# Source code for klampt.math.vectorops

```"""Allows treating tuples/lists as vectors"""

import math

if len(items) == 0: return 0
n = len(items[0])
for v in items:
if n!=len(v):
raise RuntimeError('Vector dimensions not equal')
return [sum([v[i] for v in items]) for i in range(n)]

"""Return a+c*b where a and b are vectors."""
if len(a)!=len(b):
raise RuntimeError('Vector dimensions not equal')
return [ai+c*bi for ai,bi in zip(a,b)]

[docs]def sub(a,b):
"""Subtract a vector b from a, or subtract a scalar"""
if hasattr(b,'__iter__'):
if len(a)!=len(b):
raise RuntimeError('Vector dimensions not equal')
return [ai-bi for ai,bi in zip(a,b)]
else:
return [ai-b for ai in a]

[docs]def mul(a,b):
"""Multiply a vector either elementwise with another vector, or with a
scalar."""
if hasattr(b,'__iter__'):
if len(a)!=len(b):
raise RuntimeError('Vector dimensions not equal')
return [ai*bi for ai,bi in zip(a,b)]
else:
return [ai*b for ai in a]

[docs]def div(a,b):
"""Elementwise division with another vector, or with a scalar."""
if hasattr(b,'__iter__'):
if len(a)!=len(b):
raise RuntimeError('Vector dimensions not equal')
return [ai/bi for ai,bi in zip(a,b)]
else:
return [ai/b for ai in a]

[docs]def maximum(a,b):
"""Elementwise max"""
if hasattr(b,'__iter__'):
return [max(ai,bi) for ai,bi in zip(a,b)]
else:
return [max(ai,b) for ai in a]

[docs]def minimum(a,b):
"""Elementwise min"""
if hasattr(b,'__iter__'):
return [min(ai,bi) for ai,bi in zip(a,b)]
else:
return [min(ai,b) for ai in a]

[docs]def dot(a,b):
"""Dot product."""
if len(a)!=len(b):
raise RuntimeError('Vector dimensions not equal')
return sum([a[i]*b[i] for i in range(len(a))])

[docs]def normSquared(a):
"""Returns the norm of a, squared."""
return sum(ai*ai for ai in a)

[docs]def norm(a):
"""L2 norm"""
return math.sqrt(normSquared(a))

[docs]def unit(a,epsilon=1e-5):
"""Returns the unit vector in the direction a.  If the norm of
a is less than epsilon, a is left unchanged."""
n = norm(a)
if n > epsilon:
return mul(a,1.0/n)
return a[:]

norm_L2 = norm

[docs]def norm_L1(a):
"""L1 norm"""
return sum(abs(ai) for ai in a)

[docs]def norm_Linf(a):
"""L-infinity norm"""
return max(abs(ai) for ai in a)

[docs]def distanceSquared(a,b):
"""Squared L2 distance"""
if len(a)!=len(b): raise RuntimeError('Vector dimensions not equal')
sum=0
for i in range(len(a)):
sum = sum + (a[i]-b[i])*(a[i]-b[i])
return sum

[docs]def distance(a,b):
"""L2 distance"""
return math.sqrt(distanceSquared(a,b));

[docs]def cross(a,b):
"""Cross product between a 3-vector or a 2-vector"""
if len(a)!=len(b):
raise RuntimeError('Vector dimensions not equal')
if len(a)==3:
return (a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0])
elif len(a)==2:
return a[0]*b[1]-a[1]*b[0]
else:
raise RuntimeError('Vectors must be 2D or 3D')

[docs]def interpolate(a,b,u):
"""Linear interpolation between a and b"""