## 6.2 Conversion Functions

Conversion functions between dense and sparse matrices are provided.

### 6.2.1 Dense to Sparse Conversion

Converting a dense matrix $$m$$ to a sparse representation produces a vector $$w$$ and two integer arrays, $$u$$ and $$v$$.

vector csr_extract_w(matrix a)
Return non-zero values in matrix a; see section compressed row storage.

int[] csr_extract_v(matrix a)
Return column indices for values in csr_extract_w(a); see compressed row storage.

int[] csr_extract_u(matrix a)
Return array of row starting indices for entries in csr_extract_w(a) followed by the size of csr_extract_w(a) plus one; see section compressed row storage.

### 6.2.2 Sparse to Dense Conversion

To convert a sparse matrix representation to a dense matrix, there is a single function.

matrix csr_to_dense_matrix(int m, int n, vector w, int[] v, int[] u)
Return dense $$\text{m} \times \text{n}$$ matrix with non-zero matrix entries w, column indices v, and row starting indices u; the vector w and arrays v and u must all be the same size, and the arrays v and u must have index values bounded by m and n. see section compressed row storage for more details.