Matlab学习记录06

书籍：Matlab实用教程

工具：Matlab2021a

电脑信息：Intel® Xeon® CPU E5-2603 v3 @ 1.60GHz

系统类型：64位操作系统，基于X64的处理器 windows10 专业版

第2章 MATLAB数值计算

2.5 元胞数组和结构数组

2.5.1 元胞数组

1、元胞数组的创建

复制代码

A={'This is the first cell.',[1 2;3 4],eye(3),{'Tom','Jane'}}
A =
{
  [1,1] = This is the first cell.
  [1,2] =

     1   2
     3   4

  [1,3] =

Diagonal Matrix

     1   0   0
     0   1   0
     0   0   1

  [1,4] =
  {
    [1,1] = Tom
    [1,2] = Jane
  }

}
B{1,1}={'This is the second cell.'};
B{1,2}={5+3*i};
B{1,3}={[1 2;3 4;5 6]}
B =
{
  [1,1] =
  {
    [1,1] = This is the second cell.
  }

  [1,2] =
  {
    [1,1] =  5 + 3i
  }

  [1,3] =
  {
    [1,1] =

       1   2
       3   4
       5   6

  }

}

2、元胞数组的内容显示

复制代码

B{1,1}={'This is the second cell.'};
B{1,2}={5+3*i};
B{1,3}={[1 2;3 4;5 6]};
celldisp(B)
B
B{1}{1} = 

This is the second cell.

B{2}{1} = 

 5 + 3i

B{3}{1} = 

   1   2
   3   4
   5   6

B =
{
  [1,1] =
  {
    [1,1] = This is the second cell.
  }

  [1,2] =
  {
    [1,1] =  5 + 3i
  }

  [1,3] =
  {
    [1,1] =

       1   2
       3   4
       5   6

  }

}
B{1,1}={'This is the second cell.'};
B{1,2}={5+3*i};
B{1,3}={[1 2;3 4;5 6]};
cellplot(B)

3、元胞数组的内容获取

复制代码

B{1,1}={'This is the second cell.'};
B{1,2}={5+3*i};
B{1,3}={[1 2;3 4;5 6]};
x1=B{1,2}
x2=B{1,3}
[x3,x4,x5]=deal(B{[1 2 3]})
x1 =
{
  [1,1] =  5 + 3i
}

x2 =
{
  [1,1] =

     1   2
     3   4
     5   6

}

x3 =
{
  [1,1] = This is the second cell.
}

x4 =
{
  [1,1] =  5 + 3i
}

x5 =
{
  [1,1] =

     1   2
     3   4
     5   6

}

2.5.2 结构数组

1、结构数组的创建

复制代码

ps(1).name='curve1'
ps(1).color='red'
ps(1).position=[0,0,300,300]
ps =

  scalar structure containing the fields:

    name = curve1

ps =

  scalar structure containing the fields:

    name = curve1
    color = red

ps =

  scalar structure containing the fields:

    name = curve1
    color = red
    position =

         0     0   300   300
ps(2)=struct('name','curve2','color','blue','position',[100,100,300,300])
ps =

  1x2 struct array containing the fields:

    name
    color
    position

2、结构数组数据的获取和设置

复制代码

ps(2)=struct('name','curve2','color','blue','position',[100,100,300,300])
x1=ps(2)
x2=ps(2).position
x3=ps(2).position(1,3)
x4=getfield(ps,{2},'color')
x5=getfield(ps,{2},'color',{1})
ps=setfield(ps,{2},'color','green');
ps(2)
ps =

  1x2 struct array containing the fields:

    name
    color
    position

x1 =

  scalar structure containing the fields:

    name = curve2
    color = blue
    position =

       100   100   300   300


x2 =

   100   100   300   300

x3 = 300
x4 = blue
x5 = b
ans =

  scalar structure containing the fields:

    name = curve2
    color = green
    position =

       100   100   300   300

3、结构数组域的获取

复制代码

ps(1)=struct('name','curve1','color','red','position',[0,0,300,300])
ps(2)=struct('name','curve2','color','blue','position',[100,100,300,300])
x6=fieldnames(ps)
all_x=[ps.name]
cat(1,ps.position)
cat(2,ps.position)
cat(3,ps.position)
ps =

  scalar structure containing the fields:

    name = curve1
    color = red
    position =

         0     0   300   300


ps =

  1x2 struct array containing the fields:

    name
    color
    position

x6 =
{
  [1,1] = name
  [2,1] = color
  [3,1] = position
}

all_x = curve1curve2
ans =

     0     0   300   300
   100   100   300   300

ans =

     0     0   300   300   100   100   300   300

ans =

ans(:,:,1) =

     0     0   300   300

ans(:,:,2) =

   100   100   300   300

2.6 数据分析

2.6.1 数据统计和相关分析

复制代码

X=[5.30 13.00 0.40;5.10 11.80 -1.70;3.70 8.10 0.60;1.50 7.70 -4.50]
max(X)
min(X)
mean(X)
std(X)
median(X)
var(X)
C=cov(X)
S=corrcoef(X)
[S,k]=sort(X,1)
X =

