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-rw-r--r-- | doc/C01_Matrix.dox | 217 | ||||
-rw-r--r-- | doc/examples/tut_matrix_coefficient_accessors.cpp | 19 | ||||
-rw-r--r-- | doc/examples/tut_matrix_resize.cpp | 18 | ||||
-rw-r--r-- | doc/examples/tut_matrix_resize_fixed_size.cpp | 12 |
4 files changed, 266 insertions, 0 deletions
diff --git a/doc/C01_Matrix.dox b/doc/C01_Matrix.dox new file mode 100644 index 000000000..c73bbf5cc --- /dev/null +++ b/doc/C01_Matrix.dox @@ -0,0 +1,217 @@ +namespace Eigen { + +o /** \page tut_matrix Tutorial page 1 - the Matrix class + +\ingroup Tutorial + +We assume that you have already read the \ref GettingStarted "quick \"getting started\" tutorial. +This page is the first one in a much longer multi-page tutorial. + +In Eigen, all matrices and vectors are object of the Matrix class. +Vectors are just a special case of matrices, with either 1 row or 1 column. + +\section tut_matrix_class The Matrix class + +The Matrix class takes 6 template parameters, but for now it's enough to +learn about the 3 first parameters. The 3 remaining parameters have default +values, which for now we will leave untouched, and which we +\ref tut_matrix_3_last_template_params "discuss below". + +The 3 mandatory template parameters of Matrix are: +\code +Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime> +\endcode +\li \c Scalar is the scalar type, i.e. the type of the coefficients. + That is, if you want a matrix of floats, choose \c float here. + See \ref topic_scalar_types "Scalar types" for a list of all supported + scalar types and for how to extend support to new types. +\li \c RowsAtCompileTime and \c ColsAtCompileTime are the number of rows + and columns of the matrix as known at compile-time. + +We offer a lot of convenience typedefs to cover the usual cases. For example, \c Matrix4f is +a 4x4 matrix of floats. Here is how it is defined by Eigen: +\code +typedef Matrix<float,4,4> Matrix4f; +\endcode +We discuss \ref tut_matrix_typedefs "below" these convenience typedefs. + +\section tut_matrix_vectors Vectors + +As mentioned above, in Eigen, vectors are just a special case of +matrices, with either 1 row or 1 column. The case where they have 1 column is the most common; +such vectors are called column-vectors, often abbreviated as just vectors. In the other case +where they have 1 row, they are called row-vectors. + +For example, the convenience typedef \c Vector3f is defined as follows by Eigen: +\code +typedef Matrix<float, 3, 1> Vector3f; +\endcode +and we also offer convenience typedefs for row-vectors, for example: +\code +typedef Matrix<int, 1, 2> RowVector2i; +\endcode + +\section tut_matrix_dynamic The special value Dynamic + +Of course, Eigen is not limited to matrices whose dimensions are known at compile time. +The above-discussed \c RowsAtCompileTime and \c ColsAtCompileTime can take the special +value \c Dynamic which indicates that the size is unknown at compile time, so must +be handled as a run time variable. In Eigen terminology, such a size is referred to as a +\em dynamic \em size; while a size that is known at compile time is called a +\em fixed \em size. For example, the convenience typedef \c MatrixXd, meaning +a matrix of doubles with dynamic size, is defined as follows: +\code +typedef Matrix<double,Dynamic,Dynamic> MatrixXd; +\endcode +And similarly, we define a self-explanatory typedef \c VectorXi as follows: +\code +typedef Matrix<int,Dynamic,1> VectorXi; +\endcode +You can perfectly have e.g. a fixed number of rows with a dynamic number of columns, as in: +\code +Matrix<float, 3, Dynamic> +\endcode + +\section tut_matrix_constructors Constructors + +A default constructor is always available, and always has zero runtime cost. You can do: +\code +Matrix3f a; +MatrixXf b; +\endcode +Here, +\li \c a is a 3x3 matrix, with a static float[9] array of uninitialized coefficients, +\li \c b is a dynamic-size matrix whose size is currently 0x0, and whose array of +coefficients hasn't yet been allocated at all. + +Constructors taking sizes are also available. For matrices, the number of rows is always passed first. +For vectors, just pass the vector size. They allocate the