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namespace Eigen {
/** \page QuickStartGuide
<h1>Quick start guide</h1>
<h2>Matrix creation and initialization</h2>
In Eigen all kind of dense matrices and vectors are represented by the template class Matrix, e.g.:
\code Matrix<int,Dynamic,4> m(size,4);\endcode
declares a matrix of 4 columns and having a dynamic (runtime) number of rows.
However, in most cases you can simply use one of the several convenient typedefs (\ref matrixtypedefs), e.g.:
\code Matrix3f m = Matrix3f::Identity(); \endcode
creates a 3x3 fixed size float matrix intialized to the identity matrix, while:
\code MatrixXcd m = MatrixXcd::Zero(rows,cols); \endcode
creates a rows x cols matrix of double precision complex initialized to zero where 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, e.g.:
\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<float>(6,3));
\endcode
Finally, all the coefficient of a matrix can set using the comma initializer:
<table><tr><td>
\include Tutorial_commainit_01.cpp
</td>
<td>
output:
\verbinclude Tutorial_commainit_01.out
</td></tr></table>
Eigen's comma initializer also allows to set the matrix per block making it much more powerful:
<table><tr><td>
\include Tutorial_commainit_02.cpp
</td>
<td>
output with rows=cols=5:
\verbinclude Tutorial_commainit_02.out
</td></tr></table>
<h2>Basic Linear Algebra</h2>
As long as you use mathematically well defined operators, you can basically write your matrix and vector expressions as you would do with a pen an a piece of paper:
\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 <Eigen/Geometry>
vec3 = vec1.cross(vec2);
\endcode
By default, Eigen's only allows mathematically well defined operators. However, Eigen's matrices can also be used as simple numerical containers while still offering most common coefficient wise operations via the .cwise() operator prefix:
* 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
<h2>Reductions</h2>
\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().
<h2>Sub matrices</h2>
<h2>Geometry features</h2>
<h2>Notes on performances</h2>
<h2>Advanced Linear Algebra</h2>
<h3>Solving linear problems</h3>
<h3>LU</h3>
<h3>Cholesky</h3>
<h3>QR</h3>
<h3>Eigen value problems</h3>
*/
}
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