    5.3000   13.0000    0.4000
    5.1000   11.8000   -1.7000
    3.7000    8.1000    0.6000
    1.5000    7.7000   -4.5000

ans =

    5.3000   13.0000    0.6000

ans =

   1.5000   7.7000  -4.5000

ans =

    3.9000   10.1500   -1.3000

ans =

   1.7512   2.6489   2.3735

ans =

   4.4000   9.9500  -0.6500

ans =

   3.0667   7.0167   5.6333

C =

   3.0667   4.0867   3.0667
   4.0867   7.0167   2.7100
   3.0667   2.7100   5.6333

S =

   1.0000   0.8810   0.7378
   0.8810   1.0000   0.4310
   0.7378   0.4310   1.0000

S =

    1.5000    7.7000   -4.5000
    3.7000    8.1000   -1.7000
    5.1000   11.8000    0.4000
    5.3000   13.0000    0.6000

k =

   4   4   4
   3   3   2
   2   2   1
   1   1   3

2.6.2 差分和积分

复制代码

A=[5.30 13.00 0.40;5.10 11.80 -1.70;3.70 8.10 0.60;1.50 7.70 -4.50]
diff(A,1,1)
gradient(A)
sum(A)
cumsum(A,2)
cumprod(A,2)
trapz(A)
cumtrapz(A)
A =

    5.3000   13.0000    0.4000
    5.1000   11.8000   -1.7000
    3.7000    8.1000    0.6000
    1.5000    7.7000   -4.5000

ans =

  -0.2000  -1.2000  -2.1000
  -1.4000  -3.7000   2.3000
  -2.2000  -0.4000  -5.1000

ans =

    7.7000   -2.4500  -12.6000
    6.7000   -3.4000  -13.5000
    4.4000   -1.5500   -7.5000
    6.2000   -3.0000  -12.2000

ans =

   15.6000   40.6000   -5.2000

ans =

    5.3000   18.3000   18.7000
    5.1000   16.9000   15.2000
    3.7000   11.8000   12.4000
    1.5000    9.2000    4.7000

ans =

     5.3000    68.9000    27.5600
     5.1000    60.1800  -102.3060
     3.7000    29.9700    17.9820
     1.5000    11.5500   -51.9750

ans =

   12.2000   30.2500   -3.1500

ans =

         0         0         0
    5.2000   12.4000   -0.6500
    9.6000   22.3500   -1.2000
   12.2000   30.2500   -3.1500

t=0:0.5:10;
y=exp(-0.2).*sin(t)
d=[0 diff(y)]
s1=0.5*cumsum(y)
s2=cumtrapz(t,y)

y =

 Columns 1 through 8:

        0   0.3925   0.6889   0.8167   0.7445   0.4900   0.1155  -0.2872

 Columns 9 through 16:

  -0.6196  -0.8003  -0.7851  -0.5776  -0.2288   0.1761   0.5379   0.7680

 Columns 17 through 21:

   0.8100   0.6537   0.3374  -0.0615  -0.4454

d =

 Columns 1 through 8:

        0   0.3925   0.2964   0.1277  -0.0722  -0.2545  -0.3744  -0.4027

 Columns 9 through 16:

  -0.3324  -0.1807   0.0152   0.2075   0.3489   0.4049   0.3618   0.2301

 Columns 17 through 21:

   0.0420  -0.1563  -0.3163  -0.3989  -0.3839

s1 =

 Columns 1 through 8:

        0   0.1963   0.5407   0.9491   1.3213   1.5663   1.6241   1.4805

 Columns 9 through 16:

   1.1707   0.7705   0.3779   0.0891  -0.0253   0.0628   0.3317   0.7157

 Columns 17 through 21:

   1.1207   1.4476   1.6163   1.5856   1.3629

s2 =

 Columns 1 through 8:

        0   0.0981   0.3685   0.7449   1.1352   1.4438   1.5952   1.5523

 Columns 9 through 16:

   1.3256   0.9706   0.5742   0.2335   0.0319   0.0188   0.1973   0.5237

 Columns 17 through 21:

   0.9182   1.2842   1.5320   1.6009   1.4742

2.6.3 卷积和快速傅里叶变换

复制代码

A=ones(1,10);
A(1)=0
B=ones(1,9);
B([1 2 3])=0
C=conv(A,B)
N=32;
AF=fft(A,N)
BF=fft(B,N)
CF=AF.*BF
CC=real(ifft(CF))

A =

   0   1   1   1   1   1   1   1   1   1

B =

   0   0   0   1   1   1   1   1   1

C =

   0   0   0   0   1   2   3   4   5   6   6   6   6   5   4   3   2   1

AF =

 Columns 1 through 4:

   9.0000 +      0i   4.3815 - 6.5574i  -1.9239 - 4.6447i  -1.5927 - 0.3168i

 Columns 5 through 8:

   0.7071 - 0.7071i  -0.3960 - 1.9910i  -1.3827 - 0.5727i  -0.1285 + 0.0858i

 Columns 9 through 12:

        0 - 1.0000i  -1.0704 - 0.7152i  -0.6173 + 0.2557i   0.0642 - 0.3228i

 Columns 13 through 16:

  -0.7071 - 0.7071i  -0.9039 + 0.1798i  -0.0761 + 0.1838i  -0.3542 - 0.5300i

 Columns 17 through 20:

  -1.0000 +      0i  -0.3542 + 0.5300i  -0.0761 - 0.1838i  -0.9039 - 0.1798i

 Columns 21 through 24:

  -0.7071 + 0.7071i   0.0642 + 0.3228i  -0.6173 - 0.2557i  -1.0704 + 0.7152i

 Columns 25 through 28:

        0 + 1.0000i  -0.1285 - 0.0858i  -1.3827 + 0.5727i  -0.3960 + 1.9910i

 Columns 29 through 32:

   0.7071 + 0.7071i  -1.5927 + 0.3168i  -1.9239 + 4.6447i   4.3815 + 6.5574i

BF =

 Columns 1 through 4:

   6.0000 +      0i   2.6719 - 4.9988i  -2.6310 - 3.9375i  -3.3624 + 0.3312i

 Columns 5 through 8:

  -0.7071 + 1.7071i   0.2625 + 0.3199i  -0.6756 + 0.1344i  -0.3805 + 1.2542i

 Columns 9 through 12:

   1.0000 + 1.0000i   1.0293 - 0.3122i   0.0898 - 0.4514i   0.1710 + 0.1403i

 Columns 13 through 16:

   0.7071 - 0.2929i   0.1005 - 1.0200i  -0.7832 - 0.5233i  -0.4923 + 0.2632i

 Columns 17 through 20:

        0 +      0i  -0.4923 - 0.2632i  -0.7832 + 0.5233i   0.1005 + 1.0200i

 Columns 21 through 24:

   0.7071 + 0.2929i   0.1710 - 0.1403i   0.0898 + 0.4514i   1.0293 + 0.3122i

 Columns 25 through 28:

   1.0000 - 1.0000i  -0.3805 - 1.2542i  -0.6756 - 0.1344i   0.2625 - 0.3199i

 Columns 29 through 32:

  -0.7071 - 1.7071i  -3.3624 - 0.3312i  -2.6310 + 3.9375i   2.6719 + 4.9988i

CF =

 Columns 1 through 3:

   54.0000 +       0i  -21.0721 - 39.4230i  -13.2269 + 19.7954i

 Columns 4 through 6:

    5.4603 +  0.5378i    0.7071 +  1.7071i    0.5330 -  0.6494i

 Columns 7 through 9:

    1.0111 +  0.2011i   -0.0588 -  0.1938i    1.0000 -  1.0000i

 Columns 10 through 12:

   -1.3251 -  0.4020i    0.0600 +  0.3016i    0.0563 -  0.0462i

 Columns 13 through 15:

   -0.7071 -  0.2929i    0.0926 +  0.9400i    0.1558 -  0.1041i

 Columns 16 through 18:

    0.3138 +  0.1678i         0 +       0i    0.3138 -  0.1678i

 Columns 19 through 21:

    0.1558 +  0.1041i    0.0926 -  0.9400i   -0.7071 +  0.2929i

 Columns 22 through 24:

    0.0563 +  0.0462i    0.0600 -  0.3016i   -1.3251 +  0.4020i

 Columns 25 through 27:

    1.0000 +  1.0000i   -0.0588 +  0.1938i    1.0111 -  0.2011i

 Columns 28 through 30:

    0.5330 +  0.6494i    0.7071 -  1.7071i    5.4603 -  0.5378i

 Columns 31 and 32:

  -13.2269 - 19.7954i  -21.0721 + 39.4230i

CC =

 Columns 1 through 8:

   0.0000   0.0000   0.0000   0.0000   1.0000   2.0000   3.0000   4.0000

 Columns 9 through 16:

   5.0000   6.0000   6.0000   6.0000   6.0000   5.0000   4.0000   3.0000

 Columns 17 through 24:

   2.0000   1.0000   0.0000   0.0000   0.0000        0   0.0000   0.0000

 Columns 25 through 32:

  -0.0000   0.0000   0.0000   0.0000  -0.0000   0.0000   0.0000   0.0000

2.6.4 向量函数

复制代码

a=[1 2 3];
b=[4 5 6];
c=cross(a,b)
d=dot(a,b)

c =

  -3   6  -3

d = 32