Ë ßÌPh2ãó°—ddlmZeddd«eddd«eddd«eddd«eddd«eddd «eddd «eddd «y ) é)Ú add_newdocz$scipy.sparse.linalg._dsolve._superluÚSuperLUa¦ LU factorization of a sparse matrix. Factorization is represented as:: Pr @ A @ Pc = L @ U To construct these `SuperLU` objects, call the `splu` and `spilu` functions. Attributes ---------- shape nnz perm_c perm_r L U Methods ------- solve Notes ----- .. versionadded:: 0.14.0 Examples -------- The LU decomposition can be used to solve matrix equations. Consider: >>> import numpy as np >>> from scipy.sparse import csc_array >>> from scipy.sparse.linalg import splu >>> A = csc_array([[1,2,0,4], [1,0,0,1], [1,0,2,1], [2,2,1,0.]]) This can be solved for a given right-hand side: >>> lu = splu(A) >>> b = np.array([1, 2, 3, 4]) >>> x = lu.solve(b) >>> A.dot(x) array([ 1., 2., 3., 4.]) The ``lu`` object also contains an explicit representation of the decomposition. The permutations are represented as mappings of indices: >>> lu.perm_r array([2, 1, 3, 0], dtype=int32) # may vary >>> lu.perm_c array([0, 1, 3, 2], dtype=int32) # may vary The L and U factors are sparse matrices in CSC format: >>> lu.L.toarray() array([[ 1. , 0. , 0. , 0. ], # may vary [ 0.5, 1. , 0. , 0. ], [ 0.5, -1. , 1. , 0. ], [ 0.5, 1. , 0. , 1. ]]) >>> lu.U.toarray() array([[ 2. , 2. , 0. , 1. ], # may vary [ 0. , -1. , 1. , -0.5], [ 0. , 0. , 5. , -1. ], [ 0. , 0. , 0. , 2. ]]) The permutation matrices can be constructed: >>> Pr = csc_array((np.ones(4), (lu.perm_r, np.arange(4)))) >>> Pc = csc_array((np.ones(4), (np.arange(4), lu.perm_c))) We can reassemble the original matrix: >>> (Pr.T @ (lu.L @ lu.U) @ Pc.T).toarray() array([[ 1., 2., 0., 4.], [ 1., 0., 0., 1.], [ 1., 0., 2., 1.], [ 2., 2., 1., 0.]]) )Úsolvea' solve(rhs[, trans]) Solves linear system of equations with one or several right-hand sides. Parameters ---------- rhs : ndarray, shape (n,) or (n, k) Right hand side(s) of equation trans : {'N', 'T', 'H'}, optional Type of system to solve:: 'N': A @ x == rhs (default) 'T': A^T @ x == rhs 'H': A^H @ x == rhs i.e., normal, transposed, and hermitian conjugate. Returns ------- x : ndarray, shape ``rhs.shape`` Solution vector(s) )ÚLzu Lower triangular factor with unit diagonal as a `scipy.sparse.csc_array`. .. versionadded:: 0.14.0 )ÚUz^ Upper triangular factor as a `scipy.sparse.csc_array`. .. versionadded:: 0.14.0 )Úshapez: Shape of the original matrix as a tuple of ints. )Únnzz3 Number of nonzero elements in the matrix. )Úperm_czj Permutation Pc represented as an array of indices. See the `SuperLU` docstring for details. )Úperm_rzj Permutation Pr represented as an array of indices. See the `SuperLU` docstring for details. N)Ú numpy.libr©óúsC:\Users\daisl\Desktop\realtime-object-detection\venv\Lib\site-packages\scipy/sparse/linalg/_dsolve/_add_newdocs.pyÚrs©ðÝ á Ð 1°9ðOôP ñd Ð 1°9ð? ô ñ2 Ð 1°9ð? ô ñ Ð 1°9ð? ô ñ Ð 1°9ð? ô ñ  Ð 1°9ð? ô ñ  Ð 1°9ð? ô ñ Ð 1°9ð? õ r