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How to use intersect method in fMBT

Best Python code snippet using fMBT_python

test_qp_subproblem.py

Source:test_qp_subproblem.py

1import numpy as np2from scipy.sparse import csc_matrix3from scipy.optimize._trustregion_constr.qp_subproblem \4    import (eqp_kktfact,5            projected_cg,6            box_intersections,7            sphere_intersections,8            box_sphere_intersections,9            modified_dogleg)10from scipy.optimize._trustregion_constr.projections \11    import projections12from numpy.testing import (TestCase, assert_array_almost_equal,13                           assert_array_equal, assert_array_less,14                           assert_equal, assert_,15                           run_module_suite, assert_allclose, assert_warns,16                           dec)17import pytest18class TestEQPDirectFactorization(TestCase):19    # From Example 16.2 Nocedal/Wright "Numerical20    # Optimization" p.452.21    def test_nocedal_example(self):22        H = csc_matrix([[6, 2, 1],23                        [2, 5, 2],24                        [1, 2, 4]])25        A = csc_matrix([[1, 0, 1],26                        [0, 1, 1]])27        c = np.array([-8, -3, -3])28        b = -np.array([3, 0])29        x, lagrange_multipliers = eqp_kktfact(H, c, A, b)30        assert_array_almost_equal(x, [2, -1, 1])31        assert_array_almost_equal(lagrange_multipliers, [3, -2])32class TestSphericalBoundariesIntersections(TestCase):33    def test_2d_sphere_constraints(self):34        # Interior inicial point35        ta, tb, intersect = sphere_intersections([0, 0],36                                                 [1, 0], 0.5)37        assert_array_almost_equal([ta, tb], [0, 0.5])38        assert_equal(intersect, True)39        # No intersection between line and circle40        ta, tb, intersect = sphere_intersections([2, 0],41                                                 [0, 1], 1)42        assert_equal(intersect, False)43        # Outside inicial point pointing toward outside the circle44        ta, tb, intersect = sphere_intersections([2, 0],45                                                 [1, 0], 1)46        assert_equal(intersect, False)47        # Outside inicial point pointing toward inside the circle48        ta, tb, intersect = sphere_intersections([2, 0],49                                                 [-1, 0], 1.5)50        assert_array_almost_equal([ta, tb], [0.5, 1])51        assert_equal(intersect, True)52        # Inicial point on the boundary53        ta, tb, intersect = sphere_intersections([2, 0],54                                                 [1, 0], 2)55        assert_array_almost_equal([ta, tb], [0, 0])56        assert_equal(intersect, True)57    def test_2d_sphere_constraints_line_intersections(self):58        # Interior inicial point59        ta, tb, intersect = sphere_intersections([0, 0],60                                                 [1, 0], 0.5,61                                                 entire_line=True)62        assert_array_almost_equal([ta, tb], [-0.5, 0.5])63        assert_equal(intersect, True)64        # No intersection between line and circle65        ta, tb, intersect = sphere_intersections([2, 0],66                                                 [0, 1], 1,67                                                 entire_line=True)68        assert_equal(intersect, False)69        # Outside inicial point pointing toward outside the circle70        ta, tb, intersect = sphere_intersections([2, 0],71                                                 [1, 0], 1,72                                                 entire_line=True)73        assert_array_almost_equal([ta, tb], [-3, -1])74        assert_equal(intersect, True)75        # Outside inicial point pointing toward inside the circle76        ta, tb, intersect = sphere_intersections([2, 0],77                                                 [-1, 0], 1.5,78                                                 entire_line=True)79        assert_array_almost_equal([ta, tb], [0.5, 3.5])80        assert_equal(intersect, True)81        # Inicial point on the boundary82        ta, tb, intersect = sphere_intersections([2, 0],83                                                 [1, 0], 2,84                                                 entire_line=True)85        assert_array_almost_equal([ta, tb], [-4, 0])86        assert_equal(intersect, True)87class TestBoxBoundariesIntersections(TestCase):88    def test_2d_box_constraints(self):89        # Box constraint in the direction of vector d90        ta, tb, intersect = box_intersections([2, 0], [0, 2],91                                              [1, 1], [3, 3])92        assert_array_almost_equal([ta, tb], [0.5, 1])93        assert_equal(intersect, True)94        # Negative direction95        ta, tb, intersect = box_intersections([2, 0], [0, 2],96                                              [1, -3], [3, -1])97        assert_equal(intersect, False)98        # Some constraints are absent (set to +/- inf)99        ta, tb, intersect = box_intersections([2, 0], [0, 2],100                                              [-np.inf, 1],101                                              [np.inf, np.inf])102        assert_array_almost_equal([ta, tb], [0.5, 1])103        assert_equal(intersect, True)104        # Intersect on the face of the box105        ta, tb, intersect = box_intersections([1, 0], [0, 1],106                                              [1, 1], [3, 3])107        assert_array_almost_equal([ta, tb], [1, 1])108        assert_equal(intersect, True)109        # Interior inicial pointoint110        ta, tb, intersect = box_intersections([0, 0], [4, 4],111                                              [-2, -3], [3, 2])112        assert_array_almost_equal([ta, tb], [0, 0.5])113        assert_equal(intersect, True)114        # No intersection between line and box constraints115        ta, tb, intersect = box_intersections([2, 0], [0, 2],116                                              [-3, -3], [-1, -1])117        assert_equal(intersect, False)118        ta, tb, intersect = box_intersections([2, 0], [0, 2],119                                              [-3, 3], [-1, 1])120        assert_equal(intersect, False)121        ta, tb, intersect = box_intersections([2, 0], [0, 2],122                                              [-3, -np.inf],123                                              [-1, np.inf])124        assert_equal(intersect, False)125        ta, tb, intersect = box_intersections([0, 0], [1, 100],126                                              [1, 1], [3, 3])127        assert_equal(intersect, False)128        ta, tb, intersect = box_intersections([0.99, 0], [0, 2],129                                                         [1, 1], [3, 3])130        assert_equal(intersect, False)131        # Inicial point on the boundary132        ta, tb, intersect = box_intersections([2, 2], [0, 1],133                                              [-2, -2], [2, 2])134        assert_array_almost_equal([ta, tb], [0, 0])135        assert_equal(intersect, True)136    def test_2d_box_constraints_entire_line(self):137        # Box constraint in the direction of vector d138        ta, tb, intersect = box_intersections([2, 0], [0, 2],139                                              [1, 1], [3, 3],140                                              entire_line=True)141        assert_array_almost_equal([ta, tb], [0.5, 1.5])142        assert_equal(intersect, True)143        # Negative direction144        ta, tb, intersect = box_intersections([2, 0], [0, 2],145                                              [1, -3], [3, -1],146                                              entire_line=True)147        assert_array_almost_equal([ta, tb], [-1.5, -0.5])148        assert_equal(intersect, True)149        # Some constraints are absent (set to +/- inf)150        ta, tb, intersect = box_intersections([2, 0], [0, 2],151                                              [-np.inf, 1],152                                              [np.inf, np.inf],153                                              entire_line=True)154        assert_array_almost_equal([ta, tb], [0.5, np.inf])155        assert_equal(intersect, True)156        # Intersect on the face of the box157        ta, tb, intersect = box_intersections([1, 0], [0, 1],158                                              [1, 1], [3, 3],159                                              entire_line=True)160        assert_array_almost_equal([ta, tb], [1, 3])161        assert_equal(intersect, True)162        # Interior inicial pointoint163        ta, tb, intersect = box_intersections([0, 0], [4, 4],164                                              [-2, -3], [3, 2],165                                              entire_line=True)166        assert_array_almost_equal([ta, tb], [-0.5, 0.5])167        assert_equal(intersect, True)168        # No intersection between line and box constraints169        ta, tb, intersect = box_intersections([2, 0], [0, 2],170                                              [-3, -3], [-1, -1],171                                              entire_line=True)172        assert_equal(intersect, False)173        ta, tb, intersect = box_intersections([2, 0], [0, 2],174                                              [-3, 3], [-1, 1],175                                              entire_line=True)176        assert_equal(intersect, False)177        ta, tb, intersect = box_intersections([2, 0], [0, 2],178                                              [-3, -np.inf],179                                              [-1, np.inf],180                                              entire_line=True)181        assert_equal(intersect, False)182        ta, tb, intersect = box_intersections([0, 0], [1, 100],183                                              [1, 1], [3, 3],184                                              entire_line=True)185        assert_equal(intersect, False)186        ta, tb, intersect = box_intersections([0.99, 0], [0, 2],187                                              [1, 1], [3, 3],188                                              entire_line=True)189        assert_equal(intersect, False)190        # Inicial point on the boundary191        ta, tb, intersect = box_intersections([2, 2], [0, 1],192                                              [-2, -2], [2, 2],193                                              entire_line=True)194        assert_array_almost_equal([ta, tb], [-4, 0])195        assert_equal(intersect, True)196    def test_3d_box_constraints(self):197        # Simple case198        ta, tb, intersect = box_intersections([1, 1, 0], [0, 0, 1],199                                              [1, 1, 1], [3, 3, 3])200        assert_array_almost_equal([ta, tb], [1, 1])201        assert_equal(intersect, True)202        # Negative direction203        ta, tb, intersect = box_intersections([1, 1, 0], [0, 0, -1],204                                              [1, 1, 1], [3, 3, 3])205        assert_equal(intersect, False)206        # Interior Point207        ta, tb, intersect = box_intersections([2, 2, 2], [0, -1, 1],208                                              [1, 1, 1], [3, 3, 3])209        assert_array_almost_equal([ta, tb], [0, 1])210        assert_equal(intersect, True)211    def test_3d_box_constraints_entire_line(self):212        # Simple case213        ta, tb, intersect = box_intersections([1, 1, 0], [0, 0, 1],214                                              [1, 1, 1], [3, 3, 3],215                                              entire_line=True)216        assert_array_almost_equal([ta, tb], [1, 3])217        assert_equal(intersect, True)218        # Negative direction219        ta, tb, intersect = box_intersections([1, 1, 0], [0, 0, -1],220                                              [1, 1, 1], [3, 3, 3],221                                              entire_line=True)222        assert_array_almost_equal([ta, tb], [-3, -1])223        assert_equal(intersect, True)224        # Interior Point225        ta, tb, intersect = box_intersections([2, 2, 2], [0, -1, 1],226                                              [1, 1, 1], [3, 3, 3],227                                              entire_line=True)228        assert_array_almost_equal([ta, tb], [-1, 1])229        assert_equal(intersect, True)230class TestBoxSphereBoundariesIntersections(TestCase):231    def test_2d_box_constraints(self):232        # Both constraints are active233        ta, tb, intersect = box_sphere_intersections([1, 1], [-2, 2],234                                                     [-1, -2], [1, 2], 2,235                                                     entire_line=False)236        assert_array_almost_equal([ta, tb], [0, 0.5])237        assert_equal(intersect, True)238        # None of the constraints are active239        ta, tb, intersect = box_sphere_intersections([1, 1], [-1, 1],240                                                     [-1, -3], [1, 3], 10,241                                                     entire_line=False)242        assert_array_almost_equal([ta, tb], [0, 1])243        assert_equal(intersect, True)244        # Box Constraints are active245        ta, tb, intersect = box_sphere_intersections([1, 1], [-4, 4],246                                                     [-1, -3], [1, 3], 10,247                                                     entire_line=False)248        assert_array_almost_equal([ta, tb], [0, 0.5])249        assert_equal(intersect, True)250        # Spherical Constraints are active251        ta, tb, intersect = box_sphere_intersections([1, 1], [-4, 4],252                                                     [-1, -3], [1, 3], 2,253                                                     entire_line=False)254        assert_array_almost_equal([ta, tb], [0, 0.25])255        assert_equal(intersect, True)256        # Infeasible problems257        ta, tb, intersect = box_sphere_intersections([2, 2], [-4, 4],258                                                     [-1, -3], [1, 3], 2,259                                                     entire_line=False)260        assert_equal(intersect, False)261        ta, tb, intersect = box_sphere_intersections([1, 1], [-4, 4],262                                                     [2, 4], [2, 4], 2,263                                                     entire_line=False)264        assert_equal(intersect, False)265    def