optimization fails with np.longdouble and 'tnc' or 'l-bfgs' with nevo example

[chrisconlon]

Using Nevo dataset and np.longdouble precision fails under the 'l-bfgs-b' and 'tnc' solvers immediately errors out.

Works fine with 'knitro' and 'slsqp' solver.

pyblp.options.dtype = np.longdouble
pyblp.options.digits = 3
pyblp.options.verbose = True

nevo_results_lbfgs = nevo_problem.solve(nevo_sigma,nevo_pi,steps=1,optimization=pyblp.Optimization('l-bfgs-b'))
nevo_results_tnc = nevo_problem.solve(nevo_sigma,nevo_pi,steps=1,optimization=pyblp.Optimization('tnc'))

LBFGS trace:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-30-28ef3977a353> in <module>()
      1 ### L-BFGS+TNC fails with high precision numerics
----> 2 nevo_results_lbfgs = nevo_problem.solve(nevo_sigma,nevo_pi,steps=1,optimization=pyblp.Optimization('l-bfgs-b'))
      3 #nevo_results_tnc = nevo_problem.solve(nevo_sigma,nevo_pi,steps=1,optimization=pyblp.Optimization('tnc'))

~/anaconda3/lib/python3.6/site-packages/pyblp/problem.py in solve(self, sigma, pi, sigma_bounds, pi_bounds, delta, WD, WS, steps, optimization, custom_display, error_behavior, error_punishment, iteration, linear_costs, linear_fp, center_moments, se_type, processes)
    423             bounds = [p.bounds for p in parameter_info.unfixed]
    424             verbose = options.verbose and not custom_display
--> 425             theta = optimization._optimize(objective_function, theta, bounds, verbose=verbose)
    426             end_time = time.time()
    427             output("")

~/anaconda3/lib/python3.6/site-packages/pyblp/utilities/optimization.py in _optimize(self, objective_function, start_values, bounds, verbose)
    202             if self._supports_bounds:
    203                 minimize_kwargs['bounds'] = bounds
--> 204             return scipy.optimize.minimize(objective_function, start_values, **minimize_kwargs).x
    205 
    206         # set default Knitro options

~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    485     elif meth == 'l-bfgs-b':
    486         return _minimize_lbfgsb(fun, x0, args, jac, bounds,
--> 487                                 callback=callback, **options)
    488     elif meth == 'tnc':
    489         return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,

~/anaconda3/lib/python3.6/site-packages/scipy/optimize/lbfgsb.py in _minimize_lbfgsb(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, **unknown_options)
    326         _lbfgsb.setulb(m, x, low_bnd, upper_bnd, nbd, f, g, factr,
    327                        pgtol, wa, iwa, task, iprint, csave, lsave,
--> 328                        isave, dsave, maxls)
    329         task_str = task.tostring()
    330         if task_str.startswith(b'FG'):

ValueError: failed to initialize intent(inout) array -- expected elsize=8 but got 16

TNC trace:

ValueError                                Traceback (most recent call last)
<ipython-input-31-df7d85ccaaa8> in <module>()
      1 ### L-BFGS+TNC fails with high precision numerics
      2 #nevo_results_lbfgs = nevo_problem.solve(nevo_sigma,nevo_pi,steps=1,optimization=pyblp.Optimization('l-bfgs-b'))
----> 3 nevo_results_tnc = nevo_problem.solve(nevo_sigma,nevo_pi,steps=1,optimization=pyblp.Optimization('tnc'))

~/anaconda3/lib/python3.6/site-packages/pyblp/problem.py in solve(self, sigma, pi, sigma_bounds, pi_bounds, delta, WD, WS, steps, optimization, custom_display, error_behavior, error_punishment, iteration, linear_costs, linear_fp, center_moments, se_type, processes)
    423             bounds = [p.bounds for p in parameter_info.unfixed]
    424             verbose = options.verbose and not custom_display
--> 425             theta = optimization._optimize(objective_function, theta, bounds, verbose=verbose)
    426             end_time = time.time()
    427             output("")

~/anaconda3/lib/python3.6/site-packages/pyblp/utilities/optimization.py in _optimize(self, objective_function, start_values, bounds, verbose)
    202             if self._supports_bounds:
    203                 minimize_kwargs['bounds'] = bounds
--> 204             return scipy.optimize.minimize(objective_function, start_values, **minimize_kwargs).x
    205 
    206         # set default Knitro options

~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    488     elif meth == 'tnc':
    489         return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,
--> 490                              **options)
    491     elif meth == 'cobyla':
    492         return _minimize_cobyla(fun, x0, args, constraints, **options)

~/anaconda3/lib/python3.6/site-packages/scipy/optimize/tnc.py in _minimize_tnc(fun, x0, args, jac, bounds, eps, scale, offset, mesg_num, maxCGit, maxiter, eta, stepmx, accuracy, minfev, ftol, xtol, gtol, rescale, disp, callback, **unknown_options)
    407                                         offset, messages, maxCGit, maxfun,
    408                                         eta, stepmx, accuracy, fmin, ftol,
--> 409                                         xtol, pgtol, rescale, callback)
    410 
    411     funv, jacv = func_and_grad(x)

ValueError: tnc: invalid gradient vector.