"""Sparse DIAgonal format""" __docformat__ = "restructuredtext en" __all__ = ['dia_matrix', 'isspmatrix_dia'] import numpy as np from .base import isspmatrix, _formats, spmatrix from .data import _data_matrix from .sputils import (isshape, upcast_char, getdtype, get_index_dtype, get_sum_dtype, validateaxis, check_shape, matrix) from ._sparsetools import dia_matvec class dia_matrix(_data_matrix): """Sparse matrix with DIAgonal storage This can be instantiated in several ways: dia_matrix(D) with a dense matrix dia_matrix(S) with another sparse matrix S (equivalent to S.todia()) dia_matrix((M, N), [dtype]) to construct an empty matrix with shape (M, N), dtype is optional, defaulting to dtype='d'. dia_matrix((data, offsets), shape=(M, N)) where the ``data[k,:]`` stores the diagonal entries for diagonal ``offsets[k]`` (See example below) Attributes ---------- dtype : dtype Data type of the matrix shape : 2-tuple Shape of the matrix ndim : int Number of dimensions (this is always 2) nnz Number of stored values, including explicit zeros data DIA format data array of the matrix offsets DIA format offset array of the matrix Notes ----- Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power. Examples -------- >>> import numpy as np >>> from scipy.sparse import dia_matrix >>> dia_matrix((3, 4), dtype=np.int8).toarray() array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=int8) >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0) >>> offsets = np.array([0, -1, 2]) >>> dia_matrix((data, offsets), shape=(4, 4)).toarray() array([[1, 0, 3, 0], [1, 2, 0, 4], [0, 2, 3, 0], [0, 0, 3, 4]]) >>> from scipy.sparse import dia_matrix >>> n = 10 >>> ex = np.ones(n) >>> data = np.array([ex, 2 * ex, ex]) >>> offsets = np.array([-1, 0, 1]) >>> dia_matrix((data, offsets), shape=(n, n)).toarray() array([[2., 1., 0., ..., 0., 0., 0.], [1., 2., 1., ..., 0., 0., 0.], [0., 1., 2., ..., 0., 0., 0.], ..., [0., 0., 0., ..., 2., 1., 0.], [0., 0., 0., ..., 1., 2., 1.], [0., 0., 0., ..., 0., 1., 2.]]) """ format = 'dia' def __init__(self, arg1, shape=None, dtype=None, copy=False): _data_matrix.__init__(self) if isspmatrix_dia(arg1): if copy: arg1 = arg1.copy() self.data = arg1.data self.offsets = arg1.offsets self._shape = check_shape(arg1.shape) elif isspmatrix(arg1): if isspmatrix_dia(arg1) and copy: A = arg1.copy() else: A = arg1.todia() self.data = A.data self.offsets = A.offsets self._shape = check_shape(A.shape) elif isinstance(arg1, tuple): if isshape(arg1): # It's a tuple of matrix dimensions (M, N) # create empty matrix self._shape = check_shape(arg1) self.data = np.zeros((0,0), getdtype(dtype, default=float)) idx_dtype = get_index_dtype(maxval=max(self.shape)) self.offsets = np.zeros((0), dtype=idx_dtype) else: try: # Try interpreting it as (data, offsets) data, offsets = arg1 except Exception: raise ValueError('unrecognized form for dia_matrix constructor') else: if shape is None: raise ValueError('expected a shape argument') self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy)) self.offsets = np.atleast_1d(np.array(arg1[1], dtype=get_index_dtype(maxval=max(shape)), copy=copy)) self._shape = check_shape(shape) else: #must be dense, convert to COO first, then to DIA try: arg1 = np.asarray(arg1) except Exception: raise ValueError("unrecognized form for" " %s_matrix constructor" % self.format) from .coo import coo_matrix A = coo_matrix(arg1, dtype=dtype, shape=shape).todia() self.data = A.data self.offsets = A.offsets self._shape = check_shape(A.shape) if dtype is not None: self.data = self.data.astype(dtype) #check format if self.offsets.ndim != 1: raise