Complex numbers #321
Complex numbers #321
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## master #321 +/- ##
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- Coverage 95.52% 95.48% -0.05%
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Files 47 47
Lines 3691 3789 +98
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This is how benchmark results would change (along with a 95% confidence interval in relative change) if c97b1de is merged into master:
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This is how benchmark results would change (along with a 95% confidence interval in relative change) if f70d6b9 is merged into master:
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This is how benchmark results would change (along with a 95% confidence interval in relative change) if a76290c is merged into master:
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Does this handle the automatic re-shaping if I pass something that has |
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If I understand correctly, you're asking if it matters where in the order of dimensions the dimension indexing the real and imaginary parts is? I don't think it should make a difference; array slicing should handle that. e.g. here's an rvar where the second dimension indexes the real/imaginary parts: x = rvar(array(
1:96, dim = c(4,4,2,3),
dimnames = list(NULL, NULL, c("real", "imag"), NULL)
))
x
#> rvar<4>[4,2,3] mean ± sd:
#> , , 1
#>
#> real imag
#> [1,] 2.5 ± 1.3 18.5 ± 1.3
#> [2,] 6.5 ± 1.3 22.5 ± 1.3
#> [3,] 10.5 ± 1.3 26.5 ± 1.3
#> [4,] 14.5 ± 1.3 30.5 ± 1.3
#>
#> , , 2
#>
#> real imag
#> [1,] 34.5 ± 1.3 50.5 ± 1.3
#> [2,] 38.5 ± 1.3 54.5 ± 1.3
#> [3,] 42.5 ± 1.3 58.5 ± 1.3
#> [4,] 46.5 ± 1.3 62.5 ± 1.3
#>
#> , , 3
#>
#> real imag
#> [1,] 66.5 ± 1.3 82.5 ± 1.3
#> [2,] 70.5 ± 1.3 86.5 ± 1.3
#> [3,] 74.5 ± 1.3 90.5 ± 1.3
#> [4,] 78.5 ± 1.3 94.5 ± 1.3Showing it as a as_draws_df(x)
#> # A draws_df: 4 iterations, 1 chains, and 24 variables
#> x[1,real,1] x[2,real,1] x[3,real,1] x[4,real,1] x[1,imag,1] x[2,imag,1]
#> 1 1 5 9 13 17 21
#> 2 2 6 10 14 18 22
#> 3 3 7 11 15 19 23
#> 4 4 8 12 16 20 24
#> x[3,imag,1] x[4,imag,1]
#> 1 25 29
#> 2 26 30
#> 3 27 31
#> 4 28 32
#> # ... with 16 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}We can still just slice the two components and sum them. We could also do x[,"real"] + x[,"imag"] * 1i
#> rvar<4>[4,1,3] mean ± sd:
#> , , 1
#>
#> real
#> [1,] 2+18i ± 1.8
#> [2,] 6+22i ± 1.8
#> [3,] 10+26i ± 1.8
#> [4,] 14+30i ± 1.8
#>
#> , , 2
#>
#> real
#> [1,] 34+50i ± 1.8
#> [2,] 38+54i ± 1.8
#> [3,] 42+58i ± 1.8
#> [4,] 46+62i ± 1.8
#>
#> , , 3
#>
#> real
#> [1,] 66+82i ± 1.8
#> [2,] 70+86i ± 1.8
#> [3,] 74+90i ± 1.8
#> [4,] 78+94i ± 1.8If you don't want the (now-useless) "real" dim, you can drop it: drop(x[,"real"] + x[,"imag"] * 1i)
#> rvar<4>[4,3] mean ± sd:
#> [,1] [,2] [,3]
#> [1,] 2+18i ± 1.8 34+50i ± 1.8 66+82i ± 1.8
#> [2,] 6+22i ± 1.8 38+54i ± 1.8 70+86i ± 1.8
#> [3,] 10+26i ± 1.8 42+58i ± 1.8 74+90i ± 1.8
#> [4,] 14+30i ± 1.8 46+62i ± 1.8 78+94i ± 1.8Which also looks right if we again convert to a format like draws_df: as_draws_df(drop(x[,"real"] + x[,"imag"] * 1i))
#> # A draws_df: 4 iterations, 1 chains, and 12 variables
#> x[1,1] x[2,1] x[3,1] x[4,1] x[1,2] x[2,2] x[3,2] x[4,2]
#> 1 1+17i 5+21i 9+25i 13+29i 33+49i 37+53i 41+57i 45+61i
#> 2 2+18i 6+22i 10+26i 14+30i 34+50i 38+54i 42+58i 46+62i
#> 3 3+19i 7+23i 11+27i 15+31i 35+51i 39+55i 43+59i 47+63i
#> 4 4+20i 8+24i 12+28i 16+32i 36+52i 40+56i 44+60i 48+64i
#> # ... with 4 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} |
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This is how benchmark results would change (along with a 95% confidence interval in relative change) if 8a371ac is merged into master:
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Summary
This is a draft PR to support complex numbers in draws and rvar data types. It closes #319. The main changes, plus some points of conversation:
sd(),variance(), andvar()for complex values. This fixes printing issues, especially withrvars. The implementation ofvariance()follows the definition of the variance of a complex random variable as the sum of the variances of its real and imaginary components; and its sd is taken as the square root of this.summarise_draws(), the base R approach could make sense. Conservatively I've let this throw an error, but would be curious thoughts.quantile()on complex numbers seems (like median) to just treat each component separately, which I think is wrong, but again might be okay for us (inrvar_quantileand[rvar_]quantile2) if people just want the separate point estimates for the two components. I'm not sure.is_constant()that requiresmin/max, which are not defined on complex numbers. However, some succeed but I think give incorrect answers: e.g.rhat()appears to work, but I think returns incorrect values, as it relies onrank()inz_scale(), but base R'srank()ranks complex numbers in lexicographic order, when in reality it should probably return an error. I'm not sure if there's a good definition of any of these convergence metrics for complex numbers (maybe something like max rhat of both components?) or if these should all just return errors.The main motivating example for this, inspired by @WardBrian's comment, does work now:
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