Lines Matching full:matrix
3 /** \eigenManualPage TutorialSparse Sparse matrix manipulations
11 <tr><td>\link SparseCore_Module SparseCore \endlink</td><td>\code#include <Eigen/SparseCore>\endcode</td><td>SparseMatrix and SparseVector classes, matrix assembly, basic sparse linear algebra (including sparse triangular solvers)</td></tr>
20 \section TutorialSparseIntro Sparse matrix format
22 In many applications (e.g., finite element methods) it is common to deal with very large matrices where only a few coefficients are different from zero. In such cases, memory consumption can be reduced and performance increased by using a specialized representation storing only the nonzero coefficients. Such a matrix is called a sparse matrix.
26 The class SparseMatrix is the main sparse matrix representation of Eigen's sparse module; it offers high performance and low memory usage.
33 The word \c inner refers to an \em inner \em vector that is a column for a column-major matrix, or a row for a row-major matrix.
36 This storage scheme is better explained on an example. The following matrix
71 Here is the previous matrix represented in compressed mode:
87 Such problem can be mathematically expressed as a linear problem of the form \f$ Ax=b \f$ where \f$ x \f$ is the vector of \c m unknowns (in our case, the values of the pixels), \f$ b \f$ is the right hand side vector resulting from the boundary conditions, and \f$ A \f$ is an \f$ m \times m \f$ matrix containing only a few non-zero elements resulting from the discretization of the Laplacian operator.
97 In this example, we start by defining a column-major sparse matrix type of double \c SparseMatrix<double>, and a triplet list of the same scalar type \c Triplet<double>. A triplet is a simple object representing a non-zero entry as the triplet: \c row index, \c column index, \c value.
104 Since the resulting matrix \c A is symmetric by construction, we can perform a direct Cholesky factorization via the SimplicialLDLT class which behaves like its LDLT counterpart for dense objects.
115 \b %Matrix \b and \b vector \b properties \n
122 As for dense Matrix objects, constructors takes the size of the object.
126 SparseMatrix<std::complex<float> > mat(1000,2000); // declares a 1000x2000 column-major compressed sparse matrix of complex<float>
127 SparseMatrix<double,RowMajor> mat(1000,2000); // declares a 1000x2000 row-major compressed sparse matrix of double
132 In the rest of the tutorial, \c mat and \c vec represent any sparse-matrix and sparse-vector objects, respectively.
134 The dimensions of a matrix can be queried using the following functions:
185 If the type of the sparse matrix or vector depends on a template parameter, then the \c typename keyword is
189 \section TutorialSparseFilling Filling a sparse matrix
194 The simplest way to create a sparse matrix while guaranteeing good performance is thus to first build a list of so-called \em triplets, and then convert it to a SparseMatrix.
214 In some cases, however, slightly higher performance, and lower memory consumption can be reached by directly inserting the non-zeros into the destination matrix.
227 - The line 5 suppresses the remaining empty space and transforms the matrix into a compressed column storage.
234 In Eigen's sparse module we chose to expose only the subset of the dense matrix API which can be efficiently implemented.
235 In the following \em sm denotes a sparse matrix, \em sv a sparse vector, \em dm a dense matrix, and \em dv a dense vector.
249 On the other hand, there is no restriction on the target matrix sm4.
250 For instance, this means that for computing \f$ A^T + A \f$, the matrix \f$ A^T \f$ must be evaluated into a temporary matrix of compatible storage order:
262 However, it is not yet possible to add a sparse and a dense matrix as in <tt>dm2 = sm1 + dm1</tt>.
274 \subsection TutorialSparse_Products Matrix products
276 %Eigen supports various kind of sparse matrix products which are summarize below:
283 - \b symmetric \b sparse-dense. The product of a sparse symmetric matrix with a dense matrix (or vector) can also be optimized by specifying the symmetry with selfadjointView():
312 Just as with dense matrices, the triangularView() function can be used to address a triangular part of the matrix, and perform triangular solves with a dense right hand side:
319 - optimized sparse-dense matrix products:
327 sm2 = sm1.selfadjointView<Upper>(); // makes a full selfadjoint matrix from the upper triangular part
333 sm2 = A.selfadjointView<Upper>().twistedBy(P); // compute P S P' from the upper triangular part of A, and make it a full matrix
