# Aggregating covariances matrices and/or error vectors into a single covariance matrix This function aggregates covariances matrices, single variance values or a vector of multiple variance values into one final covariance matrix suitable for `propagate`. latin1 ```r mixCov(...) ``` ## Arguments - `...`: either covariance matrices, or a vector of single/multiple variance values. ## Details 'Mixes' (aggregates) data of the following types into a final covariance matrix: 1) covariance matrices $\mathbf{\Sigma}$ that are already available. 2) single variance values $\sigma^2$. 3) a vector of variance values $\sigma^2_1, \sigma^2_2, ..., \sigma^2_n$. This is accomplished by filling a $m_1 + m_2 + \ldots + m_n$ sized square matrix $\mathbf{C}$ succesively with elements $1 \ldots m_1, m_1 + 1 \ldots m1 + m2, \ldots, m_n + 1 \ldots m_n + m_{n + 1}$ with either covariance matrices at $C_{m_n + 1 \ldots m_n + m_{n + 1}, m_n + 1 \ldots m_n + m_{n + 1}}$ or single variance values on the diagonals at $C_{m_n, m_n}$. ## Returns The aggregated covariance matrix. ## Author(s) Andrej-Nikolai Spiess ## References Evaluation of measurement data - Guide to the expression of uncertainty in measurement. JCGM 100:2008 (GUM 1995 with minor corrections). [http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf](http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf). Evaluation of measurement data - Supplement 1 to the Guide to the expression of uncertainty in measurement - Propagation of distributions using a Monte Carlo Method. JCGM 101:2008. [http://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf](http://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf). ## Examples ```r ####################################################### ## Example in Annex H.4.1 from the GUM 2008 manual ## (see 'References'), measurement of activity. ## This will give exactly the same values as Table H.8. data(H.4) attach(H.4) T0 <- 60 lambda <- 1.25894E-4 Rx <- ((Cx - Cb)/60) * exp(lambda * tx) Rs <- ((Cs - Cb)/60) * exp(lambda * ts) mRx <- mean(Rx) sRx <- sd(Rx)/sqrt(6) mRx sRx mRs <- mean(Rs) sRs <- sd(Rs)/sqrt(6) mRs sRs R <- Rx/Rs mR <- mean(R) sR <- sd(R)/sqrt(6) mR sR cor(Rx, Rs) ## Definition as in H.4.3. As <- c(0.1368, 0.0018) ms <- c(5.0192, 0.005) mx <- c(5.0571, 0.001) ## We have to scale Rs/Rx by sqrt(6) to get the ## corresponding covariances. Rs <- Rs/sqrt(6) Rx <- Rx/sqrt(6) ## Here we create an aggregated covariance matrix ## from the raw and summary data. COV1 <- cov(cbind(Rs, Rx)) COV <- mixCov(COV1, As[2]^2, ms[2]^2, mx[2]^2) COV ## Prepare the data for 'propagate'. MEANS <- c(mRs, mRx, As[1], ms[1], mx[1]) SDS <- c(sRs, sRx, As[2], ms[2], mx[2]) DAT <- rbind(MEANS, SDS) colnames(DAT) <- c("Rs", "Rx", "As", "ms", "mx") ## This will give exactly the same values as ## in H.4.3/H.4.3.1. EXPR <- expression(As * (ms/mx) * (Rx/Rs)) RES <- propagate(EXPR, data = DAT, cov = COV, nsim = 100000) RES ```

mixCov function