matrix_frac: Matrix Fraction

In anqif/CVXR: Disciplined Convex Optimization

Matrix Fraction

Description

tr(X^T P^{-1} X).

Usage

matrix_frac(X, P)

Arguments

X	An Expression or matrix. Must have the same number of rows as P.
P	An Expression or matrix. Must be an invertible square matrix.

Value

An Expression representing the matrix fraction evaluated at the input.

Examples

## 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)

anqif/CVXR documentation built on Feb. 6, 2024, 4:28 a.m.