Functions

>>> from vector import vecadd
>>> a = (5, 6, 7)
>>> b = [2]
>>> c = range(4)
>>> vecadd(a, b, c)
(7, 7, 9, 3)

Prefixed by vec... (vector).

All functions accept single exhaustible iterables.

They return vectors as tuples.

The functions are type-independent. However, the data types used must support necessary scalar operations. For instance, for vector addition, components must be addable — this may include operations with padded integer zeros. Empty operations return the zero vector (e.g. vecadd()==veczero) or integer zeros (e.g. vecdot(veczero, veczero)==int(0)).

Padding is done with int(0).

creation

• veczero = (): Zero vector.

• vecbasis(i, c=1): Return the i-th basis vector times c. The returned value is a tuple with i integer zeros followed by c.

• vecrand(n): Return a random vector of n uniform coefficients in [0, 1[.

• vecrandn(n, normed=True, mu=0, sigma=1): Return a random vector of n normal distributed coefficients.

utility

• veceq(v, w): Return if two vectors are equal.

• vectrim(v, tol=1e-9): Remove all trailing near zero (<=tol) coefficients.

• vecround(v, ndigits=None): Round all coefficients to the given precision.

• vecrshift(v, n): Pad n many zeros to the beginning of the vector.

• veclshift(v, n): Remove n many coefficients at the beginning of the vector.

Hilbert space

• vecabsq(v): Return the sum of absolute squares of the coefficients.

• vecabs(v): Return the Euclidean/L2-norm.

• vecdot(v, w): Return the inner product of two vectors without conjugation.

• vecparallel(v, w): Return if two vectors are parallel.

vector space

• vecpos(v): Return the vector with the unary positive operator applied.

• vecneg(v): Return the vector with the unary negative operator applied.

• vecaddc(v, c, i=0): Return v with c added to the i-th coefficient. More efficient than vecadd(v, vecbasis(i, c).

• vecadd(*vs): Return the sum of vectors.

• vecsub(v, w): Return the difference of two vectors.

• vecmul(a, v): Return the product of a scalar and a vector.

• vectruediv(v, a): Return the true division of a vector and a scalar.

• vecfloordiv(v, a): Return the floor division of a vector and a scalar.

• vecmod(v, a): Return the elementwise mod of a vector and a scalar.

elementwise

• vechadamard(*vs): Return the elementwise product of vectors.

• vechadamardtruediv(v, w): Return the elementwise true division of two vectors.

• vechadamardfloordiv(v, w): Return the elementwise floor division of two vectors.

• vechadamardmod(v, w): Return the elementwise mod of two vectors.

• vechadamardmin(*vs): Return the elementwise minimum of vectors.

• vechadamardmax(*vs): Return the elementwise maximum of vectors.