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1namespace Eigen {
2/** \eigenManualPage SparseQuickRefPage Quick reference guide for sparse matrices
3\eigenAutoToc
4
5<hr>
6
7In this page, we give a quick summary of the main operations available for sparse matrices in the class SparseMatrix. First, it is recommended to read the introductory tutorial at \ref TutorialSparse. The important point to have in mind when working on sparse matrices is how they are stored :
8i.e either row major or column major. The default is column major. Most arithmetic operations on sparse matrices will assert that they have the same storage order.
9
10\section SparseMatrixInit Sparse Matrix Initialization
11<table class="manual">
12<tr><th> Category </th> <th> Operations</th> <th>Notes</th></tr>
13<tr><td>Constructor</td>
14<td>
15\code
16 SparseMatrix<double> sm1(1000,1000);
17 SparseMatrix<std::complex<double>,RowMajor> sm2;
18\endcode
19</td> <td> Default is ColMajor</td> </tr>
20<tr class="alt">
21<td> Resize/Reserve</td>
22<td>
23 \code
24 sm1.resize(m,n); // Change sm1 to a m x n matrix.
25 sm1.reserve(nnz); // Allocate room for nnz nonzeros elements.
26 \endcode
27</td>
28<td> Note that when calling reserve(), it is not required that nnz is the exact number of nonzero elements in the final matrix. However, an exact estimation will avoid multiple reallocations during the insertion phase. </td>
29</tr>
30<tr>
31<td> Assignment </td>
32<td>
33\code
34 SparseMatrix<double,Colmajor> sm1;
35 // Initialize sm2 with sm1.
36 SparseMatrix<double,Rowmajor> sm2(sm1), sm3;
37 // Assignment and evaluations modify the storage order.
38 sm3 = sm1;
39 \endcode
40</td>
41<td> The copy constructor can be used to convert from a storage order to another</td>
42</tr>
43<tr class="alt">
44<td> Element-wise Insertion</td>
45<td>
46\code
47// Insert a new element;
48 sm1.insert(i, j) = v_ij;
49
50// Update the value v_ij
51 sm1.coeffRef(i,j) = v_ij;
52 sm1.coeffRef(i,j) += v_ij;
53 sm1.coeffRef(i,j) -= v_ij;
54\endcode
55</td>
56<td> insert() assumes that the element does not already exist; otherwise, use coeffRef()</td>
57</tr>
58<tr>
59<td> Batch insertion</td>
60<td>
61\code
62 std::vector< Eigen::Triplet<double> > tripletList;
63 tripletList.reserve(estimation_of_entries);
64 // -- Fill tripletList with nonzero elements...
65 sm1.setFromTriplets(TripletList.begin(), TripletList.end());
66\endcode
67</td>
68<td>A complete example is available at \link TutorialSparseFilling Triplet Insertion \endlink.</td>
69</tr>
70<tr class="alt">
71<td> Constant or Random Insertion</td>
72<td>
73\code
74sm1.setZero();
75\endcode
76</td>
77<td>Remove all non-zero coefficients</td>
78</tr>
79</table>
80
81
82\section SparseBasicInfos Matrix properties
83Beyond the basic functions rows() and cols(), there are some useful functions that are available to easily get some informations from the matrix.
84<table class="manual">
85<tr>
86 <td> \code
87 sm1.rows(); // Number of rows
88 sm1.cols(); // Number of columns
89 sm1.nonZeros(); // Number of non zero values
90 sm1.outerSize(); // Number of columns (resp. rows) for a column major (resp. row major )
91 sm1.innerSize(); // Number of rows (resp. columns) for a row major (resp. column major)
92 sm1.norm(); // Euclidian norm of the matrix
93 sm1.squaredNorm(); // Squared norm of the matrix
94 sm1.blueNorm();
95 sm1.isVector(); // Check if sm1 is a sparse vector or a sparse matrix
96 sm1.isCompressed(); // Check if sm1 is in compressed form
97 ...
98 \endcode </td>
99</tr>
100</table>
101
102\section SparseBasicOps Arithmetic operations
103It is easy to perform arithmetic operations on sparse matrices provided that the dimensions are adequate and that the matrices have the same storage order. Note that the evaluation can always be done in a matrix with a different storage order. In the following, \b sm denotes a sparse matrix, \b dm a dense matrix and \b dv a dense vector.
