Matrix Fraction
tr(X^T P^{-1} X).
matrix_frac(X, P)
X |
An Expression or matrix. Must have the same number of rows as |
P |
An Expression or matrix. Must be an invertible square matrix. |
An Expression representing the matrix fraction evaluated at the input.
## Not run: set.seed(192) m <- 100 n <- 80 r <- 70 A <- matrix(stats::rnorm(m*n), nrow = m, ncol = n) b <- matrix(stats::rnorm(m), nrow = m, ncol = 1) G <- matrix(stats::rnorm(r*n), nrow = r, ncol = n) h <- matrix(stats::rnorm(r), nrow = r, ncol = 1) # ||Ax-b||^2 = x^T (A^T A) x - 2(A^T b)^T x + ||b||^2 P <- t(A) %*% A q <- -2 * t(A) %*% b r <- t(b) %*% b Pinv <- base::solve(P) x <- Variable(n) obj <- matrix_frac(x, Pinv) + t(q) %*% x + r constr <- list(G %*% x == h) prob <- Problem(Minimize(obj), constr) result <- solve(prob) result$value ## End(Not run)
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