def test_relax_sq2norm_constr():
""" Relaxed Form of Minimize(square(norm(v0))) with v0 >= p0"""
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0))
con = [v0 >= p0] # should become -v0 + p0 <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='relax')
assert( type(c.constraints[-1]) is le)
assert( type(c.constraints[-1].expr) is sums.sum)
assert( type(c.constraints[-1].expr.args[0]) is muls.smul)
assert( type(c.constraints[-1].expr.args[1]) is muls.smul)
assert( c.objective is not obj )
assert( 'sym0' == c.objective.name )
string_equals = [
"""((-1.0 * sym1) + (1.0 * norm2(v0))) <= 0""",
"""((-1.0 * sym0) + (1.0 * square(sym1))) <= 0""",
"""((-1.0 * v0) + (p0 * 1.0)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n],'==',string,'?')
assert(str(c.constraints[n]) == string)
print('SUCCESS!')
reset_symbols()
def test_relax_sq2norm():
""" Relaxed Form of Minimize(square(norm(v0))) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0))
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='relax')
assert( c.objective is not obj )
assert( 'sym0' == c.objective.name )
# Let up on the testing rigor a bit, now that we checked core fundamentals
string_equals = [
"""((-1.0 * sym1) + (1.0 * norm2(v0))) <= 0""",
"""((-1.0 * sym0) + (1.0 * square(sym1))) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n],'==',string,'?')
assert(str(c.constraints[n]) == string)
print('SUCCESS!')
reset_symbols()
def test_relax_least_squares_constr():
""" Relaxed Form : Minimize(square(norm(F*x - g))) with x >= p0 """
x = Variable ((3,1),name='x')
F = Parameter((3,3),name='F')
g = Parameter((3,1),name='g')
objective = square(norm( F*x - g ))
objective = Minimize(objective)
problem = Problem(objective, [x >= 0])
c = Canonicalize(problem, verbose=True, only='relax')
string_equals = [
"""(sym2 + (-1.0 * matmul(F, x))) == 0""",
"""(sym3 + (-1.0 * sym2) + (g * 1.0)) == 0""",
"""((-1.0 * sym1) + (1.0 * norm2(sym3))) <= 0""",
"""((-1.0 * sym0) + (1.0 * square(sym1))) <= 0""",
"""((-1.0 * x)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n],' ???? ',string, end=' ')
assert(str(c.constraints[n]) == string)
print('... SUCCESS!')
reset_symbols()
def test_norm_inf():
x = Variable((3, 1), name='x')
objective = norm(x, kind='inf') # returns max(abs(x))
objective = Minimize(objective)
problem = Problem(objective, [])
c = Canonicalize(problem, verbose=True, only='smith')
assert (len(c.constraints) == 4)
string_equals = [
"""(sym1[0][0] + (-1.0 * abs(x[0][0]))) == 0""",
"""(sym1[1][0] + (-1.0 * abs(x[1][0]))) == 0""",
"""(sym1[2][0] + (-1.0 * abs(x[2][0]))) == 0""",
"""(sym0 + (-1.0 * max(sym1))) == 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n], ' ???? ', string, end=' ')
assert (str(c.constraints[n]) == string)
print('... SUCCESS!')
reset_symbols()
def test_matrix_sq2norm_sqcon():
""" Relaxed Form : Minimize(square(norm(v0))) with v0 >= square(v1) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0 + v1))
con = [v0 >= square(v1)] # should become -v0 + square(v1) <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True)
sym3 = [v for vn, v in c.vars.items() if vn == 'sym3'][0]
assert_A = {'row': [0, 0, 0],
'col': [0, 1, 4],
'val': [Constant(-1.0), Constant(-1.0), Constant(1.0)]}
assert_b = [Constant(0.0)]
#assert_G = {'row': [0, 0, 1, 2, 3, 4, 5, 6, 7, 8],
# 'col': [0, 5, 3, 4, 2, 2, 3, 5, 5, 1],
# 'val': [Constant(-1.0), Constant(0.0), Constant(-1.0), Constant(1.0),
# Constant(-1.0), Constant(-1.0), Constant(2.0), Constant(-1.0),
# Constant(-1.0), Constant(2.0)]}
assert_G = {'row': [0, 0, 1, 2, 3, 4, 5, 6, 7, 8],
'col': [0, 5, 3, 4, 2, 2, 3, 5, 5, 1],
'val': [Constant(-1.0), Constant(1.0), Constant(-1.0), Constant(1.0),
Constant(-1.0), Constant(-1.0), Constant(2.0), Constant(-1.0),
Constant(-1.0), Constant(2.0)]}
assert_h = [ (-1.0 * sym3), Constant(0.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0)]
assert_h = [Constant(0.0), Constant(0.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0), Constant(1.0), Constant(-1.0),
Constant(0.0)]
assert_dims = {'q': [2, 3, 3], 'l': 1}
assert_A = COO_to_CS(assert_A, (len(assert_b), len(c.c)), 'col')
assert_G = COO_to_CS(assert_G, (len(assert_h), len(c.c)), 'col')
assert_c = [0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
assert(c.c == assert_c)
assert(c.A == assert_A)
assert(c.b == assert_b)
assert(c.G == assert_G)
assert(all([c.h[n].value == t.value for n, t in enumerate(assert_h)]))
assert(c.dims == assert_dims)
reset_symbols()
def test_constraints():
v0 = Variable(name='v0')
v1 = Variable(name='v1')
p0 = Parameter(name='p0')
p1 = Parameter(name='p1')
c = (v0 == 0)
print(c)
assert (type(c) == eq)
assert (c.expr.args[0] is v0)
c = (v0 <= 0)
print(c)
assert (type(c) == le)
assert (c.expr.args[0] is v0)
c = (v0 >= 0)
print(c)
assert (type(c) == le)
assert (c.expr.args[0].args[0].value == -1)
assert (c.expr.args[0].args[1] is v0)
c = (v0 >= p0)
print(c)
assert (type(c) == le)
assert (c.expr.args[0].args[0].value == -1)
assert (c.expr.args[0].args[1] is v0)
assert (c.expr.args[1].args[0] is p0)
