MATLAB笔记1: Array Operation
变量
- ans 变量
sin(cos(pi))
等于
cos(pi)
sin(ans)
- 其他变量
- i,j: complex number
- Inf: ∞
- eps: 2.2204e-016
- NaN: not a number
- pi: π
x = 1/0 # 结果为 Inf
x = log(0) # 结果为 -Inf
x = inf/inf # 结果为 NaN
数组
- Array (Vector and Matrix) 向量和矩阵
Row Vector 行向量:
a = [1 2 3 4]
Column Vector 列向量:
a = [1; 2; 3; 4]
数组操作
- Array Indexing 索引
>> A = [1 21 6;5 17 9; 31 2 7]
A =
1 21 6
5 17 9
31 2 7
索引：
>> A(8) # 列优先
ans =
9
>> A([1 3 5])
ans =
1 31 17
>> A([1 3;1 3])
ans =
1 31
1 31
>> A(3,2)
ans =
2
>> A([1 3],[1 3]) # 第1,3行和第1,3列交叉的部分
ans =
1 6
31 7
- Colon Operator 冒号操作
>> B = 1:5
B =
1 2 3 4 5
>> B = 1:2:5
B =
1 3 5
>> B = [1:5;2:3:15;-2:0.5:0]
B =
1.0000 2.0000 3.0000 4.0000 5.0000
2.0000 5.0000 8.0000 11.0000 14.0000
-2.0000 -1.5000 -1.0000 -0.5000 0
>> str = 'a':2:'z'
str =
'acegikmoqsuwy'
- Indexing Using Colon Operator
>> A = [1 0 0; 5 0 0; 31 0 7]
A =
1 0 0
5 0 0
31 0 7
>> A(3,:)
ans =
31 0 7
>> A(3,:) = []
A =
1 0 0
5 0 0
- Array Manipulation 数组操作
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>> x1 = A+a
x1 =
3 4 5
6 7 6
11 10 9
>> x2 = A/a
x2 =
0.5000 1.0000 1.5000
2.0000 2.5000 2.0000
4.5000 4.0000 3.5000
>> x3 = A./a # 和上面结果一致
x3 =
0.5000 1.0000 1.5000
2.0000 2.5000 2.0000
4.5000 4.0000 3.5000
>> x4 = A^a # 即 A*A
x4 =
36 36 32
60 65 60
104 114 108
>> x5 = A.^a
x5 =
1 4 9
16 25 16
81 64 49
>> C = A'
C =
1 4 9
2 5 8
3 4 7
右边那五个操作为矩阵操作，点乘为每个对应元素去做操作，除法为A/B = A*inv(B),即B的逆矩阵，详细参考矩阵操作
- Array Concatenation 矩阵连接
>> D = [A B]
D =
1 2 3 3 3 3
4 5 4 2 4 9
9 8 7 1 3 1
>> E = [A;B]
E =
1 2 3
4 5 4
9 8 7
3 3 3
2 4 9
1 3 1
特殊矩阵
- linspace(a,b,c)
- eye(n): nxn identity matrix：单位矩阵
- zeros(n1,n2): n1xn2 zero matrix：零矩阵
- ones(n1,n2): n1xn2 matrix with every entry as 1
- diag(): diagonal matrix 对角矩阵
>> c = diag([2 3 4])
c =
2 0 0
0 3 0
0 0 4
>> d = linspace(0,13,6)
d =
0 2.6000 5.2000 7.8000 10.4000 13.0000
矩阵 function
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方法大多是对列column去做操作
>> A = [1 2 3;0 5 6;7 0 9]
A =
1 2 3
0 5 6
7 0 9
>> max(A) # 对每一列去求max，以下同理
ans =
7 5 9
>> max(max(A)) # 求一个矩阵最大值的方法
ans =
9
>> min(A)
ans =
0 0 3
>> sum(A)
ans =
8 7 18
>> mean(A)
ans =
2.6667 2.3333 6.0000
>> sort(A)
ans =
0 0 3
1 2 6
7 5 9
>> sortrows(A)
ans =
0 5 6
1 2 3
7 0 9
>> size(A)
ans =
3 3
>> length(A)
ans =
3
>> find(A==0)
ans =
2
6
>> find(A==2)
ans =
4
sort 和 sortrows区别是，sort对每一列进行排序，sortrows对第一列排序且 整行调换顺序
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