.. for doctests >>> import numpy as np >>> from scipy import sparse Diagonal Format (DIA) ===================== * very simple scheme * diagonals in dense NumPy array of shape `(n_diag, length)` * fixed length -> waste space a bit when far from main diagonal * subclass of :class:`_data_matrix` (sparse matrix classes with `.data` attribute) * offset for each diagonal * 0 is the main diagonal * negative offset = below * positive offset = above * fast matrix * vector (sparsetools) * fast and easy item-wise operations * manipulate data array directly (fast NumPy machinery) * constructor accepts: * dense matrix (array) * sparse matrix * shape tuple (create empty matrix) * `(data, offsets)` tuple * no slicing, no individual item access * use: * rather specialized * solving PDEs by finite differences * with an iterative solver Examples -------- * create some DIA matrices:: >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0) >>> data array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]) >>> offsets = np.array([0, -1, 2]) >>> mtx = sparse.dia_matrix((data, offsets), shape=(4, 4)) >>> mtx # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS <4x4 sparse matrix of type '<... 'numpy.int64'>' with 9 stored elements (3 diagonals) in DIAgonal format> >>> mtx.todense() matrix([[1, 0, 3, 0], [1, 2, 0, 4], [0, 2, 3, 0], [0, 0, 3, 4]]) >>> data = np.arange(12).reshape((3, 4)) + 1 >>> data array([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]]) >>> mtx = sparse.dia_matrix((data, offsets), shape=(4, 4)) >>> mtx.data # doctest: +ELLIPSIS array([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]]) >>> mtx.offsets array([ 0, -1, 2], dtype=int32) >>> print(mtx) # doctest: +NORMALIZE_WHITESPACE (0, 0) 1 (1, 1) 2 (2, 2) 3 (3, 3) 4 (1, 0) 5 (2, 1) 6 (3, 2) 7 (0, 2) 11 (1, 3) 12 >>> mtx.todense() matrix([[ 1, 0, 11, 0], [ 5, 2, 0, 12], [ 0, 6, 3, 0], [ 0, 0, 7, 4]]) * explanation with a scheme:: offset: row 2: 9 1: --10------ 0: 1 . 11 . -1: 5 2 . 12 -2: . 6 3 . -3: . . 7 4 ---------8 * matrix-vector multiplication >>> vec = np.ones((4, )) >>> vec array([1., 1., 1., 1.]) >>> mtx * vec array([12., 19., 9., 11.]) >>> mtx.toarray() * vec array([[ 1., 0., 11., 0.], [ 5., 2., 0., 12.], [ 0., 6., 3., 0.], [ 0., 0., 7., 4.]])