User data should be rCLR transformed before projection

User data will be loaded as a samples x taxon table of read counts, which we then rarefy to 3000 reads per sample see https://github.com/blekhmanlab/compendium_website/issues/34):

| Sample | Tax 1 | Tax 2 | Tax 3 | Tax 4 | Tax 5 | READ TOTAL |
| ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- |
| s123 | 300 | 150 | 600 | 650 | 1300 | 3000 |
| s124 | 0 | 0 | 1400 | 1300 | 300 | 3000 |
| s125 | 250 | 1000 | 1700 | 50 | 0 | 3000 |

At that point, we need to perform the [robust centered log-ratio transformation](https://journals.asm.org/doi/10.1128/msystems.00016-19). This is how they define it:

$rclr = log\frac{x}{g(x > 0)}$

The `g` here is a value for each sample indicating the geometric mean of the read counts found in all taxa. For `s123` above would be

$$\sqrt[5]{(300 \times 150 \times 600 \times 650 \times 1300)} = 469.5092$$

This is where the controversial step comes in. Zeroes are a problem here, for both the geometric mean (which uses multiplication, so all rows with a zero would have a mean of zero) and for the logarithms. There are a few options to replace zeroes with other numbers, but the rCLR transformation we're going with **skips the zeroes**:
* The geometric mean calculated for `s124` above would be `(1400*1300*300)^(1/3)`, for example.
* For the subsequent steps using logs, the zeroes in the matrix (s124, taxa 1 and 2; s125 taxon 5) would **remain unchanged**.

Once each sample has its geometric mean, that number is used to "center" the data in its row by dividing each read count by the geometric mean, then taking the log. So the read counts for samples mentioned here would be transformed into:

| Sample | Tax 1 | Tax 2 | Tax 3 | Tax 4 | Tax 5 |
| ------------- | ------------- | ------------- | ------------- | ------------- | ------------- |
| s123 | log(300/469.5) | log(150/469.5) | log(600/469.5) | log(650/469.5) | log(1300/469.5) |
| s124 | **0** | **0** | log(1400/817.3) | log(1300/817.3) | log(300/817.3) | log(3000/817.3)) |

Here are two helpers in R that do this. In both cases, the input is an array of read counts for a single sample:

```r
gm_mean = function(x){
exp(mean(log(x[x > 0])))
}

rclr <- function(a) {
answer <- log(a/gm_mean(a))
answer[] <- lapply(answer, function(i) if(is.numeric(i)) ifelse(is.infinite(i), 0, i) else i)
return(answer)
}
```

In case it's relevant, I'll also note that the final rCLR-transformed matrix will have negative values—taxa with fewer reads than the sample's average (s123, taxa 1 and 2; s124, taxon 4) will have negative values here. In the preliminary ordinations, the axes we visualized have generally been limited to something like `(-10, 10)` overall.

Start by locating the pipeline that loads the rarefied samples and feeds them into projection or ordination; issue 34 describes the preceding rarefaction step. Compare the implementation with the provided gm_mean and rclr helpers in R, preserving zero entries while applying the log ratio to nonzero counts. Done means the transformed matrix can be passed to the existing projection and supports negative values.

Written by the indexing model from the issue text.