Merge pull request sympy#20267 from Mohitbalwani26/refactor(test_ode)_1st_exact

oscarbenjamin · web-flow · commit 48ec7d51e4da · 2020-10-24T01:28:48.000+01:00
refactor(test_ode.py): 1st_exact examples
diff --git a/sympy/solvers/ode/tests/test_ode.py b/sympy/solvers/ode/tests/test_ode.py
@@ -1,7 +1,7 @@
-from sympy import (acos, acosh, asinh, atan, cos, Derivative, diff,
+from sympy import (acos, acosh, atan, cos, Derivative, diff,
     Dummy, Eq, Ne, exp, Function, I, Integral, LambertW, log, O, pi,
     Rational, rootof, S, sin, sqrt, Subs, Symbol, tan, asin, sinh,
-    Piecewise, symbols, Poly, sec, re, im, atan2, collect, hyper, integrate)
+    Piecewise, symbols, Poly, sec, re, im, atan2, collect, hyper)
 
 from sympy.solvers.ode import (classify_ode,
     homogeneous_order, infinitesimals, checkinfsol,
@@ -813,79 +813,6 @@ def test_old_ode_tests():
     assert checkodesol(eq11, sol11, order=1, solve_for_func=False)[0]
 
 
-@slow
-def test_1st_exact1():
-    # Type: Exact differential equation, p(x,f) + q(x,f)*f' == 0,
-    # where dp/df == dq/dx
-    eq1 = sin(x)*cos(f(x)) + cos(x)*sin(f(x))*f(x).diff(x)
-    eq2 = (2*x*f(x) + 1)/f(x) + (f(x) - x)/f(x)**2*f(x).diff(x)
-    eq3 = 2*x + f(x)*cos(x) + (2*f(x) + sin(x) - sin(f(x)))*f(x).diff(x)
-    eq4 = cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x)
-    eq5 = 2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x)
-    sol1 = [Eq(f(x), -acos(C1/cos(x)) + 2*pi), Eq(f(x), acos(C1/cos(x)))]
-    sol2 = Eq(f(x), exp(C1 - x**2 + LambertW(-x*exp(-C1 + x**2))))
-    sol2b = Eq(log(f(x)) + x/f(x) + x**2, C1)
-    sol3 = Eq(f(x)*sin(x) + cos(f(x)) + x**2 + f(x)**2, C1)
-    sol4 = Eq(x*cos(f(x)) + f(x)**3/3, C1)
-    sol5 = Eq(x**2*f(x) + f(x)**3/3, C1)
-    assert dsolve(eq1, f(x), hint='1st_exact') == sol1
-    assert dsolve(eq2, f(x), hint='1st_exact') == sol2
-    assert dsolve(eq3, f(x), hint='1st_exact') == sol3
-    assert dsolve(eq4, hint='1st_exact') == sol4
-    assert dsolve(eq5, hint='1st_exact', simplify=False) == sol5
-    assert checkodesol(eq1, sol1, order=1, solve_for_func=False)[0]
-    # issue 5080 blocks the testing of this solution
-    # FIXME: assert checkodesol(eq2, sol2, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq2, sol2b, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq3, sol3, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq4, sol4, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq5, sol5, order=1, solve_for_func=False)[0]
-
-
-@slow
-@XFAIL
-def test_1st_exact2_broken():
-    """
-    This is an exact equation that fails under the exact engine. It is caught
-    by first order homogeneous albeit with a much contorted solution.  The
-    exact engine fails because of a poorly simplified integral of q(0,y)dy,
-    where q is the function multiplying f'.  The solutions should be
-    Eq(sqrt(x**2+f(x)**2)**3+y**3, C1).  The equation below is
-    equivalent, but it is so complex that checkodesol fails, and takes a long
-    time to do so.
-    """
-    if ON_TRAVIS:
-        skip("Too slow for travis.")
-    eq = (x*sqrt(x**2 + f(x)**2) - (x**2*f(x)/(f(x) -
-          sqrt(x**2 + f(x)**2)))*f(x).diff(x))
-    sol = Eq(log(x),
-        C1 - 9*sqrt(1 + f(x)**2/x**2)*asinh(f(x)/x)/(-27*f(x)/x +
-        27*sqrt(1 + f(x)**2/x**2)) - 9*sqrt(1 + f(x)**2/x**2)*
-        log(1 - sqrt(1 + f(x)**2/x**2)*f(x)/x + 2*f(x)**2/x**2)/
-        (-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2)) +
-        9*asinh(f(x)/x)*f(x)/(x*(-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2))) +
-        9*f(x)*log(1 - sqrt(1 + f(x)**2/x**2)*f(x)/x + 2*f(x)**2/x**2)/
-        (x*(-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2))))
-    assert dsolve(eq) == sol # Slow
-    # FIXME: Checked in test_1st_exact2_broken_check below
-
-
-@slow
-def test_1st_exact2_broken_check():
-    # See test_1st_exact2_broken above
-    eq = (x*sqrt(x**2 + f(x)**2) - (x**2*f(x)/(f(x) -
-          sqrt(x**2 + f(x)**2)))*f(x).diff(x))
-    sol = Eq(log(x),
-        C1 - 9*sqrt(1 + f(x)**2/x**2)*asinh(f(x)/x)/(-27*f(x)/x +
-        27*sqrt(1 + f(x)**2/x**2)) - 9*sqrt(1 + f(x)**2/x**2)*
-        log(1 - sqrt(1 + f(x)**2/x**2)*f(x)/x + 2*f(x)**2/x**2)/
-        (-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2)) +
-        9*asinh(f(x)/x)*f(x)/(x*(-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2))) +
-        9*f(x)*log(1 - sqrt(1 + f(x)**2/x**2)*f(x)/x + 2*f(x)**2/x**2)/
-        (x*(-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2))))
-    assert checkodesol(eq, sol, order=1, solve_for_func=False)[0]
-
-
 def test_homogeneous_order():
     assert homogeneous_order(exp(y/x) + tan(y/x), x, y) == 0
     assert homogeneous_order(x**2 + sin(x)*cos(y), x, y) is None
@@ -2371,18 +2298,6 @@ def test_issue_10867():
     assert checkodesol(eq, sol, order=2, solve_for_func=False) == (True, 0)
 
