Givens rotation matlab实验

构建的乐趣2026-05-24 19:19

% 生成两个随机向量

v1 = rand(10, 1);

v2 = rand(10, 1);

% Gram-Schmidt正交化

u1 = v1;

u2 = v2 - (v2' * u1) / (u1' * u1) * u1;

u1'*u2

ans =

5.5511e-16

u1*u2'

ans =

-0.4587 0.1380 0.6883 -0.2628 0.1963 0.0453 0.1429 0.3519 -0.0446 0.0863

-0.5100 0.1534 0.7652 -0.2922 0.2182 0.0504 0.1589 0.3913 -0.0496 0.0960

-0.0715 0.0215 0.1073 -0.0410 0.0306 0.0071 0.0223 0.0549 -0.0070 0.0135

-0.5143 0.1547 0.7717 -0.2946 0.2200 0.0508 0.1602 0.3946 -0.0500 0.0968

-0.3561 0.1071 0.5342 -0.2040 0.1523 0.0352 0.1109 0.2732 -0.0346 0.0670

-0.0549 0.0165 0.0824 -0.0315 0.0235 0.0054 0.0171 0.0421 -0.0053 0.0103

-0.1568 0.0472 0.2353 -0.0898 0.0671 0.0155 0.0489 0.1203 -0.0153 0.0295

-0.3079 0.0926 0.4620 -0.1764 0.1318 0.0304 0.0959 0.2362 -0.0300 0.0580

-0.5391 0.1622 0.8089 -0.3089 0.2307 0.0532 0.1680 0.4136 -0.0524 0.1015

-0.5433 0.1634 0.8152 -0.3112 0.2325 0.0537 0.1693 0.4168 -0.0528 0.1023

rank(ans)

ans =

复制代码 
 1

p = [3 -2.1 -4.7];

r = roots§

r =

复制代码 
1.6497

-0.9497

p = [10 3 -2.1 -4.7];

r = roots§

r =

0.7687 + 0.0000i

-0.5343 + 0.5709i

-0.5343 - 0.5709i

v1=[1,0]';

v2=[0,1]'

v2 =

复制代码 
 0
 1

w1=[1/sqrt(2);1/sqrt(2)];

w2=[-1/sqrt(2);1/sqrt(2)];

v1 v2\]*\[2 0;0 0.5\]* \[v1';v2

Error using vertcat

Dimensions of arrays being concatenated are not consistent.

v1 v2

ans =

复制代码 
 1     0
 0     1

v1 v2\]*\[2 0;0 0.5\]* \[v1' ; v2

Error using vertcat

Dimensions of arrays being concatenated are not consistent.

v1 v2\]\*\[2 0;0 0.5

ans =

复制代码 
2.0000         0
     0    0.5000

v1 v2\]*\[2 0;0 0.5\]\[v1 v2\]' \[v1 v2\]* \[2 0;0 0.5\]\[v1 v2\]' ↑ Error: Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters. \[v1 v2\]*\[2 0;0 0.5\]*\[v1 v2\]'

ans =

复制代码 
2.0000         0
     0    0.5000

v1 v2\]*\[2 0;0 0.5\]* \[v1 v2\]'-\[w1 w2\]*\[2 0 0 2\]* \[w1 w2\]' Error using \* Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.\*'. \[v1 v2\]*\[2 0;0 0.5\]* \[v1 v2\]'-\[w1 w2\]*\[2 0; 0 2\]*\[w1 w2\]'

ans =

复制代码 
0.0000    0.0000
0.0000   -1.5000

v1 v2\]*\[2 0;0 0.5\]* \[v1 v2\]' - \[w1 w2\]*\[2 0; 0 2\]* \[w1 w2\]' v1=\[cos(30); -sin(30)

v1 =

复制代码 
0.1543
0.9880

v1=[sin(30); cos(30)]

v1 =

-0.9880

0.1543

v1=[cos(30); -sin(30)]

v1 =

复制代码 
0.1543
0.9880

v2=[cos(30); -sin(30)]

v2 =

复制代码 
0.1543
0.9880

v2=[sin(30); cos(30)]

v2 =

-0.9880

0.1543

v1 v2\]*\[2 0;0 0.5\]* \[v1 v2\]'-\[w1 w2\]*\[2 0; 0 2\]*\[w1 w2\]'

ans =

-1.4643 0.2286

0.2286 -0.0357

rank(ans)

ans =

复制代码 
 2

v1'*v2

ans =

复制代码 
 0

v1=[1,0]';

v2=[0,1]'

v2 =

复制代码 
 0
 1

v1 v2\]*\[4 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[4 0; 0 4\]*\[w1 w2\]'

ans =

复制代码 
0.0000    0.0000
0.0000   -3.3000

v1 v2\]*\[4 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[4 0; 0 4\]*\[w1 w2\]'

ans =

复制代码 
0.0000    0.0000
0.0000   -3.3000

v1 v2\]*\[5 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[4 0; 0 5\]*\[w1 w2\]'

ans =

复制代码 
0.5000    0.5000
0.5000   -3.8000

v1 v2\]*\[5 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[5 0; 0 5\]*\[w1 w2\]'

ans =

复制代码 
0.0000    0.0000
0.0000   -4.3000

v1=[cos(30); -sin(30)]

v1 =

复制代码 
0.1543
0.9880

v1=[cos(30); -sin(30)];

v1=[1,0]';

w1=[cos(30); -sin(30)];

w2=[sin(30); cos(30)];

v1 v2\]*\[5 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[5 0; 0 5\]*\[w1 w2\]'

ans =

复制代码 
     0   -0.0000

-0.0000 -4.3000

v1=[cos(20); -sin(20)];

v2=[sin(20); cos(20)]

v2 =

复制代码 
0.9129
0.4081

v1 v2\]*\[5 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[5 0; 0 5\]*\[w1 w2\]'

ans =

-3.5839 -1.6020

-1.6020 -0.7161

rank(ans)

ans =

复制代码 
 1

v1 v2\]*\[5 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[0.7 0; 0 0.7\]*\[w1 w2\]'

ans =

复制代码 
0.7161   -1.6020

-1.6020 3.5839

rank(ans)

ans =

复制代码 
 1

v1 v2\]*\[5 0;0 0.7\]* \[v1 v2\]'-\[w1 w2\]*\[0.7 0; 0 0.7\]*\[w1 w2\]'

ans =

复制代码 
0.7161   -1.6020

-1.6020 3.5839

v1=[1,0]';

v2=[0,1]'

v2 =

复制代码 
 0
 1

w1=[ *1/sqrt(2); *1/sqrt(2) ];

v1=[1/sqrt(2);1/sqrt(2)];

v2=[-1/sqrt(2);1/sqrt(2)];

v1=[1,0]';
v1=[1,0]';

v2=[0,1]'

v2 =

复制代码 
 0
 1

w1=[1/sqrt(2);1/sqrt(2)];

w2=[-1/sqrt(2);1/sqrt(2)];

v1 v2\]*\[5 0;0 1\]* \[v1 v2\]'-\[w1 w2\]*\[0.2 0; 0 1.6\]*\[w1 w2\]'

ans =

复制代码 
4.1000    0.7000
0.7000    0.1000

rank(ans)

ans =

复制代码 
 2

v1 v2\]*\[5 0;0 1\]* \[v1 v2\]'-\[w1 w2\]*\[0.2 0; 0 1.4\]*\[w1 w2\]'

ans =

复制代码 
4.2000    0.6000
0.6000    0.2000

rank(ans)

ans =

复制代码 
 2

v1 v2\]*\[5 0;0 1\]* \[v1 v2\]'-\[w1 w2\]*\[1.4 0; 0 0.2\]*\[w1 w2\]'

ans =

复制代码 
4.2000   -0.6000

-0.6000 0.2000

syms nu1

(nu1-0.15).^2

ans =

(nu1 - 3/20)^2

(nu1-0.15).^2-(4.1-0.5nu1-0.5 0.15)(2.2-0.5nu1-0.5*0.15)==0

ans =

(nu1 - 3/20)^2 - (nu1/2 - 17/8)*(nu1/2 - 161/40) == 0

(nu1-0.15).^2-(4.1-0.5nu1-0.5 0.15)(2.2-0.5nu1-0.5*0.15)

ans =

(nu1 - 3/20)^2 - (nu1/2 - 17/8)*(nu1/2 - 161/40)

solve(ans)

ans =

  • 13317^(1/2)/30 - 37/20
    13317^(1/2)/30 - 37/20

(nu1-0.15).^20.25-(4.1-0.5 nu1-0.50.15) (2.2-0.5nu1-0.50.15)

ans =

(nu1 - 3/20)^2/4 - (nu1/2 - 17/8)*(nu1/2 - 161/40)

solve(ans)

ans =

3419/1200

v1 v2\]*\[4.1 0;0 2.2\]* \[v1 v2\]'-\[w1 w2\]*\[ans 0; 0 0.15\]*\[w1 w2\]'

ans =

6241/2400, -3239/2400

-3239/2400, 1681/2400

rank(ans)

ans =

复制代码 
 1

givens

?? 3x3 Givens ???

