NOPY

Introduction

NOPY is an extension of scipy.optimize.least_squares. It provides a much more flexible and easier-to-use interface than the original scipy.optimize.least_squares. You will love it if you are familiar with Ceres Solver.

NOPY can solve robustified non-linear least squares problems with bounds of the form

The expression is known as a residual block, where is a residual function that depends on one or more variables .

Installation

git clone https://github.com/aipiano/NOPY.git
cd NOPY
pip install .

Example

We wanna minimize the following naive cost function

The first step is to define residual functions.

def f1(x1):
    return x1 - 1
    
def f2(x2):
    return x2 - 3

Then we define variables with some initial values.

x1 = numpy.array([-1], dtype=numpy.float64)
x2 = numpy.array([0], dtype=numpy.float64)

Next, we build the least squares problem and use the '2-point' finite difference method to estimate Jacobian matrix of each residual block.

problem = nopy.LeastSquaresProblem()
problem.add_residual_block(1, f1, x1, jac_func='2-point')
problem.add_residual_block(1, f2, x2, jac_func='2-point')

The first argument of add_residual_block is the dimension of residual function. In this example, the residual function return a scalar, so the dimension is 1.

Finally, we solve it.

problem.solve()

Now all variables should have the right value that make the cost function minimum.

print(x1)   # x1 = 1
print(x2)   # x2 = 3

If you don't want to change one or more variables during optimization, just call

problem.fix_variables(x1)

and unfix them with

problem.unfix_variables(x1)

For variable bounding, just call

problem.bound_variable(x1, 0, 1)

and unbound it with

problem.bound_variable(x1, -np.inf, np.inf)

Note that the initial value of a bounded variable must lie in the boundary.

NOPY support robust loss functions. You can specify loss function for each residual block, like bellow

problem.add_residual_block(1, f1, x1, jac_func='2-point', loss='huber')

Custom jacobian function and loss function are also supported just like scipy.optimize.least_squares. You can find more examples in the 'examples' folder.