Gaussian elimination: Difference between revisions

=={{header|R}}==

Here 'b' is a matrix. Partial pivoting is used, and the determinant of 'a' is returned as well.

<lang R>gauss <- function(a, b) {

n <- nrow(a)

det <- 1

for (i in seq_len(n - 1)) {

j <- which.max(a[i:n, i]) + i - 1

if (j != i) {

a[c(i, j), i:n] <- a[c(j, i), i:n]

b[c(i, j), ] <- b[c(j, i), ]

det <- -det

}

k <- seq(i + 1, n)

for (j in k) {

s <- a[[j, i]] / a[[i, i]]

a[j, k] <- a[j, k] - s * a[i, k]

b[j, ] <- b[j, ] - s * b[i, ]

}

}

for (i in seq(n, 1)) {

if (i < n) {

for (j in seq(i + 1, n)) {

b[i, ] <- b[i, ] - a[[i, j]] * b[j, ]

}

}

b[i, ] <- b[i, ] / a[[i, i]]

det <- det * a[[i, i]]

}

list(x=b, det=det)

}

a <- matrix(c(2, 9, 4, 7, 5, 3, 6, 1, 8), 3, 3, byrow=T)

gauss(a, diag(3))</lang>

{{out}}

<pre>$x

[,1] [,2] [,3]

[1,] -0.10277778 0.18888889 -0.01944444

[2,] 0.10555556 0.02222222 -0.06111111

[3,] 0.06388889 -0.14444444 0.14722222

$det

[1] -360</pre>