test_2d_box_constraints_entire_line(self):266        # Both constraints are active267        ta, tb, intersect = box_sphere_intersections([1, 1], [-2, 2],268                                                     [-1, -2], [1, 2], 2,269                                                     entire_line=True)270        assert_array_almost_equal([ta, tb], [0, 0.5])271        assert_equal(intersect, True)272        # None of the constraints are active273        ta, tb, intersect = box_sphere_intersections([1, 1], [-1, 1],274                                                     [-1, -3], [1, 3], 10,275                                                     entire_line=True)276        assert_array_almost_equal([ta, tb], [0, 2])277        assert_equal(intersect, True)278        # Box Constraints are active279        ta, tb, intersect = box_sphere_intersections([1, 1], [-4, 4],280                                                     [-1, -3], [1, 3], 10,281                                                     entire_line=True)282        assert_array_almost_equal([ta, tb], [0, 0.5])283        assert_equal(intersect, True)284        # Spherical Constraints are active285        ta, tb, intersect = box_sphere_intersections([1, 1], [-4, 4],286                                                     [-1, -3], [1, 3], 2,287                                                     entire_line=True)288        assert_array_almost_equal([ta, tb], [0, 0.25])289        assert_equal(intersect, True)290        # Infeasible problems291        ta, tb, intersect = box_sphere_intersections([2, 2], [-4, 4],292                                                     [-1, -3], [1, 3], 2,293                                                     entire_line=True)294        assert_equal(intersect, False)295        ta, tb, intersect = box_sphere_intersections([1, 1], [-4, 4],296                                                     [2, 4], [2, 4], 2,297                                                     entire_line=True)298        assert_equal(intersect, False)299class TestModifiedDogleg(TestCase):300    def test_cauchypoint_equalsto_newtonpoint(self):301        A = np.array([[1, 8]])302        b = np.array([-16])303        _, _, Y = projections(A)304        newton_point = np.array([0.24615385, 1.96923077])305        # Newton point inside boundaries306        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf], [np.inf, np.inf])307        assert_array_almost_equal(x, newton_point)308        # Spherical constraint active309        x = modified_dogleg(A, Y, b, 1, [-np.inf, -np.inf], [np.inf, np.inf])310        assert_array_almost_equal(x, newton_point/np.linalg.norm(newton_point))311        # Box Constraints active312        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf], [0.1, np.inf])313        assert_array_almost_equal(x, (newton_point/newton_point[0]) * 0.1)314    def test_3d_example(self):315        A = np.array([[1, 8, 1],316                      [4, 2, 2]])317        b = np.array([-16, 2])318        Z, LS, Y = projections(A)319        newton_point = np.array([-1.37090909, 2.23272727, -0.49090909])320        cauchy_point = np.array([0.11165723, 1.73068711, 0.16748585])321        origin = np.zeros_like(newton_point)322        # newton_point inside boundaries323        x = modified_dogleg(A, Y, b, 3, [-np.inf, -np.inf, -np.inf],324                            [np.inf, np.inf, np.inf])325        assert_array_almost_equal(x, newton_point)326        # line between cauchy_point and newton_point contains best point327        # (spherical constrain is active).328        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf, -np.inf],329                            [np.inf, np.inf, np.inf])330        z = cauchy_point331        d = newton_point-cauchy_point332        t = ((x-z)/(d))333        assert_array_almost_equal(t, np.full(3, 0.40807330))334        assert_array_almost_equal(np.linalg.norm(x), 2)335        # line between cauchy_point and newton_point contains best point336        # (box constrain is active).337        x = modified_dogleg(A, Y, b, 5, [-1, -np.inf, -np.inf],338                            [np.inf, np.inf, np.inf])339        z = cauchy_point340        d = newton_point-cauchy_point341        t = ((x-z)/(d))342        assert_array_almost_equal(t, np.full(3, 0.7498195))343        assert_array_almost_equal(x[0], -1)344        # line between origin and cauchy_point contains best point345        # (spherical constrain is active).346        x = modified_dogleg(A, Y, b, 1, [-np.inf, -np.inf, -np.inf],347                            [np.inf, np.inf, np.inf])348        z = origin349        d = cauchy_point350        t = ((x-z)/(d))351        assert_array_almost_equal(t, np.full(3, 0.573936265))352        assert_array_almost_equal(np.linalg.norm(x), 1)353        # line between origin and newton_point contains best point354        # (box constrain is active).355        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf, -np.inf],356                            [np.inf, 1, np.inf])357        z = origin358        d = newton_point359        t = ((x-z)/(d))360        assert_array_almost_equal(t, np.full(3, 0.4478827364))361        assert_array_almost_equal(x[1], 1)362class TestProjectCG(TestCase):363    # From Example 16.2 Nocedal/Wright "Numerical364    # Optimization" p.452.365    def test_nocedal_example(self):366        H = csc_matrix([[6, 2, 1],367                        [2, 5, 2],368                        [1, 2, 4]])369        A = csc_matrix([[1, 0, 1],370                        [0, 1, 1]])371        c = np.array([-8, -3, -3])372        b = -np.array([3, 0])373        Z, _, Y = projections(A)374        x, info = projected_cg(H, c, Z, Y, b)375        assert_equal(info["stop_cond"], 4)376        assert_equal(info["hits_boundary"], False)377        assert_array_almost_equal(x, [2, -1, 1])378    def test_compare_with_direct_fact(self):379        H = csc_matrix([[6, 2, 1, 3],380                        [2, 5, 2, 4],381                        [1, 2, 4, 5],382                        [3, 4, 5, 7]])383        A = csc_matrix([[1, 0, 1, 0],384                        [0, 1, 1, 1]])385        c = np.array([-2, -3, -3, 1])386        b = -np.array([3, 0])387        Z, _, Y = projections(A)388        x, info = projected_cg(H, c, Z, Y, b, tol=0)389        x_kkt, _ = eqp_kktfact(H, c, A, b)390        assert_equal(info["stop_cond"], 1)391        assert_equal(info["hits_boundary"], False)392        assert_array_almost_equal(x, x_kkt)393    def test_trust_region_infeasible(self):394        H = csc_matrix([[6, 2, 1, 3],395                        [2, 5, 2, 4],396                        [1, 2, 4, 5],397                        [3, 4, 5, 7]])398        A = csc_matrix([[1, 0, 1, 0],399                        [0, 1, 1, 1]])400        c = np.array([-2, -3, -3, 1])401        b = -np.array([3, 0])402        trust_radius = 1403        Z, _, Y = projections(A)404        with pytest.raises(ValueError):405            projected_cg(H, c, Z, Y, b, trust_radius=trust_radius)406    def test_trust_region_barely_feasible(self):407        H = csc_matrix([[6, 2, 1, 3],408                        [2, 5, 2, 4],409                        [1, 2, 4, 5],410                        [3, 4, 5, 7]])411        A = csc_matrix([[1, 0, 