def test_sqrt_graph():
v0 = Variable(name='v0')
s0 = Symbol(name='s0')
expr = sqrt(v0) # concave
constr = (expr >= s0) # effectively in relaxed smith form
print('Graph form of', end=' ')
print(constr)
constr = constr.graph_form()
print('-->', constr)
assert (constr.dims == 3)
assert (type(constr) is SecondOrderConeConstraint)
assert (all([type(c) is le for c in constr.constraints]))
c = constr
string_equals = [
"""(-1.0 + (-1.0 * v0)) <= 0""",
"""(1.0 + (-1.0 * v0)) <= 0""",
"""((2.0 * s0)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n], '==', string, '?')
assert (str(c.constraints[n]) == str(string))
print('SUCCESS!')
reset_symbols()
def test_matvec():
""" Test Matrix * Vector product """
a = Parameter((3, 3), name='a')
x = Variable((3, 1), name='x')
m = a * x
print(m, 'with shapes', a.shape, 'x', x.shape)
expanded = m.expand()
print_matrix(expanded)
assert (list_shape(expanded) == m.shape)
# Holds all the indices we assert must be in each ELEMENT of each atom
ind = [[
[[(0, 0), (0, 0)], [(0, 1), (1, 0)], [(0, 2), (2, 0)]],
], [
[[(1, 0), (0, 0)], [(1, 1), (1, 0)], [(1, 2), (2, 0)]],
], [
[[(2, 0), (0, 0)], [(2, 1), (1, 0)], [(2, 2), (2, 0)]],
]]
for n, row in enumerate(ind):
for m, col in enumerate(row):
for s, sumarg in enumerate(col):
for a, mularg_shape in enumerate(sumarg):
assert (
expanded[n][m].args[s].args[a].index == mularg_shape)
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_sq():
""" Relaxed Form of Minimize(square(v0)) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(v0)
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='relax')
assert( len(c.constraints) == 1 )
assert( c.objective is not obj )
assert( 'sym0' == c.objective.name )
assert(type(c.constraints[0]) is le)
assert(c.constraints[0].expr.args[0].curvature == 0)
assert(c.constraints[0].expr.args[1].curvature == +1)
assert(c.constraints[0].expr.args[1].symbol_groups()[0][0].value == 1.0)
assert(c.constraints[0].expr.args[1].symbol_groups()[2][0].name == 'square')
reset_symbols()
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_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_quad_over_lin_x1_graph():
v0 = Variable(name='v0')
s0 = Symbol(name='s0')
x = v0
expr = quad_over_lin([1], x)
constr = (expr <= s0) # effectively in relaxed smith form
print('Graph form of', end='')
print(constr)
constr = constr.graph_form()
print('-->', constr)
print()
assert (constr.dims == 3)
assert (type(constr) is SecondOrderConeConstraint)
assert (all([type(c) is le for c in constr.constraints]))
c = constr # keeps below names same as other tests
string_equals = [
"""((-1.0 * v0) + (-1.0 * s0)) <= 0""",
"""((1.0 * v0) + (-1.0 * s0)) <= 0""",
"""(2.0) <= 0""" # although this constraint is weird, it is required
]
for n, string in enumerate(string_equals):
print(c.constraints[n], '==', string, '?')
assert (str(c.constraints[n]) == str(string))
print('SUCCESS!')