cos(beta)\*cos(gamma), -cos(beta)\*sin(gamma), sin(beta)

cos(alpha)\*sin(gamma) + cos(gamma)\*sin(alpha)\*sin(beta), cos(alpha)\*cos(gamma) - sin(alpha)\*sin(beta)\*sin(gamma), -cos(beta)\*sin(alpha)

sin(alpha)\*sin(gamma) - cos(alpha)\*cos(gamma)\*sin(beta), cos(gamma)\*sin(alpha) + cos(alpha)\*sin(beta)\*sin(gamma), cos(alpha)\*cos(beta)

givens

?? 3x3 Givens ???

cos(beta), 0, sin(beta)

sin(alpha)\*sin(beta), cos(alpha), -cos(beta)\*sin(alpha)

-cos(alpha)\*sin(beta), sin(alpha), cos(alpha)\*cos(beta)

givens

?? 3x3 Givens ???

cos(beta)\*cos(gamma), -cos(beta)\*sin(gamma), sin(beta)

cos(alpha)\*sin(gamma) + cos(gamma)\*sin(alpha)\*sin(beta), cos(alpha)\*cos(gamma) - sin(alpha)\*sin(beta)\*sin(gamma), -cos(beta)\*sin(alpha)

sin(alpha)\*sin(gamma) - cos(alpha)\*cos(gamma)\*sin(beta), cos(gamma)\*sin(alpha) + cos(alpha)\*sin(beta)\*sin(gamma), cos(alpha)\*cos(beta)

givens

?? 3x3 Givens ???

cos(gamma), -sin(gamma), 0

cos(alpha)\*sin(gamma), cos(alpha)\*cos(gamma), -sin(alpha)

sin(alpha)\*sin(gamma), cos(gamma)\*sin(alpha), cos(alpha)

givens

?? 3x3 Givens ???

cos(gamma), -cos(alpha)\*sin(gamma), sin(alpha)\*sin(gamma)

sin(gamma), cos(alpha)\*cos(gamma), -cos(gamma)\*sin(alpha)

0, sin(alpha), cos(alpha)

givens2

???Q:

-0.2898 -0.1322 -0.4655 -0.2269 -0.3524 -0.0310 -0.3638 -0.5162 -0.1532 -0.2062 0.0077 0.2009

-0.3291 -0.4958 0.0181 0.1511 -0.1459 -0.2871 0.5331 -0.2212 0.3717 0.0130 -0.1052 -0.1909

-0.2931 0.1737 -0.3852 0.2475 -0.0296 -0.5340 -0.0393 0.4978 0.0048 0.1641 0.0959 0.3206

-0.3199 0.1390 0.2976 -0.4729 0.0645 -0.1133 0.4568 0.0407 -0.4818 -0.1683 -0.0547 0.2746

-0.3365 0.3436 -0.0360 0.3601 0.1410 0.0207 0.0697 -0.1789 -0.2235 -0.2683 0.4750 -0.4828

-0.3048 -0.2286 0.3371 -0.1090 0.3074 -0.3388 -0.5207 -0.0352 -0.1810 0.2968 -0.1834 -0.3051

-0.2650 0.5373 0.0639 0.0409 0.0953 0.1491 0.0763 -0.4134 0.2957 0.5216 -0.1681 0.1990

-0.2272 -0.1248 -0.2565 0.2087 0.6227 0.2895 -0.0040 0.0489 0.0365 -0.3553 -0.4405 0.1670

-0.3170 -0.1713 -0.0731 -0.4682 0.2034 0.3074 -0.0713 0.2475 0.4028 0.0790 0.5242 0.0111

-0.3135 -0.2655 0.0566 0.3173 -0.3408 0.5427 0.0195 0.2271 -0.3735 0.3488 -0.0421 0.0421

-0.2212 0.3323 -0.0908 -0.2577 -0.3574 0.0916 -0.0539 0.3379 0.1990 -0.1913 -0.4640 -0.4705

-0.2093 0.0489 0.5870 0.2603 -0.2303 -0.0025 -0.2881 0.0403 0.3055 -0.4232 0.0578 0.3579

Givens???G:

-0.7031 0 0.7111 0 0 0 0 0 0 0 0 0

0 1.0000 0 0 0 0 0 0 0 0 0 0

-0.7111 0 -0.7031 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???Q_rotated:

-0.0047 0.2165 0.0533 0.3355 0.2267 -0.3579 0.2279 0.7169 0.1111 0.2617 0.0628 0.0867

-0.3291 -0.4958 0.0181 0.1511 -0.1459 -0.2871 0.5331 -0.2212 0.3717 0.0130 -0.1052 -0.1909

0.4122 -0.0281 0.6018 -0.0127 0.2715 0.3975 0.2863 0.0171 0.1055 0.0313 -0.0729 -0.3683

-0.3199 0.1390 0.2976 -0.4729 0.0645 -0.1133 0.4568 0.0407 -0.4818 -0.1683 -0.0547 0.2746

-0.3365 0.3436 -0.0360 0.3601 0.1410 0.0207 0.0697 -0.1789 -0.2235 -0.2683 0.4750 -0.4828

-0.3048 -0.2286 0.3371 -0.1090 0.3074 -0.3388 -0.5207 -0.0352 -0.1810 0.2968 -0.1834 -0.3051

-0.2650 0.5373 0.0639 0.0409 0.0953 0.1491 0.0763 -0.4134 0.2957 0.5216 -0.1681 0.1990

-0.2272 -0.1248 -0.2565 0.2087 0.6227 0.2895 -0.0040 0.0489 0.0365 -0.3553 -0.4405 0.1670

-0.3170 -0.1713 -0.0731 -0.4682 0.2034 0.3074 -0.0713 0.2475 0.4028 0.0790 0.5242 0.0111

-0.3135 -0.2655 0.0566 0.3173 -0.3408 0.5427 0.0195 0.2271 -0.3735 0.3488 -0.0421 0.0421

-0.2212 0.3323 -0.0908 -0.2577 -0.3574 0.0916 -0.0539 0.3379 0.1990 -0.1913 -0.4640 -0.4705

-0.2093 0.0489 0.5870 0.2603 -0.2303 -0.0025 -0.2881 0.0403 0.3055 -0.4232 0.0578 0.3579

givens2

Q =

复制代码 
 1     0     0     0     0     0     0     0     0     0     0     0
 0     1     0     0     0     0     0     0     0     0     0     0
 0     0     1     0     0     0     0     0     0     0     0     0
 0     0     0     1     0     0     0     0     0     0     0     0
 0     0     0     0     1     0     0     0     0     0     0     0
 0     0     0     0     0     1     0     0     0     0     0     0
 0     0     0     0     0     0     1     0     0     0     0     0
 0     0     0     0     0     0     0     1     0     0     0     0
 0     0     0     0     0     0     0     0     1     0     0     0
 0     0     0     0     0     0     0     0     0     1     0     0
 0     0     0     0     0     0     0     0     0     0     1     0
 0     0     0     0     0     0     0     0     0     0     0     1

???Q:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

Givens???G:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

???Q_rotated:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

givens2

???Q:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

Givens???G:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

???Q_rotated:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

givens2

???Q:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

???I:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

Givens???G:

0.7071 -0.7071 0 0 0 0 0 0 0 0 0 0

0.7071 0.7071 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated:

0.7071 -0.7071 0 0 0 0 0 0 0 0 0 0

0.7071 0.7071 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

givens2

???Q:

-0.3134 -0.6182 -0.0933 -0.0422 -0.0832 0.2664 0.1669 -0.0747 -0.1832 0.3417 0.4704 0.1618

-0.2995 -0.1270 -0.3401 -0.1614 -0.5796 -0.5575 -0.0095 -0.2247 0.0665 -0.0135 -0.1912 -0.1182

