数值数组及向量化运算.ppt

XidianUniversity1数值运算

逐个构造010102030405等差数列型:,linspace等比数列型logspace,semilogx/y工作空间浏览器load/save命010203全1矩阵、全0矩阵、空矩阵、随机矩阵(均匀分布、正态分布)对角阵、单位阵、魔方数组

A,A(:),A(:,:)A(r,c),A(r,:),A(:,c)A(I)A(L)%sizeof(A)==sizeof(L)A(2:end,3:end)

reshape,repmatflipud,fliplr,rot90

A*B,A.*B,A/B,A./B,A\B,A.\BA.^a,a.^AA+B,A-BA’,A.’,

NaN,inf,01isnan,isinf02

findind2sub%单下标换全下标

size(a)size(b)size(c)4length(a)length(b)length(c)5a=[]1b=rand(0)2c=rand(1,0)3isempty(a)isempty(c)6

,=,,=,==,~=

false,true,logical,|,~,xorall,any,||isa,ishandle,ischar,islogical,isglobal,isnumericisempty,isfinite,isprime,isreal,isletter,isspace,isinf,isnan

1差分diff2梯度gradient3求和sum:sum(A,1),sum(A,2)4累计求和cumsum5近似数值积分trapz6累计近似数值积分cumtrapz

dblquad(fun,xmin,ymin,xmax,ymax,tol)trapz(x,y,tol)quad(fun,a,b,tol)

一元函数极值fminbnd(fun,x1,x2,options)01fminbnd(@(x)x^2+2*x-3,-1,1)02单纯形法求多元函数的极值fminsearch(fun,x0,options)03

数值略

高斯列主元消去法01[R,ci]=rref(A)02特征值、特征向量、行列式03X=null(A);04A矩阵零空间的全部正交基05AX=006Z=orth(A);07A矩阵值空间的全部正交基08span(A)=span(Z)09

2020fsolve(fun,x0)012021fzero(fun,x0)022022对分法03

二项式分布Binomialbino卡方分布Chisquarechi2指数分布ExponentialexpF分布Ff几何分布Geometricgeo正态分布Normalnorm泊松分布PoissonpoissT分布Tt均匀分布Uniformunif离散均匀分布DiscreteUniformunid

norm,chi2,bino,f,geo,exp,poiss,t,unif,unidnormpdf(x,mu,sigma)

normcdf(x,nu,sigma)

normrnd(nu,sigma,m,n)rand(m,n)randn(m,n)

min(X)/max(X)01mean(X)02std(X)03var(X)04cov(X)05corrcoef(X)06hist/histfit07

mu=2;sigma=0.5;x=randn(1000,1);y1=sigma*x+mu;y2=sigma*(x+mu);subplot(2,1,1);histfit(y1),;axis([-550100]);subplot(2,1,2);histfit(y2);axis([-550100]);

c=conv(p1,p2)1[q,r]=deconv(p1,p2)2poly2str(q,‘x’)3y=polyval(p,x)4

p=polyfit(x,y,n)

x0=(-10:0.5:10);x0=(-10:0.5:10);a0=[2-217];y0=polyval(a0,x0);y1=y0+(rand(size(x0))-0.5)*800;m=length(x0);n=3;X=zeros(m,n+1);fork=1:nX(:,n-k+1)=x0.^k;endX(:,n+1)=ones(m,1);aT=(X\y1);y=polyval(aT,x0);plot(x0,y0,