矩阵的存储方式

稀疏存储方式的产生

>> A = sparse(eye(5))
A =
   (1,1)        1
   (2,2)        1
   (3,3)        1
   (4,4)        1
   (5,5)        1
>> B = full(A)
B =
     1     0     0     0     0
     0     1     0     0     0
     0     0     1     0     0
     0     0     0     1     0
     0     0     0     0     1
>> whos
  Name      Size            Bytes  Class     Attributes
  A         5x5               128  double    sparse    
  B         5x5               200  double

• 注意存储的字节大小

>> A = sparse([1,2,2],[2,1,4],[4,5,-7])
A =
   (2,1)        5
   (1,2)        4
   (2,4)       -7
>> B = full(A)
B =
     0     4     0     0
     5     0     0    -7

>> A = [2,2,1;2,1,-1;2,4,3]
A =
     2     2     1
     2     1    -1
     2     4     3
>> B = spconvert(A)
B =
   (2,1)       -1
   (2,2)        1
   (2,4)        3

稀疏矩阵应用举例

>> kf1 = [1;1;2;1;0];
>> k0 = [2;4;6;6;1];
>> k1 = [0;3;1;4;2];
>> B = [kf1, k0, k1];
>> d = [-1; 0; 1];
>> A = spdiags(B, d, 5, 5);
>> f = [0;3;2;1;5];
>> x = A\f
x =
   -0.1667
    0.1111
    2.7222
   -3.6111
    8.6111