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<HTML><HEAD><TITLE>Newmat09 - binary operators</TITLE></HEAD><BODY><H2>Binary operators</H2><A HREF="matscal.html"> next</A> - <A HREF="matscal.html"> skip</A> - <A HREF="refer.html"> up</A> - <A HREF="index.html"> start</A><P>The package supports binary operations<PRE> X = A + B; // matrix addition X = A - B; // matrix subtraction X = A * B; // matrix multiplication X = A.i() * B; // equation solve (square matrix A) X = A | B; // concatenate horizontally (concatenate the rows) X = A & B; // concatenate vertically (concatenate the columns) X = SP(A, B); // elementwise product of A and B (Schur product) bool b = A == B; // test whether A and B are equal bool b = A != B; // ! (A == B) A += B; // A = A + B; A -= B; // A = A - B; A *= B; // A = A * B; A |= B; // A = A | B; A &= B; // A = A & B; <, >, <=, >= // included for compatibility with STL - see notes</PRE><P>Notes:<UL><LI>If you are doing repeated multiplication. For example <TT>A*B*C</TT>, usebrackets to force the order of evaluation to minimise the number ofoperations. If <TT>C</TT> is a column vector and <TT>A</TT> is not a vector,then it will usually reduce the number of operations to use <TT>A*(B*C)</TT>.<LI>In the equation solve example case the inverse is not explicitlycalculated. An LU decomposition of <TT>A</TT> is performed and this isapplied to <TT>B</TT>. This is more efficient than calculating the inverse andthen multiplying.See also <A HREF="solve.html">multiple matrix solving</A>.<LI>The package does not (yet?) recognise <TT>B*A.i()</TT> as an equationsolve and the inverse of <TT>A</TT> would be calculated.It is probably better to use <TT>(A.t().i()*B.t()).t()</TT>.<LI>Horizontal or vertical concatenation returns a result of type Matrix,RowVector or ColumnVector.<LI>If <TT>A</TT> is m x p, <TT>B</TT> is m x q, then <TT>A | B</TT> is m x(p+q) with the k-th row being the elements of the k-th row of <TT>A</TT>followed by the elements of the k-th row of <TT>B</TT>.<LI>If <TT>A</TT> is p x n, <TT>B</TT> is q x n, then <TT>A & B</TT> is (p+q)x n with the k-th column being the elements of the k-th column of <TT>A</TT>followed by the elements of the k-th column of <TT>B</TT>.<LI>For complicated concatenations of matrices, consider instead using<A HREF="submat.html">submatrices</A>.<LI>See the section on <A HREF="submat.html">submatrices</A> onusing a submatrix on the RHS of an expression.<LI>Two matrices are equal if their difference is zero. They may be ofdifferent types. For the CroutMatrix or BandLUMatrix they must be of thesame type and have all their elements equal. This is not a very usefuloperator and is included for compatibility with some container templates.<LI>The inequality operators are included for compatibility with the<A HREF="stl.html"> standard template library</A>. If actually called, they will throw an exception. So don'ttry to sort a <I>list</I> of matrices.</UL><P><A HREF="matscal.html"> next</A> - <A HREF="matscal.html"> skip</A> - <A HREF="refer.html"> up</A> - <A HREF="index.html"> start</A><P></BODY></HTML>?? 快捷鍵說明
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