 
-def test_issue_11290():
-    eq = cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x)
-    sol_1 = dsolve(eq, f(x), simplify=False, hint='1st_exact_Integral')
-    sol_0 = dsolve(eq, f(x), simplify=False, hint='1st_exact')
-    assert sol_1.dummy_eq(Eq(Subs(
-        Integral(u**2 - x*sin(u) - Integral(-sin(u), x), u) +
-        Integral(cos(u), x), u, f(x)), C1))
-    assert sol_1.doit() == sol_0
-    assert checkodesol(eq, sol_0, order=1, solve_for_func=False)
-    assert checkodesol(eq, sol_1, order=1, solve_for_func=False)
-
-
 def test_issue_4838():
     # Issue #15999
     eq = f(x).diff(x) - C1*f(x)
@@ -2571,21 +2486,3 @@ def test_issue_18408():
     sol = Eq(f(x), C1 + C3*exp(-x) + x*sinh(x)/2 + (C2 + x/2)*exp(x))
     assert sol == dsolve(eq, hint='nth_linear_constant_coeff_undetermined_coefficients')
     assert checkodesol(eq, sol) == (True, 0)
-
-
-def test_issue_9446():
-    f = Function('f')
-    assert dsolve(Eq(f(2 * x), sin(Derivative(f(x)))), f(x)) == \
-    [Eq(f(x), C1 + pi*x - Integral(asin(f(2*x)), x)), Eq(f(x), C1 + Integral(asin(f(2*x)), x))]
-
-    assert integrate(-asin(f(2*x)+pi), x) == -Integral(asin(pi + f(2*x)), x)
-
-def test_issue_20192():
-    # kamke ode 1.1
-    a0,a1,a2,a3,a4 = symbols('a0, a1, a2, a3, a4')
-
-    eq = f(x).diff(x)-(a4*x**4 + a3*x**3 + a2*x**2 + a1*x + a0)**(-1/2)
-    sol = Eq(f(x), C1 + Integral(1/sqrt(a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4), x))
-
-    assert sol == dsolve(eq,hint='factorable')
-    assert checkodesol(eq, sol) == (True, 0)
diff --git a/sympy/solvers/ode/tests/test_single.py b/sympy/solvers/ode/tests/test_single.py
@@ -32,8 +32,8 @@
    ODEs which raises exception.
 
