matlab中各种高斯相关函数

matlab中各种高斯相关函数

matlab， 高斯函数， 高斯分布

最常见的是产生服从一维标准正态分布的随机数

1. n=100; 
   

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2. x=randn(1,n) 
   

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实现服从任意一维高斯分布的随机数

1. u=10; 
   

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2. sigma=4; 
   

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3. x=sigma*randn(1,n)+u 
   

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产生服从多元高斯分布的随机变量函数mvnrnd,[multivarite normal random]

1. n=100; %产生随机数的个数 
   

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2. mu=[1 -1]; 
   

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3. Sigma=[.9,.4;.4,.3]; 
   

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4. r=mvnrnd(mu,Sigma,n); 
   

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将产生的随机数绘制在二维平面

1. scatter(r(:,1),r(:,2)); 
   

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1474457688429.jpg

当然mvnrnd函数还可以产生更高维数的高斯随机数，具体参见matlab help。

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产生多元高斯分布概率密度函数

Y=mvnpdf(X,[MU,Sigma])

其中可省参数MU,Sigma默认值分别为零向量和单位阵，X是的矩阵，N是样本个数，D是样本维数。

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

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

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3. X = [X1(:) X2(:)]; 
   

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4. p = mvnpdf(X, mu, Sigma); 
   

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5. surf(X1,X2,reshape(p,25,25)); 
   

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和下面代码产生的趋势相同

1. mu = [1 -1]; 
   

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2. Sigma = [.9 .4; .4 .3]; 
   

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

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4. for i=1:25 
   

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5. for j=1:25 
   

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6. XY=[X(i,j),Y(i,j)]; 
   

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

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8. end 
   

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9. end 
   

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10. surf(X,Y,Z); 
    

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1474460161935.jpg

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高斯分布函数

Y=mvncdf(X,[Mu],[Sigma]) , cumulative probability of the multivariate norm distribution with mean Mu and covariance Sigma.

具体使用看代码

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

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

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3. X = [X1(:) X2(:)]; 
   

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4. p = mvncdf(X, mu, Sigma); 
   

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5. surf(X1,X2,reshape(p,25,25)); 
   

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1474460555428.jpg

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高斯隶属函数

gaussmf(X,[Sigma,Mu])

1. x = (0:0.1:10)'; 
   

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2. y1 = gaussmf(x, [0.5 5]); 
   

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3. y2 = gaussmf(x, [1 5]); 
   

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4. y3 = gaussmf(x, [2 5]); 
   

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5. y4 = gaussmf(x, [3 5]); 
   

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6. plot(x, [y1 y2 y3 y4]); 
   

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