Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.8/site-packages/scipy/sparse/linalg/_dsolve/_add_newdocs.py: 100%

1from numpy.lib import add_newdoc 

2 

3add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', 

4 """ 

5 LU factorization of a sparse matrix. 

6 

7 Factorization is represented as:: 

8 

9 Pr @ A @ Pc = L @ U 

10 

11 To construct these `SuperLU` objects, call the `splu` and `spilu` 

12 functions. 

13 

14 Attributes 

15 ---------- 

16 shape 

17 nnz 

18 perm_c 

19 perm_r 

20 L 

21 U 

22 

23 Methods 

24 ------- 

25 solve 

26 

27 Notes 

28 ----- 

29 

30 .. versionadded:: 0.14.0 

31 

32 Examples 

33 -------- 

34 The LU decomposition can be used to solve matrix equations. Consider: 

35 

36 >>> import numpy as np 

37 >>> from scipy.sparse import csc_matrix, linalg as sla 

38 >>> A = csc_matrix([[1,2,0,4],[1,0,0,1],[1,0,2,1],[2,2,1,0.]]) 

39 

40 This can be solved for a given right-hand side: 

41 

42 >>> lu = sla.splu(A) 

43 >>> b = np.array([1, 2, 3, 4]) 

44 >>> x = lu.solve(b) 

45 >>> A.dot(x) 

46 array([ 1., 2., 3., 4.]) 

47 

48 The ``lu`` object also contains an explicit representation of the 

49 decomposition. The permutations are represented as mappings of 

50 indices: 

51 

52 >>> lu.perm_r 

53 array([0, 2, 1, 3], dtype=int32) 

54 >>> lu.perm_c 

55 array([2, 0, 1, 3], dtype=int32) 

56 

57 The L and U factors are sparse matrices in CSC format: 

58 

59 >>> lu.L.A 

60 array([[ 1. , 0. , 0. , 0. ], 

61 [ 0. , 1. , 0. , 0. ], 

62 [ 0. , 0. , 1. , 0. ], 

63 [ 1. , 0.5, 0.5, 1. ]]) 

64 >>> lu.U.A 

65 array([[ 2., 0., 1., 4.], 

66 [ 0., 2., 1., 1.], 

67 [ 0., 0., 1., 1.], 

68 [ 0., 0., 0., -5.]]) 

69 

70 The permutation matrices can be constructed: 

71 

72 >>> Pr = csc_matrix((np.ones(4), (lu.perm_r, np.arange(4)))) 

73 >>> Pc = csc_matrix((np.ones(4), (np.arange(4), lu.perm_c))) 

74 

75 We can reassemble the original matrix: 

76 

77 >>> (Pr.T @ (lu.L @ lu.U) @ Pc.T).A 

78 array([[ 1., 2., 0., 4.], 

79 [ 1., 0., 0., 1.], 

80 [ 1., 0., 2., 1.], 

81 [ 2., 2., 1., 0.]]) 

82 """) 

83 

84add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('solve', 

85 """ 

86 solve(rhs[, trans]) 

87 

88 Solves linear system of equations with one or several right-hand sides. 

89 

90 Parameters 

91 ---------- 

92 rhs : ndarray, shape (n,) or (n, k) 

93 Right hand side(s) of equation 

94 trans : {'N', 'T', 'H'}, optional 

95 Type of system to solve:: 

96 

97 'N': A @ x == rhs (default) 

98 'T': A^T @ x == rhs 

99 'H': A^H @ x == rhs 

100 

101 i.e., normal, transposed, and hermitian conjugate. 

102 

103 Returns 

104 ------- 

105 x : ndarray, shape ``rhs.shape`` 

106 Solution vector(s) 

107 """)) 

108 

109add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('L', 

110 """ 

111 Lower triangular factor with unit diagonal as a 

112 `scipy.sparse.csc_matrix`. 

113 

114 .. versionadded:: 0.14.0 

115 """)) 

116 

117add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('U', 

118 """ 

119 Upper triangular factor as a `scipy.sparse.csc_matrix`. 

120 

121 .. versionadded:: 0.14.0 

122 """)) 

123 

124add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('shape', 

125 """ 

126 Shape of the original matrix as a tuple of ints. 

127 """)) 

128 

129add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('nnz', 

130 """ 

131 Number of nonzero elements in the matrix. 

132 """)) 

133 

134add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('perm_c', 

135 """ 

136 Permutation Pc represented as an array of indices. 

137 

138 The column permutation matrix can be reconstructed via: 

139 

140 >>> Pc = np.zeros((n, n)) 

141 >>> Pc[np.arange(n), perm_c] = 1 

142 """)) 

143 

144add_newdoc('scipy.sparse.linalg._dsolve._superlu', 'SuperLU', ('perm_r', 

145 """ 

146 Permutation Pr represented as an array of indices. 

147 

148 The row permutation matrix can be reconstructed via: 

149 

150 >>> Pr = np.zeros((n, n)) 

151 >>> Pr[perm_r, np.arange(n)] = 1 

152 """))