-0.4132 0.3577 0.1519 0.0652 0.0166 0.1438 0.3585 -0.0849 -0.2054 0.5029 -0.4634 0.0864

-0.3404 0.2281 0.4277 -0.0128 -0.2495 0.0622 -0.1451 0.1026 0.6575 0.1133 0.3253 -0.0183

-0.2395 0.0466 0.3334 -0.3257 -0.2947 0.2966 -0.3632 -0.0553 -0.4519 -0.4145 -0.0944 0.1687

-0.2282 -0.2919 -0.0859 -0.0505 0.0085 0.0743 0.2779 0.6986 0.2118 -0.3048 -0.3398 0.1691

-0.2743 0.1036 -0.2647 -0.3142 0.3366 -0.1007 -0.5182 0.3855 -0.1371 0.3152 0.0516 -0.2896

-0.1862 0.3264 -0.0406 -0.0291 -0.0361 -0.0545 0.4939 0.1556 -0.2851 -0.3094 0.4405 -0.4613

-0.3154 -0.2028 0.3074 -0.2540 0.6006 -0.3664 0.1261 -0.3475 0.1040 -0.2334 -0.0316 0.0490

-0.2641 0.3002 -0.6199 -0.0228 0.1624 0.3588 -0.0264 -0.2914 0.2471 -0.2612 0.0707 0.2834

-0.2351 -0.2811 0.0200 0.4506 0.0460 0.3158 -0.1770 -0.1894 0.0866 -0.1512 -0.2598 -0.6287

-0.2857 0.0820 0.0166 0.7011 0.0618 -0.3528 -0.2299 0.1438 -0.2426 -0.1092 0.1643 0.3468

???I:

-0.3134 -0.6182 -0.0933 -0.0422 -0.0832 0.2664 0.1669 -0.0747 -0.1832 0.3417 0.4704 0.1618

-0.2995 -0.1270 -0.3401 -0.1614 -0.5796 -0.5575 -0.0095 -0.2247 0.0665 -0.0135 -0.1912 -0.1182

-0.4132 0.3577 0.1519 0.0652 0.0166 0.1438 0.3585 -0.0849 -0.2054 0.5029 -0.4634 0.0864

-0.3404 0.2281 0.4277 -0.0128 -0.2495 0.0622 -0.1451 0.1026 0.6575 0.1133 0.3253 -0.0183

-0.2395 0.0466 0.3334 -0.3257 -0.2947 0.2966 -0.3632 -0.0553 -0.4519 -0.4145 -0.0944 0.1687

-0.2282 -0.2919 -0.0859 -0.0505 0.0085 0.0743 0.2779 0.6986 0.2118 -0.3048 -0.3398 0.1691

-0.2743 0.1036 -0.2647 -0.3142 0.3366 -0.1007 -0.5182 0.3855 -0.1371 0.3152 0.0516 -0.2896

-0.1862 0.3264 -0.0406 -0.0291 -0.0361 -0.0545 0.4939 0.1556 -0.2851 -0.3094 0.4405 -0.4613

-0.3154 -0.2028 0.3074 -0.2540 0.6006 -0.3664 0.1261 -0.3475 0.1040 -0.2334 -0.0316 0.0490

-0.2641 0.3002 -0.6199 -0.0228 0.1624 0.3588 -0.0264 -0.2914 0.2471 -0.2612 0.0707 0.2834

-0.2351 -0.2811 0.0200 0.4506 0.0460 0.3158 -0.1770 -0.1894 0.0866 -0.1512 -0.2598 -0.6287

-0.2857 0.0820 0.0166 0.7011 0.0618 -0.3528 -0.2299 0.1438 -0.2426 -0.1092 0.1643 0.3468

Givens???G:

0.7071 -0.7071 0 0 0 0 0 0 0 0 0 0

0.7071 0.7071 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated:

-0.0098 -0.3473 0.1745 0.0842 0.3510 0.5825 0.1247 0.1061 -0.1765 0.2512 0.4678 0.1980

-0.4334 -0.5270 -0.3064 -0.1440 -0.4687 -0.2058 0.1113 -0.2117 -0.0825 0.2320 0.1974 0.0308

-0.4132 0.3577 0.1519 0.0652 0.0166 0.1438 0.3585 -0.0849 -0.2054 0.5029 -0.4634 0.0864

-0.3404 0.2281 0.4277 -0.0128 -0.2495 0.0622 -0.1451 0.1026 0.6575 0.1133 0.3253 -0.0183

-0.2395 0.0466 0.3334 -0.3257 -0.2947 0.2966 -0.3632 -0.0553 -0.4519 -0.4145 -0.0944 0.1687

-0.2282 -0.2919 -0.0859 -0.0505 0.0085 0.0743 0.2779 0.6986 0.2118 -0.3048 -0.3398 0.1691

-0.2743 0.1036 -0.2647 -0.3142 0.3366 -0.1007 -0.5182 0.3855 -0.1371 0.3152 0.0516 -0.2896

-0.1862 0.3264 -0.0406 -0.0291 -0.0361 -0.0545 0.4939 0.1556 -0.2851 -0.3094 0.4405 -0.4613

-0.3154 -0.2028 0.3074 -0.2540 0.6006 -0.3664 0.1261 -0.3475 0.1040 -0.2334 -0.0316 0.0490

-0.2641 0.3002 -0.6199 -0.0228 0.1624 0.3588 -0.0264 -0.2914 0.2471 -0.2612 0.0707 0.2834

-0.2351 -0.2811 0.0200 0.4506 0.0460 0.3158 -0.1770 -0.1894 0.0866 -0.1512 -0.2598 -0.6287

-0.2857 0.0820 0.0166 0.7011 0.0618 -0.3528 -0.2299 0.1438 -0.2426 -0.1092 0.1643 0.3468

I_rotated-I

ans =

复制代码 
0.3036    0.2709    0.2678    0.1265    0.4342    0.3162   -0.0422    0.1808    0.0066   -0.0905   -0.0025    0.0362

-0.1339 -0.4000 0.0336 0.0174 0.1109 0.3516 0.1208 0.0130 -0.1490 0.2456 0.3886 0.1490

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

givens2

???Q:

-0.2130 0.0966 0.1171 -0.5760 0.1782 0.3133 0.4710 -0.2193 -0.0375 0.0206 -0.4123 -0.1677

-0.2695 -0.2314 -0.5204 -0.0443 -0.4201 0.0597 0.2122 0.4199 -0.4266 -0.0920 -0.0510 -0.0811

-0.3410 -0.0916 0.3243 0.2849 0.2953 0.1115 0.3091 -0.0351 -0.4656 0.2041 0.3493 0.3349

-0.2813 0.5158 -0.2399 0.3797 -0.0357 0.1903 -0.1194 -0.4441 -0.1657 -0.3916 -0.0492 -0.1444

-0.2480 0.3619 -0.0605 -0.5813 0.0797 -0.4437 -0.2283 0.0345 -0.1723 -0.0649 0.4148 0.0585

-0.3531 0.3370 0.1563 0.1026 -0.1279 -0.0698 -0.2879 0.2980 0.0310 0.3682 -0.5459 0.3152

-0.2905 -0.1577 0.1975 0.1988 0.4357 -0.3727 0.0238 0.3340 0.0540 -0.3706 -0.1996 -0.4373

-0.2439 -0.1041 -0.0269 -0.0538 0.1349 0.4828 -0.4496 0.0983 0.0387 0.3873 0.2478 -0.5001

-0.2866 -0.1435 -0.2506 0.1511 -0.1126 -0.4751 0.2327 -0.4259 0.2238 0.4917 0.0062 -0.2140

-0.2890 -0.1475 -0.4756 -0.0367 0.3929 0.1824 0.0030 0.0704 0.4921 -0.1436 0.0682 0.4551

-0.3086 0.1552 0.3622 0.0324 -0.4882 0.1288 0.2775 0.1809 0.4897 -0.1744 0.3318 -0.0587

-0.3092 -0.5620 0.2545 -0.1574 -0.2591 -0.0176 -0.3930 -0.3833 -0.0728 -0.2760 -0.1300 0.1785

???I:

-0.2130 0.0966 0.1171 -0.5760 0.1782 0.3133 0.4710 -0.2193 -0.0375 0.0206 -0.4123 -0.1677

-0.2695 -0.2314 -0.5204 -0.0443 -0.4201 0.0597 0.2122 0.4199 -0.4266 -0.0920 -0.0510 -0.0811

