From: Guido Kanschat Date: Tue, 22 Mar 2005 21:57:18 +0000 (+0000) Subject: more documentation update for doxygen X-Git-Tag: v8.0.0~14334 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=7c6ec7643dc55427a7af9723a5d004d85d9547d5;p=dealii.git more documentation update for doxygen git-svn-id: https://svn.dealii.org/trunk@10204 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/lac/include/lac/full_matrix.h b/deal.II/lac/include/lac/full_matrix.h index e018c0f3ae..196c1f4982 100644 --- a/deal.II/lac/include/lac/full_matrix.h +++ b/deal.II/lac/include/lac/full_matrix.h @@ -30,8 +30,6 @@ template class Vector; /** - * @brief Rectangular/quadratic full matrix. - * * Implementation of a classical rectangular scheme of numbers. The * data type of the entries is provided in the template argument * number. The interface is quite fat and in fact has grown every @@ -109,7 +107,7 @@ class FullMatrix : public Table<2,number> */ unsigned short a_col; - /** + /* * Make enclosing class a * friend. */ @@ -353,14 +351,14 @@ class FullMatrix : public Table<2,number> /** * Number of rows of this matrix. * To remember: this matrix is an - * $m \times n$-matrix. + * m x n-matrix. */ unsigned int m () const; /** * Number of columns of this matrix. * To remember: this matrix is an - * $m \times n$-matrix. + * m x n-matrix. */ unsigned int n () const; @@ -399,52 +397,55 @@ class FullMatrix : public Table<2,number> number2 matrix_norm_square (const Vector &v) const; /** - * Build the matrix scalar product - * u^T M v. This function is mostly - * useful when building the cellwise - * scalar product of two functions in - * the finite element context. + * Build the matrix scalar + * product uT M + * v. This function is + * mostly useful when building + * the cellwise scalar product of + * two functions in the finite + * element context. */ template number2 matrix_scalar_product (const Vector &u, const Vector &v) const; /** - * Return the $l_1$-norm of the matrix, i.e. - * $|M|_1=max_{all columns j}\sum_{all - * rows i} |M_ij|$, - * (max. sum of columns). This is the - * natural matrix norm that is compatible - * to the $l_1$-norm for vectors, i.e. - * $|Mv|_1\leq |M|_1 |v|_1$. - * (cf. Rannacher Numerik0) + * Return the + * l1-norm of + * the matrix, where + * $||M||_1 = \max_j \sum_i + * |M_{ij}|$ (maximum of + * the sums over columns). */ number l1_norm () const; /** - * Return the $l_\infty$-norm of the - * matrix, i.e. - * $|M|_\infty=\max_{all rows i}\sum_{all - * columns j} |M_{ij}|$, - * (max. sum of rows). - * This is the - * natural matrix norm that is compatible - * to the $l_\infty$-norm of vectors, i.e. - * $|Mv|_\infty \leq |M|_\infty |v|_\infty$. - * (cf. Rannacher Numerik0) + * Return the + * l-norm + * of the matrix, where + * $||M||_\infty = \max_i \sum_j + * |M_{ij}|$ (maximum of the sums + * over rows). */ number linfty_norm () const; /** - * Compute the quadratic matrix norm. - * Return value is the root of the square - * sum of all matrix entries. Also called - * Frobenius norm. - * - * This norm is compatible with the $l_2$ - * vector norm. But it is not a natural - * matrix norm (cf Rannacher Numeric0), - * therefore it is not called $l_2$-norm. + * Compute the Frobenius norm of + * the matrix. Return value is + * the root of the square sum of + * all matrix entries. + * + * @note For the timid among us: + * this norm is not the norm + * compatible with the + * l2-norm of + * the vector space. + */ + number frobenius_norm () const; + + /** + * @deprecated Old name for + * frobenius_norm(). */ number norm2 () const; @@ -635,9 +636,10 @@ class FullMatrix : public Table<2,number> /** * Weighted addition of the - * transpose of B to this. + * transpose of B to + * this. * - * $A += s B^T$ + * A += s BT */ template void Tadd (const number s, @@ -674,23 +676,25 @@ class FullMatrix : public Table<2,number> const unsigned int src_offset_j = 0); /** - * $A(i,1...n)+=s*A(j,1...n)$. - * Simple addition of rows of this + * A(i,1...n) += + * s*A(j,1...n). Simple + * addition of rows of this */ void add_row (const unsigned int i, const number s, const unsigned int j); /** - * $A(i,1...n)+=s*A(j,1...n)+t*A(k,1...n)$. - * Multiple addition of rows of this. + * A(i,1...n) += s*A(j,1...n) + * + t*A(k,1...n). Multiple + * addition of rows of this. */ void add_row (const unsigned int i, const number s, const unsigned int j, const number t, const unsigned int k); /** - * $A(1...n,i)+=s*A(1...n,j)$. + * A(1...n,i) += s*A(1...n,j). * Simple addition of columns of this. */ void add_col (const unsigned int i, @@ -698,31 +702,36 @@ class FullMatrix : public Table<2,number> const unsigned int j); /** - * $A(1...n,i)+=s*A(1...n,j)+t*A(1...n,k)$. - * Multiple addition of columns of this. + * A(1...n,i) += s*A(1...n,j) + * + t*A(1...n,k). Multiple + * addition of columns of this. */ void add_col (const unsigned int i, const number s, const unsigned int j, const number t, const unsigned int k); /** - * Swap A(i,1...n) <-> A(j,1...n). - * Swap rows i and j of this + * Swap A(i,1...n) <-> + * A(j,1...n). Swap rows i + * and j of this */ void swap_row (const unsigned int i, const unsigned int j); /** - * Swap A(1...n,i) <-> A(1...n,j). - * Swap columns i and j of this + * Swap A(1...n,i) <-> + * A(1...n,j). Swap columns + * i and j of this */ void swap_col (const unsigned int i, const unsigned int j); /** - * A(i,i)+=B(i,1...n). Addition of complete - * rows of B to diagonal-elements of this ;

- * ( i = 1 ... m ) + * A(i,i) += + * B(i,1...n). Addition of + * complete rows of B to + * diagonal-elements of this ; + *

( i = 1 ... m ) */ template void add_diag (const number s, @@ -740,7 +749,8 @@ class FullMatrix : public Table<2,number> * Symmetrize the matrix by * forming the mean value between * the existing matrix and its - * transpose, $A = \frac 12(A+A^T)$. + * transpose, A = + * 1/2(A+AT). * * Obviously the matrix must be * quadratic for this operation. @@ -808,10 +818,10 @@ class FullMatrix : public Table<2,number> * to C. * * if (adding) - * $C += A*B$ + * C += A*B * * if (!adding) - * $C = A*B$ + * C = A*B * * Assumes that A and B have * compatible sizes and that C @@ -832,13 +842,14 @@ class FullMatrix : public Table<2,number> * to C. * * if (adding) - * $C += A^T*B$ + * C += AT*B * * if (!adding) - * $C = A^T*B$ + * C = AT*B * - * Assumes that A and B have - * compatible sizes and that C + * Assumes that A and + * B have compatible + * sizes and that C * already has the right size. */ template @@ -855,10 +866,10 @@ class FullMatrix : public Table<2,number> * to w. * * if (adding) - * $w += A*v$ + * w += A*v * * if (!adding) - * $w = A*v$ + * w = A*v * * Source and destination must * not be the same vector. @@ -870,7 +881,7 @@ class FullMatrix : public Table<2,number> /** * Adding Matrix-vector-multiplication. - * $w += A*v$ + * w += A*v * * Source and destination must * not be the same vector. @@ -882,7 +893,18 @@ class FullMatrix : public Table<2,number> /** * Transpose * matrix-vector-multiplication. - * See vmult() above. + * + * The optional parameter + * adding determines, whether the + * result is stored in w or added + * to w. + * + * if (adding) + * w += AT*v + * + * if (!adding) + * w = AT*v + * * * Source and destination must * not be the same vector. @@ -895,7 +917,7 @@ class FullMatrix : public Table<2,number> /** * Adding transpose * matrix-vector-multiplication. - * See vmult() above. + * w += AT*v * * Source and destination must * not be the same vector.