matlab中各種高斯相關函數

matlab， 高斯函數， 高斯分布

最常見的是產生服從一維標准正態分布的隨機數

1. n=100; 

   ---

2. x=randn(1,n) 

   ---

實現服從任意一維高斯分布的隨機數

1. u=10; 

   ---

2. sigma=4; 

   ---

3. x=sigma*randn(1,n)+u 

   ---

---

產生服從多元高斯分布的隨機變量函數mvnrnd,[multivarite normal random]

1. n=100; %產生隨機數的個數 

   ---

2. mu=[1 -1]; 

   ---

3. Sigma=[.9,.4;.4,.3]; 

   ---

4. r=mvnrnd(mu,Sigma,n); 

   ---

將產生的隨機數繪制在二維平面

1. scatter(r(:,1),r(:,2)); 

   ---

1474457688429.jpg

當然mvnrnd函數還可以產生更高維數的高斯隨機數，具體參見matlab help。

---

產生多元高斯分布概率密度函數
Y=mvnpdf(X,[MU,Sigma])
其中可省參數MU,Sigma默認值分別為零向量和單位陣，X是的矩陣，N是樣本個數，D是樣本維數。

1. mu = [1 -1]; Sigma = [.9 .4; .4 .3]; 

   ---

2. [X1,X2] = meshgrid(linspace(-1,3,25)', linspace(-3,1,25)'); 

   ---

3. X = [X1(:) X2(:)]; 

   ---

4. p = mvnpdf(X, mu, Sigma); 

   ---

5. surf(X1,X2,reshape(p,25,25)); 

   ---

和下面代碼產生的趨勢相同

1. mu = [1 -1]; 

   ---

2. Sigma = [.9 .4; .4 .3]; 

   ---

3. [X,Y] = meshgrid(linspace(-1,3,25)', linspace(-3,1,25)'); 

   ---

4. for i=1:25 

   ---

5. for j=1:25 

   ---

6. XY=[X(i,j),Y(i,j)]; 

   ---

7. Z(i,j)=exp(-0.5*(XY-mu)/Sigma*(XY-mu)'); 

   ---

8. end 

   ---

9. end 

   ---

10. surf(X,Y,Z); 

    ---

1474460161935.jpg

---

高斯分布函數
Y=mvncdf(X,[Mu],[Sigma]) , cumulative probability of the multivariate norm distribution with mean Mu and covariance Sigma.
具體使用看代碼

1. mu = [1 -1]; Sigma = [.9 .4; .4 .3]; 

   ---

2. [X1,X2] = meshgrid(linspace(-1,3,25)', linspace(-3,1,25)'); 

   ---

3. X = [X1(:) X2(:)]; 

   ---

4. p = mvncdf(X, mu, Sigma); 

   ---

5. surf(X1,X2,reshape(p,25,25)); 

   ---

1474460555428.jpg

---

高斯隸屬函數
gaussmf(X,[Sigma,Mu])

1. x = (0:0.1:10)'; 

   ---

2. y1 = gaussmf(x, [0.5 5]); 

   ---

3. y2 = gaussmf(x, [1 5]); 

   ---

4. y3 = gaussmf(x, [2 5]); 

   ---

5. y4 = gaussmf(x, [3 5]); 

   ---

6. plot(x, [y1 y2 y3 y4]); 

   ---

1474460751315.jpg