matlab入门一基本操作
//学习笔记，侵删，参考书西安电子科技大学出版社程序设计，学长传下来的书
一、矩阵的几种处理
1.生成矩阵与基本处理
中矩阵元素按列存储，可以仅用一个下标寻址，如下例中对于矩阵a，a(2)=4,a(6)=8;
若要对复数矩阵com做转置，com' 表示共轭转置，若要实现非共轭转置，用com.'
triu(),tril()分别是对矩阵（未必是方阵）进行取上三角，下三角矩阵。
clc;close all;
a=[1 2 3;4 5 6;7 8 9];%3*3 matrix
b=[6 2 4];
c = diag(a)%without ";" in the end means show the output on command window
d = diag(b)%diag()to extract the diagonal or generate diagonal matrix
e = diag(b,1)%generate 4*4 matrix,and the identity matrix in the upper right corner
f = diag(b,-1)%generate 4*4 matrix,and the identity matrix in the lower left corner
g = fliplr(a)%flip left and right
h = flipud(a)%flip up and downa11 = eye(5)%generate 5*5 identity matrix
a12 = eye(3,4)%generate 3*4 matrix with the identity matrix in the left
a13 = zeros(2,5)%generate 2*5 all zero matrix
a14 = ones(3,2)%generate 3*2 all one matrix%运行结果如下
c =159d =6 0 00 2 00 0 4e =0 6 0 00 0 2 00 0 0 40 0 0 0f =0 0 0 06 0 0 00 2 0 00 0 4 0g =3 2 16 5 49 8 7h =7 8 94 5 61 2 3a11 =1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1a12 =1 0 0 00 1 0 00 0 1 0a13 =0 0 0 0 00 0 0 0 0a14 =1 11 11 12.矩阵处理进阶
2.1矩阵扩大
clc;close all;
a=[1 2;3 4];
b=[a a+2;a-2 zeros(size(a))]%size(a)=[2 2],generate 4*4 matrix by matrix a
c=[a;5 10]%increase one row below a
d=[a [5;10]]%increase one column on the right of a
e=[[5;10] a]%increase one column on the left of aa1=[5 6;7 8];
f=cat(1,a,a1)%link by first dimension (to the row)
g=cat(2,a,a1)%link by second dimension
h=cat(3,a,a1)%link by third dimensioni=repmat(a,2,3)%generate 2*3 matrix which is formed by repeat matrix a%结果如下
b =1 2 3 43 4 5 6-1 0 0 01 2 0 0c =1 23 45 10d =1 2 53 4 10e =5 1 210 3 4f =1 23 45 67 8g =1 2 5 63 4 7 8h(:,:,1) =1 23 4h(:,:,2) =5 67 8i =1 2 1 2 1 23 4 3 4 3 41 2 1 2 1 23 4 3 4 3 4
2.2矩阵缩小
clc;close all;
a=[1:4;5:8;9:12;13:16]
%extraction
b=a(2:3,3:4)%to extract row:2 to 3,column:3 to 4
c=a([2 4],[1 3])%to extract row:2 and 4,column:1 and 3
%delete
a(2,:)=[]%to delete the second row
a(:,[1 3])=[]%to delete the first and the third column%运行结果如下
a =1 2 3 45 6 7 89 10 11 1213 14 15 16b =7 811 12c =5 713 15a =1 2 3 49 10 11 1213 14 15 16a =2 410 1214 16
2.3逻辑函数
(a):如果a是一个向量，若其中所有元素都是非零，返回1，若有一个元素为零，返回0；如果a是一个矩阵，则返回一个行向量，用于检测每一列是否全为非零元素，如果某一列有一个值为零，则返回0，若某一列全为非零，才返回1.
fun2 any():规则与all类似，有非零返回1，全零才返回0.
2.4基本运算
左右除与矩阵的逆
inv(A):对矩阵A求逆，且A必须为方阵。如果A是非奇异方阵，则B/A = B*inv(A)，A\B = inv(A)*B。/表示右除，\表示左除。
2.5特殊形式矩阵生成
线性间距向量
y=(a,b)可在a和b之间等间隔产生100个点，y=(a,b,n)则生成n个点。ps：含端点。
对数间距向量
y=(a,b,n)默认是50个，从
到
。(a,pi)表示在
和pi之间生成这些点，这在DSP领域很有用。
二、随机数生成函数
clc;close all;
%Generate a 2*3 matrix in which the elements
%are uniformly distributed on [0,1]
a=rand(2,3)%Generate a 3*2 matrix in which the elements
%are uniformly distributed on [-5,5]
b=10*rand(3,2)-5%Generate a 3*5 matrix in which the elements
%follow a standard normal distribution
c=randn(3,5)%Generate a 2*3 matrix in which the elements
%follow a normal distribution N(3,4)
d=2*randn(2,3)+3%generate 2*5 integer matrix in which the elements
%are uniformly distributed on [10,50]
e=randi([10 50],2,5)%generate a random complex number in which the real part
%and the imaginary part are uniformly distributed on (0,1)
f=rand+1i*rand%运行结果如下
a =0.0423 0.1892 0.58640.9730 0.6671 0.6751b =-1.3898 -4.80741.2028 -4.16133.1115 4.7480c =0.3998 -1.4969 -0.7258 -0.9427 1.8179-0.6548 -0.9048 -0.8665 1.3419 -0.3744-0.2963 -0.4042 -0.4218 -0.9884 -1.4517d =1.7626 5.1119 3.57484.8690 3.3205 4.2658e =12 11 39 45 1222 18 39 33 47f =0.8004 + 0.2859i三、常用几个取整函数区别
fix向零方向取整，floor向负无穷方向取整，ceil向正无穷方向取整，round进行四舍五入。
四、取余函数
mod(X,Y) 返回值为X-Y.*floor(X./Y)
rem(X,Y) 返回值为X-Y.*fix(X./Y)