reset_symbols()
def test_smith_sq():
""" Smith Form of Minimize(square(v0)) """
v0 = Variable(name='v0')
v1 = Variable(name='v1')
p0 = Parameter(name='p0')
p1 = Parameter(name='p1')
obj = square(v0)
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='smith')
assert (len(c.constraints) == 1)
assert (c.objective is not obj)
assert ('sym0' == c.objective.name)
assert (hasattr(c.constraints[0].expr.args[0], 'name'))
assert (c.constraints[0].expr.args[0].name == 'sym0')
assert (hasattr(c.constraints[0].expr.args[1], 'args'))
assert (hasattr(c.constraints[0].expr.args[1].args[0], 'value'))
assert (c.constraints[0].expr.args[1].args[0].value == -1.0)
assert (hasattr(c.constraints[0].expr.args[1].args[1], 'name'))
assert (c.constraints[0].expr.args[1].args[1].name == 'square')
reset_symbols()
def test_ecos_trivial_geomean():
x = cvx.Variable( (2), name='x')
constraints = [x[0] >= 0]
constraints += [x[1] <= cvx.geo_mean(x[0], 5)]
constraints += [x[1] >= 5]
objective = x[0] + x[1] # farthest down and left
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
canon.assign_values({})
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'][0:2])
assert( np.allclose(solution['x'][0:2], [5.0, 5.0]) )
reset_symbols()
def test_ecos_leastsquares():
x = cvx.Variable (name='x')
F = cvx.Parameter(name='F')
g = cvx.Parameter(name='g')
objective = cvx.square(cvx.norm( F*x - g ))
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, [])
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'F' : 42,
'g' : 42,
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'][0])
assert( np.isclose(solution['x'][0], 1.0) )
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_elementwisesymbol_into_function():
""" Test a shaped symbol input to a scalar function and
the elementwise output """
x = Variable((3, 1), name='x')
expr = square(x)
print(expr)
constr = (expr <= 0)
print(constr)
expand = constr.expand()
print(expand)
assert (type(constr.expr) is sums.sum)
assert (type(constr.expr.args[0]) is Vector)
assert (len(constr.expr.args[0].args) == 3)
assert (len(expand) == 3)
assert (all([type(a) is le for a in expand]))
reset_symbols()
def test_square_graph():
v0 = Variable(name='v0')
s0 = Symbol(name='s0')
expr = square(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 + 2)
assert (type(constr) is SecondOrderConeConstraint)
assert (all([type(c) is le for c in constr.constraints]))
c = constr # keeps below names same as other tests
string_equals = [
"""(-1.0 + (-1.0 * s0)) <= 0""", """(1.0 + (-1.0 * s0)) <= 0""",
"""((2.0 * v0)) <= 0"""
]
for n, string in enumerate(string_equals):
print(c.constraints[n], '==', string, '?')
assert (str(c.constraints[n]) == str(string))
print('SUCCESS!')
reset_symbols()
def test_matrix_sq():
""" Matrix Form of Minimize(square(v0)) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(v0)
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True)
assert(c.c == [0, 0, 1])
assert(c.A is None)
assert(c.b is None)
assert_G = {
'row':[0, 1, 2],
'col':[2, 2, 0],
'val':[Constant(-1.0), Constant(-1.0), Constant(2.0)]
}
assert_h = [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.G == assert_G)
assert(all([c.h[n].value == t.value for n, t in enumerate(assert_h)]))
assert(c.dims == {'q': [3], 'l': 0})
reset_symbols()
def test_ecos_trivial_invpos():
x = cvx.Variable( (2), name='x')
constraints = [x[0] >= 0]
constraints += [x[1] >= x[0]]
constraints += [x[1] >= cvx.inv_pos(x[0])]
objective = x[1]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
canon.assign_values({})
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'][0:2])
assert( np.allclose(solution['x'][0:2], [1.0, 1.0]) )
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_symbol_curvature():
v = Variable(name='v')
assert (v.curvature == 0)
p = Parameter(name='p')
assert (p.curvature == 0)
reset_symbols()
def test_ecos_polyhedradist():
import cvx_sym as cvx
n = 2 # number of dimensions
m = 3 # number of lines defining polyhedron 1
p = 3 # number of lines defining polyhedron 2
x1 = cvx.Variable ((n,1),name='x1')
x2 = cvx.Variable ((n,1),name='x2')
A1 = cvx.Parameter((m,n),name='A1')
A2 = cvx.Parameter((p,n),name='A2')
B1 = cvx.Parameter((m,1),name='B1')
B2 = cvx.Parameter((p,1),name='B2')
objective = cvx.square(cvx.norm(x1 - x2))
constraints = [ A1[i,:].T * x1 <= B1[i] for i in range(m) ]
constraints += [ A2[i,:].T * x2 <= B2[i] for i in range(p) ]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'A1' : np.array([[-1,1],[1,1],[0,-1]]),
'B1' : np.array([[3],[3],[0]]),
