def test_genexpr_op_genexpr(model):
m, x, y, z = model
genexpr = x**1.5 + y
assert isinstance(genexpr, GenExpr)
genexpr **= 2.2
assert isinstance(genexpr, GenExpr)
genexpr += exp(x)
assert isinstance(genexpr, GenExpr)
genexpr -= exp(x)
assert isinstance(genexpr, GenExpr)
genexpr /= log(x + 1)
assert isinstance(genexpr, GenExpr)
genexpr *= (x + y)**1.2
assert isinstance(genexpr, GenExpr)
genexpr /= exp(2)
assert isinstance(genexpr, GenExpr)
genexpr /= x + y
assert isinstance(genexpr, GenExpr)
genexpr = x**1.5 + y
assert isinstance(genexpr, GenExpr)
assert isinstance(sqrt(x) + genexpr, GenExpr)
assert isinstance(exp(x) + genexpr, GenExpr)
assert isinstance(1/x + genexpr, GenExpr)
assert isinstance(1/x**1.5 - genexpr, GenExpr)
assert isinstance(y/x - exp(genexpr), GenExpr)
# sqrt(2) is not a constant expression and
# we can only power to constant expressions!
with pytest.raises(NotImplementedError):
genexpr **= sqrt(2)
def test_genexpr_op_genexpr(model):
m, x, y, z = model
genexpr = x**1.5 + y
assert isinstance(genexpr, GenExpr)
genexpr **= 2.2
assert isinstance(genexpr, GenExpr)
genexpr += exp(x)
assert isinstance(genexpr, GenExpr)
genexpr -= exp(x)
assert isinstance(genexpr, GenExpr)
genexpr /= log(x + 1)
assert isinstance(genexpr, GenExpr)
genexpr *= (x + y)**1.2
assert isinstance(genexpr, GenExpr)
genexpr /= exp(2)
assert isinstance(genexpr, GenExpr)
genexpr /= x + y
assert isinstance(genexpr, GenExpr)
genexpr = x**1.5 + y
assert isinstance(genexpr, GenExpr)
assert isinstance(sqrt(x) + genexpr, GenExpr)
assert isinstance(exp(x) + genexpr, GenExpr)
assert isinstance(1 / x + genexpr, GenExpr)
assert isinstance(1 / x**1.5 - genexpr, GenExpr)
assert isinstance(y / x - exp(genexpr), GenExpr)
# sqrt(2) is not a constant expression and
# we can only power to constant expressions!
with pytest.raises(NotImplementedError):
genexpr **= sqrt(2)
def test_circle():
points = [(2.802686, 1.398947), (4.719673, 4.792101), (1.407758, 7.769566),
(2.253320, 2.373641), (8.583144, 9.769102), (3.022725, 5.470335),
(5.791380, 1.214782), (8.304504, 8.196392), (9.812677, 5.284600),
(9.445761, 9.541600)]
m = Model()
a = m.addVar('a', lb=None)
b = m.addVar('b', ub=None)
r = m.addVar('r')
# minimize radius
m.setObjective(r, 'minimize')
for i, p in enumerate(points):
# NOTE: SCIP will not identify this as SOC constraints!
m.addCons(sqrt((a - p[0])**2 + (b - p[1])**2) <= r,
name='point_%d' % i)
m.optimize()
bestsol = m.getBestSol()
assert abs(m.getSolVal(bestsol, r) - 5.2543) < 1.0e-3
assert abs(m.getSolVal(bestsol, a) - 6.1230) < 1.0e-3
assert abs(m.getSolVal(bestsol, b) - 5.4713) < 1.0e-3
def test_circle():
points =[
(2.802686, 1.398947),
(4.719673, 4.792101),
(1.407758, 7.769566),
(2.253320, 2.373641),
(8.583144, 9.769102),
(3.022725, 5.470335),
(5.791380, 1.214782),
(8.304504, 8.196392),
(9.812677, 5.284600),
(9.445761, 9.541600)]
m = Model()
a = m.addVar('a', lb=None)
b = m.addVar('b', ub=None)
r = m.addVar('r')
# minimize radius
m.setObjective(r, 'minimize')
for i,p in enumerate(points):