# TODO: ADD TESTS FOR ATOMS AND FUNCTIONS IN CONSTRAINTS!
# ATOMS in Constraints
c = (v1 + v0 == p0)
print(c)
assert (type(c) == eq)
assert (str(c) == '(p0 + (-1.0 * v1) + (-1.0 * v0)) == 0')
# FUNCTIONS in Constraints
c = (norm(v1) <= v0)
print(c)
assert (type(c) == le)
assert (c.expr.nterms == 2)
assert (c.expr.args[1].args[1] is v0)
reset_symbols()
def test_norm_value_expr():
p = Parameter((3, 1), name='p')
expr = norm(p)
value = expr.value({'p[0][0]': 3, 'p[1][0]': 2, 'p[2][0]': 1})
assert (np.isclose(value, np.linalg.norm([[3], [2], [1]])))
reset_symbols()
p = Parameter((1, 3), name='p')
expr = norm(p)
value = expr.value({'p[0][0]': 3, 'p[0][1]': 2, 'p[0][2]': 1})
assert (np.isclose(value, np.linalg.norm([3, 2, 1])))
reset_symbols()
def test_matrix_least_squares_constr():
""" Minimize(square(norm(F*x - g))) with x >= p0 """
x = Variable ((3,1),name='x')
F = Parameter((3,3),name='F')
g = Parameter((3,1),name='g')
objective = square(norm( F*x - g ))
objective = Minimize(objective)
problem = Problem(objective, [x >= 1])
c = Canonicalize(problem, verbose=True)
# Test for errors, not asserts, and for solution outcome (via ecos_solution)
reset_symbols()
def test_matrix_sq2norm():
""" Matrix Form of Minimize(square(norm(v0))) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0))
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True)
assert_c = [0.0, 0.0, 1.0, 0.0]
assert_A = COO_to_CS({'row':[],'col':[],'val':[]}, (0,4), 'col')
assert_G = {'row':[0, 1, 2, 3, 4],
'col':[3, 0, 2, 2, 3],
'val':[Constant(-1.0), Constant(1.0), Constant(-1.0),
Constant(-1.0), Constant(2.0)]}
assert_h = [Constant(0.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0)]
assert_G = COO_to_CS(assert_G, (len(assert_h), len(c.c)), 'col')
assert(c.c == assert_c)
assert(c.A is None)
assert(c.b is None)
assert(c.G == assert_G)
assert(all([c.h[n].value == t.value for n, t in enumerate(assert_h)]))
assert(c.dims == {'q': [2,3], 'l': 0})
reset_symbols()
def test_norm_graph():
v0 = Variable(name='v0')
s0 = Symbol(name='s0')
expr = norm(v0)
constr = (expr <= s0) # effectively in relaxed smith form
print('Graph form of', end='')
print(constr)
constr = constr.graph_form()
print('-->', constr)
print()
n = max(v0.shape[0], v0.shape[1])
assert (constr.dims == n + 1)
assert (type(constr) is SecondOrderConeConstraint)
assert (all([type(c) is le for c in constr.constraints]))
assert (constr.constraints[1].expr.args[0] is v0)
assert (constr.constraints[0].expr.args[0].args[1] is s0)
reset_symbols()
def test_smith_sq2norm_sqcon():
""" Smith Form : Minimize(square(norm(v0))) with v0 >= square(v1) """
v0 = Variable(name='v0')
v1 = Variable(name='v1')
p0 = Parameter(name='p0')
p1 = Parameter(name='p1')
obj = square(norm(v0 + v1))
con = [v0 >= square(v1)] # should become -v0 + square(v1) <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='smith')
assert (type(c.constraints[-1]) is le)
assert (type(c.constraints[-1].expr) is sums.sum)
assert (type(c.constraints[-1].expr.args[0]) is muls.smul)
assert (type(c.constraints[-1].expr.args[1]) is muls.smul)
assert (c.objective is not obj)
assert ('sym0' == c.objective.name)
string_equals = [
"""(sym2 + (-1.0 * v0) + (-1.0 * v1)) == 0""",
"""(sym1 + (-1.0 * norm2(sym2))) == 0""",
"""(sym0 + (-1.0 * square(sym1))) == 0""",
"""(sym3 + (-1.0 * square(v1))) == 0""",
"""((-1.0 * v0) + (1.0 * sym3)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n], ' ???? ', string, end=' ')
assert (str(c.constraints[n]) == string)
print('... SUCCESS!')
reset_symbols()
def sum_squares(*args):
return square(norms.norm(*args, kind=2))