ValueError('offsets array must have rank 1') if self.data.ndim != 2: raise ValueError('data array must have rank 2') if self.data.shape[0] != len(self.offsets): raise ValueError('number of diagonals (%d) ' 'does not match the number of offsets (%d)' % (self.data.shape[0], len(self.offsets))) if len(np.unique(self.offsets)) != len(self.offsets): raise ValueError('offset array contains duplicate values') def __repr__(self): format = _formats[self.getformat()][1] return "<%dx%d sparse matrix of type '%s'\n" \ "\twith %d stored elements (%d diagonals) in %s format>" % \ (self.shape + (self.dtype.type, self.nnz, self.data.shape[0], format)) def _data_mask(self): """Returns a mask of the same shape as self.data, where mask[i,j] is True when data[i,j] corresponds to a stored element.""" num_rows, num_cols = self.shape offset_inds = np.arange(self.data.shape[1]) row = offset_inds - self.offsets[:,None] mask = (row >= 0) mask &= (row < num_rows) mask &= (offset_inds < num_cols) return mask def count_nonzero(self): mask = self._data_mask() return np.count_nonzero(self.data[mask]) def getnnz(self, axis=None): if axis is not None: raise NotImplementedError("getnnz over an axis is not implemented " "for DIA format") M,N = self.shape nnz = 0 for k in self.offsets: if k > 0: nnz += min(M,N-k) else: nnz += min(M+k,N) return int(nnz) getnnz.__doc__ = spmatrix.getnnz.__doc__ count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__ def sum(self, axis=None, dtype=None, out=None): validateaxis(axis) if axis is not None and axis < 0: axis += 2 res_dtype = get_sum_dtype(self.dtype) num_rows, num_cols = self.shape ret = None if axis == 0: mask = self._data_mask() x = (self.data * mask).sum(axis=0) if x.shape[0] == num_cols: res = x else: res = np.zeros(num_cols, dtype=x.dtype) res[:x.shape[0]] = x ret = matrix(res, dtype=res_dtype) else: row_sums = np.zeros(num_rows, dtype=res_dtype) one = np.ones(num_cols, dtype=res_dtype) dia_matvec(num_rows, num_cols, len(self.offsets), self.data.shape[1], self.offsets, self.data, one, row_sums) row_sums = matrix(row_sums) if axis is None: return row_sums.sum(dtype=dtype, out=out) if axis is not None: row_sums = row_sums.T ret = matrix(row_sums.sum(axis=axis)) if out is not None and out.shape != ret.shape: raise ValueError("dimensions do not match") return ret.sum(axis=(), dtype=dtype, out=out) sum.__doc__ = spmatrix.sum.__doc__ def _mul_vector(self, other): x = other y = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char, x.dtype.char)) L = self.data.shape[1] M,N = self.shape dia_matvec(M,N, len(self.offsets), L, self.offsets, self.data, x.ravel(), y.ravel()) return y def _mul_multimatrix(self, other): return np.hstack([self._mul_vector(col).reshape(-1,1) for col in other.T]) def _setdiag(self, values, k=0): M, N = self.shape if values.ndim == 0: # broadcast values_n = np.inf else: values_n = len(values) if k < 0: n = min(M + k, N, values_n) min_index = 0 max_index = n else: n = min(M, N - k, values_n) min_index = k max_index = k + n if values.ndim != 0: # allow also longer sequences values = values[:n] if k in self.offsets: self.data[self.offsets == k, min_index:max_index] = values else: self.offsets = np.append(self.offsets, self.offsets.dtype.type(k)) m = max(max_index, self.data.shape[1]) data = np.zeros((self.data.shape[0]+1, m), dtype=self.data.dtype) data[:-1,:self.data.shape[1]] = self.data data[-1, min_index:max_index] = values self.data = data def todia(self, copy=False): if copy: return self.copy() else: return self todia.__doc__ = spmatrix.todia.