Quick reference guide for sparse matrices

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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 Sparse matrix manipulations. The important point to have in mind when working on sparse matrices is how they are stored : 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.

Sparse Matrix Initialization

Category	Operations	Notes
Constructor	SparseMatrix<double> sm1(1000,1000); SparseMatrix<std::complex<double>,RowMajor> sm2; Code	Default is ColMajor
Resize/Reserve	sm1.resize(m,n); // Change sm1 to a m x n matrix. sm1.reserve(nnz); // Allocate room for nnz nonzeros elements. Code	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.
Assignment	SparseMatrix<double,Colmajor> sm1; // Initialize sm2 with sm1. SparseMatrix<double,Rowmajor> sm2(sm1), sm3; // Assignment and evaluations modify the storage order. sm3 = sm1; Code	The copy constructor can be used to convert from a storage order to another
Element-wise Insertion	// Insert a new element; sm1.insert(i, j) = v_ij; // Update the value v_ij sm1.coeffRef(i,j) = v_ij; sm1.coeffRef(i,j) += v_ij; sm1.coeffRef(i,j) -= v_ij; Code	insert() assumes that the element does not already exist; otherwise, use coeffRef()
Batch insertion	std::vector< Eigen::Triplet<double> > tripletList; tripletList.reserve(estimation_of_entries); // -- Fill tripletList with nonzero elements... sm1.setFromTriplets(TripletList.begin(), TripletList.end()); Code	A complete example is available at Triplet Insertion .
Constant or Random Insertion	sm1.setZero(); Code	Remove all non-zero coefficients

Matrix properties

Beyond the basic functions rows() and cols(), there are some useful functions that are available to easily get some information from the matrix.

sm1.rows(); // Number of rows sm1.cols(); // Number of columns sm1.nonZeros(); // Number of non zero values sm1.outerSize(); // Number of columns (resp. rows) for a column major (resp. row major ) sm1.innerSize(); // Number of rows (resp. columns) for a row major (resp. column major) sm1.norm(); // Euclidian norm of the matrix sm1.squaredNorm(); // Squared norm of the matrix sm1.blueNorm(); sm1.isVector(); // Check if sm1 is a sparse vector or a sparse matrix sm1.isCompressed(); // Check if sm1 is in compressed form ... Code

Arithmetic operations

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, sm denotes a sparse matrix, dm a dense matrix and dv a dense vector.

Operations	Code	Notes
add subtract	sm3 = sm1 + sm2; sm3 = sm1 - sm2; sm2 += sm1; sm2 -= sm1; Code	sm1 and sm2 should have the same storage order
scalar product	sm3 = sm1 * s1; sm3 *= s1; sm3 = s1 * sm1 + s2 * sm2; sm3 /= s1; Code	Many combinations are possible if the dimensions and the storage order agree.
Sparse Product	sm3 = sm1 * sm2; dm2 = sm1 * dm1; dv2 = sm1 * dv1; Code
transposition, adjoint	sm2 = sm1.transpose(); sm2 = sm1.adjoint(); Code	Note that the transposition change the storage order. There is no support for transposeInPlace().
Permutation	perm.indices(); // Reference to the vector of indices sm1.twistedBy(perm); // Permute rows and columns sm2 = sm1 * perm; // Permute the rows sm2 = perm * sm1; // Permute the columns Code
Component-wise ops	sm1.cwiseProduct(sm2); sm1.cwiseQuotient(sm2); sm1.cwiseMin(sm2); sm1.cwiseMax(sm2); sm1.cwiseAbs(); sm1.cwiseSqrt(); Code	sm1 and sm2 should have the same storage order

Other supported operations

Code	Notes
Sub-matrices
sm1.block(startRow, startCol, rows, cols); sm1.block(startRow, startCol); sm1.topLeftCorner(rows, cols); sm1.topRightCorner(rows, cols); sm1.bottomLeftCorner( rows, cols); sm1.bottomRightCorner( rows, cols); Code	Contrary to dense matrices, here all these methods are read-only. See Block operations and below for read-write sub-matrices.
Range
sm1.innerVector(outer); // RW sm1.innerVectors(start, size); // RW sm1.leftCols(size); // RW sm2.rightCols(size); // RO because sm2 is row-major sm1.middleRows(start, numRows); // RO because sm1 is column-major sm1.middleCols(start, numCols); // RW sm1.col(j); // RW Code	A inner vector is either a row (for row-major) or a column (for column-major). As stated earlier, for a read-write sub-matrix (RW), the evaluation can be done in a matrix with different storage order.
Triangular and selfadjoint views
sm2 = sm1.triangularview<Lower>(); sm2 = sm1.selfadjointview<Lower>(); Code	Several combination between triangular views and blocks views are possible Code
Triangular solve
dv2 = sm1.triangularView<Upper>().solve(dv1); dv2 = sm1.topLeftCorner(size, size) .triangularView<Lower>().solve(dv1); Code	For general sparse solve, Use any suitable module described at Solving Sparse Linear Systems
Low-level API
sm1.valuePtr(); // Pointer to the values sm1.innerIndexPtr(); // Pointer to the indices. sm1.outerIndexPtr(); // Pointer to the beginning of each inner vector Code	If the matrix is not in compressed form, makeCompressed() should be called before. Note that these functions are mostly provided for interoperability purposes with external libraries. A better access to the values of the matrix is done by using the InnerIterator class as described in the Tutorial Sparse section
Mapping external buffers
int outerIndexPtr[cols+1]; int innerIndices[nnz]; double values[nnz]; Map<SparseMatrix<double> > sm1(rows,cols,nnz,outerIndexPtr, // read-write innerIndices,values); Map<const SparseMatrix<double> > sm2(...); // read-only Code	As for dense matrices, class Map<SparseMatrixType> can be used to see external buffers as an Eigen's SparseMatrix object.