### LCI results (OpenLCA method)

Posted:

**21 May 2012 11:05**I would like to understand how the LCI results are calculated in openLCA.

I know one of the more used way to do that is throughout the use of matrices and vectors and the formula generally used are:

Where:

A = technology matrix

s = scaling vector

f = final demand vector

B = intervention matrix

g = inventory vector

from the first equation, once the A^-1 (inverse matrix) is calculated, it is possible to figure out the scaling vector:

Therefore, substituting the scaling factor in the second equation, the inventory vector, that is the LCI result, is solved:

I think OpenLCA software uses the same method to solve the LCI results because in the source code (...unluckily I couldn't import correctly the sources and I haven't received any answers on this topic) there are some references to such matrices and vectors.

Looking at the software, I do not understand the relationship between OpenLCA elements (process, flow, flow property, …) and the terms of the formula for the LCI results evaluation.

I would really appreciate for any help or comment on topic.

Thank you in advance

marco

I know one of the more used way to do that is throughout the use of matrices and vectors and the formula generally used are:

**A x s = f**

B x s = gB x s = g

Where:

A = technology matrix

s = scaling vector

f = final demand vector

B = intervention matrix

g = inventory vector

from the first equation, once the A^-1 (inverse matrix) is calculated, it is possible to figure out the scaling vector:

**s = A^-1 x f**Therefore, substituting the scaling factor in the second equation, the inventory vector, that is the LCI result, is solved:

**g = B x s = B x A^-1 x f**I think OpenLCA software uses the same method to solve the LCI results because in the source code (...unluckily I couldn't import correctly the sources and I haven't received any answers on this topic) there are some references to such matrices and vectors.

Looking at the software, I do not understand the relationship between OpenLCA elements (process, flow, flow property, …) and the terms of the formula for the LCI results evaluation.

I would really appreciate for any help or comment on topic.

Thank you in advance

marco