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author | Gael Guennebaud <g.gael@free.fr> | 2008-08-20 13:07:46 +0000 |
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committer | Gael Guennebaud <g.gael@free.fr> | 2008-08-20 13:07:46 +0000 |
commit | 8afaeb4ad5fbcde1fb25ab5c8f9a9d120db4b13b (patch) | |
tree | feecc82c87cfe6534bcc0e2039bdc48578a18aec /doc/QuickStartGuide.dox | |
parent | db8fbf2b397f632f0ccc1260b7e2a50eb6d6ef82 (diff) |
doc fixes, and extended Basic Linear Algebra and Reductions sections
Diffstat (limited to 'doc/QuickStartGuide.dox')
-rw-r--r-- | doc/QuickStartGuide.dox | 141 |
1 files changed, 109 insertions, 32 deletions
diff --git a/doc/QuickStartGuide.dox b/doc/QuickStartGuide.dox index cff5cafe5..0128ded7b 100644 --- a/doc/QuickStartGuide.dox +++ b/doc/QuickStartGuide.dox @@ -153,53 +153,130 @@ Eigen's comma initializer usually yields to very optimized code without any over <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: +In short all mathematically well defined operators can be used right away as in the following exemple: \code -mat1 = mat1*1.5 + mat2 * mat3/4; +mat4 -= mat1*1.5 + mat2 * mat3/4; \endcode +which includes two matrix scalar products ("mat1*1.5" and "mat3/4"), a matrix-matrix product ("mat2 * mat3/4"), +a matrix addition ("+") and substraction with assignment ("-="). -\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 +<table> +<tr><td> +matrix/vector product</td><td>\code +col2 = mat1 * col1; +row2 = row1 * mat1; row1 *= mat1; +mat3 = mat1 * mat2; mat3 *= mat1; \endcode +</td></tr> +<tr><td> +add/subtract</td><td>\code +mat3 = mat1 + mat2; mat3 += mat1; +mat3 = mat1 - mat2; mat3 -= mat1;\endcode +</td></tr> +<tr><td> +scalar product</td><td>\code +mat3 = mat1 * s1; mat3 = s1 * mat1; mat3 *= s1; +mat3 = mat1 / s1; mat3 /= s1;\endcode +</td></tr> +<tr><td> +dot product (inner product)</td><td>\code +scalar = vec1.dot(vec2);\endcode +</td></tr> +<tr><td> +outer product</td><td>\code +mat = vec1 * vec2.transpose();\endcode +</td></tr> +<tr><td> +cross product</td><td>\code #include <Eigen/Geometry> -vec3 = vec1.cross(vec2); -\endcode +vec3 = vec1.cross(vec2);\endcode</td></tr> +</table> -By default, Eigen's only allows mathematically well defined operators. -However, thanks to the .cwise() operator prefix, Eigen's matrices also provide +In Eigen only mathematically well defined operators can be used right away, +but don't worry, thanks to the .cwise() operator prefix, Eigen's matrices also provide a very powerful numerical container supporting most common coefficient wise operators: <table> -<tr><td></td><td></td><tr> + +<tr><td>Coefficient wise product</td> +<td>\code mat3 = mat1.cwise() * mat2; \endcode +</td></tr> +<tr><td> +Add a scalar to all coefficients</td><td>\code +mat3 = mat1.cwise() + scalar; +mat3.cwise() += scalar; +mat3.cwise() -= scalar; +\endcode +</td></tr> +<tr><td> +Coefficient wise division</td><td>\code +mat3 = mat1.cwise() / mat2; \endcode +</td></tr> +<tr><td> +Coefficient wise reciprocal</td><td>\code +mat3 = mat1.cwise().inverse(); \endcode +</td></tr> +<tr><td> +Coefficient wise comparisons \n +(support all operators)</td><td>\code +mat3 = mat1.cwise() < mat2; +mat3 = mat1.cwise() <= mat2; +mat3 = mat1.cwise() > mat2; +etc. +\endcode +</td></tr> +<tr><td> +Trigo:\n sin, cos, tan</td><td>\code +mat3 = mat1.cwise().sin(); +etc. +\endcode +</td></tr> +<tr><td> +Power:\n pow, square, cube, sqrt, exp, log</td><td>\code +mat3 = mat1.cwise().square(); +mat3 = mat1.cwise().pow(5); +mat3 = mat1.cwise().log(); +etc. +\endcode +</td></tr> +<tr><td> +min, max, absolute value</td><td>\code +mat3 = mat1.cwise().min(mat2); +mat3 = mat1.cwise().max(mat2); +mat3 = mat1.cwise().abs(mat2); +mat3 = mat1.cwise().abs2(mat2); +\endcode</td></tr> </table> -* 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(); +Reductions can be done matrix-wise, column-wise or row-wise, e.g.: +<table> +<tr><td>\code mat \endcode +</td><td>\code +5 3 1 +2 7 8 +9 4 6 \endcode -Other natively supported reduction operations include maxCoeff(), norm2(), all() and any(). +</td></tr> +<tr><td>\code mat.minCoeff(); \endcode</td><td>\code 1 \endcode</td></tr> +<tr><td>\code mat.maxCoeff(); \endcode</td><td>\code 9 \endcode</td></tr> +<tr><td>\code mat.colwise().minCoeff(); \endcode</td><td>\code 2 3 1 \endcode</td></tr> +<tr><td>\code mat.colwise().maxCoeff(); \endcode</td><td>\code 9 7 8 \endcode</td></tr> +<tr><td>\code mat.rowwise().minCoeff(); \endcode</td><td>\code +1 +2 +4 +\endcode</td></tr> +<tr><td>\code mat.rowwise().maxCoeff(); \endcode</td><td>\code +5 +8 +9 +\endcode</td></tr> +</table> +Eigen provides several other reduction methods such as sum(), norm(), norm2(), all(), and any(). +The all() and any() functions are especially useful in combinaison with coeff-wise comparison operators. <h2>Sub matrices</h2> |