# LCA#

## Specifying a functional unit#

The functional unit for any LCA calculation is a dictionary of keys and amounts:

```
{
("a database", "the answer"): 42,
("a database", "pi"): 3.14159265358979
}
```

However, you can also use a `Activity`

proxy:

```
In [1]: from brightway2 import *
In [2]: activity = Database("ecoinvent 3.2 cutoff").random()
In [3]: type(activity), activity
Out[3]:
(bw2data.backends.peewee.proxies.Activity,
'quicklime production, milled, packed' (kilogram, CH, None))
In [4]: lca = LCA({activity: 1})
In [5]: lca.demand
Out[5]: {'quicklime production, milled, packed' (kilogram, CH, None): 1}
```

How does this work? It is quite simple - the `Activity`

proxy knows how
to pretend to be a key tuple:

```
In [7]: activity[0], activity[1]
Out[7]: ('ecoinvent 3.2 cutoff', 'ab2f7a551a06a59de9191065128233e4')
In [8]: activity == ('ecoinvent 3.2 cutoff', 'ab2f7a551a06a59de9191065128233e4')
Out[8]: True
```

This is an instance of duck typing - if it walks like a duck and quacks like a duck, then we can treat it like a duck.

If you are interested in the details, see how
`bw2data.proxies.ActivityProxyBase`

defines `__getitem__`

and other `__`

magic methods.

## Turning processed data arrays in matrices {#building-matrices}#

A parameter array is a NumPy structured or record array, where each column has a label and data type. Here is an sample of the parameter array for the US LCI:

input output row col type amount

9829 9829 4294967295 4294967295 0 1.0 9708 9708 4294967295 4294967295 0 1.0 9633 9633 4294967295 4294967295 0 1.0 9276 9276 4294967295 4294967295 0 3.0999 8778 8778 4294967295 4294967295 0 1.0 9349 9349 4294967295 4294967295 0 1000.0 5685 9349 4294967295 4294967295 2 14.895 9516 9349 4294967295 4294967295 1 1032.7 9433 9349 4294967295 4294967295 1 4.4287 8838 9349 4294967295 4294967295 1 1.5490

There are also some columns for uncertainty information, but these would only be a distraction for now. The complete spec for the uncertainty fields is given in the stats_arrays documentation.

We notice several things:

Both the

`input`

and`output`

columns have numbers, but we don’t know what they mean yetBoth the

`row`

and`col`

columns are filled with a large numberThe

`type`

column has only a few values, but they are also mysteriousThe

`amount`

column is the only one that seems reasonable, and gives the values that should be inserted into the matrix

### Input and Output#

The `input`

and `output`

columns gives values for biosphere flows or
transforming activity data sets. The `mapping`

is used to translate keys like `("Douglas Adams", 42)`

into
integer values. So, each mapping number uniquely identifies an activity
dataset.

If the `input`

and `output`

values are the same, then this is a
production exchange - it describes how much product is produced by the
transforming activity dataset.

```
::: title
Warning
```

Integer mapping ids are not transferable from machine to machine or
installation to installation, as the order of insertion (and hence the
integer id) is more or less at random. Always `.process()`

datasets on a
new machine.

```
### Rows and columns
The `row` and `col` columns have the data type *unsigned integer, 32
bit*, and the maximum value is therefore $2^{32} - 1$, i.e. 4294967295.
This is just a dummy value telling Brightway2 to insert better data.
The method `MatrixBuilder.build_dictionary` is used to take `input` and
`output` values, respectively, and figure out which rows and columns
they correspond to. The actual code is succinct - only one line - but
what it does is:
> 1. Get all unique values, as each value will appear multiple times
> 2. Sort these values
> 3. Give them integer indices, starting with zero
For our example parameter array, the dictionary from `input` values to
`row` would be:
``` python
{5685: 0,
8778: 1,
8838: 2,
9276: 3,
9349: 4,
9433: 5,
9516: 6,
9633: 7,
9708: 8,
9829: 9}
```
And the dictionary from `output` to `col` would be:
``` python
{8778: 0,
9276: 1,
9349: 2,
9633: 3,
9708: 4,
9829: 5}
```
The method `MatrixBuilder.add_matrix_indices` would replace the
4294967295 values with dictionary values based on `input` and `output`.
At this point, we have enough to build a sparse matrix using
`MatrixBuilder.build_matrix`:
row col amount
----- ----- --------
9 5 1.0
8 4 1.0
7 3 1.0
3 1 3.0999
1 0 1.0
4 2 1000.0
0 2 14.895
6 2 1032.7
5 2 4.4287
2 2 1.5490
Indeed, the [coordinate (coo)
matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_matrix.html)
takes as inputs exactly the row and column indices, and the values to
insert.
Of course, there are some details for specific matrices - technosphere
matrices need to be square, and should have ones by default on the
diagonal, etc. etc., but this is the general idea.
### Types
The `type` column indicates whether a value should be in the
technosphere or biosphere matrix: `0` is a transforming activity
production amount, `1` is a technosphere exchange, and `2` is a
biosphere exchange.
## Brightway2 LCA Reports
The Brightway2 report data format is evolving, and this section should
not be understood as definitive.
```

LCA reports calculated with `bw2analyzer.report.SerializedLCAReport`

are
written as a JSON file to disk. It has the following data format:

```
{
"monte carlo": {
"statistics": {
"interval": [lower, upper values],
"median": median,
"mean": mean
},
"smoothed": [ ## This is smoothed values for drawing empirical PDF
[x, y],
],
"histogram": [ ## This are point coordinates for each point when drawing histogram bins
[x, y],
]
},
"score": LCA score,
"activity": [
[name, amount, unit],
],
"contribution": {
"hinton": {
"xlabels": [
label,
],
"ylabels": [
label,
],
"total": LCA score,
"results": [
[x index, y index, score], ## See hinton JS implementation in bw2ui source code
],
},
"treemap": {
"size:" LCA score,
"name": "LCA result",
"children": [
{
"name": activity name,
"size": activity LCA score
},
]
}
"herfindahl": herfindahl score,
"concentration": concentration score
},
"method": {
"name": method name,
"unit": method unit
},
"metadata": {
"version": report data format version number (this is 1),
"type": "Brightway2 serialized LCA report",
"uuid": the UUID of this report,
"online": URL where this report can be accessed. Optional.
}
}
```