def test_merge(self): """Test merging functions. """ # sum_entries x = Variable(10) fn1 = sum_entries(x, gamma=1.0) fn2 = norm1(x) assert can_merge(fn1, fn2) merged = merge_fns(fn1, fn2) v = np.arange(10) * 1.0 - 5.0 prox_val1 = merged.prox(1.0, v.copy()) tmp = norm1(x, c=np.ones(10), gamma=1.0) prox_val2 = tmp.prox(1.0, v.copy()) self.assertItemsAlmostEqual(prox_val1, prox_val2) # sum_squares x = Variable(10) val = np.arange(10) fn1 = sum_squares(x, gamma=1.0, beta=2.0, alpha=3.0, b=val) fn2 = norm1(x) assert can_merge(fn1, fn2) merged = merge_fns(fn1, fn2) v = np.arange(10) * 1.0 - 5.0 prox_val1 = merged.prox(1.0, v.copy()) tmp = norm1(x, c=-12 * val, gamma=1.0 + 12, d=val.dot(val)) prox_val2 = tmp.prox(1.0, v.copy()) self.assertItemsAlmostEqual(prox_val1, prox_val2)
def test_sum_entries(self): """Sum of entries of lin op. """ tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = sum_entries(tmp) x = fn.prox(1.0, v.copy()) self.assertItemsAlmostEqual(x, v - 1)
def test_merge_all(self): """Test function to merge all prox operators possible. """ # merge all x = Variable(10) lin_op = grad(x) fns = [sum_squares(lin_op), sum_entries(lin_op), nonneg(lin_op)] merged = merge_all(fns) assert len(merged) == 1 v = np.reshape(np.arange(10) * 1.0 - 5.0, (10, 1)) prox_val1 = merged[0].prox(1.0, v.copy()) tmp = nonneg(lin_op, c=np.ones((10, 1)), gamma=1.0) prox_val2 = tmp.prox(1.0, v.copy()) self.assertItemsAlmostEqual(prox_val1, prox_val2)
def test_absorb_lin_op(self): """Test absorb lin op operator. """ # norm1. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = norm1(mul_elemwise(-v, tmp), alpha=5.) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0)) fn = norm1(mul_elemwise(-v, mul_elemwise(2 * v, tmp)), alpha=5.) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0)) new_prox = absorb_lin_op(new_prox)[0] x = new_prox.prox(rho, v.copy()) new_v = 2 * v * v self.assertItemsAlmostEqual(x, np.sign(new_v) * np.maximum(np.abs(new_v) - 5. * np.abs(new_v) / rho, 0)) # nonneg. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = nonneg(mul_elemwise(-v, tmp), alpha=5.) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) self.assertItemsAlmostEqual(x, fn.prox(rho, -np.abs(v))) # sum_squares. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 alpha = 5. val = np.arange(10) fn = sum_squares(mul_elemwise(-v, tmp), alpha=alpha, c=val) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) cvx_x = cvx.Variable(10) prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) * (rho / 2) + 5 * cvx.sum_squares(cvx.mul_elemwise(-v, cvx_x)) + (val * -v).T * cvx_x )) prob.solve() self.assertItemsAlmostEqual(x, cvx_x.value, places=3) # Test scale. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = norm1(10 * tmp) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) cvx_x = cvx.Variable(10) prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x, 1))) prob.solve() self.assertItemsAlmostEqual(x, cvx_x.value, places=3) val = np.arange(10) fn = norm1(10 * tmp, c=val, b=val, gamma=0.01) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) cvx_x = cvx.Variable(10) prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x - val, 1) + 10 * val.T * \ cvx_x + cvx.sum_squares(cvx_x) )) prob.solve() self.assertItemsAlmostEqual(x, cvx_x.value, places=2) # sum_entries tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = sum_entries(sum([10 * tmp, mul_elemwise(v, tmp)])) funcs = absorb.absorb_all_lin_ops([fn]) c = __builtins__['sum']([func.c for func in funcs]) self.assertItemsAlmostEqual(c, v + 10, places=3)
def test_absorb_lin_op(self): """Test absorb lin op operator. """ # norm1. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = norm1(mul_elemwise(-v, tmp), alpha=5.) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) self.assertItemsAlmostEqual( x, np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0)) fn = norm1(mul_elemwise(-v, mul_elemwise(2 * v, tmp)), alpha=5.) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) self.assertItemsAlmostEqual( x, np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0)) new_prox = absorb_lin_op(new_prox)[0] x = new_prox.prox(rho, v.copy()) new_v = 2 * v * v self.assertItemsAlmostEqual( x, np.sign(new_v) * np.maximum(np.abs(new_v) - 5. * np.abs(new_v) / rho, 0)) # nonneg. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = nonneg(mul_elemwise(-v, tmp), alpha=5.) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) self.assertItemsAlmostEqual(x, fn.prox(rho, -np.abs(v))) # sum_squares. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 alpha = 5. val = np.arange(10) fn = sum_squares(mul_elemwise(-v, tmp), alpha=alpha, c=val) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) cvx_x = cvx.Variable(10) prob = cvx.Problem( cvx.Minimize( cvx.sum_squares(cvx_x - v) * (rho / 2) + 5 * cvx.sum_squares(cvx.mul_elemwise(-v, cvx_x)) + (val * -v).T * cvx_x)) prob.solve() self.assertItemsAlmostEqual(x, cvx_x.value, places=3) # Test scale. tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = norm1(10 * tmp) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) cvx_x = cvx.Variable(10) prob = cvx.Problem( cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x, 1))) prob.solve() self.assertItemsAlmostEqual(x, cvx_x.value, places=3) val = np.arange(10) fn = norm1(10 * tmp, c=val, b=val, gamma=0.01) rho = 2 new_prox = absorb_lin_op(fn)[0] x = new_prox.prox(rho, v.copy()) cvx_x = cvx.Variable(10) prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x - val, 1) + 10 * val.T * \ cvx_x + cvx.sum_squares(cvx_x) )) prob.solve() self.assertItemsAlmostEqual(x, cvx_x.value, places=2) # sum_entries tmp = Variable(10) v = np.arange(10) * 1.0 - 5.0 fn = sum_entries(sum([10 * tmp, mul_elemwise(v, tmp)])) funcs = absorb.absorb_all_lin_ops([fn]) c = __builtins__['sum']([func.c for func in funcs]) self.assertItemsAlmostEqual(c, v + 10, places=3)