Why are the results different when calculating a 10 x 3 matrix and a 1 x 3 matrix?

Question

BRAND HUN 2020-5-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/536263-why-are-the-results-different-when-calculating-a-10-x-3-matrix-and-a-1-x-3-matrix

回答： Walter Roberson 2020-5-28

There is a problem.

The result calculated using a for loop as a 125-row matrix and the result calculated using a 1-row matrix are different.

What is the reason ??

clear all;
Lcam_ang1 = -pi/4;
Rcam_ang1 = pi/4;
A1 = [cos(Lcam_ang1) 0 sin(Lcam_ang1); 0 1 0; (-sin(Lcam_ang1)) 0 cos(Lcam_ang1)];
B1 = [cos(Rcam_ang1) 0 sin(Rcam_ang1); 0 1 0; (-sin(Rcam_ang1)) 0 cos(Rcam_ang1)];
XYZ_rwd21t = [1.30937778204061e-14,-13.8617246105272,22.6275000000000;
    4.98412069706843,-14.0972221725972,22.6275000000000;
    10.1405192035478,-14.3408597871621,22.6275000000000;
    15.4782848683395,-14.5930669220533,22.6275000000000;
    21.0071578899899,-14.8543037974684,22.6275000000000;
    5.61569879271913e-15,-6.93086230526358,22.6275000000000;
    4.98412069706842,-7.04861108629860,22.6275000000000;
    10.1405192035478,-7.17042989358107,22.6275000000000;
    15.4782848683395,-7.29653346102667,22.6275000000000;
    21.0071578899899,-7.42715189873418,22.6275000000000;
    2.93832502315486e-15,-1.32495437644941e-15,22.6275000000000;
    4.98412069706841,-1.80157025904491e-15,22.6275000000000;
    10.1405192035478,-1.88965753591222e-15,22.6275000000000;
    15.4782848683395,-1.54697382149079e-15,22.6275000000000;
    21.0071578899899,-7.26667087945844e-16,22.6275000000000;
    5.06165651171334e-15,6.93086230526358,22.6275000000000;
    4.98412069706842,7.04861108629860,22.6275000000000;
    10.1405192035478,7.17042989358107,22.6275000000000;
    15.4782848683395,7.29653346102667,22.6275000000000;
    21.0071578899899,7.42715189873418,22.6275000000000];
for i = 1 : 20
    XYZ_rwt212t(i, 1) = (XYZ_rwd21t(i, 1) * B1(1,1) + XYZ_rwd21t(i, 3) * B1(1,3));
    XYZ_rwt212t(i, 2) = XYZ_rwd21t(1, 2);
    XYZ_rwt212t(i, 3) = (XYZ_rwd21t(i, 1) * B1(3,1) + XYZ_rwd21t(i, 3) * B1(3,3));
end
XYZ_rwt211t = zeros(1, 3);
XYZ_rwd2t=[XYZ_rwd21t(15, 1), XYZ_rwd21t(15, 2), XYZ_rwd21t(15, 3)];
for i = 1 : 1
    XYZ_rwt211t(i, 1) = (XYZ_rwd2t(i, 1) * B1(1,1) + XYZ_rwd2t(i, 3) * B1(1,3));
    XYZ_rwt211t(i, 2) = XYZ_rwd2t(1, 2);
    XYZ_rwt211t(i, 3) = (XYZ_rwd2t(i, 1) * B1(3,1) + XYZ_rwd2t(i, 3) * B1(3,3));
end
test_errorX = XYZ_rwt212t(15, 1) - XYZ_rwt211t(1, 1)
test_errorY = XYZ_rwt212t(15, 2) - XYZ_rwt211t(1, 2)
test_errorZ = XYZ_rwt212t(15, 3) - XYZ_rwt211t(1, 3)

The desired answer is the answer from XYZ_rwt211t below.

Why is the Y value different?

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Answer 1

Walter Roberson 2020-5-28

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/536263-why-are-the-results-different-when-calculating-a-10-x-3-matrix-and-a-1-x-3-matrix#answer_441631

在 MATLAB Online 中打开

XYZ_rwd21t = [1.30937778204061e-14,-13.8617246105272,22.6275000000000;
    
XYZ_rwt212t(i, 2) = XYZ_rwd21t(1, 2);

Okay, so for the first series, the second column will be a copy of -13.8617246105272

    21.0071578899899,-7.26667087945844e-16,22.6275000000000;
    
XYZ_rwd2t=[XYZ_rwd21t(15, 1), XYZ_rwd21t(15, 2), XYZ_rwd21t(15, 3)];
    XYZ_rwt211t(i, 2) = XYZ_rwd2t(1, 2);

For the second one, the second column will be a copy of 7.26667087945844e-16

You are copying from different places; it is not surprising that the results are different.