def hops_config():
N = int(sys.argv[3])
x0 = nice_coeff(N, border='no')
curve = bspline.BasisSpline(3, numpy.linspace(0.0, 4.0, N - 2))
# Ineq. constraints
lowvec = numpy.r_[numpy.zeros(N - 1), pi / 2.0]
upvec = numpy.r_[numpy.ones(N - 1) * 2.0, pi]
xvals = numpy.linspace(0.0, 4.0, N - 1)
B = curve.compute_basis_matrix(xvals)
I = curve.compute_basis_integrals()
A = numpy.vstack([B, I])
configfile = sys.argv[2]
cur_file = os.path.abspath(__file__)
numpy2hopspack.makecfg(N,
cur_file,
configfile,
x0=x0,
Aineq=A,
lineq=lowvec,
uineq=upvec,
P=8,
gss_step_top=0.01)
def nice_coeff(N, border='yes'):
curve = bspline.BasisSpline(3, numpy.linspace(0.0, 4.0, N - 2))
xvals = numpy.linspace(0.0, 4.0, N)
# Matrix with values of basis functions at xvals
# so that B*c gives a vector with the evaluations of the spline with
# coefficients c at each x \in xvals
B = curve.compute_basis_matrix(xvals)
# Prepare vector with desired values at xvals
f = []
for x in xvals:
f.append(half_circle(x))
f = numpy.array(f)
if border == 'no':
f = f[1:N - 1]
B = B[1:N - 1, 1:N - 1]
Bineq = curve.compute_basis_matrix(numpy.linspace(0.0, 4.0, N - 1))
Bineq = Bineq[1:N - 2, 1:N - 1]
def grad_func(c):
return 0.5 * numpy.dot(c, numpy.dot(B, c)) - numpy.dot(c, f)
def dgrad_func(c):
return numpy.dot(B, c) - f
def ineq_func(c):
if border == 'no':
return numpy.dot(Bineq, c)
return numpy.dot(B, c)
# mini = scipy.optimize.fmin_slsqp(grad_func, f)
mini = scipy.optimize.fmin_slsqp(grad_func,
f,
fprime=dgrad_func,
f_ieqcons=ineq_func)
return mini
def obstacle_chi(c):
N, = c.shape
# For N degrees of freedom we need N-2 knots
curve = bspline.BasisSpline(3, numpy.linspace(0.0, 4.0, N-2))
def chi(x):
if x[0] <= 4.0:
return 0
if x[0] >= 8.0:
return 0
sval = curve.evaluate(c, x[0]-4.0)
if abs(x[1] - 4.0) <= sval:
return 1
else:
return 0
return chi
def apps_config():
N = int(sys.argv[3])
x0 = nice_coeff(N, border='no')
curve = bspline.BasisSpline(3, numpy.linspace(0.0, 4.0, N - 2))
with open(sys.argv[2], "w") as cf:
cf.write('# SAMPLE APPSPACK INPUT FILE\n')
cf.write('@ "Linear"\n')
# cf.write('"Upper" vector 4 10 10 10 10\n')
# cf.write('"Lower" vector 4 -10 0 0 0\n')
# cf.write('"Scaling" vector 4 1 1 1 1\n')
# cf.write('"Inequality Upper" vector 2 DNE -1\n')
# cf.write('"Inequality Lower" vector 2 -10 DNE\n')
# cf.write('"Equality Bound" vector 1 3\n')
# cf.write('"Inequality Matrix" matrix 2 4 \n')
# cf.write('-1 -1 -1 -1\n')
# cf.write(' 1 -1 1 -1\n')
# cf.write('"Equality Matrix" matrix 1 4\n')
# cf.write('2 0 2 -7\n')
# Upper
# Scaling vector
cf.write('"Scaling" vector %d ' % (N - 2))
for i in range(1, N - 1):
cf.write('1.0 ')
cf.write('\n')
# Pointwise inequalities + Volume bounds
cf.write('"Inequality Upper" vector %d ' % (N - 2))
for i in range(1, N - 2):
cf.write('2.0 ')
cf.write('%f ' % pi)
cf.write('\n')
cf.write('"Inequality Lower" vector %d ' % (N - 2))
for i in range(1, N - 2):
cf.write('0.0 ')
cf.write('%f ' % (pi / 2.0))
cf.write('\n')
xvals = numpy.linspace(0.0, 4.0, N - 1)
B = curve.compute_basis_matrix(xvals)
I = curve.compute_basis_integrals()
cf.write('"Inequality Matrix" matrix %d %d \n' % (N - 2, N - 2))
for i in range(1, N - 2):
for j in range(1, N - 1):
cf.write('%f ' % B[i, j])
cf.write('\n')
for j in range(1, N - 1):
cf.write('%f ' % I[j])
cf.write('\n')
cf.write('@@\n')
cf.write('@ "Evaluator"\n')
cf.write('"Executable Name" string "run_obstacle.py"\n')
cf.write('"Input Prefix" string "obstacle_input"\n')
cf.write('"Output Prefix" string "obstacle_output"\n')
cf.write('@@\n')
cf.write('@ "Solver" \n')
cf.write('"Debug" int 3\n')
# Initial vector
cf.write('"Initial X" vector %d ' % (N - 2))
for i in range(0, N - 2):
cf.write("%f " % x0[i])
cf.write('\n')
cf.write('"Step Tolerance" double 1e-3\n')
cf.write('@@\n')
print numpy.dot(I[1:N - 1], x0)
#print numpy.dot(B[1:N-1,1:N-1], x0)
print str(pi / 2.0)