-0.3410 -0.0916 0.3243 0.2849 0.2953 0.1115 0.3091 -0.0351 -0.4656 0.2041 0.3493 0.3349

-0.2813 0.5158 -0.2399 0.3797 -0.0357 0.1903 -0.1194 -0.4441 -0.1657 -0.3916 -0.0492 -0.1444

-0.2480 0.3619 -0.0605 -0.5813 0.0797 -0.4437 -0.2283 0.0345 -0.1723 -0.0649 0.4148 0.0585

-0.3531 0.3370 0.1563 0.1026 -0.1279 -0.0698 -0.2879 0.2980 0.0310 0.3682 -0.5459 0.3152

-0.2905 -0.1577 0.1975 0.1988 0.4357 -0.3727 0.0238 0.3340 0.0540 -0.3706 -0.1996 -0.4373

-0.2439 -0.1041 -0.0269 -0.0538 0.1349 0.4828 -0.4496 0.0983 0.0387 0.3873 0.2478 -0.5001

-0.2866 -0.1435 -0.2506 0.1511 -0.1126 -0.4751 0.2327 -0.4259 0.2238 0.4917 0.0062 -0.2140

-0.2890 -0.1475 -0.4756 -0.0367 0.3929 0.1824 0.0030 0.0704 0.4921 -0.1436 0.0682 0.4551

-0.3086 0.1552 0.3622 0.0324 -0.4882 0.1288 0.2775 0.1809 0.4897 -0.1744 0.3318 -0.0587

-0.3092 -0.5620 0.2545 -0.1574 -0.2591 -0.0176 -0.3930 -0.3833 -0.0728 -0.2760 -0.1300 0.1785

Givens???G:

0.5000 -0.8660 0 0 0 0 0 0 0 0 0 0

0.8660 0.5000 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated:

0.1269 0.2487 0.5092 -0.2497 0.4530 0.1050 0.0517 -0.4733 0.3507 0.0900 -0.1620 -0.0136

-0.3193 -0.0320 -0.1588 -0.5210 -0.0558 0.3012 0.5140 0.0200 -0.2458 -0.0281 -0.3825 -0.1858

-0.3410 -0.0916 0.3243 0.2849 0.2953 0.1115 0.3091 -0.0351 -0.4656 0.2041 0.3493 0.3349

-0.2813 0.5158 -0.2399 0.3797 -0.0357 0.1903 -0.1194 -0.4441 -0.1657 -0.3916 -0.0492 -0.1444

-0.2480 0.3619 -0.0605 -0.5813 0.0797 -0.4437 -0.2283 0.0345 -0.1723 -0.0649 0.4148 0.0585

-0.3531 0.3370 0.1563 0.1026 -0.1279 -0.0698 -0.2879 0.2980 0.0310 0.3682 -0.5459 0.3152

-0.2905 -0.1577 0.1975 0.1988 0.4357 -0.3727 0.0238 0.3340 0.0540 -0.3706 -0.1996 -0.4373

-0.2439 -0.1041 -0.0269 -0.0538 0.1349 0.4828 -0.4496 0.0983 0.0387 0.3873 0.2478 -0.5001

-0.2866 -0.1435 -0.2506 0.1511 -0.1126 -0.4751 0.2327 -0.4259 0.2238 0.4917 0.0062 -0.2140

-0.2890 -0.1475 -0.4756 -0.0367 0.3929 0.1824 0.0030 0.0704 0.4921 -0.1436 0.0682 0.4551

-0.3086 0.1552 0.3622 0.0324 -0.4882 0.1288 0.2775 0.1809 0.4897 -0.1744 0.3318 -0.0587

-0.3092 -0.5620 0.2545 -0.1574 -0.2591 -0.0176 -0.3930 -0.3833 -0.0728 -0.2760 -0.1300 0.1785

givens2

???Q:

-0.2935 -0.0259 0.0015 0.2139 -0.0489 -0.4611 -0.0891 -0.2036 -0.6467 -0.3041 0.2289 0.1999

-0.3037 -0.0615 -0.1874 -0.2406 0.2362 0.0268 -0.2428 0.2005 -0.1746 0.3861 -0.4321 0.5376

-0.3455 -0.3862 0.1578 0.1785 -0.2248 -0.0386 -0.3199 0.2316 -0.1084 0.3842 -0.0105 -0.5543

-0.3650 -0.1271 -0.5569 -0.2529 0.1877 0.3898 0.1955 -0.0517 -0.0955 -0.0231 0.4591 -0.1677

-0.2849 0.1755 0.1211 0.2692 -0.3494 0.2497 0.6156 0.4143 -0.1554 -0.0274 -0.1525 0.1329

-0.2116 0.3814 -0.5207 0.5441 -0.1360 -0.0979 -0.1781 -0.2132 0.3283 0.0967 -0.1400 -0.0256

-0.3355 0.0619 0.3723 -0.0735 -0.2563 0.0732 -0.1891 -0.0833 0.3997 0.1296 0.5196 0.4234

-0.2471 0.6489 0.3768 -0.0343 0.4325 0.2163 -0.1426 -0.0702 -0.1793 0.0251 -0.0270 -0.2864

-0.2030 -0.0385 0.1106 -0.1972 0.0478 -0.3801 0.5376 -0.5018 0.0998 0.4225 -0.1292 -0.1157

-0.3064 0.1983 -0.1045 -0.5447 -0.2783 -0.3393 -0.0835 0.2278 0.2172 -0.4220 -0.2028 -0.2035

-0.2580 -0.3258 0.1656 0.0465 -0.0949 0.4386 -0.0866 -0.5030 0.0529 -0.3924 -0.4224 0.0233

-0.2604 -0.2865 0.1138 0.2963 0.6115 -0.2391 0.1492 0.2762 0.3830 -0.2686 0.0112 0.0263

???I:

-0.2935 -0.0259 0.0015 0.2139 -0.0489 -0.4611 -0.0891 -0.2036 -0.6467 -0.3041 0.2289 0.1999

-0.3037 -0.0615 -0.1874 -0.2406 0.2362 0.0268 -0.2428 0.2005 -0.1746 0.3861 -0.4321 0.5376

-0.3455 -0.3862 0.1578 0.1785 -0.2248 -0.0386 -0.3199 0.2316 -0.1084 0.3842 -0.0105 -0.5543

-0.3650 -0.1271 -0.5569 -0.2529 0.1877 0.3898 0.1955 -0.0517 -0.0955 -0.0231 0.4591 -0.1677

-0.2849 0.1755 0.1211 0.2692 -0.3494 0.2497 0.6156 0.4143 -0.1554 -0.0274 -0.1525 0.1329

-0.2116 0.3814 -0.5207 0.5441 -0.1360 -0.0979 -0.1781 -0.2132 0.3283 0.0967 -0.1400 -0.0256

-0.3355 0.0619 0.3723 -0.0735 -0.2563 0.0732 -0.1891 -0.0833 0.3997 0.1296 0.5196 0.4234

-0.2471 0.6489 0.3768 -0.0343 0.4325 0.2163 -0.1426 -0.0702 -0.1793 0.0251 -0.0270 -0.2864

-0.2030 -0.0385 0.1106 -0.1972 0.0478 -0.3801 0.5376 -0.5018 0.0998 0.4225 -0.1292 -0.1157

-0.3064 0.1983 -0.1045 -0.5447 -0.2783 -0.3393 -0.0835 0.2278 0.2172 -0.4220 -0.2028 -0.2035

-0.2580 -0.3258 0.1656 0.0465 -0.0949 0.4386 -0.0866 -0.5030 0.0529 -0.3924 -0.4224 0.0233

-0.2604 -0.2865 0.1138 0.2963 0.6115 -0.2391 0.1492 0.2762 0.3830 -0.2686 0.0112 0.0263

Givens???G:

0.5000 -0.8660 0 0 0 0 0 0 0 0 0 0

0.8660 0.5000 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

0.4098 0.0662 0.1615 0.1014 -0.1801 0.2074 0.2548 -0.0718 0.4746 -0.1823 0.2598 -0.5655

-0.1023 0.0083 0.0950 0.3055 -0.1604 -0.4127 0.0442 -0.2766 -0.4727 -0.4564 0.4143 -0.0957

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

givens2

???Q:

-0.2851 -0.0269 0.5495 0.5628 0.0184 0.0385 0.0681 0.0405 -0.2550 0.3847 0.2166 0.1768

