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 = <float> - size: [3 4] Columns 1 to 4 0.426610678 0.075468481 0.871337116 0.487616807 0.879925549 0.154911667 0.373149037 0.475030541 0.041696656 0.165778294 0.552217603 0.506726503 --> norm(A,1) ans = <float> - size: [1 1] 1.7967038 --> norm(A,2) ans = <float> - size: [1 1] 1.5921172 --> norm(A,inf) ans = <float> - size: [1 1] 1.8830168 --> norm(A,'fro') ans = <float> - size: [1 1] 1.7142895
Next, we calculate some vector norms.
--> A = float(rand(4,1)) A = <float> - size: [4 1] Columns 1 to 1 0.68404633 0.20355032 0.90988815 0.69708711 --> norm(A,1) ans = <double> - size: [1 1] 2.4945719242095947 --> norm(A,2) ans = <float> - size: [1 1] 1.3502514 --> norm(A,7) ans = <double> - size: [1 1] 0.9436675093733905 --> norm(A,inf) ans = <float> - size: [1 1] 0.90988815 --> norm(A,-inf) ans = <float> - size: [1 1] 0.20355032