1, 0],412                        [0, 1, 1, 1]])413        c = np.array([-2, -3, -3, 1])414        b = -np.array([3, 0])415        trust_radius = 2.32379000772445021283416        Z, _, Y = projections(A)417        x, info = projected_cg(H, c, Z, Y, b,418                               tol=0,419                               trust_radius=trust_radius)420        assert_equal(info["stop_cond"], 2)421        assert_equal(info["hits_boundary"], True)422        assert_array_almost_equal(np.linalg.norm(x), trust_radius)423        assert_array_almost_equal(x, -Y.dot(b))424    def test_hits_boundary(self):425        H = csc_matrix([[6, 2, 1, 3],426                        [2, 5, 2, 4],427                        [1, 2, 4, 5],428                        [3, 4, 5, 7]])429        A = csc_matrix([[1, 0, 1, 0],430                        [0, 1, 1, 1]])431        c = np.array([-2, -3, -3, 1])432        b = -np.array([3, 0])433        trust_radius = 3434        Z, _, Y = projections(A)435        x, info = projected_cg(H, c, Z, Y, b,436                               tol=0,437                               trust_radius=trust_radius)438        assert_equal(info["stop_cond"], 2)439        assert_equal(info["hits_boundary"], True)440        assert_array_almost_equal(np.linalg.norm(x), trust_radius)441    def test_negative_curvature_unconstrained(self):442        H = csc_matrix([[1, 2, 1, 3],443                        [2, 0, 2, 4],444                        [1, 2, 0, 2],445                        [3, 4, 2, 0]])446        A = csc_matrix([[1, 0, 1, 0],447                        [0, 1, 0, 1]])448        c = np.array([-2, -3, -3, 1])449        b = -np.array([3, 0])450        Z, _, Y = projections(A)451        with pytest.raises(ValueError):452            projected_cg(H, c, Z, Y, b, tol=0)453    def test_negative_curvature(self):454        H = csc_matrix([[1, 2, 1, 3],455                        [2, 0, 2, 4],456                        [1, 2, 0, 2],457                        [3, 4, 2, 0]])458        A = csc_matrix([[1, 0, 1, 0],459                        [0, 1, 0, 1]])460        c = np.array([-2, -3, -3, 1])461        b = -np.array([3, 0])462        Z, _, Y = projections(A)463        trust_radius = 1000464        x, info = projected_cg(H, c, Z, Y, b,465                               tol=0,466                               trust_radius=trust_radius)467        assert_equal(info["stop_cond"], 3)468        assert_equal(info["hits_boundary"], True)469        assert_array_almost_equal(np.linalg.norm(x), trust_radius)470    # The box constraints are inactive at the solution but471    # are active during the iterations.472    def test_inactive_box_constraints(self):473        H = csc_matrix([[6, 2, 1, 3],474                        [2, 5, 2, 4],475                        [1, 2, 4, 5],476                        [3, 4, 5, 7]])477        A = csc_matrix([[1, 0, 1, 0],478                        [0, 1, 1, 1]])479        c = np.array([-2, -3, -3, 1])480        b = -np.array([3, 0])481        Z, _, Y = projections(A)482        x, info = projected_cg(H, c, Z, Y, b,483                               tol=0,484                               lb=[0.5, -np.inf,485                                   -np.inf, -np.inf],486                               return_all=True)487        x_kkt, _ = eqp_kktfact(H, c, A, b)488        assert_equal(info["stop_cond"], 1)489        assert_equal(info["hits_boundary"], False)490        assert_array_almost_equal(x, x_kkt)491    # The box constraints active and the termination is492    # by maximum iterations (infeasible iteraction).493    def test_active_box_constraints_maximum_iterations_reached(self):494        H = csc_matrix([[6, 2, 1, 3],495                        [2, 5, 2, 4],496                        [1, 2, 4, 5],497                        [3, 4, 5, 7]])498        A = csc_matrix([[1, 0, 1, 0],499                        [0, 1, 1, 1]])500        c = np.array([-2, -3, -3, 1])501        b = -np.array([3, 0])502        Z, _, Y = projections(A)503        x, info = projected_cg(H, c, Z, Y, b,504                               tol=0,505                               lb=[0.8, -np.inf,506                                   -np.inf, -np.inf],507                               return_all=True)508        assert_equal(info["stop_cond"], 1)509        assert_equal(info["hits_boundary"], True)510        assert_array_almost_equal(A.dot(x), -b)511        assert_array_almost_equal(x[0], 0.8)512    # The box constraints are active and the termination is513    # because it hits boundary (without infeasible iteraction).514    def test_active_box_constraints_hits_boundaries(self):515        H = csc_matrix([[6, 2, 1, 3],516                        [2, 5, 2, 4],517                        [1, 2, 4, 5],518                        [3, 4, 5, 7]])519        A = csc_matrix([[1, 0, 1, 0],520                        [0, 1, 1, 1]])521        c = np.array([-2, -3, -3, 1])522        b = -np.array([3, 0])523        trust_radius = 3524        Z, _, Y = projections(A)525        x, info = projected_cg(H, c, Z, Y, b,526                               tol=0,527                               ub=[np.inf, np.inf, 1.6, np.inf],528                               trust_radius=trust_radius,529                               return_all=True)530        assert_equal(info["stop_cond"], 2)531        assert_equal(info["hits_boundary"], True)532        assert_array_almost_equal(x[2], 1.6)533    # The box constraints are active and the termination is534    # because it hits boundary (infeasible iteraction).535    def test_active_box_constraints_hits_boundaries_infeasible_iter(self):536        H = csc_matrix([[6, 2, 1, 3],537                        [2, 5, 2, 4],538                        [1, 2, 4, 5],539                        [3, 4, 5, 7]])540        A = csc_matrix([[1, 0, 1, 0],541                        [0, 1, 1, 1]])542        c = np.array([-2, -3, -3, 1])543        b = -np.array([3, 0])544        trust_radius = 4545        Z, _, Y = projections(A)546        x, info = projected_cg(H, c, Z, Y, b,547                               tol=0,548                               ub=[np.inf, 0.1, np.inf, np.inf],549                               trust_radius=trust_radius,550                               return_all=True)551        assert_equal(info["stop_cond"], 2)552        assert_equal(info["hits_boundary"], True)553        assert_array_almost_equal(x[1], 0.1)554    # The box constraints are active and the termination is555    # because it hits boundary (no infeasible iteraction).556    def test_active_box_constraints_negative_curvature(self):557        H = csc_matrix([[1, 2, 1, 3],558                        [2, 0, 2, 4],559                        [1, 2, 0, 2],560                        [3, 4, 2, 0]])561        A = csc_matrix([[1, 0, 1, 0],562                        [0, 1, 0, 1]])563        c = np.array([-2, -3, -3, 1])564        b = -np.array([3, 0])565        Z, _, Y = projections(A)566        trust_radius = 1000567        x, info = projected_cg(H, c, Z, Y, b,568                               tol=0,569                               ub=[np.inf, np.inf, 100, np.inf],570                               trust_radius=trust_radius)571        assert_equal(info["stop_cond"], 3)572        assert_equal(info["hits_boundary"], True)...

