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 = 0.4266 0.0755 0.8713 0.4876 0.8799 0.1549 0.3731 0.4750 0.0417 0.1658 0.5522 0.5067 --> norm(A,1) ans = 1.7967 --> norm(A,2) ans = 1.5921 --> norm(A,inf) ans = 1.8830 --> norm(A,'fro') ans = 1.7143
Next, we calculate some vector norms.
--> A = float(rand(4,1)) A = 0.6840 0.2036 0.9099 0.6971 --> norm(A,1) ans = 2.4946 --> norm(A,2) ans = 1.3503 --> norm(A,7) ans = 0.9437 --> norm(A,inf) ans = 0.9099 --> norm(A,-inf) ans = 0.2036