Section: Array Generation and Manipulations
norm
function. The general syntax is
y = norm(A,p)
where A
is the matrix to analyze, and p
is the
type norm to compute. The following choices of p
are supported
p = 1
returns the 1-norm, or the max column sum of A
p = 2
returns the 2-norm (largest singular value of A)
p = inf
returns the infinity norm, or the max row sum of A
p = 'fro'
returns the Frobenius-norm (vector Euclidean norm, or RMS value)
1 <= p < inf
returns sum(abs(A).^p)^(1/p)
p
unspecified returns norm(A,2)
p = inf
returns max(abs(A))
p = -inf
returns min(abs(A))
--> A = float(rand(3,4)) A = 0.2751 0.5250 0.0532 0.8315 0.9886 0.7171 0.6396 0.5145 0.5634 0.9679 0.7133 0.0706 --> norm(A,1) ans = 2.2099 --> norm(A,2) ans = 2.0674 --> norm(A,inf) ans = 2.8597 --> norm(A,'fro') ans = 2.2313 --> quit
Next, we calculate some vector norms.
--> A = float(rand(4,1)) A = 0.0288 0.6311 0.4853 0.6145 --> norm(A,1) ans = 1.7596 --> norm(A,2) ans = 1.0061 --> norm(A,7) ans = 0.6962 --> norm(A,inf) ans = 0.6311 --> norm(A,-inf) ans = 2.8751e-02 --> quit