# NOTE: SCIP will not identify this as SOC constraints!
m.addCons( sqrt((a - p[0])**2 + (b - p[1])**2) <= r, name = 'point_%d'%i)
m.optimize()
bestsol = m.getBestSol()
assert abs(m.getSolVal(bestsol, r) - 5.2543) < 1.0e-3
assert abs(m.getSolVal(bestsol, a) - 6.1242) < 1.0e-3
assert abs(m.getSolVal(bestsol, b) - 5.4702) < 1.0e-3
def test_upgrade(model):
m, x, y, z = model
expr = x + y
assert isinstance(expr, Expr)
expr += exp(z)
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr -= exp(z)
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr /= x
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr *= sqrt(x)
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr **= 1.5
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
assert isinstance(expr + exp(x), GenExpr)
assert isinstance(expr - exp(x), GenExpr)
assert isinstance(expr / x, GenExpr)
assert isinstance(expr * x**1.2, GenExpr)
assert isinstance(sqrt(expr), GenExpr)
assert isinstance(abs(expr), GenExpr)
assert isinstance(log(expr), GenExpr)
assert isinstance(exp(expr), GenExpr)
with pytest.raises(ZeroDivisionError):
expr /= 0.0
def test_upgrade(model):
m, x, y, z = model
expr = x + y
assert isinstance(expr, Expr)
expr += exp(z)
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr -= exp(z)
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr /= x
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr *= sqrt(x)
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
expr **= 1.5
assert isinstance(expr, GenExpr)
expr = x + y
assert isinstance(expr, Expr)
assert isinstance(expr + exp(x), GenExpr)
assert isinstance(expr - exp(x), GenExpr)
assert isinstance(expr/x, GenExpr)
assert isinstance(expr * x**1.2, GenExpr)
assert isinstance(sqrt(expr), GenExpr)
assert isinstance(abs(expr), GenExpr)
assert isinstance(log(expr), GenExpr)
assert isinstance(exp(expr), GenExpr)
with pytest.raises(ZeroDivisionError):
expr /= 0.0
def test_equation(model):
m, x, y, z = model
equat = 2 * x**1.2 - 3 * sqrt(y) == 1
assert isinstance(equat, ExprCons)
assert equat._lhs == equat._rhs
assert equat._lhs == 1.0
equat = exp(x + 2 * y) == 1 + x**1.2
assert isinstance(equat, ExprCons)
assert isinstance(equat.expr, GenExpr)
assert equat._lhs == equat._rhs
assert equat._lhs == 0.0
equat = x == 1 + x**1.2
assert isinstance(equat, ExprCons)
assert isinstance(equat.expr, GenExpr)
assert equat._lhs == equat._rhs
assert equat._lhs == 0.0
def test_equation(model):
m, x, y, z = model
equat = 2*x**1.2 - 3*sqrt(y) == 1
assert isinstance(equat, ExprCons)
assert equat._lhs == equat._rhs
assert equat._lhs == 1.0
equat = exp(x+2*y) == 1 + x**1.2
assert isinstance(equat, ExprCons)
assert isinstance(equat.expr, GenExpr)
assert equat._lhs == equat._rhs
assert equat._lhs == 0.0
equat = x == 1 + x**1.2
assert isinstance(equat, ExprCons)
assert isinstance(equat.expr, GenExpr)
assert equat._lhs == equat._rhs
assert equat._lhs == 0.0
scip.addCons(y[0] == 0.0)
scip.addCons(x[0] == 0.0)
scip.addCons(y[N] == -1.0)
scip.addCons(x[N] == 1.0)
#
# Optional constraint: y_i are decreasing, x_i are increasing
#
for i in range(N):
scip.addCons(y[i+1] <= y[i])
scip.addCons(x[i] <= x[i+1])
#
# discretization expression and time constraint
#
disc = sqrt(2/g) * sum(sqrt(( (x[i+1] - x[i])**2 + (y[i+1] - y[i])**2 )) / ((sqrt(-y[i+1]) + sqrt(-y[i])) ) for i in range(N))
scip.addCons(disc <= t)
#scip.writeProblem()
#scip.setPresolve(SCIP_PARAMSETTING.OFF)
#
# Solve problem
#
scip.optimize()
#
# Get values for plotting
#
for i in range(N+1):
print(i, scip.getVal(x[i]), scip.getVal(y[i]))
