nimble.calculate.leastSquaresSolution

nimble.calculate.leastSquaresSolution(aObj, bObj)

Compute least-squares solution to equation A x = b.

Compute a vector x such that the 2-norm determinant of b - Ax is minimized. The matrix A may be square or rectangular (over-determined or under-determined).

Parameters:

• aObj ((M, N) nimble Base object.) – Left hand side object in A x = b.

• bObj – Right-hand side nimble Base object in A x = b. (1-D)

Returns:

xObj ((N) nimble Base object.) – Least-squares solution.

Raises:

• InvalidArgumentType – If aObj or bObj is not a nimble Base Object. If aObj elements types are not supported.

• InvalidArgumentValue – If bObj is not a vector. 1-D.

• InvalidArgumentValueCombination – If aObj and bObj have incompatible dimensions.

Examples

>>> a = [[0, 1],
...      [1, 1],
...      [2, 1],
...      [3, 1],
...      [4, 1]]
>>> b = [6, 9, 12, 15, 18]
>>> aObj = nimble.data(a)
>>> bObj = nimble.data(b)
>>> nimble.calculate.leastSquaresSolution(aObj, bObj)
<Matrix 1pt x 2ft
       0      1
   ┌─────────────
 0 │ 3.000  6.000
>