-0.2455 0.1682 -0.0918 0.0336 0.1393 0.6881 0.0523 0.1941 0.0567 -0.3481 -0.0587 0.4906

-0.2914 0.1207 0.4956 -0.6709 0.1199 -0.0737 -0.3068 0.0896 -0.1788 0.0758 -0.2009 0.0685

-0.2185 -0.1883 0.0383 -0.2504 -0.7516 0.2563 0.0330 -0.0478 0.0163 -0.0376 0.4484 -0.1260

-0.2903 -0.5451 -0.0237 -0.0900 0.4298 -0.1592 -0.0971 -0.2815 0.3202 -0.1387 0.3969 0.1785

-0.2758 -0.1599 0.2695 0.1641 -0.1014 0.1596 0.1041 -0.0791 0.5764 -0.0142 -0.5332 -0.3594

-0.3419 -0.3473 -0.2849 -0.1790 0.0861 -0.0463 0.6170 0.1790 -0.3777 0.1680 -0.2308 -0.0538

-0.2936 0.2558 0.1246 0.1566 -0.1503 -0.4247 0.1947 -0.2511 -0.1965 -0.6800 -0.0508 0.0291

-0.2827 0.0778 -0.1144 0.1332 0.1279 -0.1503 -0.2151 0.7397 0.0849 -0.1679 0.2464 -0.3934

-0.3403 -0.1578 -0.4172 0.2193 -0.2448 -0.0967 -0.6026 -0.1137 -0.1850 0.1313 -0.3284 0.1804

-0.2486 0.4372 -0.1901 -0.1057 -0.1449 -0.3390 0.2205 0.0703 0.4781 0.3654 0.0808 0.3764

-0.3241 0.4361 -0.2222 -0.0258 0.2804 0.2715 -0.0235 -0.4525 -0.1164 0.1859 0.1880 -0.4623

???I:

-0.2851 -0.0269 0.5495 0.5628 0.0184 0.0385 0.0681 0.0405 -0.2550 0.3847 0.2166 0.1768

-0.2455 0.1682 -0.0918 0.0336 0.1393 0.6881 0.0523 0.1941 0.0567 -0.3481 -0.0587 0.4906

-0.2914 0.1207 0.4956 -0.6709 0.1199 -0.0737 -0.3068 0.0896 -0.1788 0.0758 -0.2009 0.0685

-0.2185 -0.1883 0.0383 -0.2504 -0.7516 0.2563 0.0330 -0.0478 0.0163 -0.0376 0.4484 -0.1260

-0.2903 -0.5451 -0.0237 -0.0900 0.4298 -0.1592 -0.0971 -0.2815 0.3202 -0.1387 0.3969 0.1785

-0.2758 -0.1599 0.2695 0.1641 -0.1014 0.1596 0.1041 -0.0791 0.5764 -0.0142 -0.5332 -0.3594

-0.3419 -0.3473 -0.2849 -0.1790 0.0861 -0.0463 0.6170 0.1790 -0.3777 0.1680 -0.2308 -0.0538

-0.2936 0.2558 0.1246 0.1566 -0.1503 -0.4247 0.1947 -0.2511 -0.1965 -0.6800 -0.0508 0.0291

-0.2827 0.0778 -0.1144 0.1332 0.1279 -0.1503 -0.2151 0.7397 0.0849 -0.1679 0.2464 -0.3934

-0.3403 -0.1578 -0.4172 0.2193 -0.2448 -0.0967 -0.6026 -0.1137 -0.1850 0.1313 -0.3284 0.1804

-0.2486 0.4372 -0.1901 -0.1057 -0.1449 -0.3390 0.2205 0.0703 0.4781 0.3654 0.0808 0.3764

-0.3241 0.4361 -0.2222 -0.0258 0.2804 0.2715 -0.0235 -0.4525 -0.1164 0.1859 0.1880 -0.4623

Givens???G:

0.5000 -0.8660 0 0 0 0 0 0 0 0 0 0

0.8660 0.5000 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

0.3551 -0.1322 -0.1953 -0.3105 -0.1298 -0.6152 -0.0793 -0.1883 0.0784 0.1091 -0.0575 -0.5133

-0.1241 -0.1074 0.5218 0.4706 -0.0537 -0.3107 0.0328 -0.0620 -0.2492 0.5072 0.2170 -0.0922

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

givens2

???Q:

-0.4172 0.3098 -0.0432 -0.4060 -0.1495 -0.0635 0.3103 0.4877 0.4094 0.0241 0.0201 -0.1847

-0.2677 0.2842 -0.1482 0.4556 -0.3896 0.2669 0.2289 -0.0390 -0.3860 -0.2547 0.2635 -0.2404

-0.3062 -0.0656 0.2187 0.3566 -0.4508 -0.3825 -0.1306 0.0929 0.0838 0.3154 -0.0063 0.4953

-0.2401 0.0738 -0.5365 0.3563 0.4626 0.2442 -0.1155 0.1806 0.0963 0.4270 -0.0342 0.0983

-0.2105 -0.3243 -0.1932 -0.1103 -0.3783 0.1164 -0.0387 -0.4052 0.0983 0.3356 -0.4115 -0.4324

-0.2901 -0.3313 0.1413 0.3893 0.2300 -0.2038 -0.1960 0.1789 0.2423 -0.5138 -0.2175 -0.3157

-0.3550 0.1570 -0.4199 -0.2909 -0.0100 -0.1358 -0.3130 -0.4205 0.0712 -0.4167 0.0745 0.3329

-0.2345 0.3629 0.3089 -0.1705 0.1205 -0.0742 -0.5960 0.0924 -0.4172 0.2045 -0.0571 -0.2930

-0.3332 0.1542 0.5519 0.0647 0.2744 0.3929 0.2007 -0.4443 0.2602 0.0579 0.0198 0.1329

-0.2006 0.0461 -0.0282 -0.0588 0.2352 -0.2696 0.4810 -0.0178 -0.4892 -0.0462 -0.5663 0.1778

-0.2752 -0.3930 -0.0085 -0.1226 0.2429 -0.3625 0.2101 -0.1483 -0.1870 0.2056 0.6181 -0.1972

-0.2577 -0.5118 0.0776 -0.2709 -0.0919 0.5304 -0.1099 0.3436 -0.2786 -0.1132 0.0188 0.2857

???I:

-0.4172 0.3098 -0.0432 -0.4060 -0.1495 -0.0635 0.3103 0.4877 0.4094 0.0241 0.0201 -0.1847

-0.2677 0.2842 -0.1482 0.4556 -0.3896 0.2669 0.2289 -0.0390 -0.3860 -0.2547 0.2635 -0.2404

-0.3062 -0.0656 0.2187 0.3566 -0.4508 -0.3825 -0.1306 0.0929 0.0838 0.3154 -0.0063 0.4953

-0.2401 0.0738 -0.5365 0.3563 0.4626 0.2442 -0.1155 0.1806 0.0963 0.4270 -0.0342 0.0983

-0.2105 -0.3243 -0.1932 -0.1103 -0.3783 0.1164 -0.0387 -0.4052 0.0983 0.3356 -0.4115 -0.4324

-0.2901 -0.3313 0.1413 0.3893 0.2300 -0.2038 -0.1960 0.1789 0.2423 -0.5138 -0.2175 -0.3157

-0.3550 0.1570 -0.4199 -0.2909 -0.0100 -0.1358 -0.3130 -0.4205 0.0712 -0.4167 0.0745 0.3329

-0.2345 0.3629 0.3089 -0.1705 0.1205 -0.0742 -0.5960 0.0924 -0.4172 0.2045 -0.0571 -0.2930

-0.3332 0.1542 0.5519 0.0647 0.2744 0.3929 0.2007 -0.4443 0.2602 0.0579 0.0198 0.1329

-0.2006 0.0461 -0.0282 -0.0588 0.2352 -0.2696 0.4810 -0.0178 -0.4892 -0.0462 -0.5663 0.1778

-0.2752 -0.3930 -0.0085 -0.1226 0.2429 -0.3625 0.2101 -0.1483 -0.1870 0.2056 0.6181 -0.1972

-0.2577 -0.5118 0.0776 -0.2709 -0.0919 0.5304 -0.1099 0.3436 -0.2786 -0.1132 0.0188 0.2857

Givens???G:

0.8660 -0.5000 0 0 0 0 0 0 0 0 0 0

0.5000 0.8660 0 0 0 0 0 0 0 0 0 0

0 0 1.0000 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

0.1897 -0.1836 0.0799 -0.1734 0.2148 -0.1249 -0.1560 -0.0458 0.1381 0.1241 -0.1345 0.1450

-0.1727 0.1168 -0.0018 -0.2640 -0.0226 -0.0675 0.1245 0.2491 0.2564 0.0462 -0.0253 -0.0602

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

givens2

???Q:

-0.3029 0.1078 -0.5232 -0.0478 0.1955 -0.1514 -0.2248 -0.2935 -0.2631 0.1133 0.5027 0.2967

-0.2730 -0.1300 -0.0435 0.6010 0.0238 -0.1963 -0.1146 -0.2408 -0.2028 -0.3026 -0.1042 -0.5400

-0.1758 -0.1925 -0.2748 0.0930 -0.0215 -0.0575 -0.3600 0.0738 0.7152 -0.3091 -0.1801 0.2637

-0.2996 -0.1389 0.6946 -0.1496 -0.2213 -0.3563 -0.1276 -0.1945 0.0832 -0.0971 0.3410 0.1533

-0.3687 -0.0504 -0.2240 -0.4481 -0.6399 0.2612 -0.0813 -0.1220 -0.1407 -0.0323 -0.2014 -0.2237

-0.2984 0.2113 0.2195 0.0356 0.1979 0.3515 -0.5411 0.5602 -0.1484 0.0356 0.1037 -0.1163

-0.1782 0.4492 0.1777 0.0133 0.2252 0.3163 -0.0155 -0.5569 0.3838 0.2965 -0.1139 -0.1594

-0.3447 -0.3626 0.0803 -0.0199 0.2640 -0.1709 -0.0212 -0.0079 -0.2104 0.4477 -0.5779 0.2545

-0.2793 -0.2402 0.0875 -0.1129 0.3563 0.4771 0.4037 -0.0870 -0.1025 -0.5217 0.0548 0.1821

-0.2859 0.0698 -0.1369 -0.4121 0.3193 -0.4042 0.2992 0.2827 0.2500 0.0165 0.0878 -0.4686

-0.3374 -0.1320 -0.0598 0.4463 -0.2968 0.1860 0.4230 0.2509 0.2200 0.3966 0.3037 0.0581

-0.2528 0.6744 0.0128 0.1450 -0.1605 -0.2485 0.2427 0.1525 -0.1278 -0.2649 -0.2941 0.3427

???I:

-0.3029 0.1078 -0.5232 -0.0478 0.1955 -0.1514 -0.2248 -0.2935 -0.2631 0.1133 0.5027 0.2967

-0.2730 -0.1300 -0.0435 0.6010 0.0238 -0.1963 -0.1146 -0.2408 -0.2028 -0.3026 -0.1042 -0.5400

-0.1758 -0.1925 -0.2748 0.0930 -0.0215 -0.0575 -0.3600 0.0738 0.7152 -0.3091 -0.1801 0.2637

-0.2996 -0.1389 0.6946 -0.1496 -0.2213 -0.3563 -0.1276 -0.1945 0.0832 -0.0971 0.3410 0.1533

-0.3687 -0.0504 -0.2240 -0.4481 -0.6399 0.2612 -0.0813 -0.1220 -0.1407 -0.0323 -0.2014 -0.2237

-0.2984 0.2113 0.2195 0.0356 0.1979 0.3515 -0.5411 0.5602 -0.1484 0.0356 0.1037 -0.1163

-0.1782 0.4492 0.1777 0.0133 0.2252 0.3163 -0.0155 -0.5569 0.3838 0.2965 -0.1139 -0.1594

-0.3447 -0.3626 0.0803 -0.0199 0.2640 -0.1709 -0.0212 -0.0079 -0.2104 0.4477 -0.5779 0.2545

-0.2793 -0.2402 0.0875 -0.1129 0.3563 0.4771 0.4037 -0.0870 -0.1025 -0.5217 0.0548 0.1821

-0.2859 0.0698 -0.1369 -0.4121 0.3193 -0.4042 0.2992 0.2827 0.2500 0.0165 0.0878 -0.4686

-0.3374 -0.1320 -0.0598 0.4463 -0.2968 0.1860 0.4230 0.2509 0.2200 0.3966 0.3037 0.0581

-0.2528 0.6744 0.0128 0.1450 -0.1605 -0.2485 0.2427 0.1525 -0.1278 -0.2649 -0.2941 0.3427

Givens???G:

0.8660 0 -0.5000 0 0 0 0 0 0 0 0 0

0 1.0000 0 0 0 0 0 0 0 0 0 0

0.5000 0 0.8660 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

0.1285 0.0818 0.2075 -0.0401 -0.0154 0.0490 0.2101 0.0024 -0.3224 0.1393 0.0227 -0.1716

0 0 0 0 0 0 0 0 0 0 0 0

-0.1279 0.0797 -0.2248 -0.0363 0.1007 -0.0680 -0.0642 -0.1567 -0.2274 0.0981 0.2755 0.1130

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

givens2

???Q:

-0.3135 -0.0778 -0.4246 -0.3232 0.1638 -0.5077 -0.1003 -0.3049 0.1660 0.0696 0.3109 0.3071

-0.2680 -0.5169 0.0444 0.3857 0.1039 -0.0091 -0.1409 0.2194 -0.2598 -0.3927 0.4532 -0.0653

-0.2798 0.3129 -0.0598 0.1167 0.0234 0.4478 -0.2342 -0.3587 0.4205 -0.1013 0.3009 -0.3799

-0.2557 -0.3182 -0.5402 -0.3698 -0.2005 0.4161 0.0443 0.0591 -0.2690 0.0452 -0.2534 -0.2179

-0.2832 -0.0576 0.2939 -0.3712 0.0044 -0.2463 0.5071 0.2231 0.3026 -0.2480 -0.0034 -0.4143

-0.4090 -0.0807 0.1652 0.0077 0.4462 0.2384 -0.1455 0.4305 0.2595 0.4246 -0.1545 0.2545

-0.2963 0.5686 -0.2737 0.2706 -0.0452 -0.0008 0.4597 0.2470 -0.3160 0.0980 0.2205 0.0913

-0.3151 0.3158 0.0051 0.0265 0.2122 -0.1952 -0.3368 -0.0360 -0.2080 -0.5077 -0.5489 -0.0054

-0.2491 -0.0444 0.0453 0.1256 -0.7198 0.0443 -0.0370 0.1151 0.3537 -0.1961 -0.1121 0.4554

-0.2876 0.1163 0.4024 -0.2046 -0.3740 -0.1936 -0.3793 -0.0091 -0.3788 0.3982 0.1611 -0.2252

-0.2072 -0.0772 0.4110 -0.1768 0.1250 0.3380 0.3339 -0.5128 -0.2850 -0.1072 0.0300 0.3911

-0.2528 -0.2706 -0.0295 0.5438 -0.0426 -0.2433 0.2311 -0.3912 0.0631 0.3332 -0.3605 -0.2320

???I:

-0.3135 -0.0778 -0.4246 -0.3232 0.1638 -0.5077 -0.1003 -0.3049 0.1660 0.0696 0.3109 0.3071

-0.2680 -0.5169 0.0444 0.3857 0.1039 -0.0091 -0.1409 0.2194 -0.2598 -0.3927 0.4532 -0.0653

-0.2798 0.3129 -0.0598 0.1167 0.0234 0.4478 -0.2342 -0.3587 0.4205 -0.1013 0.3009 -0.3799

-0.2557 -0.3182 -0.5402 -0.3698 -0.2005 0.4161 0.0443 0.0591 -0.2690 0.0452 -0.2534 -0.2179

-0.2832 -0.0576 0.2939 -0.3712 0.0044 -0.2463 0.5071 0.2231 0.3026 -0.2480 -0.0034 -0.4143

-0.4090 -0.0807 0.1652 0.0077 0.4462 0.2384 -0.1455 0.4305 0.2595 0.4246 -0.1545 0.2545

-0.2963 0.5686 -0.2737 0.2706 -0.0452 -0.0008 0.4597 0.2470 -0.3160 0.0980 0.2205 0.0913

-0.3151 0.3158 0.0051 0.0265 0.2122 -0.1952 -0.3368 -0.0360 -0.2080 -0.5077 -0.5489 -0.0054

-0.2491 -0.0444 0.0453 0.1256 -0.7198 0.0443 -0.0370 0.1151 0.3537 -0.1961 -0.1121 0.4554

