beta = 1.0000000 S = 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 h = 0.0000000 0.0000000 0.0000000 Probabilities and CDF for IID fair: [ 1 1 1 ] 0.1250000 0.1250000 [ 1 1 -1 ] 0.1250000 0.2500000 [ 1 -1 1 ] 0.1250000 0.3750000 [ 1 -1 -1 ] 0.1250000 0.5000000 [ -1 1 1 ] 0.1250000 0.6250000 [ -1 1 -1 ] 0.1250000 0.7500000 [ -1 -1 1 ] 0.1250000 0.8750000 [ -1 -1 -1 ] 0.1250000 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 3.0000000 volume = 8.0000000 Probabilities and CDF for IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7290000 [ 1 1 -1 ] 0.0810000 0.8100000 [ 1 -1 1 ] 0.0810000 0.8910000 [ 1 -1 -1 ] 0.0090000 0.9000000 [ -1 1 1 ] 0.0810000 0.9810000 [ -1 1 -1 ] 0.0090000 0.9900000 [ -1 -1 1 ] 0.0090000 0.9990000 [ -1 -1 -1 ] 0.0010000 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 1.4069868 volume = 2.6518272 Probabilities and CDF for indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.3360000 [ 1 1 -1 ] 0.0840000 0.4200000 [ 1 -1 1 ] 0.1440000 0.5640000 [ 1 -1 -1 ] 0.0360000 0.6000000 [ -1 1 1 ] 0.2240000 0.8240000 [ -1 1 -1 ] 0.0560000 0.8800000 [ -1 -1 1 ] 0.0960000 0.9760000 [ -1 -1 -1 ] 0.0240000 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 2.5741696 volume = 5.9552810 Probabilities and CDF for Ising model: [ 1 1 1 ] 0.3879017 0.3879017 [ 1 1 -1 ] 0.0524968 0.4403985 [ 1 -1 1 ] 0.0071047 0.4475032 [ 1 -1 -1 ] 0.0524968 0.5000000 [ -1 1 1 ] 0.0524968 0.5524968 [ -1 1 -1 ] 0.0071047 0.5596015 [ -1 -1 1 ] 0.0524968 0.6120983 [ -1 -1 -1 ] 0.3879017 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 2.0541307 volume = 4.1529332 ---------------------------------------------------------------- Getting 20 samples using independence sampling ps = 0.5000000 0.5000000 0.5000000 Sample 0 state = 1 -1 -1 Sample 1 state = 1 1 1 Sample 2 state = -1 -1 -1 Sample 3 state = 1 -1 1 Sample 4 state = 1 1 1 Sample 5 state = -1 -1 -1 Sample 6 state = 1 -1 1 Sample 7 state = 1 -1 1 Sample 8 state = 1 1 -1 Sample 9 state = 1 -1 1 Sample 10 state = 1 1 -1 Sample 11 state = -1 1 -1 Sample 12 state = -1 -1 -1 Sample 13 state = -1 1 -1 Sample 14 state = -1 1 -1 Sample 15 state = 1 -1 -1 Sample 16 state = -1 1 1 Sample 17 state = -1 1 -1 Sample 18 state = -1 -1 -1 Sample 19 state = -1 -1 1 P's and Q's: 20 samples, indep. sampling, IID fair: [ 1 1 1 ] 0.1250000 0.1000000 diff = 0.0250000 [ 1 1 -1 ] 0.1250000 0.1000000 diff = 0.0250000 [ 1 -1 1 ] 0.1250000 0.2000000 diff = -0.0750000 [ 1 -1 -1 ] 0.1250000 0.1000000 diff = 0.0250000 [ -1 1 1 ] 0.1250000 0.0500000 diff = 0.0750000 [ -1 1 -1 ] 0.1250000 0.2000000 diff = -0.0750000 [ -1 -1 1 ] 0.1250000 0.0500000 diff = 0.0750000 [ -1 -1 -1 ] 0.1250000 0.2000000 diff = -0.0750000 Getting 20 samples using independence sampling ps = 0.9000000 0.9000000 0.9000000 Sample 0 state = 1 1 1 Sample 1 state = 1 1 1 Sample 2 state = 1 1 1 Sample 3 state = 1 -1 1 Sample 4 state = 1 -1 1 Sample 5 state = 1 1 1 Sample 6 state = 1 1 1 Sample 7 state = 1 1 1 Sample 8 state = 1 1 1 Sample 9 state = 1 1 1 Sample 10 state = 1 -1 1 Sample 11 state = 1 1 1 Sample 12 state = 1 1 1 Sample 13 state = 