Compute the distance in the L2-norm of two complexes viewed as a sequence of matrices
i1 : needsPackage "RandomComplexes" o1 = RandomComplexes o1 : Package |
i2 : setRandomSeed "a good example"; |
i3 : h={2,3,5,2}
o3 = {2, 3, 5, 2}
o3 : List
|
i4 : r={4,3,3}
o4 = {4, 3, 3}
o4 : List
|
i5 : elapsedTime C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
-- 0.00323298 seconds elapsed
6 10 11 5
o5 = ZZ <-- ZZ <-- ZZ <-- ZZ
0 1 2 3
o5 : ChainComplex
|
i6 : C.dd^2
6 11
o6 = 0 : ZZ <----- ZZ : 2
0
10 5
1 : ZZ <----- ZZ : 3
0
o6 : ChainComplexMap
|
i7 : CR=(C**RR_53)
6 10 11 5
o7 = RR <-- RR <-- RR <-- RR
53 53 53 53
0 1 2 3
o7 : ChainComplex
|
i8 : h=(SVDHomology CR)_0
o8 = HashTable{0 => 2}
1 => 3
2 => 5
3 => 2
o8 : HashTable
|
i9 : D=disturb(C,1e-2,Strategy=>Discrete)
6 10 11 5
o9 = RR <-- RR <-- RR <-- RR
53 53 53 53
0 1 2 3
o9 : ChainComplex
|
i10 : C.dd_1
o10 = | -3 4 -4 -2 0 2 -4 -1 -1 -2 |
| -4 4 -3 -1 -2 1 -2 -1 1 -6 |
| -1 -4 2 2 0 -2 0 5 -1 -2 |
| 2 -2 3 -1 4 1 -1 -3 7 5 |
| -5 2 -3 -3 4 3 -9 0 4 -1 |
| 2 4 -3 -3 2 3 -2 -5 -1 6 |
6 10
o10 : Matrix ZZ <--- ZZ
|
i11 : D.dd_1
o11 = | -3.03 4.04 -3.96 -2.02 0 2.02 -3.96 -.99 -1.01 -1.98 |
| -4.04 4.04 -3.03 -1.01 -1.98 1.01 -1.98 -.99 1.01 -5.94 |
| -.99 -4.04 1.98 1.98 0 -2.02 0 4.95 -1.01 -2.02 |
| 1.98 -2.02 3.03 -.99 4.04 .99 -1.01 -2.97 6.93 5.05 |
| -4.95 2.02 -3.03 -2.97 4.04 2.97 -9.09 0 4.04 -.99 |
| 2.02 4.04 -2.97 -3.03 2.02 3.03 -1.98 -4.95 -1.01 5.94 |
6 10
o11 : Matrix RR <--- RR
53 53
|
i12 : D.dd^2
6 11
o12 = 0 : RR <------------------------------------------------------------------------------------------------- RR : 2
53 | .404 -1.0068 1.5192 1.1538 1.9168 -.96 .463 -.5122 .6336 -2.0516 1.8312 | 53
| .0646 -1.1216 .8444 1.6532 1.8214 -.2892 .4242 -1.2694 -7.10543e-15 -2.2028 1.676 |
| -.1616 .2424 -1.3062 -.932 -1.1766 .5156 -.524 .4172 -1.12 2.0808 -.198 |
| .4674 -.5608 .3608 -1.2064 -.004 -.7272 .1204 1.2226 1.0408 -.1148 -.3548 |
| -1.0218 -.7936 -.4102 -.2552 -.0934 -.1212 -.1192 1.031 -2.0768 1.2952 -.2756 |
| -.1818 1.23 1.303 1.7906 .596 .1688 .5644 -1.0064 .3944 -1.2468 -.3224 |
10 5
1 : RR <----------------------------------------------- RR : 3
53 | -.6666 -.2352 -3.0378 .1148 -.2808 | 53
| -4.9212 -3.1936 3.2648 -.5656 -.0446 |
| -.948 -.2004 1.4232 -.4356 -1.6118 |
| .0082 .7928 -.6338 .6336 -3.4756 |
| -.96 -1.0344 -.906 -.5544 1.8058 |
