From f0238cfb6997c4acfc2bd200de7295f3fa36968f Mon Sep 17 00:00:00 2001 From: Stanislaw Halik Date: Sun, 3 Mar 2019 21:09:10 +0100 Subject: don't index Eigen --- eigen/doc/TutorialArrayClass.dox | 192 --------------------------------------- 1 file changed, 192 deletions(-) delete mode 100644 eigen/doc/TutorialArrayClass.dox (limited to 'eigen/doc/TutorialArrayClass.dox') diff --git a/eigen/doc/TutorialArrayClass.dox b/eigen/doc/TutorialArrayClass.dox deleted file mode 100644 index f6f3510..0000000 --- a/eigen/doc/TutorialArrayClass.dox +++ /dev/null @@ -1,192 +0,0 @@ -namespace Eigen { - -/** \eigenManualPage TutorialArrayClass The Array class and coefficient-wise operations - -This page aims to provide an overview and explanations on how to use -Eigen's Array class. - -\eigenAutoToc - -\section TutorialArrayClassIntro What is the Array class? - -The Array class provides general-purpose arrays, as opposed to the Matrix class which -is intended for linear algebra. Furthermore, the Array class provides an easy way to -perform coefficient-wise operations, which might not have a linear algebraic meaning, -such as adding a constant to every coefficient in the array or multiplying two arrays coefficient-wise. - - -\section TutorialArrayClassTypes Array types -Array is a class template taking the same template parameters as Matrix. -As with Matrix, the first three template parameters are mandatory: -\code -Array -\endcode -The last three template parameters are optional. Since this is exactly the same as for Matrix, -we won't explain it again here and just refer to \ref TutorialMatrixClass. - -Eigen also provides typedefs for some common cases, in a way that is similar to the Matrix typedefs -but with some slight differences, as the word "array" is used for both 1-dimensional and 2-dimensional arrays. -We adopt the convention that typedefs of the form ArrayNt stand for 1-dimensional arrays, where N and t are -the size and the scalar type, as in the Matrix typedefs explained on \ref TutorialMatrixClass "this page". For 2-dimensional arrays, we -use typedefs of the form ArrayNNt. Some examples are shown in the following table: - - - - - - - - - - - - - - - - - - - - - - -
Type Typedef
\code Array \endcode \code ArrayXf \endcode
\code Array \endcode \code Array3f \endcode
\code Array \endcode \code ArrayXXd \endcode
\code Array \endcode \code Array33d \endcode
- - -\section TutorialArrayClassAccess Accessing values inside an Array - -The parenthesis operator is overloaded to provide write and read access to the coefficients of an array, just as with matrices. -Furthermore, the \c << operator can be used to initialize arrays (via the comma initializer) or to print them. - - - - -
Example:Output:
-\include Tutorial_ArrayClass_accessors.cpp - -\verbinclude Tutorial_ArrayClass_accessors.out -
- -For more information about the comma initializer, see \ref TutorialAdvancedInitialization. - - -\section TutorialArrayClassAddSub Addition and subtraction - -Adding and subtracting two arrays is the same as for matrices. -The operation is valid if both arrays have the same size, and the addition or subtraction is done coefficient-wise. - -Arrays also support expressions of the form array + scalar which add a scalar to each coefficient in the array. -This provides a functionality that is not directly available for Matrix objects. - - - - -
Example:Output:
-\include Tutorial_ArrayClass_addition.cpp - -\verbinclude Tutorial_ArrayClass_addition.out -
- - -\section TutorialArrayClassMult Array multiplication - -First of all, of course you can multiply an array by a scalar, this works in the same way as matrices. Where arrays -are fundamentally different from matrices, is when you multiply two together. Matrices interpret -multiplication as matrix product and arrays interpret multiplication as coefficient-wise product. Thus, two -arrays can be multiplied if and only if they have the same dimensions. - - - - -
Example:Output:
-\include Tutorial_ArrayClass_mult.cpp - -\verbinclude Tutorial_ArrayClass_mult.out -
- - -\section TutorialArrayClassCwiseOther Other coefficient-wise operations - -The Array class defines other coefficient-wise operations besides the addition, subtraction and multiplication -operators described above. For example, the \link ArrayBase::abs() .abs() \endlink method takes the absolute -value of each coefficient, while \link ArrayBase::sqrt() .sqrt() \endlink computes the square root of the -coefficients. If you have two arrays of the same size, you can call \link ArrayBase::min(const Eigen::ArrayBase&) const .min(.) \endlink to -construct the array whose coefficients are the minimum of the corresponding coefficients of the two given -arrays. These operations are illustrated in the following example. - - - - -
Example:Output:
-\include Tutorial_ArrayClass_cwise_other.cpp - -\verbinclude Tutorial_ArrayClass_cwise_other.out -
- -More coefficient-wise operations can be found in the \ref QuickRefPage. - - -\section TutorialArrayClassConvert Converting between array and matrix expressions - -When should you use objects of the Matrix class and when should you use objects of the Array class? You cannot -apply Matrix operations on arrays, or Array operations on matrices. Thus, if you need to do linear algebraic -operations such as matrix multiplication, then you should use matrices; if you need to do coefficient-wise -operations, then you should use arrays. However, sometimes it is not that simple, but you need to use both -Matrix and Array operations. In that case, you need to convert a matrix to an array or reversely. This gives -access to all operations regardless of the choice of declaring objects as arrays or as matrices. - -\link MatrixBase Matrix expressions \endlink have an \link MatrixBase::array() .array() \endlink method that -'converts' them into \link ArrayBase array expressions\endlink, so that coefficient-wise operations -can be applied easily. Conversely, \link ArrayBase array expressions \endlink -have a \link ArrayBase::matrix() .matrix() \endlink method. As with all Eigen expression abstractions, -this doesn't have any runtime cost (provided that you let your compiler optimize). -Both \link MatrixBase::array() .array() \endlink and \link ArrayBase::matrix() .matrix() \endlink -can be used as rvalues and as lvalues. - -Mixing matrices and arrays in an expression is forbidden with Eigen. For instance, you cannot add a matrix and -array directly; the operands of a \c + operator should either both be matrices or both be arrays. However, -it is easy to convert from one to the other with \link MatrixBase::array() .array() \endlink and -\link ArrayBase::matrix() .matrix()\endlink. The exception to this rule is the assignment operator: it is -allowed to assign a matrix expression to an array variable, or to assign an array expression to a matrix -variable. - -The following example shows how to use array operations on a Matrix object by employing the -\link MatrixBase::array() .array() \endlink method. For example, the statement -result = m.array() * n.array() takes two matrices \c m and \c n, converts them both to an array, uses -* to multiply them coefficient-wise and assigns the result to the matrix variable \c result (this is legal -because Eigen allows assigning array expressions to matrix variables). - -As a matter of fact, this usage case is so common that Eigen provides a \link MatrixBase::cwiseProduct const -.cwiseProduct(.) \endlink method for matrices to compute the coefficient-wise product. This is also shown in -the example program. - - - - -
Example:Output:
-\include Tutorial_ArrayClass_interop_matrix.cpp - -\verbinclude Tutorial_ArrayClass_interop_matrix.out -
- -Similarly, if \c array1 and \c array2 are arrays, then the expression array1.matrix() * array2.matrix() -computes their matrix product. - -Here is a more advanced example. The expression (m.array() + 4).matrix() * m adds 4 to every -coefficient in the matrix \c m and then computes the matrix product of the result with \c m. Similarly, the -expression (m.array() * n.array()).matrix() * m computes the coefficient-wise product of the matrices -\c m and \c n and then the matrix product of the result with \c m. - - - - -
Example:Output:
-\include Tutorial_ArrayClass_interop.cpp - -\verbinclude Tutorial_ArrayClass_interop.out -
- -*/ - -} -- cgit v1.2.3