ResourceAreaCharacterization.py

Source:ResourceAreaCharacterization.py

1import config2import arcpy3import time45# This script does intersections of multiple inputs to determine the areas of treated stormwater in a given resource area.6# Output is provided as a time stamped gdb.7# Currently all intermediate steps are saved out as feature classes8# ==> Program is meant to be run using the ArcPro version of Python <==91011def characterize_resource():1213    #create new time stamped gdb14    gdb_name = time.strftime("ResourceAreas_%m_%d_%Y_%H_%M")1516    arcpy.CreateFileGDB_management(config.output_folder, gdb_name, "10.0")17    gdb_path = config.output_folder + r"/" + gdb_name + r".gdb/"1819    working_resource_areas_path = gdb_path + config.resource_area_characterization20    imp_intersect_path = gdb_path + 'imp_intersect'21    imp_intersect_dissolved_path = gdb_path + 'imp_intersect_dissolved'2223    mem = 'memory/'24    #feature_classes_in_memory = []2526    #this copies the resource area and removes extra fields27    arcpy.Dissolve_management(config.resource_areas, gdb_path + config.resource_area_characterization, 'NewSiteNum')2829    working_resource_areas_layer = arcpy.MakeFeatureLayer_management(gdb_path + config.resource_area_characterization, 'working_resource_areas_layer')30    #add all the new fields31    arcpy.AddField_management(working_resource_areas_layer,'Resource_Area_sqft', 'DOUBLE')32    arcpy.CalculateField_management(working_resource_areas_layer,'Resource_Area_sqft',0)3334    arcpy.AddField_management(working_resource_areas_layer,'ImpA_sqft', 'DOUBLE')35    arcpy.CalculateField_management(working_resource_areas_layer,'ImpA_sqft',0)3637    arcpy.AddField_management(gdb_path + config.resource_area_characterization,'Total_Treated_sqft', 'DOUBLE')38    arcpy.CalculateField_management(gdb_path + config.resource_area_characterization,'Total_Treated_sqft',0)3940    arcpy.AddField_management(gdb_path + config.resource_area_characterization,'Total_Untreated_sqft', 'DOUBLE')41    arcpy.CalculateField_management(gdb_path + config.resource_area_characterization,'Total_Untreated_sqft',0)4243    arcpy.AddField_management(gdb_path + config.resource_area_characterization,'ImpA_BMP_Treated_sqft', 'DOUBLE')44    arcpy.CalculateField_management(gdb_path + config.resource_area_characterization,'ImpA_BMP_Treated_sqft',0)4546    arcpy.AddField_management(gdb_path + config.resource_area_characterization,'ImpA_UIC_Treated_sqft', 'DOUBLE')47    arcpy.CalculateField_management(gdb_path + config.resource_area_characterization,'ImpA_UIC_Treated_sqft',0)4849    arcpy.AddField_management(working_resource_areas_layer,'Combined_ImpA_sqft', 'DOUBLE')50    arcpy.CalculateField_management(working_resource_areas_layer, 'Combined_ImpA_sqft', 0)5152    arcpy.AddField_management(gdb_path + config.resource_area_characterization,'Sanitary_ImpA_sqft', 'DOUBLE')53    arcpy.CalculateField_management(gdb_path + config.resource_area_characterization,'Sanitary_ImpA_sqft', 0)5455    ##Impervious Area565758    #intersect impervious areas and resource areas in memory59    #imp_intersect = arcpy.Intersect_analysis([working_resource_areas_path, config.modeled_impervious_areas], imp_intersect_path)60    imp_intersect = arcpy.PairwiseIntersect_analysis([working_resource_areas_path, config.modeled_impervious_areas], imp_intersect_path)6162    #dissolve on NewSiteNum63    imp_intersect_dissolved = arcpy.Dissolve_management(imp_intersect_path, imp_intersect_dissolved_path, 'NewSiteNum')6465    #make a feature layer66    imp_intersect_dissolved_layer = arcpy.MakeFeatureLayer_management(imp_intersect_dissolved, 'imp_intersect_dissolved_layer')6768    # join the impervious area to the resource area and transfer area to 'ImpA_sqft'69    joined = arcpy.AddJoin_management(working_resource_areas_layer, 'NewSiteNum', imp_intersect_dissolved_layer, 'NewSiteNum')70    arcpy.CalculateField_management(working_resource_areas_layer, "ImpA_sqft", "!imp_intersect_dissolved.Shape_Area!")71    arcpy.RemoveJoin_management(working_resource_areas_layer)7273    ##BMP Areas74    #get intersection of bmp and resource areas, dissolve the result, make a feature layer so it can be joined75    bmp_intersect_resource = arcpy.Intersect_analysis([working_resource_areas_layer, config.bmp_areas], gdb_path + 'bmp_intersect_resource')76    bmp_intersect_resource_dissolved = arcpy.Dissolve_management(bmp_intersect_resource, gdb_path + 'bmp_intersect_resource_dissolved', 'NewSiteNum')77    bmp_intersect_resource_dissolved_layer = arcpy.MakeFeatureLayer_management(bmp_intersect_resource_dissolved, 'bmp_intersect_resource_dissolved_layer')7879    ##BMPs intersected with impervious areas80    bmp_intersect_impervious = arcpy.Intersect_analysis([bmp_intersect_resource_dissolved, imp_intersect_dissolved_layer], gdb_path + 'bmp_intersect_impervious')81    bmp_intersect_impervious_dissolved = arcpy.Dissolve_management(bmp_intersect_impervious, gdb_path + 'bmp_intersect_impervious_dissolved', 'NewSiteNum')82    bmp_intersect_impervious_dissolved_layer = arcpy.MakeFeatureLayer_management(bmp_intersect_impervious_dissolved, 'bmp_intersect_impervious_dissolved_layer')8384    ##UIC Areas85    #get intersection of uic and resource areas, dissolve the result, make a feature layer so it can be joined8687    uic_intersect_resource = arcpy.Intersect_analysis([working_resource_areas_layer, config.uic_areas], gdb_path + 'uic_intersect_resource')88    uic_intersect_dissolved = arcpy.Dissolve_management(uic_intersect_resource, gdb_path + 'uic_intersect_dissolved', 'NewSiteNum')89    uic_intersect_dissolved_layer = arcpy.MakeFeatureLayer_management(uic_intersect_dissolved, 'uic_intersect_dissolved_layer')9091    ##UICs intersected with impervious areas92    uic_intersect_impervious = arcpy.Intersect_analysis([uic_intersect_dissolved, imp_intersect_dissolved_layer], gdb_path + 'uic_intersect_impervious')93    uic_intersect_impervious_dissolved = arcpy.Dissolve_management(uic_intersect_impervious, gdb_path + 'uic_intersect_impervious_dissolved', 'NewSiteNum')94    uic_intersect_impervious_dissolved_layer = arcpy.MakeFeatureLayer_management(uic_intersect_impervious_dissolved, 