2018东三省数学建模联赛E优秀论文(5)

380 225 236 217 188 326 358 325 404 439 410 347 280 553 551 173 166 320 513 748 840 990 332 394 389 377 587 287 487 565 688 608

52.8 9.9 7.6 16.6 32.0 22.4 29.2 33.6 56.0 90.2 83.7 26.9 94.0 59.5 81.6 11.5 29.9 74.6 79.6 34.2 73.7 65.5 50.9 48.3 69.7 52.7 164.3 18.3 64.5 28.4 42.1 44.4 ];

s = size(x) len = s(2); num = s(1); for i = 1: num

x(i,:) = x(i,:)./x(i,1); end

dx(num,len-1) = 0; for i = 1 : num

for j = 1 : len - 1

dx(i,j) = x(i,j+1) - x(i,j); end end

r(1,1:len-1) = 1; for i = 2 : num

for k = 1 : len - 1

r(i,k) = 1/(1 + abs(dx(1,k) - dx(i,k))); end end

r1 = sum(r(2:num,:),2)/(len - 1) s =

3 32 r1 =

0.6180 0.7222

附件三 非线性回归方程Matlab程序

clear clc

data = [90 17 16 63 57 103 49 94 236 42 82 43 131 77 147 34 60 102 114 61 178 124 50 88 93 109 300 50 175 111 242 619

394 227 218 213 186 327 389 351 442 431 427 355 282 617 547 177 165 430 517 753

18

873 995 339 406 384 393 612 282 497 565 753 617

58.3 10.5 7.7 17.8 31.3 23.6 18.4 35.9 58.8 90.9 85.4 30.0 96.8 66.0 88.2 11.4 32.6 80.9 81.3 37.3 87.5 66.7 58.5 45.8 76.9 58.5 206.6 18.6 65.1 32.0 44.4 43.9 ]';

x1 = data(:,1); x2 = data(:,2); y = data(:,3);

X = [ones(size(x1)) x1.*x1 x1 x2.*x2 x2 x1.*x2]; [b,bint,r,rint,stats] = regress(y,X) scatter3(x1,x2,y,'filled') hold on

x1fit = min(x1):0.5:max(x1); x2fit = min(x2):0.5:max(x2);

[X1FIT,X2FIT] = meshgrid(x1fit,x2fit);

YFIT = b(1)+ b(2)*X1FIT.*X1FIT+b(3)*X1FIT + b(4)*X2FIT.*X2FIT + b(5)*X2FIT + b(6)*X1FIT.*X2FIT;

mesh(X1FIT,X2FIT,YFIT) xlabel('x1') ylabel('x2') zlabel('Y') view(140,30) b =

-28.0861 -0.0008 0.4900 -0.0002 0.1759 0.0001

bint =

-91.5312 35.3590 -0.0014 -0.0001 -0.2534 1.2335 -0.0004 0.0001 -0.1025 0.4542 -0.0013 0.0014

19

r =

0.4908 -1.9169 -3.2500 -13.3480 5.8312 -34.0032 -22.4542 -20.4043 -40.0697 50.8412 28.7424 -5.9395 34.1762 6.8611 4.9844 -3.0558 8.5618 16.6230 9.3367 -11.4702 4.6839 12.4885 20.6742 -11.9880 18.6204 -6.0701 95.3076 -14.3564 -24.2742 -39.8736 -58.7484 -7.0007

rint =

-63.4205 64.4022 -61.4065 57.5728 -62.3486 55.8485 -74.7076 48.0116 -54.3658 66.0281 -95.5291 27.5228

20

-84.2480 39.3397 -83.6959 42.8873 -91.9602 11.8207 -6.4934 108.1758 -33.6700 91.1548 -68.4176 56.5386 -21.3410 89.6933 -53.6216 67.3438 -57.7698 67.7386 -62.5173 56.4058 -49.6934 66.8170 -46.7019 79.9479 -53.6774 72.3509 -64.1926 41.2521 -48.8265 58.1944 -23.1044 48.0814 -41.9803 83.3287 -75.6242 51.6482 -44.8507 82.0915 -69.6353 57.4951 55.8451 134.7700 -77.4349 48.7221 -85.3185 36.7701 -100.4235 20.6764 -101.1035 -16.3934 -13.9492 -0.0523

stats =

0.4472 4.2064 0.0062 972.1002

21

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