'A2' : np.array([[.5,-1],[0,1],[+1,0]]),
'B2' : np.array([[-3],[3],[5]]),
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
# Solution is found at intersection of polyhedra
assert( np.allclose(x_solution, [0,3, 0,3], atol=1e-4) )
# So therefore the objective should be near zero
assert( np.allclose(solution['info']['pcost'], 0.0 ) )
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_mul_redirect():
""" Test that mul redirects properly to matmul """
a = Parameter((10, 1), name='a')
b = Variable((1, 10), name='b')
m = a * b
assert (type(m) is matmul)
assert (m.args[0] is a)
assert (m.args[1] is b)
reset_symbols()
def test_ecos_robustlp():
import cvx_sym as cvx
n = 2 # number of dimensions
m = 3 # number of elementwise elements
x = cvx.Variable ((n,1),name='x')
A = cvx.Parameter((m,n),name='A')
B = cvx.Parameter((m,1),name='B')
C = cvx.Parameter((n,1),name='C')
P = cvx.Parameter((m,n),name='P')
objective = C.T * x
constraints = [A[i].T * x + cvx.norm(P[i].T * x) <= B[i] for i in range(m)]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'A' : np.array([[1,1],[1,1],[1,1]]),
'B' : np.array([[3],[3],[3]]),
'C' : np.array([[.1],[.2]]),
'P' : np.array([[1,2],[3,4],[5,6]])
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.allclose(x_solution, [3,-3] ) )
reset_symbols()
def test_ecos_leastsquares_constr():
x = cvx.Variable ((3,1),name='x')
F = cvx.Parameter((3,3),name='F')
g = cvx.Parameter((3,1),name='g')
U = cvx.Parameter((3,1),name='U')
L = cvx.Parameter((3,1),name='L')
constraints = []
objective = cvx.square(cvx.norm( F*x - g ))
constraints += [ x <= U ]
constraints += [ L <= x ]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'F' : np.array([[1,2,3],[4,5,6],[7,8,9]]),
'g' : np.array([[1],[2],[3]]),
'U' : np.array([[42],[42],[42]]),
'L' : np.array([[1],[2],[3]])
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.allclose(x_solution, [1,2,3] ) )
reset_symbols()
def test_ecos_chebyshevcenter():
import cvx_sym as cvx
n = 2
m = 3
r = cvx.Variable((1,1),name='r')
x = cvx.Variable((n,1),name='x')
A = cvx.Parameter((m,n),name='A')
B = cvx.Parameter((m,1),name='B')
objective = -r
constraints = [A[i,:].T * x + r * cvx.norm(A[i,:]) <= B[i] for i in range(m)]
constraints += [r >= 0]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'A' : np.array([[-1,1],[1,1],[0,-1]]),
'B' : np.array([[3],[3],[0]]),
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.allclose(x_solution, [0, 1.242641] ) )
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_reshaping_vector():
""" Test reshaping a vector (slice of a symbol in this case)"""
p = Parameter((2, (2 * 2)), name='p')
sliced = p[1, :]
print(sliced)
shaped = reshape(sliced, (2, 2))
print(shaped)
assert (str(shaped[0, 0]) == str(p[1][0]))
assert (str(shaped[0, 1]) == str(p[1][1]))
assert (str(shaped[1, 0]) == str(p[1][2]))
assert (str(shaped[1, 1]) == str(p[1][3]))
reset_symbols()
def check_curvy_function(function, asserted_curvature):
print('Testing Curvature of', function.name)
v = Variable(name='v')
e = function(v)
if asserted_curvature > 0:
assert (e.curvature > 0)
else:
assert (e.curvature < 0)
e = -1 * function(v)
if asserted_curvature > 0:
assert (e.curvature < 0)
else:
assert (e.curvature > 0)
reset_symbols()
def test_matmul_constraint():
""" Test that constraints with matmul are expanded elementwise in canon """
p = Parameter((3, 1), name='p')
a = Parameter((3, 3), name='a')
x = Variable((3, 1), name='x')
expr = a * x
print('expr', expr)
constr = (expr <= p)
print('constr', constr)
constr = constr.expand()
print('-->', constr)
print()
assert (len(constr) == 3)
assert (all([type(a) is le for a in constr]))
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_sq2norm_constr():
""" Matrix 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)
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, 5], 'col': [0, 3, 0, 2, 2, 3],
'val': [Constant(-1.0), Constant(-1.0), Constant(1.0),
Constant(-1.0), Constant(-1.0), Constant(2.0)]}
assert_h = [(-1.0 * p0), 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': 1})
reset_symbols()
def test_elementwiselist_into_function():
""" Test a list input to a scalar function and the elementwise output """
x = Variable(name='x')
y = Variable(name='y')
z = Variable(name='z')
a = Variable(name='a')
b = Variable(name='b')
c = Variable(name='c')
expr = square([x, y, z, a, b, c])
print(expr)
constr = (expr <= 0)
print(constr)
assert (type(constr.expr) is sums.sum)
assert (type(constr.expr.args[0]) is Vector)
assert (len(constr.expr.args[0].args) == 6)
reset_symbols()