'uic_intersect_impervious_dissolved_layer')959697    arcpy.AddJoin_management(working_resource_areas_layer, 'NewSiteNum', bmp_intersect_impervious_dissolved_layer, 'NewSiteNum')98    arcpy.CalculateField_management(working_resource_areas_layer, "ImpA_BMP_Treated_sqft", "!bmp_intersect_impervious_dissolved.Shape_Area!")99    #copy out the join to see whats up100    arcpy.CopyFeatures_management(working_resource_areas_layer, gdb_path + 'watershed_resource_combined_intersect_dissolved_bmp_join')101    arcpy.RemoveJoin_management(working_resource_areas_layer)102103104    arcpy.AddJoin_management(working_resource_areas_layer, 'NewSiteNum', uic_intersect_impervious_dissolved_layer, 'NewSiteNum')105    arcpy.CalculateField_management(working_resource_areas_layer, "ImpA_UIC_Treated_sqft", "!uic_intersect_impervious_dissolved.Shape_Area!")106    #copy out the join to see whats up107    arcpy.CopyFeatures_management(working_resource_areas_layer, gdb_path + 'watershed_resource_combined_intersect_dissolved_uic_join')108109    arcpy.RemoveJoin_management(working_resource_areas_layer)110111112    ##UICs intersected with impervious areas113    ##Combined Sewer114    #Make layer to filter by sewer area, dissolve, make layer on the dissolved result so it can be joined115    combined_sewer_area = arcpy.MakeFeatureLayer_management(config.sewer_basin_areas, 'combined_sewer_area', "TYPE =  'C'")116    combined_sewer_area_dissolved = arcpy.Dissolve_management(combined_sewer_area, "memory/combined_dissolved", "TYPE")117    combined_sewer_area_dissolved_layer = arcpy.MakeFeatureLayer_management(combined_sewer_area_dissolved, 'combined_sewer_area_dissolved_layer')118119120    #Sanitary Sewer121    #Make layer to filter by sewer area, dissolve, make layer on the dissolved result so it can be joined122    sanitary_sewer_area = arcpy.MakeFeatureLayer_management(config.sewer_basin_areas, 'sanitary_sewer_area', "TYPE =  'S'")123    sanitary_sewer_area_dissolved = arcpy.Dissolve_management(sanitary_sewer_area, "memory/sanitary_dissolved", "TYPE")124    sanitary_sewer_area_dissolved_layer = arcpy.MakeFeatureLayer_management(sanitary_sewer_area_dissolved, 'sanitary_sewer_area_dissolved_layer')125126127    #intersect watershed areas and combined sewer areas128    watershed_resource_combined_intersect = arcpy.Intersect_analysis([working_resource_areas_layer, combined_sewer_area_dissolved_layer], "memory/watershed_resource_combined_intersect")129    watershed_resource_combined_intersect_dissolved = arcpy.Dissolve_management(watershed_resource_combined_intersect, "memory/watershed_resource_combined_intersect_dissolved",'NewSiteNum' )130    arcpy.CopyFeatures_management(watershed_resource_combined_intersect_dissolved, gdb_path + 'watershed_resource_combined_intersect_dissolved')131132    watershed_resource_combined_intersect_dissolved_layer = arcpy.MakeFeatureLayer_management(watershed_resource_combined_intersect_dissolved, 'watershed_resource_combined_intersect_dissolved_layer')133    ##134    #135    #intersect new combined areas with impervious areas and dissolve136    watershed_resource_combined_intersect_impervious = arcpy.Intersect_analysis([watershed_resource_combined_intersect_dissolved, imp_intersect_dissolved_layer], "memory/watershed_resource_combined_intersect_impervious")137    watershed_resource_combined_intersect_impervious_dissolved = arcpy.Dissolve_management(watershed_resource_combined_intersect_impervious, "memory/watershed_resource_combined_intersect_impervious_dissolved", 'NewSiteNum')138    arcpy.CopyFeatures_management(watershed_resource_combined_intersect_impervious_dissolved, gdb_path + 'watershed_resource_combined_intersect_impervious_dissolved')139    watershed_resource_combined_intersect_impervious_dissolved_layer = arcpy.MakeFeatureLayer_management(watershed_resource_combined_intersect_impervious_dissolved, 'watershed_resource_combined_intersect_impervious_dissolved_layer')140141    #intersect watershed areas and sanitary sewer areas142    watershed_resource_sanitary_intersect = arcpy.Intersect_analysis([working_resource_areas_layer, sanitary_sewer_area_dissolved_layer], "memory/watershed_resource_sanitary_intersect")143    watershed_resource_sanitary_intersect_dissolved = arcpy.Dissolve_management(watershed_resource_sanitary_intersect, "memory/watershed_resource_sanitary_intersect_dissolved",'NewSiteNum' )144145    arcpy.CopyFeatures_management(watershed_resource_sanitary_intersect_dissolved, gdb_path + 'watershed_resource_sanitary_intersect_dissolved')146147    watershed_resource_sanitary_intersect_dissolved_layer = arcpy.MakeFeatureLayer_management(watershed_resource_sanitary_intersect_dissolved, 'watershed_resource_sanitary_intersect_dissolved_layer')148    #149    #150    #intersect new sanitary areas with impervious areas and dissolve151    watershed_resource_sanitary_intersect_impervious = arcpy.Intersect_analysis([watershed_resource_sanitary_intersect_dissolved, imp_intersect_dissolved_layer], "memory/watershed_resource_sanitary_intersect_impervious")152    watershed_resource_sanitary_intersect_impervious_dissolved = arcpy.Dissolve_management(watershed_resource_sanitary_intersect_impervious, "memory/watershed_resource_sanitary_intersect_impervious_dissolved", 'NewSiteNum')153    arcpy.CopyFeatures_management(watershed_resource_sanitary_intersect_impervious_dissolved, gdb_path + 'watershed_resource_sanitary_intersect_impervious_dissolved')154    watershed_resource_sanitary_intersect_impervious_dissolved_layer = arcpy.MakeFeatureLayer_management(watershed_resource_sanitary_intersect_impervious_dissolved, 'watershed_resource_sanitary_intersect_impervious_dissolved_layer')155156    #join combined and sanitary impervious areas and transfer the areas157158    arcpy.AddJoin_management(working_resource_areas_layer, 'NewSiteNum', gdb_path + 'watershed_resource_combined_intersect_impervious_dissolved', 'NewSiteNum')159    arcpy.CalculateField_management(working_resource_areas_layer, 'Combined_ImpA_sqft', '!watershed_resource_combined_intersect_impervious_dissolved.Shape_Area!')160    arcpy.RemoveJoin_management(working_resource_areas_layer)161162    arcpy.AddJoin_management(working_resource_areas_layer, 