| -2.7814 -.6764 1.3226 .358 -3.0424 |
| -2.8502 -1.7236 1.2766 -.8808 .2148 |
| -1.7776 -.9696 -.6352 -1.2024 1.158 |
| -.5156 -.4808 .1528 -.4008 .7854 |
| -2.7992 -1.0312 2.1204 .2796 -2.8468 |
o12 : ChainComplexMap
|
i13 : C'=projectToComplex(D,h)
6 10 11 5
o13 = RR <-- RR <-- RR <-- RR
53 53 53 53
0 1 2 3
o13 : ChainComplex
|
i14 : C'.dd^2
6 11
o14 = 0 : RR <----------------------------------------------------------------------------------------------------------------------------------------------------- RR : 2
53 | 1.06581e-14 -1.06581e-14 1.42109e-14 -7.10543e-15 1.06581e-14 -2.13163e-14 0 1.06581e-14 2.13163e-14 -2.13163e-14 1.42109e-14 | 53
| 3.19744e-14 -3.55271e-14 1.06581e-14 -6.39488e-14 1.77636e-14 -4.9738e-14 -1.24345e-14 6.75016e-14 2.84217e-14 -2.13163e-14 7.10543e-15 |
| 2.30926e-14 -1.06581e-14 1.59872e-14 -2.93099e-14 1.95399e-14 -3.55271e-14 -2.77556e-15 4.26326e-14 1.06581e-14 -2.13163e-14 1.86517e-14 |
| -2.13163e-14 7.10543e-15 -1.24345e-14 -5.32907e-15 -2.4869e-14 1.42109e-14 -2.66454e-15 -1.77636e-14 -1.42109e-14 3.90799e-14 -2.4869e-14 |
| 3.90799e-14 -4.9738e-14 3.55271e-14 -2.84217e-14 4.9738e-14 -4.9738e-14 -8.88178e-16 3.55271e-14 7.81597e-14 -4.9738e-14 5.68434e-14 |
| -2.4869e-14 1.42109e-14 0 5.68434e-14 -8.88178e-15 4.26326e-14 1.19904e-14 -7.99361e-14 3.55271e-15 0 3.55271e-15 |
10 5
1 : RR <------------------------------------------------------------------------ RR : 3
53 | -4.89053e-14 -2.52576e-14 3.19189e-16 7.10543e-15 -5.50671e-14 | 53
| 1.32449e-14 1.52524e-14 -4.77302e-14 3.21965e-15 -3.33067e-16 |
| 1.50019e-14 1.55986e-14 5.6205e-15 -3.55271e-15 2.30926e-14 |
| 1.78e-14 2.53617e-15 1.41727e-15 -3.10862e-15 6.66134e-15 |
| 8.51402e-15 1.12965e-14 -5.00572e-14 7.10543e-15 -2.30926e-14 |
| 1.59872e-14 1.04639e-14 -1.70003e-14 0 1.42109e-14 |
| 9.24955e-15 6.89726e-15 -3.305e-14 3.55271e-15 -5.32907e-15 |
| 1.54633e-14 1.71946e-14 -7.05581e-14 2.13163e-14 7.10543e-15 |
| 8.13141e-15 3.10429e-15 -1.6048e-14 2.08167e-15 -4.02456e-15 |
| 2.68743e-14 1.06443e-14 -3.12181e-14 -7.10543e-15 1.95399e-14 |
o14 : ChainComplexMap
|
i15 : euclideanDistance(C',D) o15 = .448104803679259 o15 : RR (of precision 53) |
i16 : euclideanDistance(CR,D) o16 = .320600000000001 o16 : RR (of precision 53) |
i17 : euclideanDistance(C',CR) o17 = .476857690728904 o17 : RR (of precision 53) |