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))