1 1 1 Sample 14 state = 1 1 1 Sample 15 state = 1 1 1 Sample 16 state = 1 1 1 Sample 17 state = 1 1 1 Sample 18 state = 1 1 1 Sample 19 state = 1 1 1 P's and Q's: 20 samples, indep. sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.8500000 diff = -0.1210000 [ 1 1 -1 ] 0.0810000 0.0000000 diff = 0.0810000 [ 1 -1 1 ] 0.0810000 0.1500000 diff = -0.0690000 [ 1 -1 -1 ] 0.0090000 0.0000000 diff = 0.0090000 [ -1 1 1 ] 0.0810000 0.0000000 diff = 0.0810000 [ -1 1 -1 ] 0.0090000 0.0000000 diff = 0.0090000 [ -1 -1 1 ] 0.0090000 0.0000000 diff = 0.0090000 [ -1 -1 -1 ] 0.0010000 0.0000000 diff = 0.0010000 Getting 20 samples using independence sampling ps = 0.6000000 0.7000000 0.8000000 Sample 0 state = 1 1 1 Sample 1 state = 1 1 1 Sample 2 state = 1 -1 1 Sample 3 state = 1 -1 1 Sample 4 state = -1 1 1 Sample 5 state = 1 1 1 Sample 6 state = -1 1 1 Sample 7 state = 1 -1 1 Sample 8 state = 1 1 -1 Sample 9 state = 1 1 1 Sample 10 state = 1 -1 -1 Sample 11 state = 1 1 1 Sample 12 state = -1 1 1 Sample 13 state = -1 -1 1 Sample 14 state = 1 -1 1 Sample 15 state = 1 1 1 Sample 16 state = 1 1 1 Sample 17 state = 1 1 1 Sample 18 state = 1 1 1 Sample 19 state = 1 1 1 P's and Q's: 20 samples, indep. sampling, indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.5000000 diff = -0.1640000 [ 1 1 -1 ] 0.0840000 0.0500000 diff = 0.0340000 [ 1 -1 1 ] 0.1440000 0.2000000 diff = -0.0560000 [ 1 -1 -1 ] 0.0360000 0.0500000 diff = -0.0140000 [ -1 1 1 ] 0.2240000 0.1500000 diff = 0.0740000 [ -1 1 -1 ] 0.0560000 0.0000000 diff = 0.0560000 [ -1 -1 1 ] 0.0960000 0.0500000 diff = 0.0460000 [ -1 -1 -1 ] 0.0240000 0.0000000 diff = 0.0240000 ---------------------------------------------------------------- Getting 20 samples using CDF sampling Sample 0 state = -1 -1 1 Sample 1 state = 1 -1 1 Sample 2 state = 1 1 -1 Sample 3 state = 1 -1 1 Sample 4 state = 1 1 1 Sample 5 state = 1 -1 1 Sample 6 state = 1 -1 1 Sample 7 state = 1 1 -1 Sample 8 state = 1 1 1 Sample 9 state = 1 -1 1 Sample 10 state = 1 -1 -1 Sample 11 state = 1 1 1 Sample 12 state = 1 1 -1 Sample 13 state = -1 1 -1 Sample 14 state = -1 1 1 Sample 15 state = 1 -1 -1 Sample 16 state = -1 -1 1 Sample 17 state = 1 -1 -1 Sample 18 state = 1 -1 1 Sample 19 state = 1 1 1 P's and Q's: 20 samples, CDF sampling, IID fair: [ 1 1 1 ] 0.1250000 0.2000000 diff = -0.0750000 [ 1 1 -1 ] 0.1250000 0.1500000 diff = -0.0250000 [ 1 -1 1 ] 0.1250000 0.3000000 diff = -0.1750000 [ 1 -1 -1 ] 0.1250000 0.1500000 diff = -0.0250000 [ -1 1 1 ] 0.1250000 0.0500000 diff = 0.0750000 [ -1 1 -1 ] 0.1250000 0.0500000 diff = 0.0750000 [ -1 -1 1 ] 0.1250000 0.1000000 diff = 0.0250000 [ -1 -1 -1 ] 0.1250000 0.0000000 diff = 0.1250000 Getting 20 samples using CDF sampling Sample 0 state = 1 -1 1 Sample 1 state = 1 1 1 Sample 2 state = 1 1 -1 Sample 3 state = 1 1 1 Sample 4 state = -1 1 1 Sample 5 state = 1 1 1 Sample 6 state = 1 -1 1 Sample 7 state = 1 1 -1 Sample 8 state = 1 1 1 Sample 9 state = -1 -1 1 Sample 10 state = 1 1 1 Sample 11 state = 1 1 1 Sample 12 state = 1 1 1 Sample 13 state = 1 1 1 Sample 14 state = 1 -1 1 Sample 15 state = -1 1 -1 Sample 