-0.2876 0.1163 0.4024 -0.2046 -0.3740 -0.1936 -0.3793 -0.0091 -0.3788 0.3982 0.1611 -0.2252

-0.2072 -0.0772 0.4110 -0.1768 0.1250 0.3380 0.3339 -0.5128 -0.2850 -0.1072 0.0300 0.3911

-0.2528 -0.2706 -0.0295 0.5438 -0.0426 -0.2433 0.2311 -0.3912 0.0631 0.3332 -0.3605 -0.2320

复制代码 
0.8660         0   -0.5000         0         0         0         0         0         0         0         0         0
     0    1.0000         0         0         0         0         0         0         0         0         0         0
0.5000         0    0.8660         0         0         0         0         0         0         0         0         0
     0         0         0    1.0000         0         0         0         0         0         0         0         0
     0         0         0         0    1.0000         0         0         0         0         0         0         0
     0         0         0         0         0    1.0000         0         0         0         0         0         0
     0         0         0         0         0         0    1.0000         0         0         0         0         0
     0         0         0         0         0         0         0    1.0000         0         0         0         0
     0         0         0         0         0         0         0         0    1.0000         0         0         0
     0         0         0         0         0         0         0         0         0    1.0000         0         0
     0         0         0         0         0         0         0         0         0         0    1.0000         0
     0         0         0         0         0         0         0         0         0         0         0    1.0000

givens2

???Q:

-0.2636 0.3766 -0.2845 -0.2814 0.2787 0.1600 -0.1239 -0.4145 0.0815 -0.0925 0.5199 0.2295

-0.2721 -0.0120 0.0085 -0.1484 -0.5354 0.0850 0.1319 0.2094 -0.4722 0.4205 0.3830 0.0455

-0.2486 0.1738 0.4987 -0.0728 0.0476 0.2685 0.5410 -0.2589 -0.2614 -0.3292 -0.2043 -0.0394

-0.3251 -0.2302 0.4850 -0.0324 0.1713 -0.0377 -0.3842 0.0770 0.1068 -0.0678 0.3462 -0.5338

-0.2866 0.2531 0.2511 -0.1317 -0.3787 -0.5180 0.0610 0.0991 0.5050 -0.1116 -0.0303 0.2824

-0.2702 -0.2126 -0.1688 0.4473 -0.3285 -0.2127 -0.1707 -0.6557 -0.1382 -0.0613 -0.1101 -0.0776

-0.3080 -0.4579 -0.0126 0.0780 0.3400 0.0108 0.4272 -0.0916 0.3292 0.4951 0.0156 0.1696

-0.1796 0.1301 -0.3073 -0.5584 -0.0042 -0.1582 0.0481 -0.1193 0.0119 0.2184 -0.4173 -0.5301

-0.2348 0.2490 -0.3565 0.4297 0.2002 -0.2958 0.3682 0.3445 -0.0968 -0.2136 0.1976 -0.3085

-0.3312 -0.3238 -0.3374 -0.0837 -0.2796 0.5014 -0.0216 0.2529 0.2688 -0.4345 -0.0965 0.0132

-0.3270 0.4842 0.0862 0.3736 0.0571 0.3662 -0.3086 0.1412 0.0958 0.3679 -0.3366 0.0351

-0.3676 -0.1940 -0.0244 -0.1606 0.3399 -0.2862 -0.2795 0.2155 -0.4660 -0.1511 -0.2690 0.4081

???I:

-0.2636 0.3766 -0.2845 -0.2814 0.2787 0.1600 -0.1239 -0.4145 0.0815 -0.0925 0.5199 0.2295

-0.2721 -0.0120 0.0085 -0.1484 -0.5354 0.0850 0.1319 0.2094 -0.4722 0.4205 0.3830 0.0455

-0.2486 0.1738 0.4987 -0.0728 0.0476 0.2685 0.5410 -0.2589 -0.2614 -0.3292 -0.2043 -0.0394

-0.3251 -0.2302 0.4850 -0.0324 0.1713 -0.0377 -0.3842 0.0770 0.1068 -0.0678 0.3462 -0.5338

-0.2866 0.2531 0.2511 -0.1317 -0.3787 -0.5180 0.0610 0.0991 0.5050 -0.1116 -0.0303 0.2824

-0.2702 -0.2126 -0.1688 0.4473 -0.3285 -0.2127 -0.1707 -0.6557 -0.1382 -0.0613 -0.1101 -0.0776

-0.3080 -0.4579 -0.0126 0.0780 0.3400 0.0108 0.4272 -0.0916 0.3292 0.4951 0.0156 0.1696

-0.1796 0.1301 -0.3073 -0.5584 -0.0042 -0.1582 0.0481 -0.1193 0.0119 0.2184 -0.4173 -0.5301

-0.2348 0.2490 -0.3565 0.4297 0.2002 -0.2958 0.3682 0.3445 -0.0968 -0.2136 0.1976 -0.3085

-0.3312 -0.3238 -0.3374 -0.0837 -0.2796 0.5014 -0.0216 0.2529 0.2688 -0.4345 -0.0965 0.0132

-0.3270 0.4842 0.0862 0.3736 0.0571 0.3662 -0.3086 0.1412 0.0958 0.3679 -0.3366 0.0351

-0.3676 -0.1940 -0.0244 -0.1606 0.3399 -0.2862 -0.2795 0.2155 -0.4660 -0.1511 -0.2690 0.4081

复制代码 
0.8660         0   -0.5000         0         0         0         0         0         0         0         0         0
     0    1.0000         0         0         0         0         0         0         0         0         0         0
0.5000         0    0.8660         0         0         0         0         0         0         0         0         0
     0         0         0    1.0000         0         0         0         0         0         0         0         0
     0         0         0         0    1.0000         0         0         0         0         0         0         0
     0         0         0         0         0    1.0000         0         0         0         0         0         0
     0         0         0         0         0         0    1.0000         0         0         0         0         0
     0         0         0         0         0         0         0    1.0000         0         0         0         0
     0         0         0         0         0         0         0         0    1.0000         0         0         0
     0         0         0         0         0         0         0         0         0    1.0000         0         0
     0         0         0         0         0         0         0         0         0         0    1.0000         0
     0         0         0         0         0         0         0         0         0         0         0    1.0000

Givens???G:

0.8660 0 -0.5000 0 0 0 0 0 0 0 0 0

0 1.0000 0 0 0 0 0 0 0 0 0 0

0.5000 0 0.8660 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

-0.1069 0 0.1699 0 0 0 0 0 0 0 0 0

0.0407 0 0.1349 0 0 0 0 0 0 0 0 0

0.2826 0 0.0575 0 0 0 0 0 0 0 0 0

0.2860 0 0.0976 0 0 0 0 0 0 0 0 0

0.1639 0 0.1096 0 0 0 0 0 0 0 0 0

-0.0482 0 0.1577 0 0 0 0 0 0 0 0 0

0.0350 0 0.1557 0 0 0 0 0 0 0 0 0

-0.1296 0 0.1309 0 0 0 0 0 0 0 0 0

-0.1468 0 0.1652 0 0 0 0 0 0 0 0 0

-0.1243 0 0.2108 0 0 0 0 0 0 0 0 0

0.0869 0 0.1519 0 0 0 0 0 0 0 0 0

0.0371 0 0.1871 0 0 0 0 0 0 0 0 0

givens2

???Q:

-0.2427 -0.4000 0.0453 0.3648 0.0497 0.3207 0.1316 -0.4307 -0.2574 -0.4198 0.3082 -0.0176

-0.2509 -0.0232 -0.2816 0.4106 0.5708 -0.1450 -0.2632 0.1693 0.1762 -0.2127 -0.4086 -0.0239

-0.2734 -0.3568 0.5163 0.3055 -0.0043 -0.4555 0.0383 0.2043 0.0692 0.3640 0.1883 0.1209

-0.3042 -0.0542 -0.4038 0.0973 -0.4188 0.1398 -0.0278 0.3933 -0.1801 -0.0006 0.0002 0.5909

-0.3324 -0.3830 -0.0868 -0.4305 -0.0346 -0.1692 0.2189 -0.2930 -0.2239 0.1357 -0.5622 -0.0417

-0.3119 -0.0465 0.1732 -0.3345 -0.2061 -0.1359 -0.3847 0.3573 -0.1157 -0.4862 0.1213 -0.3970

