1 namespace Eigen { 2 /** \eigenManualPage SparseQuickRefPage Quick reference guide for sparse matrices 3 \eigenAutoToc 4 5 <hr> 6 7 In 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 : 8 i.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 74 sm1.setZero(); 75 \endcode 76 </td> 77 <td>Remove all non-zero coefficients</td> 78 </tr> 79 </table> 80 81 82 \section SparseBasicInfos Matrix properties 83 Beyond 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 103 It 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 154 perm.indices(); // Reference to the vector of indices 155 sm1.twistedBy(perm); // Permute rows and columns 156 sm2 = sm1 * perm; // Permute the columns 157 sm2 = 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> 197 Contrary to dense matrices, here <strong>all these methods are read-only</strong>.\n 198 See \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 because sm1 is column-major 210 sm1.middleCols(start, numCols); // RW 211 sm1.col(j); // RW 212 \endcode 213 </td> 214 <td> 215 A inner vector is either a row (for row-major) or a column (for column-major).\n 216 As 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 246 sm1.valuePtr(); // Pointer to the values 247 sm1.innerIndextr(); // Pointer to the indices. 248 sm1.outerIndexPtr(); // Pointer to the beginning of each inner vector 249 \endcode 250 </td> 251 <td> 252 If the matrix is not in compressed form, makeCompressed() should be called before.\n 253 Note that these functions are mostly provided for interoperability purposes with external libraries.\n 254 A 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 <tr class="alt"><td colspan="2">Mapping external buffers</td></tr> 257 <tr class="alt"> 258 <td> 259 \code 260 int outerIndexPtr[cols+1]; 261 int innerIndices[nnz]; 262 double values[nnz]; 263 Map<SparseMatrix<double> > sm1(rows,cols,nnz,outerIndexPtr, // read-write 264 innerIndices,values); 265 Map<const SparseMatrix<double> > sm2(...); // read-only 266 \endcode 267 </td> 268 <td>As for dense matrices, class Map<SparseMatrixType> can be used to see external buffers as an %Eigen's SparseMatrix object. </td> 269 </tr> 270 </table> 271 */ 272 } 273