array of coefficients +with the given size, but don't initialize the coefficients themselves: +\code +MatrixXf a(10,15); +VectorXf b(30); +\endcode +Here, +\li \c a is a 10x15 dynamic-size matrix, with allocated but currently uninitialized coefficients. +\li \c b is a dynamic-size vector of size 30, with allocated but currently uninitialized coefficients. + +In order to offer a uniform API across fixed-size and dynamic-size matrices, it is legal to use these +constructors on fixed-size matrices, even if passing the sizes is useless in this case. So this is legal: +\code +Matrix3f a(3,3); +\endcode +and is a no-operation. + +Finally, we also offer some constructors to initialize the coefficients of small fixed-size vectors up to size 4: +\code +Vector2d a(5.0, 6.0); +Vector3d b(5.0, 6.0, 7.0); +Vector4d c(5.0, 6.0, 7.0, 8.0); +\endcode + +\section tut_matrix_coefficient_accessors Coefficient accessors + +The primary coefficient accessors and mutators in Eigen are the overloaded parenthesis operators. +For matrices, the row index is always passed first. For vectors, just pass one index. +The numbering starts at 0. This example is self-explanatory: +\include tut_matrix_coefficient_accessors.cpp +Output: \verbinclude tut_matrix_coefficient_accessors.out + +Note that the syntax +\code +m(index) +\endcode +is not restricted to vectors, it is also available for general matrices, meaning index-based access +in the array of coefficients. This however depends on the matrix's storage order. All Eigen matrices default to +column-major storage order, but this can be changed to row-major, see \ref topic_storage_orders "Storage orders". + +The operator[] is also overloaded for index-based access in vectors, but keep in mind that C++ doesn't allow operator[] to +take more than one argument. We restrict operator[] to vectors, because an awkwardness in the C++ language +would make matrix[i,j] compile to the same thing as matrix[j] ! + +\section tut_matrix_sizes_and_resizing Resizing + +The current sizes can be retrieved by rows(), cols() and size(). Resizing a dynamic-size matrix is done by the resize() method. +For example: \include tut_matrix_resize.cpp +Output: \verbinclude tut_matrix_resize.out + +The resize() method is a no-operation if the actual array size doesn't change; otherwise it is destructive. +If you want a conservative variant of resize(), use conservativeResize(). + +All these methods are still available on fixed-size matrices, for the sake of API uniformity. Of course, you can't actually +resize a fixed-size matrix. Trying to change a fixed size to an actually different value will trigger an assertion failure; +but the following code is legal: +\include tut_matrix_resize_fixed_size.cpp +Output: \verbinclude tut_matrix_resize_fixed_size.out + +\section tut_matrix_fixed_vs_dynamic Fixed vs. Dynamic size + +When should one use fixed sizes (e.g. \c Matrix4f), and when should one prefer dynamic sizes (e.g. \c MatrixXf) ? +The simple answer is: use fixed +sizes for very small sizes where you can, and use dynamic sizes for larger sizes or where you have to. For small sizes, +especially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial +to performance, as it allows Eigen to avoid dynamic memory allocation and to unroll +loops. Internally, a fixed-size Eigen matrix is just a plain static array, i.e. doing +\code Matrix4f mymatrix; \endcode +really amounts to just doing +\code float mymatrix[16]; \endcode +so this really has zero runtime cost. By constrast, the array of a dynamic-size matrix +is always allocated on the heap, so doing +\code MatrixXf mymatrix(rows,columns); \endcode +amounts to doing +\code float *mymatrix = new float[rows*columns]; \endcode +and in addition to that, the MatrixXf object stores its number of rows and columns as +member variables. + +The limitation of using fixed sizes, of course, is that this is only possible +when you know the sizes at compile time. Also, for large enough sizes, say for sizes +greater than (roughly) 32, the performance benefit of using fixed sizes becomes negligible. +Worse, trying to create a very large matrix using fixed sizes could result in a stack overflow, +since Eigen will try