__doc__ def transpose(self, axes=None, copy=False): if axes is not None: raise ValueError(("Sparse matrices do not support " "an 'axes' parameter because swapping " "dimensions is the only logical permutation.")) num_rows, num_cols = self.shape max_dim = max(self.shape) # flip diagonal offsets offsets = -self.offsets # re-align the data matrix r = np.arange(len(offsets), dtype=np.intc)[:, None] c = np.arange(num_rows, dtype=np.intc) - (offsets % max_dim)[:, None] pad_amount = max(0, max_dim-self.data.shape[1]) data = np.hstack((self.data, np.zeros((self.data.shape[0], pad_amount), dtype=self.data.dtype))) data = data[r, c] return dia_matrix((data, offsets), shape=( num_cols, num_rows), copy=copy) transpose.__doc__ = spmatrix.transpose.__doc__ def diagonal(self, k=0): rows, cols = self.shape if k <= -rows or k >= cols: return np.empty(0, dtype=self.data.dtype) idx, = np.nonzero(self.offsets == k) first_col, last_col = max(0, k), min(rows + k, cols) if idx.size == 0: return np.zeros(last_col - first_col, dtype=self.data.dtype) return self.data[idx[0], first_col:last_col] diagonal.__doc__ = spmatrix.diagonal.__doc__ def tocsc(self, copy=False): from .csc import csc_matrix if self.nnz == 0: return csc_matrix(self.shape, dtype=self.dtype) num_rows, num_cols = self.shape num_offsets, offset_len = self.data.shape offset_inds = np.arange(offset_len) row = offset_inds - self.offsets[:,None] mask = (row >= 0) mask &= (row < num_rows) mask &= (offset_inds < num_cols) mask &= (self.data != 0) idx_dtype = get_index_dtype(maxval=max(self.shape)) indptr = np.zeros(num_cols + 1, dtype=idx_dtype) indptr[1:offset_len+1] = np.cumsum(mask.sum(axis=0)) indptr[offset_len+1:] = indptr[offset_len] indices = row.T[mask.T].astype(idx_dtype, copy=False) data = self.data.T[mask.T] return csc_matrix((data, indices, indptr), shape=self.shape, dtype=self.dtype) tocsc.__doc__ = spmatrix.tocsc.__doc__ def tocoo(self, copy=False): num_rows, num_cols = self.shape num_offsets, offset_len = self.data.shape offset_inds = np.arange(offset_len) row = offset_inds - self.offsets[:,None] mask = (row >= 0) mask &= (row < num_rows) mask &= (offset_inds < num_cols) mask &= (self.data != 0) row = row[mask] col = np.tile(offset_inds, num_offsets)[mask.ravel()] data = self.data[mask] from .coo import coo_matrix A = coo_matrix((data,(row,col)), shape=self.shape, dtype=self.dtype) A.has_canonical_format = True return A tocoo.__doc__ = spmatrix.tocoo.__doc__ # needed by _data_matrix def _with_data(self, data, copy=True): """Returns a matrix with the same sparsity structure as self, but with different data. By default the structure arrays are copied. """ if copy: return dia_matrix((data, self.offsets.copy()), shape=self.shape) else: return dia_matrix((data,self.offsets), shape=self.shape) def resize(self, *shape): shape = check_shape(shape) M, N = shape # we do not need to handle the case of expanding N self.data = self.data[:, :N] if (M > self.shape[0] and np.any(self.offsets + self.shape[0] < self.data.shape[1])): # explicitly clear values that were previously hidden mask = (self.offsets[:, None] + self.shape[0] <= np.arange(self.data.shape[1])) self.data[mask] = 0 self._shape = shape resize.__doc__ = spmatrix.resize.__doc__ def isspmatrix_dia(x): """Is x of dia_matrix type? Parameters ---------- x object to check for being a dia matrix Returns ------- bool True if x is a dia matrix, False otherwise Examples -------- >>> from scipy.sparse import dia_matrix, isspmatrix_dia >>> isspmatrix_dia(dia_matrix([[5]])) True >>> from scipy.sparse import dia_matrix, csr_matrix, isspmatrix_dia >>> isspmatrix_dia(csr_matrix([[5]])) False """ return isinstance(x, dia_matrix)