How do I normalize the columns of a matrix?
such as A=matrix(5,5,[some numbers])
The simplest way to normalize the column of a matrix is probably to replace each column of a matrix by itself divided by its norm.
Create a matrix:
sage: a = matrix(RDF, 4, [randint(-10, 10) for _ in range(16)])
sage: a
[-2.0 6.0 -6.0 -2.0]
[ 6.0 1.0 -8.0 4.0]
[-7.0 4.0 -3.0 9.0]
[ 6.0 -9.0 9.0 -5.0]Normalize each column:
sage: for j in range(a.ncols()):
....: v = a.column(j)
....: a[:,j] = v/v.norm()
....:Show the result:
sage: a
[-0.17888543819998318 0.5183210553488161 -0.435285750066007 -0.1781741612749496]
[ 0.5366563145999496 0.08638684255813601 -0.5803810000880093 0.3563483225498992]
[ -0.6260990336999411 0.34554737023254406 -0.2176428750330035 0.8017837257372732]
[ 0.5366563145999496 -0.7774815830232241 0.6529286250990105 -0.44543540318737396]Check the norms of the new columns:
sage: [c.norm() for c in a.columns()]
[1.0, 1.0, 1.0, 1.0]carefully,I would add an if ?:
for j in range(a.ncols()):
v = a.column(j)
if v.norm() <> 0 :
a[:,j] = v/v.norm()Asked: 6 years ago
Seen: 5,322 times
Last updated: Jun 13 '18
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