# Osborne 1, a data-fitting problem (33 points, the sum of two decaying
# exponentials, 5 parameters), solved by lmder1 from the standard start, to
# read as a story:
#
#     viv story lib/minpack/story_osborne1.viv
#
from minpack.lmder import H_X, lmder1
from minpack.enorm import enorm, EPSMCH
from minpack.mgh import mgh_data, mgh_fcn, mgh_start

# problem 17 of the test driver: 33 residuals in 5 unknowns
SO_NPROB = 17.0
SO_M = 33.0
SO_N = 5.0
so_x = mgh_start(SO_NPROB, SO_N, 1.0)
so_fvec = zeros(SO_M)
so_counts = zeros(2)
so_info = lmder1(mgh_fcn, mgh_data(SO_NPROB, SO_M, SO_N), so_x, so_fvec, zeros(SO_M, SO_N), sqrt(EPSMCH), zeros(SO_N), so_counts, zeros(1, H_X + SO_N))
print(so_info)
print(enorm(len(so_fvec), so_fvec))

test "lmder1 stops with info 1 after 18 evaluations of f and 15 of J, at the Fortran's norm 7.3924926e-3" {
    assert_near(so_info, 1.0, 0.0)
    assert_near(so_counts[0], 18.0, 0.0)
    assert_near(so_counts[1], 15.0, 0.0)
    assert_near(enorm(len(so_fvec), so_fvec), 0.007392492609048511, 1.0e-15)
    assert_near(so_x[0], 0.375410049244025656, 1.0e-13)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors