code: """Compressed Sparse Column matrix format"""
  from __future__ import division, print_function, absolute_import
  
  __docformat__ = "restructuredtext en"
  
  __all__ = ['csc_matrix', 'isspmatrix_csc']
  
  from warnings import warn
  
  import numpy as np
  from scipy.lib.six import xrange
  
  from .base import isspmatrix
  from .sparsetools import csc_tocsr
  from . import sparsetools
  from .sputils import upcast, isintlike, IndexMixin, get_index_dtype
  
  from .compressed import _cs_matrix
  
  
  class csc_matrix(_cs_matrix, IndexMixin):
      """
      Compressed Sparse Column matrix
  
      This can be instantiated in several ways:
  
          csc_matrix(D)
              with a dense matrix or rank-2 ndarray D
  
          csc_matrix(S)
              with another sparse matrix S (equivalent to S.tocsc())
  
          csc_matrix((M, N), [dtype])
              to construct an empty matrix with shape (M, N)
              dtype is optional, defaulting to dtype='d'.
  
          csc_matrix((data, ij), [shape=(M, N)])
              where ``data`` and ``ij`` satisfy the relationship
              ``a[ij[0, k], ij[1, k]] = data[k]``
  
          csc_matrix((data, indices, indptr), [shape=(M, N)])
              is the standard CSC representation where the row indices for
              column i are stored in ``indices[indptr[i]:indptr[i+1]]``
              and their corresponding values are stored in
              ``data[indptr[i]:indptr[i+1]]``.  If the shape parameter is
              not supplied, the matrix dimensions are inferred from
              the index arrays.
  
      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
          Data array of the matrix
      indices
          CSC format index array
      indptr
          CSC format index pointer array
      has_sorted_indices
          Whether indices are sorted
  
      Notes
      -----
  
      Sparse matrices can be used in arithmetic operations: they support
      addition, subtraction, multiplication, division, and matrix power.
  
      Advantages of the CSC format
          - efficient arithmetic operations CSC + CSC, CSC * CSC, etc.
          - efficient column slicing
          - fast matrix vector products (CSR, BSR may be faster)
  
      Disadvantages of the CSC format
        - slow row slicing operations (consider CSR)
        - changes to the sparsity structure are expensive (consider LIL or DOK)
  
  
      Examples
      --------
  
      >>> from scipy.sparse import *
      >>> from scipy import *
      >>> csc_matrix( (3,4), dtype=int8 ).todense()
      matrix([[0, 0, 0, 0],
              [0, 0, 0, 0],
              [0, 0, 0, 0]], dtype=int8)
  
      >>> row = array([0,2,2,0,1,2])
      >>> col = array([0,0,1,2,2,2])
      >>> data = array([1,2,3,4,5,6])
      >>> csc_matrix( (data,(row,col)), shape=(3,3) ).todense()
      matrix([[1, 0, 4],
              [0, 0, 5],
              [2, 3, 6]])
  
      >>> indptr = array([0,2,3,6])
      >>> indices = array([0,2,2,0,1,2])
      >>> data = array([1,2,3,4,5,6])
      >>> csc_matrix( (data,indices,indptr), shape=(3,3) ).todense()
      matrix([[1, 0, 4],
              [0, 0, 5],
              [2, 3, 6]])
  
      """
  
      def transpose(self, copy=False):
          from .csr import csr_matrix
          M,N = self.shape
          return csr_matrix((self.data,self.indices,self.indptr),(N,M),copy=copy)
  
      def __iter__(self):
          csr = self.tocsr()
          for r in xrange(self.shape[0]):
              yield csr[r,:]
  
      def tocsc(self, copy=False):
          if copy:
              return self.copy()
          else:
              return self
  
      def tocsr(self):
          M,N = self.shape
          idx_dtype = get_index_dtype((self.indptr, self.indices),
                                      maxval=max(self.nnz, N))
          indptr = np.empty(M + 1, dtype=idx_dtype)
          indices = np.empty(self.nnz, dtype=idx_dtype)
          data = np.empty(self.nnz, dtype=upcast(self.dtype))
  
          csc_tocsr(M, N,
                    self.indptr.astype(idx_dtype),
                    self.indices.astype(idx_dtype),
                    self.data,
                    indptr,
                    indices,
                    data)
  
          from .csr import csr_matrix
          A = csr_matrix((data, indices, indptr), shape=self.shape)
          A.has_sorted_indices = True
          return A
  
      def __getitem__(self, key):
          # Use CSR to implement fancy indexing.
  
          row, col = self._unpack_index(key)
          # Things that return submatrices. row or col is a int or slice.
          if (isinstance(row, slice) or isinstance(col, slice) or
              isintlike(row) or isintlike(col)):
              return self.T[col, row].T
          # Things that return a sequence of values.
          else:
              return self.T[col, row]
  
      def nonzero(self):
          # CSC can't use _cs_matrix's .nonzero method because it
          # returns the indices sorted for self transposed.
  
          # Get row and col indices, from _cs_matrix.tocoo
          major_dim, minor_dim = self._swap(self.shape)
          minor_indices = self.indices
          major_indices = np.empty(len(minor_indices), dtype=self.indptr.dtype)
          sparsetools.expandptr(major_dim, self.indptr, major_indices)
          row, col = self._swap((major_indices, minor_indices))
  
          # Sort them to be in C-style order
          ind = np.lexsort((col, row))
          row = row[ind]
          col = col[ind]
  
          return row, col
  
      nonzero.__doc__ = _cs_matrix.nonzero.__doc__
  
      def getrow(self, i):
          """Returns a copy of row i of the matrix, as a (1 x n)
          CSR matrix (row vector).
          """
          # transpose to use CSR code
          # we convert to CSR to maintain compatibility with old impl.
          # in spmatrix.getrow()
          return self.T.getcol(i).T.tocsr()
  
      def getcol(self, i):
          """Returns a copy of column i of the matrix, as a (m x 1)
          CSC matrix (column vector).
          """
          # transpose to use CSR code
          return self.T.getrow(i).T
  
      # these functions are used by the parent class (_cs_matrix)
      # to remove redudancy between csc_matrix and csr_matrix
      def _swap(self,x):
          """swap the members of x if this is a column-oriented matrix
          """
          return (x[1],x[0])
  
  
  def isspmatrix_csc(x):
      return isinstance(x, csc_matrix)
  
apis: numpy.lexsort scipy.lib.six.xrange numpy.empty