namespace Eigen { /** \page QuickStartGuide

Quick start guide

Matrix creation and initialization

In Eigen all kind of dense matrices and vectors are represented by the template class Matrix. For instance \code Matrix m(size,4);\endcode declares a matrix of 4 columns with a dynamic number of rows. However, in most cases you can simply use one of the several convenient typedefs (\ref matrixtypedefs). For instance \code Matrix3f m = Matrix3f::Identity(); \endcode creates a 3x3 fixed size matrix of float which is initialized to the identity matrix. Similarly \code MatrixXcd m = MatrixXcd::Zero(rows,cols); \endcode creates a rows x cols matrix of double precision complex which is initialized to zero. Here rows and cols do not have to be known at runtime. In "MatrixXcd", "X" stands for dynamic, "c" for complex, and "d" for double. You can also initialize a matrix with all coefficients equal to one: \code MatrixXi m = MatrixXi::Ones(rows,cols); \endcode or to any constant value: \code MatrixXi m = MatrixXi::Constant(rows,cols,66); Matrix4d m = Matrix4d::Constant(6.6); \endcode All these 4 matrix creation functions also exist with the "set" prefix: \code Matrix3f m3; MatrixXi mx; VectorXcf vec; m3.setZero(); mx.setZero(rows,cols); vec.setZero(size); m3.setIdentity(); mx.setIdentity(rows,cols); vec.setIdentity(size); m3.setOnes(); mx.setOnes(rows,cols); vec.setOnes(size); m3.setConstant(6.6); mx.setConstant(rows,cols,6.6); vec.setConstant(size,complex(6,3)); \endcode Finally, all the coefficients of a matrix can set using the comma initializer syntax:
\include Tutorial_commainit_01.cpp output: \verbinclude Tutorial_commainit_01.out
Eigen's comma initializer also allows to set the matrix per block making it much more powerful:
\include Tutorial_commainit_02.cpp output with rows=cols=5: \verbinclude Tutorial_commainit_02.out

Basic Linear Algebra

As long as you use mathematically well defined operators, you can basically write your matrix and vector expressions using standard arithmetic operators: \code mat1 = mat1*1.5 + mat2 * mat3/4; \endcode \b dot \b product (inner product): \code scalar = vec1.dot(vec2); \endcode \b outer \b product: \code mat = vec1 * vec2.transpose(); \endcode \b cross \b product: The cross product is defined in the Geometry module, you therefore have to include it first: \code #include vec3 = vec1.cross(vec2); \endcode By default, Eigen's only allows mathematically well defined operators. However, thanks to the .cwise() operator prefix, Eigen's matrices also provide a very powerful numerical container supporting most common coefficient wise operators: * Coefficient wise product: \code mat3 = mat1.cwise() * mat2; \endcode * Coefficient wise division: \code mat3 = mat1.cwise() / mat2; \endcode * Coefficient wise reciprocal: \code mat3 = mat1.cwise().inverse(); \endcode * Add a scalar to a matrix: \code mat3 = mat1.cwise() + scalar; \endcode * Coefficient wise comparison: \code mat3 = mat1.cwise() < mat2; \endcode * Finally, \c .cwise() offers many common numerical functions including abs, pow, exp, sin, cos, tan, e.g.: \code mat3 = mat1.cwise().sin(); \endcode

Reductions

\code scalar = mat.sum(); scalar = mat.norm(); scalar = mat.minCoeff(); vec = mat.colwise().sum(); vec = mat.colwise().norm(); vec = mat.colwise().minCoeff(); vec = mat.rowwise().sum(); vec = mat.rowwise().norm(); vec = mat.rowwise().minCoeff(); \endcode Other natively supported reduction operations include maxCoeff(), norm2(), all() and any().

Sub matrices

Geometry features

Notes on performances

Advanced Linear Algebra

Solving linear problems

LU

Cholesky

QR

Eigen value problems

*/ }