Introduction to Sparse Matrices In Scilab - Projects

sp2adjspeyesponessprandspzerosfullsparsemtlb sparsennzspcompackspgetconverts sparse matrix into adjacency formsparse identity matrixsparse matrixsparse random matrixsparse zero matrixsparse to full matrix conversionsparse matrix definitionconvert sparse matrixnumber of non zero entries in a matrixconverts a compressed adjacency representationretrieves entries of sparse matrixFigure 1 – Basic features for sparse matrices.matrix is stored internally.2.1 Creating sparse matricesThe figure 1 present several functions to create sparse matrices.In the following session, we use the sprand function to create a 100×1000sparse matrix with density 0.001. The density parameter makes so that thenumber of non-zero entries in the sparse matrix is approximately equal to100 · 1000 · 0.001 = 100. Then we use the size function to compute the sizeof the matrix. Finally, we compute the number of non-zero entries with thennz function.-->A= sprand (100 ,1000 ,0.001);--> size (A)ans =100. 1000.-->nnz (A)ans =100.The sparse and full functions works as complementary functions. Indeed,the sparse function converts a full matrix into a sparse one, while thefull function converts a sparse matrix into a full one.In the following session, we create a 3 × 5 dense matrix. Then we use thesparse function to convert it into a sparse matrix. Scilab then displays all6