knitr::opts_chunk$set( error = TRUE, collapse = TRUE, comment = "#>", out.width = "100%" )
alpha <- runif(n = 1, min = -1, max = 1) beta <- runif(n = 1, min = -1, max = 1) sigmax2 <- runif(n = 1, min = 0, max = 1) sigmae2 <- runif(n = 1, min = 0, max = 1) mux <- runif(n = 1, min = -1, max = 1) muepsilon <- 0 A <- S <- matrixR::ZeroMatrix(3) A[1, ] <- c(0, beta, 1) diag(S) <- c(0, sigmax2, sigmae2) colnames(A) <- rownames(A) <- c("y", "x", "e") I <- matrixR::IdentityFrom(A) IminusA <- I - A E <- Ryacas::as_r(solve(Ryacas::ysym(I) - Ryacas::ysym(A))) Filter <- diag(2) Filter <- cbind(Filter, 0) colnames(Filter) <- c("y", "x", "e") rownames(Filter) <- c("y", "x") u <- as.matrix(c(alpha, mux, 0)) v <- as.matrix(c(alpha + (beta * mux), mux, 0.00)) rownames(u) <- rownames(v) <- c("y", "x", "e") colnames(u) <- "u" colnames(v) <- "v" C <- Ryacas::as_r( solve( Ryacas::ysym(I) - Ryacas::ysym(A) ) * Ryacas::ysym(S) * t( solve(Ryacas::ysym(I) - Ryacas::ysym(A)) ) ) C.scaled <- stats::cov2cor(C) M <- Ryacas::as_r( Ryacas::ysym(Filter) * solve( Ryacas::ysym(I) - Ryacas::ysym(A) ) * Ryacas::ysym(S) * t( solve(Ryacas::ysym(I) - Ryacas::ysym(A)) ) * t(Ryacas::ysym(Filter)) ) M.scaled <- Filter %*% C.scaled %*% t(Filter) g <- as.matrix( Ryacas::as_r( Ryacas::ysym(Filter) * Ryacas::ysym(v) ) )
\begin{equation}
\begin{split}
y &= \alpha + \beta x + \varepsilon \
y &= r alpha
+ \left( r beta
x \right) + \varepsilon
\end{split}
\end{equation}
NumericIminusA <- round( ramR::IminusA(A), digits = 4 ) SymbolicIminusA <- round( Ryacas::as_r( ramR::IminusA( Ryacas::ysym(A), R = FALSE, simplify = TRUE ) ), digits = 4 ) SymbolicIminusAExpr <- round( eval( ramR::IminusA( Ryacas::ysym(A), R = TRUE, simplify = TRUE ) ), digits = 4 )
ramR::IminusA( Ryacas::ysym(A), R = FALSE, format = "ysym", simplify = TRUE )
cat( "\\begin{align*}", ramR::IminusA( Ryacas::ysym(A), R = FALSE, format = "tex" ), "\\end{align*}", sep = "" )
IminusA <- round(IminusA, digits = 4)
testthat::test_that("IminusA.", { for (i in seq_len(nrow(IminusA))) { for (j in seq_len(ncol(IminusA))) { testthat::expect_equal( IminusA[i, j], NumericIminusA[i, j], SymbolicIminusA[i, j], SymbolicIminusAExpr[i, j], check.attributes = FALSE ) } } })
ramR::IminusA( Ryacas::ysym(A), exe = FALSE, check = FALSE )
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