16 state = 1 1 1 Sample 17 state = 1 1 1 Sample 18 state = 1 1 -1 Sample 19 state = 1 1 1 P's and Q's: 20 samples, CDF sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.5500000 diff = 0.1790000 [ 1 1 -1 ] 0.0810000 0.1500000 diff = -0.0690000 [ 1 -1 1 ] 0.0810000 0.1500000 diff = -0.0690000 [ 1 -1 -1 ] 0.0090000 0.0000000 diff = 0.0090000 [ -1 1 1 ] 0.0810000 0.0500000 diff = 0.0310000 [ -1 1 -1 ] 0.0090000 0.0500000 diff = -0.0410000 [ -1 -1 1 ] 0.0090000 0.0500000 diff = -0.0410000 [ -1 -1 -1 ] 0.0010000 0.0000000 diff = 0.0010000 Getting 20 samples using CDF sampling Sample 0 state = -1 1 1 Sample 1 state = 1 1 1 Sample 2 state = -1 1 1 Sample 3 state = 1 1 -1 Sample 4 state = -1 -1 1 Sample 5 state = 1 1 -1 Sample 6 state = -1 1 1 Sample 7 state = 1 1 1 Sample 8 state = 1 1 1 Sample 9 state = -1 -1 1 Sample 10 state = 1 1 1 Sample 11 state = -1 1 1 Sample 12 state = -1 1 1 Sample 13 state = 1 -1 1 Sample 14 state = 1 1 -1 Sample 15 state = -1 1 1 Sample 16 state = -1 1 1 Sample 17 state = -1 1 1 Sample 18 state = 1 1 -1 Sample 19 state = 1 1 -1 P's and Q's: 20 samples, CDF sampling, indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.2000000 diff = 0.1360000 [ 1 1 -1 ] 0.0840000 0.2500000 diff = -0.1660000 [ 1 -1 1 ] 0.1440000 0.0500000 diff = 0.0940000 [ 1 -1 -1 ] 0.0360000 0.0000000 diff = 0.0360000 [ -1 1 1 ] 0.2240000 0.4000000 diff = -0.1760000 [ -1 1 -1 ] 0.0560000 0.0000000 diff = 0.0560000 [ -1 -1 1 ] 0.0960000 0.1000000 diff = -0.0040000 [ -1 -1 -1 ] 0.0240000 0.0000000 diff = 0.0240000 Getting 20 samples using CDF sampling Sample 0 state = 1 -1 -1 Sample 1 state = 1 1 1 Sample 2 state = -1 -1 -1 Sample 3 state = -1 -1 -1 Sample 4 state = -1 -1 -1 Sample 5 state = -1 -1 -1 Sample 6 state = -1 -1 -1 Sample 7 state = 1 -1 -1 Sample 8 state = -1 -1 -1 Sample 9 state = -1 -1 1 Sample 10 state = 1 1 1 Sample 11 state = -1 -1 -1 Sample 12 state = 1 1 1 Sample 13 state = -1 -1 -1 Sample 14 state = 1 1 1 Sample 15 state = -1 -1 -1 Sample 16 state = 1 1 1 Sample 17 state = 1 1 -1 Sample 18 state = -1 -1 -1 Sample 19 state = 1 1 1 P's and Q's: 20 samples, CDF sampling, Ising model: [ 1 1 1 ] 0.3879017 0.3000000 diff = 0.0879017 [ 1 1 -1 ] 0.0524968 0.0500000 diff = 0.0024968 [ 1 -1 1 ] 0.0071047 0.0000000 diff = 0.0071047 [ 1 -1 -1 ] 0.0524968 0.1000000 diff = -0.0475032 [ -1 1 1 ] 0.0524968 0.0000000 diff = 0.0524968 [ -1 1 -1 ] 0.0071047 0.0000000 diff = 0.0071047 [ -1 -1 1 ] 0.0524968 0.0500000 diff = 0.0024968 [ -1 -1 -1 ] 0.3879017 0.5000000 diff = -0.1120983 ---------------------------------------------------------------- P's and Q's: 10000 samples, Metro sampling, Ising model: [ 1 1 1 ] 0.3879017 0.3862000 diff = 0.0017017 [ 1 1 -1 ] 0.0524968 0.0520000 diff = 0.0004968 [ 1 -1 1 ] 0.0071047 0.0075000 diff = -0.0003953 [ 1 -1 -1 ] 0.0524968 0.0502000 diff = 0.0022968 [ -1 1 1 ] 0.0524968 0.0494000 diff = 0.0030968 [ -1 1 -1 ] 0.0071047 0.0085000 diff = -0.0013953 [ -1 -1 1 ] 0.0524968 0.0542000 diff = -0.0017032 [ -1 -1 -1 ] 0.3879017 0.3920000 diff = -0.0040983 ----------------------------------------------------------------