Lines Matching full:matrix
39 The Eigen header files define many types, but for simple applications it may be enough to use only the \c MatrixXd type. This represents a matrix of arbitrary size (hence the \c X in \c MatrixXd), in which every entry is a \c double (hence the \c d in \c MatrixXd). See the \ref QuickRef_Types "quick reference guide" for an overview of the different types you can use to represent a matrix.
43 The first line of the \c main function declares a variable of type \c MatrixXd and specifies that it is a matrix with 2 rows and 2 columns (the entries are not initialized). The statement <tt>m(0,0) = 3</tt> sets the entry in the top-left corner to 3. You need to use round parentheses to refer to entries in the matrix. As usual in computer science, the index of the first index is 0, as opposed to the convention in mathematics that the first index is 1.
45 The following three statements sets the other three entries. The final line outputs the matrix \c m to the standard output stream.
68 The second example starts by declaring a 3-by-3 matrix \c m which is initialized using the \link DenseBase::Random(Index,Index) Random() \endlink method with random values between -1 and 1. The next line applies a linear mapping such that the values are between 10 and 110. The function call \link DenseBase::Constant(Index,Index,const Scalar&) MatrixXd::Constant\endlink(3,3,1.2) returns a 3-by-3 matrix expression having all coefficients equal to 1.2. The rest is standard arithmetics.
81 The final line of the program multiplies the matrix \c m with the vector \c v and outputs the result.
83 Now look back at the second example program. We presented two versions of it. In the version in the left column, the matrix is of type \c MatrixXd which represents matrices of arbitrary size. The version in the right column is similar, except that the matrix is of type \c Matrix3d, which represents matrices of a fixed size (here 3-by-3). Because the type already encodes the size of the matrix, it is not necessary to specify the size in the constructor; compare <tt>MatrixXd m(3,3)</tt> with <tt>Matrix3d m</tt>. Similarly, we have \c VectorXd on the left (arbitrary size) versus \c Vector3d on the right (fixed size). Note that here the coefficients of vector \c v are directly set in the constructor, though the same syntax of the left example could be used too.
85 The use of fixed-size matrices and vectors has two advantages. The compiler emits better (faster) code because it knows the size of the matrices and vectors. Specifying the size in the type also allows for more rigorous checking at compile-time. For instance, the compiler will complain if you try to multiply a \c Matrix4d (a 4-by-4 matrix) with a \c Vector3d (a vector of size 3). However, the use of many types increases compilation time and the size of the executable. The size of the matrix may also not be known at compile-time. A rule of thumb is to use fixed-size matrices for size 4-by-4 and smaller.
