数值数组及向量化运算.ppt

Xidian University,1,数值运算,hjT,Xidian University,2,数组创建,逐个构造 等差数列型 :, linspace 等比数列型 logspace, semilogx/y 工作空间浏览器 load/save命令,Xidian University,3,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,Xidian University,4,数组的访问,A, A(:), A(:, :) A(r, c), A(r, :), A(:, c) A(I) A(L) %sizeof(A) = sizeof(L) A(2:end, 3:end),Xidian University,5,reshape, repmat flipud, fliplr, rot90,Xidian University,6,数组运算,A, A., A+B, A-B A*B, A.*B, A/B, A./B, AB, A.B A.a, a.A,Xidian University,7,非数,NaN, inf, isnan, isinf,Xidian University,8,特殊操作,find ind2sub %单下标换全下标,Xidian University,9,空数组,a= b=rand(0) c=rand(1, 0) size(a) size(b) size(c) length(a) length(b) length(c) isempty(a) isempty(c),Xidian University,10,关系操作, =, =, =,Xidian University,11,逻辑操作,&, |, , xor &, | all, any false, true, logical isempty, isfinite, isprime, isreal, isletter, isspace, isinf, isnan isa, ishandle, ischar, islogical, isglobal, isnumeric,Xidian University,12,数值计算,差分 diff 梯度 gradient 求和 sum: sum(A, 1), sum(A, 2) 累计求和 cumsum 近似数值积分 trapz 累计近似数值积分 cumtrapz,Xidian University,13,数值积分,trapz(x, y, tol) quad(fun, a, b, tol) dblquad(fun, xmin, ymin, xmax, ymax, tol),Xidian University,14,求极值,一元函数极值 fminbnd(fun, x1, x2, options) fminbnd(x)x2+2*x-3, -1, 1) 单纯形法求多元函数的极值fminsearch(fun, x0, options),Xidian University,15,常微分方程,数值略,Xidian University,16,矩阵和代数方程,高斯列主元消去法 R, ci = rref(A) 特征值、特征向量、行列式 X=null(A); A矩阵零空间的全部正交基 AX=0 Z=orth(A); A矩阵值空间的全部正交基 span(A) = span(Z),Xidian University,17,代数方程的求解,fsolve(fun, x0) fzero(fun, x0) 对分法,Xidian University,18,概率分布图,Xidian University,19,norm, chi2, bino, f, geo, exp, poiss, t, unif, unid normpdf(x, mu, sigma) normcdf(x, nu, sigma) normrnd(nu, sigma, m, n) rand(m, n) randn(m, n),Xidian University,20,统计指令,min(X)/max(X) mean(X) std(X) var(X) cov(X) corrcoef(X) hist/histfit,Xidian University,21,P159 例4.3-5,mu=2; sigma=0.5; x=randn(1000, 1); y1=sigma*x + mu; y2=sigma*(x+mu); subplot(2, 1, 1); histfit(y1),; axis(-5 5 0 100); subplot(2, 1, 2); histfit(y2); axis(-5 5 0 100);,Xidian University,22,多项式运算,c = conv(p1, p2) q, r = deconv(p1, p2) poly2str(q, x) y = polyval(p, x),Xidian University,23,多项式拟合,p = polyfit(x, y, n),Xidian University,24,最小二乘法,x0=(-10:0.5:10); x0=(-10:0.5:10); a0 = 2 -2 1 7; y0 = polyval(a0, x0); y1 = y0 + (rand(size(x0)-0.5)*800; m=length(x0); n=3; X=zeros(m, n+1); for k=1:n X(:, n-k+1)=x0.k; end X(:, n+1)=ones(m, 1); aT = (Xy1); y = polyval(aT, x0)