to allocate the array as a static array, which by default goes on the stack. +Finally, depending on circumstances, Eigen can also be more aggressive trying to vectorize +(use SIMD instructions) when dynamic sizes are used, see \ref topic_vectorization "Vectorization". + +\section tut_matrix_optional_template_params Optional template parameters + +We mentioned at the beginning of this page that the Matrix class takes 6 template parameters, +but so far we only discussed the first 3. The remaining 3 parameters are optional. Here is +the complete list of template parameters: +\code +Matrix<typename Scalar, + int RowsAtCompileTime, + int ColsAtCompileTime, + int Options = 0, + int MaxRowsAtCompileTime = RowsAtCompileTime, + int MaxColsAtCompileTime = ColsAtCompileTime> +\endcode +\li \c Options is a bit field; let us only mention here one bit: \c RowMajor. It specifies that the matrices + of this type use row-major storage order; the default is column-major. See the page on + \ref topic_storage_orders "storage orders". For example, this type means row-major 3x3 matrices: + \code + Matrix<float,3,3,RowMajor> + \endcode +\li \c MaxRowsAtCompileTime and \c MaxColsAtCompileTime are useful when you want to specify that, even though + the exact sizes of your matrices are unknown at compile time, a fixed upper bound is known at + compile time. The biggest reason why you might want to do that is to avoid dynamic memory allocation. + For example the following matrix type uses a static array of 12 floats, without dynamic memory allocation: + \code + Matrix<float,Dynamic,Dynamic,0,3,4> + \endcode + +\section tut_matrix_typedefs Convenience typedefs + +Eigen defines the following Matrix typedefs: +\li MatrixNT for Matrix<T, N, N>. For example, MatrixXi for Matrix<int, Dynamic, Dynamic>. +\li VectorNT for Matrix<T, N, 1>. For example, Vector2f for Matrix<float, 2, 1>. +\li MatrixNT for Matrix<T, 1, N>. For example, RowVector3d for Matrix<double, 1, 3>. + +Where: +\li N can be any one of \c 2,\c 3,\c 4, or \c Dynamic. +\li T can be any one of \c i (meaning int), \c f (meaning float), \c d (meaning double), + \c cf (meaning complex<float>), or \c cd (meaning complex<double>). The fact that typedefs are only + defined for these 5 types doesn't mean that they are the only supported scalar types. For example, + all standard integer types are supported, see \ref topic_scalar_types "Scalar types". + +*/ + +}
\ No newline at end of file diff --git a/doc/examples/tut_matrix_coefficient_accessors.cpp b/doc/examples/tut_matrix_coefficient_accessors.cpp new file mode 100644 index 000000000..6d982b6e1 --- /dev/null +++ b/doc/examples/tut_matrix_coefficient_accessors.cpp @@ -0,0 +1,19 @@ +#include <iostream> +#include <Eigen/Dense> + +using namespace Eigen; + +int main() +{ + MatrixXd m(2,2); + m(0,0) = 3; + m(1,0) = 2.5; + m(0,1) = -1; + m(1,1) = m(1,0) + m(0,1); + std::cout << "Here is the matrix m:\n" << m << std::endl; + VectorXd v(2); + v(0) = 4; + v(1) = v(0) - 1; + std::cout << "Here is the vector v:\n" << v << std::endl; + +} diff --git a/doc/examples/tut_matrix_resize.cpp b/doc/examples/tut_matrix_resize.cpp new file mode 100644 index 000000000..0392c3aa5 --- /dev/null +++ b/doc/examples/tut_matrix_resize.cpp @@ -0,0 +1,18 @@ +#include <iostream> +#include <Eigen/Dense> + +using namespace Eigen; + +int main() +{ + MatrixXd m(2,5); + m.resize(4,3); + std::cout << "The matrix m is of size " + << m.rows() << "x" << m.cols() << std::endl; + std::cout << "It has " << m.size() << " coefficients" << std::endl; + VectorXd v(2); + v.resize(5); + std::cout << "The vector v is of size " << v.size() << std::endl; + std::cout << "As a matrix, v is of size " + << v.rows() << "x" << v.cols() << std::endl; +} diff --git a/doc/examples/tut_matrix_resize_fixed_size.cpp b/doc/examples/tut_matrix_resize_fixed_size.cpp new file mode 100644 index 000000000..dcbdfa783 --- /dev/null +++ b/doc/examples/tut_matrix_resize_fixed_size.cpp @@ -0,0 +1,12 @@ +#include <iostream> +#include <Eigen/Dense> + +using namespace Eigen; + +int main() +{ + Matrix4d m; + m.resize(4,4); // no operation + std::cout << "The matrix m is of size " + << m.rows() << "x" << m.cols() << std::endl; +} |