norm: Matrix Norm

In CVXR: Disciplined Convex Optimization

Matrix Norm

Description

The matrix norm, which can be the 1-norm ("1"), infinity-norm ("I"), Frobenius norm ("F"), maximum modulus of all the entries ("M"), or the spectral norm ("2"), as determined by the value of type.

Usage

## S4 method for signature 'Expression,character'
norm(x, type)

Arguments

x

An Expression.

type

A character indicating the type of norm desired. "O", "o" or "1" specifies the 1-norm (maximum absolute column sum). "I" or "i" specifies the infinity-norm (maximum absolute row sum). "F" or "f" specifies the Frobenius norm (Euclidean norm of the vectorized x). "M" or "m" specifies the maximum modulus of all the elements in x. "2" specifies the spectral norm, which is the largest singular value of x.

Value

An Expression representing the norm of the input.

See Also

The p_norm function calculates the vector p-norm.

Examples

C <- Variable(3,2)
val <- Constant(rbind(c(1,2), c(3,4), c(5,6)))
prob <- Problem(Minimize(norm(C, "F")), list(C == val))
result <- solve(prob, solver = "SCS")
result$value

CVXR documentation built on June 27, 2024, 5:11 p.m.