-0.2853 0.4893 -0.1365 0.0105 0.2857 -0.2103 0.1241 -0.0231 -0.6260 0.2109 0.2632 -0.1143

-0.3427 0.1460 0.1333 -0.1555 0.1954 0.2952 0.6739 0.3286 0.3363 -0.1174 0.0342 -0.0622

-0.2327 0.0484 -0.2351 0.3620 -0.4176 0.1917 -0.0108 -0.0254 0.1479 0.3717 -0.0828 -0.6151

-0.2935 -0.0307 0.1842 -0.2566 0.2811 0.5575 -0.4842 -0.0696 0.0607 0.3966 0.0875 0.1239

-0.2631 0.5382 0.4497 0.1833 -0.2794 -0.0087 -0.0801 -0.3247 0.0637 -0.1910 -0.3512 0.2268

-0.3077 0.0823 -0.3517 -0.2086 -0.0366 -0.3507 -0.0692 -0.3956 0.5171 -0.0330 0.4042 0.1177

???I:

-0.2427 -0.4000 0.0453 0.3648 0.0497 0.3207 0.1316 -0.4307 -0.2574 -0.4198 0.3082 -0.0176

-0.2509 -0.0232 -0.2816 0.4106 0.5708 -0.1450 -0.2632 0.1693 0.1762 -0.2127 -0.4086 -0.0239

-0.2734 -0.3568 0.5163 0.3055 -0.0043 -0.4555 0.0383 0.2043 0.0692 0.3640 0.1883 0.1209

-0.3042 -0.0542 -0.4038 0.0973 -0.4188 0.1398 -0.0278 0.3933 -0.1801 -0.0006 0.0002 0.5909

-0.3324 -0.3830 -0.0868 -0.4305 -0.0346 -0.1692 0.2189 -0.2930 -0.2239 0.1357 -0.5622 -0.0417

-0.3119 -0.0465 0.1732 -0.3345 -0.2061 -0.1359 -0.3847 0.3573 -0.1157 -0.4862 0.1213 -0.3970

-0.2853 0.4893 -0.1365 0.0105 0.2857 -0.2103 0.1241 -0.0231 -0.6260 0.2109 0.2632 -0.1143

-0.3427 0.1460 0.1333 -0.1555 0.1954 0.2952 0.6739 0.3286 0.3363 -0.1174 0.0342 -0.0622

-0.2327 0.0484 -0.2351 0.3620 -0.4176 0.1917 -0.0108 -0.0254 0.1479 0.3717 -0.0828 -0.6151

-0.2935 -0.0307 0.1842 -0.2566 0.2811 0.5575 -0.4842 -0.0696 0.0607 0.3966 0.0875 0.1239

-0.2631 0.5382 0.4497 0.1833 -0.2794 -0.0087 -0.0801 -0.3247 0.0637 -0.1910 -0.3512 0.2268

-0.3077 0.0823 -0.3517 -0.2086 -0.0366 -0.3507 -0.0692 -0.3956 0.5171 -0.0330 0.4042 0.1177

复制代码 
0.8660         0   -0.5000         0         0         0         0         0         0         0         0         0
     0    1.0000         0         0         0         0         0         0         0         0         0         0
0.5000         0    0.8660         0         0         0         0         0         0         0         0         0
     0         0         0    1.0000         0         0         0         0         0         0         0         0
     0         0         0         0    1.0000         0         0         0         0         0         0         0
     0         0         0         0         0    1.0000         0         0         0         0         0         0
     0         0         0         0         0         0    1.0000         0         0         0         0         0
     0         0         0         0         0         0         0    1.0000         0         0         0         0
     0         0         0         0         0         0         0         0    1.0000         0         0         0
     0         0         0         0         0         0         0         0         0    1.0000         0         0
     0         0         0         0         0         0         0         0         0         0    1.0000         0
     0         0         0         0         0         0         0         0         0         0         0    1.0000

Givens???G:

0.8660 0 -0.5000 0 0 0 0 0 0 0 0 0

0 1.0000 0 0 0 0 0 0 0 0 0 0

0.5000 0 0.8660 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

0.1692 0.2320 -0.2642 -0.2016 -0.0045 0.1848 -0.0368 -0.0444 -0.0001 -0.1257 -0.1354 -0.0581

0 0 0 0 0 0 0 0 0 0 0 0

-0.0847 -0.1522 -0.0465 0.1415 0.0254 0.2214 0.0607 -0.2427 -0.1380 -0.2586 0.1289 -0.0250

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

givens2

???Q:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

???I:

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 1

复制代码 
0.8660         0   -0.5000         0         0         0         0         0         0         0         0         0
     0    1.0000         0         0         0         0         0         0         0         0         0         0
0.5000         0    0.8660         0         0         0         0         0         0         0         0         0
     0         0         0    1.0000         0         0         0         0         0         0         0         0
     0         0         0         0    1.0000         0         0         0         0         0         0         0
     0         0         0         0         0    1.0000         0         0         0         0         0         0
     0         0         0         0         0         0    1.0000         0         0         0         0         0
     0         0         0         0         0         0         0    1.0000         0         0         0         0
     0         0         0         0         0         0         0         0    1.0000         0         0         0
     0         0         0         0         0         0         0         0         0    1.0000         0         0
     0         0         0         0         0         0         0         0         0         0    1.0000         0
     0         0         0         0         0         0         0         0         0         0         0    1.0000

Givens???G:

0.8660 0 -0.5000 0 0 0 0 0 0 0 0 0

0 1.0000 0 0 0 0 0 0 0 0 0 0

0.5000 0 0.8660 0 0 0 0 0 0 0 0 0

0 0 0 1.0000 0 0 0 0 0 0 0 0

0 0 0 0 1.0000 0 0 0 0 0 0 0

0 0 0 0 0 1.0000 0 0 0 0 0 0

0 0 0 0 0 0 1.0000 0 0 0 0 0

0 0 0 0 0 0 0 1.0000 0 0 0 0

0 0 0 0 0 0 0 0 1.0000 0 0 0

0 0 0 0 0 0 0 0 0 1.0000 0 0

0 0 0 0 0 0 0 0 0 0 1.0000 0

0 0 0 0 0 0 0 0 0 0 0 1.0000

???I_rotated-I:

-0.1340 0 -0.5000 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0.5000 0 -0.1340 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

相关推荐
Deep-w7 小时前
【MATLAB】基于 MATLAB/Simulink 的无刷直流电机（BLDC）转速控制模糊 PID 算法
开发语言·算法·matlab
Evand J8 小时前
【MATLAB代码介绍】到达时间（TOA）定位，三维空间，带EKF的轨迹滤波与误差分析
开发语言·matlab
吃好睡好便好12 小时前
用if…elseif…end语句输出成绩等级
开发语言·前端·javascript·数据库·学习·matlab·信息可视化
Deep-w12 小时前
【MATLAB】基于遗传算法的直流电机 PI 控制器参数优化研究
开发语言·算法·matlab
吃好睡好便好1 天前
用if…end…语句计算分段函数
开发语言·人工智能·学习·算法·matlab
Matlab程序猿小助手1 天前
【MATLAB源码-第319期】基于matlab的帝王蝶优化算法(MBO)无人机三维路径规划，输出做短路径图和适应度曲线.
开发语言·算法·matlab
Evand J1 天前
【MATLAB控制例程】（9）多无人机编队协同控制与三维轨迹规划仿真，附下载链接
开发语言·分布式·matlab·无人机·控制
吃好睡好便好1 天前
在Matlab中绘制质点三维运动轨迹图
开发语言·学习·matlab·信息可视化
茗创科技1 天前
脑室周围扩散率（PVeD）专题：一种评估类淋巴系统功能的DTI新方法（附高分文献下载）
深度学习·机器学习·matlab·脑网络
热门推荐
01GitHub 镜像站点02Codex 接入 DeepSeek API 完整配置文档03【踩坑记录 | 第一篇】微软商店无法使用时，如何手动安装 OpenAI Codex？附`.msix`文件系统错误解决方法04裂开！ChatGPT 居然开始要手机号验证，附详细解决方法05CC-Switch & Claude 基于 Linux 服务器安装使用指南06【AI】2026 年具身智能模型和世界模型总结07几个好用的ip纯净度检测网站08codex app每次打开重连5次Reconnecting问题解决09装上就回不去了：CodeGraph 让 AI 编程效率飙升 92%，它到底做了什么？10CC-Switch 全平台下载、安装与使用全指南（Windows/macOS/Linux）