'NewSiteNum', gdb_path + 'watershed_resource_sanitary_intersect_impervious_dissolved', 'NewSiteNum')163    arcpy.CalculateField_management(working_resource_areas_layer, 'Sanitary_ImpA_sqft', '!watershed_resource_sanitary_intersect_impervious_dissolved.Shape_Area!')164    arcpy.RemoveJoin_management(working_resource_areas_layer)165166167168    #prior to calculating total treated, need to merge UIC and BMP areas and then dissolve to remove duplicates169    merged_uic_and_bmp = arcpy.Merge_management([bmp_intersect_impervious_dissolved_layer, uic_intersect_impervious_dissolved_layer], 'memory/merged_uic_and_bmp')170    merged_uic_and_bmp_dissolved = arcpy.Dissolve_management(merged_uic_and_bmp, 'memory/merged_uic_and_bmp_dissolved', 'NewSiteNum')171    merged_uic_and_bmp_dissolved_layer = arcpy.MakeFeatureLayer_management(merged_uic_and_bmp_dissolved, 'merged_uic_and_bmp_dissolved_layer')172    arcpy.CopyFeatures_management(merged_uic_and_bmp_dissolved_layer,  gdb_path + 'merged_uic_and_bmp_dissolved')173174    new_join = arcpy.AddJoin_management(working_resource_areas_layer, 'NewSiteNum', gdb_path + 'merged_uic_and_bmp_dissolved', 'NewSiteNum')175    arcpy.CopyFeatures_management(new_join, gdb_path + 'new_join')176177    arcpy.CalculateField_management(working_resource_areas_layer, 'Total_Treated_sqft', '!merged_uic_and_bmp_dissolved.Shape_Area!')178    arcpy.RemoveJoin_management(working_resource_areas_layer)179180    arcpy.CalculateField_management(working_resource_areas_layer, 'Total_Untreated_sqft', "!ImpA_sqft!- !Total_Treated_sqft!", "PYTHON3")181    arcpy.CalculateField_management(working_resource_areas_layer, 'Resource_Area_sqft', "!Shape_Area!", "PYTHON3")182183    #create copies of feature classes184    arcpy.CopyFeatures_management(combined_sewer_area_dissolved_layer, gdb_path + 'combined_sewer_area_dissolved_layer')185    arcpy.CopyFeatures_management(sanitary_sewer_area_dissolved_layer, gdb_path + 'sanitary_sewer_area_dissolved_layer')186187if __name__ == "__main__":
...

Fractal Images & Chaotic Scattering.py

Source:Fractal Images & Chaotic Scattering.py

1## This code will model chaotic scattering in a 3 disk system2from numpy import *3import matplotlib.pyplot as plt4import time as time5#########################################################################################################6###### This Portion Is For The RunTimeWarning Created By Complex Numbers in IntersectTimes Function######7#########################################################################################################8import warnings9warnings.simplefilter("ignore", RuntimeWarning)10    11######################################12######FUNCTIONS FOR PROGRAM###########13######################################14def Intersect(xcoordinates,ycoordinates,paramsr,theta,x0,y0): # This function returns the minimum intersection time and circle hit and intersection points15    16    #########FINDING LEAST TIME###############17    18    numintersects = numdisks * 2 # we intersect at each disk twice19    timeintersect = zeros(numintersects)20    21    22    # Unpack parameters we will be using23    24    r1 = paramsr[0]25    r2 = paramsr[1]26    r3 = paramsr[2]27    28    x1 = xcoordinates[0]29    x2 = xcoordinates[1]30    x3 = xcoordinates[2]31    y1 = ycoordinates[0]32    y2 = ycoordinates[1]33    y3 = ycoordinates[2]34    35    # create a,b,c for quadratic formula for finding time36    37    a1 = cos(theta)**2 + sin(theta)**238    a2 = a139    a3 = a140    41    b1 = 2*x0*cos(theta) + 2*y0*sin(theta) - 2*x1*cos(theta) - 2*y1*sin(theta)42    b2 = 2*x0*cos(theta) + 2*y0*sin(theta) - 2*x2*cos(theta) - 2*y2*sin(theta)43    b3 = 2*x0*cos(theta) + 2*y0*sin(theta) - 2*x3*cos(theta) - 2*y3*sin(theta)44    45    c1 = x0**2 + y0**2 + x1**2 + y1**2 - 2*x1*x0 - 2*y1*y0 - r1**246    c2 = x0**2 + y0**2 + x2**2 + y2**2 - 2*x2*x0 - 2*y2*y0 - r2**247    c3 = x0**2 + y0**2 + x3**2 + y3**2 - 2*x3*x0 - 2*y3*y0 - r3**248    49    #first disk intersect points50    51    timeintersect[0] = (-b1 + sqrt(b1**2 - 4*a1*c1))/(2*a1)52    timeintersect[1] = (-b1 - sqrt(b1**2 - 4*a1*c1))/(2*a1)53    54    #second disk intersect points55    56    timeintersect[2] = (-b2 + sqrt(b2**2 - 4*a2*c2))/(2*a2)57    timeintersect[3] = (-b2 - sqrt(b2**2 - 4*a2*c2))/(2*a2)58    59    #third disk intersect points60    61    timeintersect[4] = (-b3 + sqrt(b3**2 - 4*a3*c3))/(2*a3)62    timeintersect[5] = (-b3 - sqrt(b3**2 - 4*a3*c3))/(2*a3)63    64     # We are only concerned with finding the minimum t to the point we are crossing65     66     # If t is complex, we will change that number to a really large one67     # if t is approximately 0 or negative, we will change that to a really large number68    69    reallylargenumber = 10**870    reallysmallnumber = 10 ** -871    72    timeintersect[isnan(timeintersect)] = reallylargenumber 73    timeintersect[timeintersect < reallysmallnumber] = reallylargenumber74    75    IntersectTime = min(timeintersect)76    IntersectCircle = 077    78    if IntersectTime == timeintersect[0] or IntersectTime == timeintersect[1]:79        IntersectCircle = 180    if IntersectTime == timeintersect[2] or IntersectTime == timeintersect[3]:81        IntersectCircle = 282    if IntersectTime == timeintersect[4] or IntersectTime == timeintersect[5]:83        IntersectCircle = 384    if IntersectTime == reallylargenumber:85        IntersectCircle = 086    87    #### FIND INTERSECTING POINTS ####88    89    IntersectPointX = LastImpactX + IntersectTime*cos(theta)90    IntersectPointY = LastImpactY + IntersectTime*sin(theta)91    92    IntersectPoints = [IntersectPointX,IntersectPointY]93    return [IntersectTime,IntersectCircle,IntersectPoints]94def flipvectorgettheta(ImpactPoints,LastImpactX,LastImpactY,IntersectCircle): #this function flips the vector and computes our new angle theta95    96    xp = ImpactPoints[0]97    yp = ImpactPoints[1]98    99    x0 = LastImpactX100    y0 = LastImpactY101    102    103    CircleIntersect = IntersectCircle104    105    if CircleIntersect == 1 : # we hit upper disk106        xc = x1107        yc = y1108    109    if CircleIntersect == 2: # we hit right disk110        