Sparse matrices are stored in compressed column storage (CCS) format. For a general nrows by ncols sparse matrix with nnz nonzero entries this means the following. The sparsity pattern and the nonzero values are stored in three fields:
For example, for the matrix
the elements of values, rowind and colptr are:
values: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, rowind: 0, 1,3, 1, 0, 2, colptr: 0, 3, 3, 4, 6.
It is crucial that for each column the row indices in rowind are sorted; the equivalent representation
values: 3.0, 2.0, 1.0, 4.0, 5.0, 6.0, rowind: 3, 1, 0, 1, 0, 2, colptr: 0, 3, 3, 4, 6
is not allowed (and will likely cause the program to crash).
The nzmax field specifies the number of non-zero elements the matrix can store. It is equal to the length of rowind and values; this number can be larger that colptr[nrows], but never less. This field makes it possible to preallocate a certain amount of memory to avoid reallocations if the matrix is constructed sequentially by filling in elements. In general the nzmax field can safely be ignored, however, since it will always be adjusted automatically as the number of non-zero elements grows.
The id field controls the type of the matrix and can have values DOUBLE and COMPLEX.
Sparse matrices are created using the following functions from the API.
spmatrix *SpMatrix_New(int nrows, int ncols, int nzmax, int id)
Returns a sparse zero matrix with nrows rows and ncols columns. nzmax is the number of elements that will be allocated (the length of the values and rowind fields).
spmatrix *SpMatrix_NewFromMatrix(spmatrix *src, int id)
Returns a copy the sparse matrix src.
spmatrix *SpMatrix_NewFromIJV(matrix *I, matrix *J, matrix *V, int nrows, int ncols, int nzmax, int id)
Creates a sparse matrix with nrows rows and ncols columns from a triplet description. I and J must be integer matrices and V either a double or complex matrix, or NULL. If V is NULL the values of the entries in the matrix are undefined, otherwise they are specified by V. Repeated entries in V are summed. The number of allocated elements is given by nzmax, which is adjusted if it is smaller than the required amount.
We illustrate use of the sparse matrix class by listing the source code for the real() method, which returns the real part of a sparse matrix:
static PyObject * spmatrix_real(spmatrix *self) {
if (SP_ID(self) != COMPLEX) return (PyObject *)SpMatrix_NewFromMatrix(self, 0, SP_ID(self)); spmatrix *ret = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self), SP_NNZ(self), DOUBLE); if (!ret) return PyErr_NoMemory(); int i; for (i=0; i < SP_NNZ(self); i++) SP_VALD(ret)[i] = creal(SP_VALZ(self)[i]); memcpy(SP_COL(ret), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t)); memcpy(SP_ROW(ret), SP_ROW(self), SP_NNZ(self)*sizeof(int_t)); return (PyObject *)ret; } |