#!/usr/bin/env python3
"``naginterfaces.library.opt.qpconvex2_sparse_solve`` Python Example."
# NAG Copyright 2017-2019.
# pylint: disable=invalid-name,too-many-locals
from naginterfaces.library import opt
[docs]def main():
"""
Example for :func:`naginterfaces.library.opt.qpconvex2_sparse_solve`.
Sparse QP/LP.
>>> main()
naginterfaces.library.opt.qpconvex2_sparse_solve Python Example Results.
Sparse QP/LP.
Function value at lowest point found is -1847784.67712.
The corresponding x is:
(0.00, 349.40, 648.85, 172.85, 407.52, 271.36, 150.02).
"""
print(
'naginterfaces.library.opt.qpconvex2_sparse_solve '
'Python Example Results.'
)
print('Sparse QP/LP.')
# Cold start:
start = 'Cold'
cb_qphx = lambda x, _nstate: (
[
2*x[0], 2*x[1],
2*(x[2] + x[3]), 2*(x[2] + x[3]),
2*x[4],
2*(x[5] + x[6]), 2*(x[5] + x[6]),
]
)
# The sparse A stored by column:
a = [
0.02, 0.02, 0.03, 1.00, 0.70, 0.02, 0.15, -200.00,
0.06, 0.75, 0.03, 0.04, 0.05, 0.04, 1.00, -2000.00,
0.02, 1.00, 0.01, 0.08, 0.08, 0.80, -2000.00,
1.00, 0.12, 0.02, 0.02, 0.75, 0.04, -2000.00,
0.01, 0.80, 0.02, 1.00, 0.02, 0.06, 0.02, -2000.00,
1.00, 0.01, 0.01, 0.97, 0.01, 400.00,
0.97, 0.03, 1.00, 400.00,
]
# The index information for the packed A:
loca = [1, 9, 17, 24, 31, 39, 45, 49]
inda = [
7, 5, 3, 1, 6, 4, 2, 8, 7, 6, 5, 4, 3, 2, 1, 8, 2, 1, 4,
3, 7, 6, 8, 1, 7, 3, 4, 6, 2, 8, 5, 6, 7, 1, 2, 3, 4, 8,
1, 2, 3, 6, 7, 8, 7, 2, 1, 8,
]
# In this example, we make the objective vector the final column of A:
c = [0.]
iobj = 8
# The number of leading nonzero columns of the Hessian matrix:
ncolh = 7
# The bounds on x and on the linear constraints:
m = 8
bl = [
0., 0., 400., 100., 0., 0., 0.,
2000., -1.e20, -1.e20, -1.e20, -1.e20, 1500., 250., -1.e20,
]
bu = [
200., 2500., 800., 700., 1500., 1.e20, 1.e20,
2000., 60., 100., 40., 30., 1.e20, 300., 1.e20,
]
# No constant objective term:
objadd = 0.
# Row and column names:
names = [
'...X1...', '...X2...', '...X3...', '...X4...', '...X5...',
'...X6...', '...X7...', '..ROW1..', '..ROW2..', '..ROW3..',
'..ROW4..', '..ROW5..', '..ROW6..', '..ROW7..', '..COST..',
]
# Blank problem name:
prob = ''
# No elastic variables:
n = len(loca) - 1
helast = [0]*(n+m)
# Initial state for cold start:
hs = [0]*(n+m)
x = [0.]*(n+m)
# No superbasics to specify:
ns = 0
# Initialize the communication structure:
comm = opt.qpconvex2_sparse_init()
qp_soln = opt.qpconvex2_sparse_solve(
start, m, ncolh, iobj, objadd, prob,
a, inda, loca, bl, bu, names, helast, hs, x, ns, comm,
qphx=cb_qphx, c=c,
)
print(
'Function value at lowest point found is {:.5f}.'.format(qp_soln.obj)
)
print('The corresponding x is:')
print('(' + ', '.join(['{:.2f}']*n).format(*qp_soln.x[:n]) + ').')
if __name__ == '__main__':
import doctest
import sys
sys.exit(
doctest.testmod(
None, verbose=True, report=False,
optionflags=doctest.REPORT_NDIFF,
).failed
)
