From: Matthias Maier <tamiko@43-1.org>
Date: Sun, 10 May 2015 12:19:27 +0000 (+0200)
Subject: update documentation
X-Git-Tag: v8.3.0-rc1~179^2~3
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a7c2bfecd8b75f338972da7526f65562c4b116a8;p=dealii.git

update documentation
---

diff --git a/doc/doxygen/headers/laoperators.h b/doc/doxygen/headers/laoperators.h
index 1616826357..f52ed2c168 100644
--- a/doc/doxygen/headers/laoperators.h
+++ b/doc/doxygen/headers/laoperators.h
@@ -96,6 +96,79 @@
  * InverseMatrixRichardson, SchurMatrix, ShiftedMatrix,
  * ShiftedMatrixGeneralized, TransposeMatrix
  *
+ *
+ * <h3>Packaged Operation</h3>
+ *
+ * An  application of a LinearOperator object to a vector via
+ * <code>operator*</code> yields a PackagedOperation object that stores
+ * this computation.
+ *
+ * The PackagedOperation class allows lazy evaluation of expressions
+ * involving vectors and linear operators. This is done by storing the
+ * computational expression and only performing the computation when either
+ * the object is implicitly converted to a vector object, or
+ * <code>apply</code> (or <code>apply_add</code>) is invoked by hand. This
+ * avoids unnecessary temporary storage of intermediate results.
+ *
+ * As an example consider the addition of multiple vectors:
+ * @code
+ *   dealii::Vector<double> a, b, c, d;
+ *   // ..
+ *   dealii::Vector<double> result = a + b - c + d;
+ * @endcode
+ * Converting the PackagedOperation <code>a + b - c + d</code> to a vector
+ * results in code equivalent to the following code
+ * @code
+ *   dealii::Vector<double> a, b, c, d;
+ *   // ..
+ *   dealii::Vector<double> result = a;
+ *   result += b;
+ *   result -= c;
+ *   result += d;
+ * @endcode
+ * that avoids any intermediate storage. As a second example (involving a
+ * LinearOperator object) consider the computation of a residual $b-Ax$:
+ *
+ * @code
+ *   dealii::SparseMatrix<double> A;
+ *   dealii::Vector<double> b, x;
+ *   // ..
+ *   const auto op_a = linear_operator(A);
+ *
+ *   dealii::Vector<double> residual =  b - op_a * x;
+ * @endcode
+ *
+ * @note
+ * Lazy evaluation of a computational expression necessarily involves
+ * references to the underlying vector and matrix objects. For example, the
+ * creation of a <code>residual_expr</code> object
+ * @code
+ *   auto residual_expr =  b - op_a * x;
+ * @endcode
+ * stores the computational expression of the residual with references to
+ * the vector <code>b</code> and matrix <code>A</code>. It does not perform
+ * any computation at this point. In particular, if <code>b</code> or
+ * <code>A</code> are changed <b>after</b> the creation of
+ * <code>residual_expr</code> every subsequent evaluation of the expression
+ * is performed with the new values
+ * @code
+ *   auto residual_expr =  b - op_a * x;
+ *   residual_expr.apply(tmp);  // tmp is a Vector<double>
+ *
+ *   // modify b, or A
+ *
+ *   residual_expr.apply(tmp2); // tmp2 is a Vector<double>
+ *
+ *   // tmp and tmp2 are different
+ * @endcode
+ * Thus, as a safeguard, if you want to compute the result of an expression
+ * right away, always explicitly use a vector type on the left side (and
+ * not <code>auto</code>):
+ * @code
+ *   Vector<double> residual =  b - op_a * x; // computes the residual at this point
+ * @endcode
+ *
+ *
  * @ingroup LAC
  * @ingroup MATRICES
  */
diff --git a/include/deal.II/lac/linear_operator.h b/include/deal.II/lac/linear_operator.h
index f3b1c69662..324df3df3b 100644
--- a/include/deal.II/lac/linear_operator.h
+++ b/include/deal.II/lac/linear_operator.h
@@ -1314,6 +1314,13 @@ block_diagonal_operator(const LinearOperator<typename Range::BlockType, typename
 /**
  * A class to store a computation.
  *
+ * The PackagedOperation class allows lazy evaluation of expressions
+ * involving vectors and linear operators. This is done by storing the
+ * computational expression and only performing the computation when either
+ * the object is implicitly converted to a vector object, or
+ * <code>apply</code> (or <code>apply_add</code>) is invoked by hand. This
+ * avoids unnecessary temporary storage of intermediate results.
+ *
  * The class essentially consists of <code>std::function</code> objects
  * that store the knowledge of how to generate the result of a computation
  * and store it in a vector:
@@ -1328,9 +1335,7 @@ block_diagonal_operator(const LinearOperator<typename Range::BlockType, typename
  *   std::function<void(Range &, bool)> reinit_vector;
  * @endcode
  *
- * The primary purpose of this class is to allow lazy evaluation of
- * expressions involving vectors and linear operators. As an example
- * consider the addition of multiple vectors
+ * As an example consider the addition of multiple vectors
  * @code
  *   dealii::Vector<double> a, b, c, d;
  *   // ..
@@ -1343,7 +1348,7 @@ block_diagonal_operator(const LinearOperator<typename Range::BlockType, typename
  *   // ..
  *   const auto op_a = linear_operator(A);
  *
- *   const auto residual =  b - op_a * x;
+ *   dealii::Vector<double> residual =  b - op_a * x;
  * @endcode
  * The expression <code>residual</code> is of type
  * <code>PackagedOperation<dealii::Vector<double>></code>. It stores