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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.
For instance \code Matrix<int,Dynamic,4> 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<float>(6,3));
\endcode
Finally, all the coefficients of a matrix can set using the comma initializer syntax:
<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 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 <Eigen/Geometry>
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
<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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