def norm(x, y=2):
"""
Norm of a matrix or a vector according to Matlab.
The description is taken from Matlab:
For matrices...
NORM(X) is the largest singular value of X, max(svd(X)).
NORM(X,2) is the same as NORM(X).
NORM(X,1) is the 1-norm of X, the largest column sum,
= max(sum(abs((X)))).
NORM(X,inf) is the infinity norm of X, the largest row sum,
= max(sum(abs((X')))).
NORM(X,'fro') is the Frobenius norm, sqrt(sum(diag(X'*X))).
NORM(X,P) is available for matrix X only if P is 1, 2, inf or 'fro'.
For vectors...
NORM(V,P) = sum(abs(V).^P)^(1/P).
NORM(V) = norm(V,2).
NORM(V,inf) = max(abs(V)).
NORM(V,-inf) = min(abs(V)).
"""
x = numerix.asarray(x)
if MLab.rank(x) == 2:
if y == 2:
return MLab.max(MLab.svd(x)[1])
elif y == 1:
return MLab.max(MLab.sum(numerix.absolute((x))))
elif y == 'inf':
return MLab.max(MLab.sum(numerix.absolute((MLab.transpose(x)))))
elif y == 'fro':
return MLab.sqrt(
MLab.sum(
MLab.diag(numerix.matrixmultiply(MLab.transpose(x), x))))
else:
verbose.report_error('Second argument not permitted for matrices')
return None
else:
if y == 'inf':
return MLab.max(numerix.absolute(x))
elif y == '-inf':
return MLab.min(numerix.absolute(x))
else:
return numerix.power(
MLab.sum(numerix.power(numerix.absolute(x), y)), 1 / float(y))
def norm(x,y=2):
"""
Norm of a matrix or a vector according to Matlab.
The description is taken from Matlab:
For matrices...
NORM(X) is the largest singular value of X, max(svd(X)).
NORM(X,2) is the same as NORM(X).
NORM(X,1) is the 1-norm of X, the largest column sum,
= max(sum(abs((X)))).
NORM(X,inf) is the infinity norm of X, the largest row sum,
= max(sum(abs((X')))).
NORM(X,'fro') is the Frobenius norm, sqrt(sum(diag(X'*X))).
NORM(X,P) is available for matrix X only if P is 1, 2, inf or 'fro'.
For vectors...
NORM(V,P) = sum(abs(V).^P)^(1/P).
NORM(V) = norm(V,2).
NORM(V,inf) = max(abs(V)).
NORM(V,-inf) = min(abs(V)).
"""
x = numerix.asarray(x)
if MLab.rank(x)==2:
if y==2:
return MLab.max(MLab.svd(x)[1])
elif y==1:
return MLab.max(MLab.sum(numerix.absolute((x))))
elif y=='inf':
return MLab.max(MLab.sum(numerix.absolute((MLab.transpose(x)))))
elif y=='fro':
return MLab.sqrt(MLab.sum(MLab.diag(numerix.matrixmultiply(MLab.transpose(x),x))))
else:
verbose.report_error('Second argument not permitted for matrices')
return None
else:
if y == 'inf':
return MLab.max(numerix.absolute(x))
elif y == '-inf':
return MLab.min(numerix.absolute(x))
else:
return numerix.power(MLab.sum(numerix.power(numerix.absolute(x),y)),1/float(y))