - - <i>Matrix assignment</i></tt></li><li><tt><a href="#matrixO25">operator*</a> - - <i>Matrix multiplication e.g.matrix m1,m2,m3; .... m3 = m1 * m2;</i></tt></li><li><tt><a href="#matrixO26">operator*</a> - - <i>Postmultiplication of a Matrixby a numeric_vector. e.g. matrix m; numeric_vector v1,v2; ... v2 = m *v1;</i></tt></li><li><tt><a href="#matrixO27">operator*=</a> - - <i>Multiple each element bya number.</i></tt></li><li><tt><a href="#matrixO28">operator*</a> - - <i>Multiple each element bya number</i></tt></li><li><tt><a href="#matrixO29">operator/=</a> - - <i>Divide each element by anumber</i></tt></li><li><tt><a href="#matrixO30">operator/</a> - - <i>Divide each element by anumber</i></tt></li><li><tt><a href="#matrixO31">operator-=</a> - - <i>Subtraction of a numberfrom each element.</i></tt></li><li><tt><a href="#matrixO32">operator-</a> - - <i>Subtraction of a number fromeach element.</i></tt></li><li><tt><a href="#matrixO33">operator+=</a> - - <i>Addition of a number to