xc = x2111        yc = y2112        113    if CircleIntersect == 3: # we hit bottom disk114        xc = x3115        yc = y3116    if CircleIntersect == 0: # We Have Not Hit Any Circles, We return 'NaN' because we cant compute it117        return float('NaN')118        119    incomingx = xp-x0120    incomingy = yp-y0121    122    normalx = xp-xc123    normaly = yp-yc124    125    normalmag = sqrt(normalx**2 + normaly**2)126    127    vectorincoming = array([incomingx,incomingy])128    normal_direction = array([(normalx),(normaly)])129    normal_direction = normal_direction/normalmag130    131    vectorreflect = vectorincoming - 2*normal_direction*(dot(vectorincoming,normal_direction))132    133    ycomponent = vectorreflect[1]134    xcomponent = vectorreflect[0]135    136    theta = arctan(ycomponent/xcomponent)137    138    if xcomponent <= 0.0 and ycomponent >= 0.0:139        theta += pi140    elif xcomponent <= 0.0 and ycomponent <= 0.0:141        theta += -pi142        143    return theta144    145#####################146####Create Disks#####147#####################148numdisks = 3149paramsr = zeros(numdisks)150for i in range(numdisks):151    paramsr[i] = 3152d = 5 # distance between disks153# Disk Up #154x1 = -d/6.0 * sqrt(3.0)155y1 = d/2.0156# Disk Right #157x2 = d/3.0 * sqrt(3.0)158y2 = 0159# Disk Left # 160x3 = -d/6.0 * sqrt(3.0)161y3 = -d/2.0162xcoordinates = zeros(numdisks)163ycoordinates = zeros(numdisks)164xcoordinates[0] = x1165xcoordinates[1] = x2166xcoordinates[2] = x3167ycoordinates[0] = y1168ycoordinates[1] = y2169ycoordinates[2] = y3170#####################171####Shoot Particle#####172#####################173# Parameters of Problem #174xp = -4 # starting point of particle175ystart = -0.5 # beginning impact parameter176yend = 0.5 # ending impact parameter177interval = 100000 # points between ystart and yend and how many times we will run the code178impact = linspace(ystart,yend,interval)179theta = 0180# WHAT ARE WE GRAPHING? #181ExitAngle = zeros(interval) # How many exit angles we have is how many times we run the code182BounceCount = zeros(interval) # How Many Times We Bounce For Each Trajectory183TimeSpent = zeros(interval) # Time Spent For Each Trajectory184NumParticles = linspace(0,interval,interval)185##### STARTING ALGORITHM #####186IntersectPointsHeld = zeros([16,2]) # We Use This For Plotting A Single Trajectory187SimulationCounter = 1 # Simulation Counter188Counter = 0 # Initialze Counter For Things We Will Be Graphing189PlotNow = False # This is only used for Plotting A Single Trajectory190for i in impact: 191    exitParticle = False192       193    # Every time we run the code we need to initialize the beginning values #194    LastImpactX = xp195    LastTheta = theta196    LastImpactY = i197    198    199   # if LastImpactY == impact[91]: # scatter number200        #PlotNow = True201        #IntersectPointsHeld[0] = [LastImpactX,LastImpactY]202    #else:203        #PlotNow = False204        #IntersectPointsHeld[15] = IntersectPointsHeld[14]205        206    IntersectArray = Intersect(xcoordinates,ycoordinates,paramsr,LastTheta,LastImpactX,LastImpactY)207    IntersectTime = IntersectArray[0]208    IntersectCircle = IntersectArray[1]209    IntersectPoints = IntersectArray[2]210    211    if IntersectCircle == 0:212        exitParticle = True213        print("We Have Exited")214        timespentthistrajectory = IntersectTime215        216    print("Running Simulation %s" % SimulationCounter)217    218    BounceCounter = 1219    220    timespentthistrajectory = 0221    222    while exitParticle == False:223        224        225        226        print("Projectile has bounced %s times" % BounceCounter) # Sanity Check #227        228        # Use Intersect Function #229        230        IntersectArray = Intersect(xcoordinates,ycoordinates,paramsr,LastTheta,LastImpactX,LastImpactY) 231        232        # Unpack Intersect Function #233        234        IntersectTime = IntersectArray[0]235        IntersectCircle = IntersectArray[1]236        IntersectPoints = IntersectArray[2]237        238        239        240        if PlotNow == True: # IF WE WANT TO PLOT A TRAJECTORY WE USE THIS LINE OF CODE #241            IntersectPointsHeld[BounceCounter] = IntersectPoints242    243        244        if IntersectCircle == 0: # This is our exit condition245            ExitAngle[Counter] = LastTheta246            exitParticle = True247            print("We Have Exited")248            249        250        251        NewAngle = flipvectorgettheta(IntersectPoints,LastImpactX,LastImpactY,IntersectCircle)252        253        LastImpactX = IntersectPoints[0]254        LastImpactY = IntersectPoints[1]255        LastTheta = NewAngle256        257        if exitParticle == False:258            timespentthistrajectory += IntersectTime259        260        261        262        BounceCounter += 1263  264    265    TimeSpent[Counter] = timespentthistrajectory266    267    268    BounceCount[Counter] = BounceCounter269     270    Counter += 1271    SimulationCounter += 1272    273#####################274######Plots##########275#####################276ax=plt.gca()277plt.plot(IntersectPointsHeld[:,0],IntersectPointsHeld[:,1],)278circle1 = plt.Circle((x1,ycoordinates[0]), radius=1, color='g', fill=False)279circle2 = plt.Circle((x2,ycoordinates[1]), radius=1, color='b', fill=False)280circle3 = plt.Circle((x3,ycoordinates[2]), radius=1, color='r', fill=False)281ax.add_patch(circle1)282ax.add_patch(circle2)283ax.add_patch(circle3)284plt.axis('scaled')285plt.title('Trajectory Plot')286plt.show()287plt.figure()288plt.plot(impact,ExitAngle)289plt.xlabel('Impact Parameter (''$\it{b}$)')290plt.ylabel('Exit Angle ('r'$\theta$)')291plt.title('Output ('r'$\theta$) vs Input Ordinate')292plt.show()293plt.figure()294plt.plot(impact,BounceCount)295plt.title("Bounce Count vs Input Ordinate")296plt.xlabel('Impact Parameter (''$\it{b}$)')297plt.ylabel('Number Bounces')298plt.show()299plt.figure()300plt.plot(impact,TimeSpent)301plt.xlabel('Impact Parameter (''$\it{b}$)')302plt.ylabel('Time Spent')303plt.title('Time Spent vs Input Ordinate')...

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