104<table class="manual">
105<tr><th> Operations </th> <th> Code </th> <th> Notes </th></tr>
106
107<tr>
108 <td> add subtract </td>
109 <td> \code
110 sm3 = sm1 + sm2;
111 sm3 = sm1 - sm2;
112 sm2 += sm1;
113 sm2 -= sm1; \endcode
114 </td>
115 <td>
116 sm1 and sm2 should have the same storage order
117 </td>
118</tr>
119
120<tr class="alt"><td>
121 scalar product</td><td>\code
122 sm3 = sm1 * s1; sm3 *= s1;
123 sm3 = s1 * sm1 + s2 * sm2; sm3 /= s1;\endcode
124 </td>
125 <td>
126 Many combinations are possible if the dimensions and the storage order agree.
127</tr>
128
129<tr>
130 <td> %Sparse %Product </td>
131 <td> \code
132 sm3 = sm1 * sm2;
133 dm2 = sm1 * dm1;
134 dv2 = sm1 * dv1;
135 \endcode </td>
136 <td>
137 </td>
138</tr>
139
140<tr class='alt'>
141 <td> transposition, adjoint</td>
142 <td> \code
143 sm2 = sm1.transpose();
144 sm2 = sm1.adjoint();
145 \endcode </td>
146 <td>
147 Note that the transposition change the storage order. There is no support for transposeInPlace().
148 </td>
149</tr>
150<tr>
151<td> Permutation </td>
152<td>
153\code
154perm.indices(); // Reference to the vector of indices
155sm1.twistedBy(perm); // Permute rows and columns
156sm2 = sm1 * perm; // Permute the columns
157sm2 = perm * sm1; // Permute the columns
158\endcode
159</td>
160<td>
161
162</td>
163</tr>
164<tr>
165 <td>
166 Component-wise ops
167 </td>
168 <td>\code
169 sm1.cwiseProduct(sm2);
170 sm1.cwiseQuotient(sm2);
171 sm1.cwiseMin(sm2);
172 sm1.cwiseMax(sm2);
173 sm1.cwiseAbs();
174 sm1.cwiseSqrt();
175 \endcode</td>
176 <td>
177 sm1 and sm2 should have the same storage order
178 </td>
179</tr>
180</table>
181
182\section sparseotherops Other supported operations
183<table class="manual">
184<tr><th style="min-width:initial"> Code </th> <th> Notes</th> </tr>
185<tr><td colspan="2">Sub-matrices</td></tr>
186<tr>
187<td>
188\code
189 sm1.block(startRow, startCol, rows, cols);
190 sm1.block(startRow, startCol);
191 sm1.topLeftCorner(rows, cols);
192 sm1.topRightCorner(rows, cols);
193 sm1.bottomLeftCorner( rows, cols);
194 sm1.bottomRightCorner( rows, cols);
195 \endcode
196</td><td>
197Contrary to dense matrices, here <strong>all these methods are read-only</strong>.\n
198See \ref TutorialSparse_SubMatrices and below for read-write sub-matrices.
199</td>
200</tr>
201<tr class="alt"><td colspan="2"> Range </td></tr>
202<tr class="alt">
203<td>
204\code
205 sm1.innerVector(outer); // RW
206 sm1.innerVectors(start, size); // RW
207 sm1.leftCols(size); // RW
208 sm2.rightCols(size); // RO because sm2 is row-major
209 sm1.middleRows(start, numRows); // RO becasue sm1 is column-major
210 sm1.middleCols(start, numCols); // RW
211 sm1.col(j); // RW
212\endcode
213</td>
214<td>
215A inner vector is either a row (for row-major) or a column (for column-major).\n
216As stated earlier, for a read-write sub-matrix (RW), the evaluation can be done in a matrix with different storage order.
217</td>
218</tr>
219<tr><td colspan="2"> Triangular and selfadjoint views</td></tr>
220<tr>
221<td>
222\code
223 sm2 = sm1.triangularview<Lower>();
224 sm2 = sm1.selfadjointview<Lower>();
225\endcode
226</td>
227<td> Several combination between triangular views and blocks views are possible
228\code
229 \endcode </td>
230</tr>
231<tr class="alt"><td colspan="2">Triangular solve </td></tr>
232<tr class="alt">
233<td>
234\code
235 dv2 = sm1.triangularView<Upper>().solve(dv1);
236 dv2 = sm1.topLeftCorner(size, size)
237 .triangularView<Lower>().solve(dv1);
238\endcode
239</td>
240<td> For general sparse solve, Use any suitable module described at \ref TopicSparseSystems </td>
241</tr>
242<tr><td colspan="2"> Low-level API</td></tr>
243<tr>
244<td>
245\code
246sm1.valuePtr(); // Pointer to the values
247sm1.innerIndextr(); // Pointer to the indices.
248sm1.outerIndexPtr(); // Pointer to the beginning of each inner vector
249\endcode
250</td>
251<td>
252If the matrix is not in compressed form, makeCompressed() should be called before.\n
253Note that these functions are mostly provided for interoperability purposes with external libraries.\n
254A better access to the values of the matrix is done by using the InnerIterator class as described in \link TutorialSparse the Tutorial Sparse \endlink section</td>
255</tr>
256</table>
257*/
258}
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