# scipy/scipy

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 """Sparse DIAgonal format""" from __future__ import division, print_function, absolute_import __docformat__ = "restructuredtext en" __all__ = ['dia_matrix', 'isspmatrix_dia'] import numpy as np from .base import isspmatrix, _formats from .data import _data_matrix from .sputils import isshape, upcast, upcast_char, getdtype 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 nonzero elements 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 -------- >>> from scipy.sparse import * >>> from scipy import * >>> dia_matrix( (3,4), dtype=int8).todense() matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=int8) >>> data = array([[1,2,3,4]]).repeat(3,axis=0) >>> offsets = array([0,-1,2]) >>> dia_matrix( (data,offsets), shape=(4,4)).todense() matrix([[1, 0, 3, 0], [1, 2, 0, 4], [0, 2, 3, 0], [0, 0, 3, 4]]) """ 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 = 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 = A.shape elif isinstance(arg1, tuple): if isshape(arg1): # It's a tuple of matrix dimensions (M, N) # create empty matrix self.shape = arg1 #spmatrix checks for errors here self.data = np.zeros( (0,0), getdtype(dtype, default=float)) self.offsets = np.zeros( (0), dtype=np.intc) else: try: # Try interpreting it as (data, offsets) data, offsets = arg1 except: 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=np.intc, copy=copy)) self.shape = shape else: #must be dense, convert to COO first, then to DIA try: arg1 = np.asarray(arg1) except: raise ValueError("unrecognized form for" \ " %s_matrix constructor" % self.format) from .coo import coo_matrix A = coo_matrix(arg1, dtype=dtype).todia() self.data = A.data self.offsets = A.offsets self.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): nnz = self.getnnz() format = self.getformat() return "<%dx%d sparse matrix of type '%s'\n" \ "\twith %d stored elements (%d diagonals) in %s format>" % \ ( self.shape + (self.dtype.type, nnz, self.data.shape[0], \ _formats[format][1],) ) def getnnz(self): """number of nonzero values explicit zero values are included in this number """ 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 nnz nnz = property(fget=getnnz) 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 todia(self,copy=False): if copy: return self.copy() else: return self def tocsr(self): #this could be faster return self.tocoo().tocsr() def tocsc(self): #this could be faster return self.tocoo().tocsc() def tocoo(self): num_data = len(self.data) len_data = self.data.shape[1] row = np.arange(len_data).reshape(1,-1).repeat(num_data,axis=0) col = row.copy() for i,k in enumerate(self.offsets): row[i,:] -= k row,col,data = row.ravel(),col.ravel(),self.data.ravel() mask = (row >= 0) mask &= (row < self.shape[0]) mask &= (col < self.shape[1]) mask &= data != 0 row,col,data = row[mask],col[mask],data[mask] from .coo import coo_matrix return coo_matrix((data,(row,col)), shape=self.shape) # 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 isspmatrix_dia(x): return isinstance(x, dia_matrix)
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