MATLAB示例

目录

1

矩阵基础................................................................................................................................................ 3 1.1

创建矩阵 ................................................................................................................................... 3 1.1.1 1.1.2 1.1.3 1.2 1.3

直接输入法 ................................................................................................................... 3 构造序列 ....................................................................................................................... 3 函数构造法 ................................................................................................................... 3

获取矩阵信息 ........................................................................................................................... 5 矩阵元素的访问 ....................................................................................................................... 5 1.3.1 1.3.2

利用下标访问 ............................................................................................................... 5 利用逻辑矩阵访问 ....................................................................................................... 6 矩阵拼接 ....................................................................................................................... 7 矩阵变形 ....................................................................................................................... 8 矩阵90度旋转 ............................................................................................................. 9 矩阵翻转 ....................................................................................................................... 9 矩阵转置 ......................................................................................................................10 矩阵扩容 ......................................................................................................................10 矩阵收缩 ......................................................................................................................11 矩阵复制 ......................................................................................................................11 元素的和与积 ..............................................................................................................12 平均值和中位数 ..........................................................................................................13 最大最小值 ..................................................................................................................14 累计求和、积 ..............................................................................................................15 矩阵排序 ......................................................................................................................15

1.4 矩阵拼接、变形，改变大小 ................................................................................................... 7 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 1.4.7 1.4.8

1.5 简单数据处理 ..........................................................................................................................12 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5

2 MATLAB运算符 ..................................................................................................................................16 2.1

算术运算符 ..............................................................................................................................16 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.1.7 2.2 2.3

加、减法[M×N]±[M×N]，[M×N]±a ...........................................................................16 数组乘法[M×N].*[M×N]，[M×N].*a ..........................................................................17 数组除法[M×N]./[M×N]，[M×N].\\[M×N]，[M×N]./a，[M×N].\\a .........................17 数组乘方[M×N].^[M×N]，a.^[M×N]，[M×N].^a .....................................................18 矩阵乘法[M×N]*[N×M]，[M×N]*a ............................................................................18 矩阵乘方[M×M]^a ......................................................................................................19 线性方程求解[M×N]\\[M×1]，[1×M]/[N×M] ...........................................................19

关系运算符 ..............................................................................................................................20 逻辑运算符 ..............................................................................................................................20 多项式计算 ..............................................................................................................................21 3.1.1

多项式的根与系数 ......................................................................................................21

3 MATLAB 数值计算 ..............................................................................................................................21 3.1

3.1.2 3.1.3 3.1.4 3.1.5 3.2 3.3

多项式求值 ..................................................................................................................21 多项式导数 ..................................................................................................................21 多项式乘法和除法 ......................................................................................................22 部分分式分解 ..............................................................................................................22

数值积分 ..................................................................................................................................23 代数方程数值解 ......................................................................................................................24 3.3.1 3.3.2

一元非线性方程 ..........................................................................................................24 多元非线性方程及方程组 ..........................................................................................24

1 矩阵基础

1.1 创建矩阵

1.1.1 直接输入法

x = [1 2 3]

y = [1 2 3;4 5 6] x =

1 2 3 y =

1 2 3 4 5 6

1.1.2 构造序列

A = 0:0.1:1

B = linspace(0,1,10) A =

Columns 1 through 6

0 0.1000 0.2000 0.3000 0.4000 0.5000 Columns 7 through 11

0.6000 0.7000 0.8000 0.9000 1.0000 B =

Columns 1 through 6

0 0.1111 0.2222 0.3333 0.4444 0.5556 Columns 7 through 10

0.6667 0.7778 0.8889 1.0000

1.1.3 函数构造法

x = eye(3), y = eye(2,4) %单位矩阵

x =

1 0 0 0 1 0 0 0 1 y =

1 0 0 0 0 1 0 0

x = rand(3), y = rand(2,4) %随机矩阵 x =

0.9157 0.6557 0.9340 0.7922 0.0357 0.6787 0.9595 0.8491 0.7577 y =

0.7431 0.6555 0.7060 0.2769 0.3922 0.1712 0.0318 0.0462

x = zeros(3), y = zeros(2,4) %全0矩阵 x =

0 0 0 0 0 0 0 0 0 y =

0 0 0 0 0 0 0 0

x = ones(3), y = ones(2,4) %全1矩阵 x =

1 1 1 1 1 1 1 1 1 y =

1 1 1 1 1 1 1 1

x = [1 3 5 6 8] A = diag(x)%对角矩阵 x =

1 3 5 6 8 A =

1 0 0 0 0

0 3 0 0 0 0 0 5 0 0 0 0 0 6 0 0 0 0 0 8

1.2 获取矩阵信息

x = 1:10; A = ones(4);

L = length(x)%获取向量长度 [m,n] = size(A)%获取矩阵各维大小 N = numel(A)%获取矩阵元素个数 L = 10 m = 4 n = 4 N = 16

1.3 矩阵元素的访问

1.3.1 利用下标访问

A = [1:4;5:8;9:12;13:16] x = A(3,2)%单个元素访问方式1 y = A(7)%单个元素访问方式2 A =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 x = 10 y = 10