读取cc.matlab建立mex,matlab第二天学习笔记

落日映苍穹つ 2023-01-16 02:44 127阅读 0赞

A=magic(3)，3\*3魔方矩阵，

A =

8     1     6

3     5     7

4     9     2

sum(A),求和，

ans =

15    15    15

sum(A)'转置

ans =

sum(diag(A))主对角线求和

sum(diag(flipud(A)))反对角线求和

det(A)求解行列式

X= inv (A)求A的逆矩阵

format short

>> X               用有理分数表示X

r = norm(A)     矩阵范数

r =

>> e = eig(A)  特征值

e =

15.0000

4.8990

\-4.8990

>> s=svd(A)    奇异值

s =

15.0000

6.9282

3.4641

A=sym(A)     使A转变为符号表达形式

A =

\[ 8, 1, 6\]

\[ 3, 5, 7\]

\[ 4, 9, 2\]

inv(A)   矩阵的逆

ans =

\[  53/360, -13/90,  23/360\]

\[ -11/180,   1/45,  19/180\]

load detail

image(X)

>> colormap(map)

>> axis image

>> A=magic(4)

![280db80020904172dbd48c8b4697b0ef.png][]

>> A=magic(4)

A =

16     2     3    13

5    11    10     8

9     7     6    12

4    14    15     1

A = A(:,\[1 3 2 4\])    将第2列和第3列对换

A =

16     3     2    13

5    10    11     8

9     6     7    12

4    15    14     1

for n = 1:24,r(n) = rank(magic(n));end

>> \[(1:24)'r'\]

bar(r)

>> title('Rank of magic squares')

![ada07fc5ce3307d8c57b76d69fcf080b.png][]

>> edit magic.m

>> for n = 8:11

subplot(2,2,n-7)

surf(magic(n))

title(num2str(n))

axis off

view(30,45)

axis tight

end

![d0ecbf72f836a2348bfabefb491033c8.png][]

一下保存在m文件中

function \[L,U,p\] = lutx(A)

%LU三角分解

%下三角矩阵L,上三角矩阵U，排列向量p

%使L\*U = A(p,:)

\[n,n\] = size(A);

p = (1:n)'

for k = 1:n-1

\[r,m\] = max(abs(A(k:n,k)));

m = m+k-1;

if(A(m,k)~=0)

if(m~=k)

A(\[k m\],:) = A(\[m k\],:);

p(\[k m\]) = p(\[m k\]);

end

i=k+1:n;

A(i,k)=A(i,k)/A(k,k);

j=k+1:n;

A(i,j) = A(i,j)-A(i,k)\*A(k,j);

end

L = tril(A,-1) + eye(n,n);

U = triu(A);

lutx(A)   这里A是magic(4)

p =

ans =

1.0000         0         0         0

0.2500    1.0000         0         0

0.3125    0.6360    1.0000         0

0.5625    0.3026    1.0000    1.0000

matlab自带函数是lu

lu(A)

ans =

16.0000    3.0000    2.0000   13.0000

0.2500   14.2500   13.5000   -2.2500

0.3125    0.6360    1.7895    5.3684

0.5625    0.3026    1.0000    0.0000

lutx是lu的可读版

x=(1:4)/5

x =

0.2000    0.4000    0.6000    0.8000

>> norm1 = norm(x,1)    L1范数是曼哈顿范数

norm1 =

>> norm2 = norm(x)   L2范数是欧几里得距离

norm2 =

1.0954

>> norminf = norm(x,inf)   L3范数是切比雪夫范数

norminf =

0.8000

density = nnz(A)/prod(size(A))   nnz计算矩阵中非零元素

density =

>> \[i,j\]=find(A)

i =

j =

>> bandwidth=max(abs(i-j))        矩阵带宽是指非零元素到主对角线的最大距离，带状矩阵指矩阵带宽很小的矩阵

bandwidth =

>> S=sparse(A)    将矩阵转换为稀疏形式

S =

(1,1)       16

(2,1)        5

(3,1)        9

(4,1)        4

(1,2)        2

(2,2)       11

(3,2)        7

(4,2)       14

(1,3)        3

(2,3)       10

(3,3)        6

(4,3)       15

(1,4)       13

(2,4)        8

(3,4)       12

(4,4)        1

>> A=full(S)  相反操作

A =

16     2     3    13

5    11    10     8

9     7     6    12

4    14    15     1

[280db80020904172dbd48c8b4697b0ef.png]: /images/20221022/8a0a4df83459467980518df25e82f603.png
[ada07fc5ce3307d8c57b76d69fcf080b.png]: /images/20221022/81b270f00782496ebe60d9f7010def23.png
[d0ecbf72f836a2348bfabefb491033c8.png]: /images/20221022/d6012668f7e64905a680f32e3b88acea.png