 """
-from sympy import (acos, asin, atan, cos, Derivative, Dummy, diff,
-    E, Eq, exp, I, log, pi, Piecewise, Rational, S, sin, sinh, tan,
+from sympy import (acos, asin, asinh, atan, cos, Derivative, Dummy, diff,
+    E, Eq, exp, I, Integral, integrate, LambertW, log, pi, Piecewise, Rational, S, sin, sinh, tan,
     sqrt, symbols, Ei, erfi)
 
 from sympy.core import Function, Symbol
@@ -46,7 +46,7 @@
 
 from sympy.solvers.ode.subscheck import checkodesol
 
-from sympy.testing.pytest import raises, slow
+from sympy.testing.pytest import raises, slow, ON_TRAVIS
 import traceback
 
 
@@ -150,7 +150,10 @@ def _ode_solver_test(ode_examples, run_slow_test=False):
             'func': ode_examples['examples'][example].get('func',ode_examples['func']),
             'example_name': example,
             'slow': ode_examples['examples'][example].get('slow', False),
-            'checkodesol_XFAIL': ode_examples['examples'][example].get('checkodesol_XFAIL', False)
+            'simplify_flag':ode_examples['examples'][example].get('simplify_flag',True),
+            'checkodesol_XFAIL': ode_examples['examples'][example].get('checkodesol_XFAIL', False),
+            'dsolve_too_slow':ode_examples['examples'][example].get('dsolve_too_slow',False),
+            'checkodesol_too_slow':ode_examples['examples'][example].get('checkodesol_too_slow',False),
         }
         if (not run_slow_test) and temp['slow']:
             continue
@@ -191,7 +194,10 @@ def _test_particular_example(our_hint, ode_example, solver_flag=False):
     xfail = our_hint in ode_example['XFAIL']
     func = ode_example['func']
     result = {'msg': '', 'xpass_msg': ''}
+    simplify_flag=ode_example['simplify_flag']
     checkodesol_XFAIL = ode_example['checkodesol_XFAIL']
+    dsolve_too_slow = ode_example['dsolve_too_slow']
+    checkodesol_too_slow = ode_example['checkodesol_too_slow']
     xpass = True
     if solver_flag:
         if our_hint not in classify_ode(eq, func):
@@ -201,7 +207,13 @@ def _test_particular_example(our_hint, ode_example, solver_flag=False):
     if our_hint in classify_ode(eq, func):
         result['match_list'] = example
         try:
-            dsolve_sol = dsolve(eq, func, hint=our_hint)
+            if not (dsolve_too_slow and ON_TRAVIS):
+                dsolve_sol = dsolve(eq, func, simplify=simplify_flag,hint=our_hint)
+            else:
+                if len(expected_sol)==1:
+                    dsolve_sol = expected_sol[0]
+                else:
+                    dsolve_sol = expected_sol
 
         except Exception as e:
             dsolve_sol = []
@@ -235,16 +247,17 @@ def _test_particular_example(our_hint, ode_example, solver_flag=False):
             if len(expected_sol) == 1:
                 expected_checkodesol = (True, 0)
 
-            if not checkodesol_XFAIL:
-                if checkodesol(eq, dsolve_sol, solve_for_func=False) != expected_checkodesol:
-                    result['unsolve_list'] = example
-                    xpass = False
-                    message = dsol_incorrect_msg.format(hint=our_hint, eq=eq, sol=expected_sol,dsolve_sol=dsolve_sol)
-                    if solver_flag:
-                        message = checkodesol_msg.format(example=example, eq=eq)
-                        raise AssertionError(message)
-                    else:
-                        result['msg'] = 'AssertionError: ' + message
+            if not (checkodesol_too_slow and ON_TRAVIS):
+                if not checkodesol_XFAIL:
+                    if checkodesol(eq, dsolve_sol, solve_for_func=False) != expected_checkodesol:
+                        result['unsolve_list'] = example
+                        xpass = False
+                        message = dsol_incorrect_msg.format(hint=our_hint, eq=eq, sol=expected_sol,dsolve_sol=dsolve_sol)
+                        if solver_flag:
+                            message = checkodesol_msg.format(example=example, eq=eq)
+                            raise AssertionError(message)
+                        else:
+                            result['msg'] = 'AssertionError: ' + message
 
         if xpass and xfail:
             result['xpass_msg'] = example + "is now passing for the hint" + our_hint
@@ -318,6 +331,14 @@ def test_nth_algebraic():
     _ode_solver_test(_get_examples_ode_sol_nth_algebraic())
 
 
+@slow
+def test_slow_examples_1st_exact():
+    eq = cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x)
+    sol_1 = dsolve(eq, f(x), simplify=False, hint='1st_exact_Integral')
+    assert checkodesol(eq, sol_1, order=1, solve_for_func=False)
+    _ode_solver_test(_get_examples_ode_sol_1st_exact(), run_slow_test=True)
+
+
 @slow
 def test_slow_examples_nth_order_reducible():
     _ode_solver_test(_get_examples_ode_sol_nth_order_reducible(), run_slow_test=True)
@@ -357,6 +378,7 @@ def test_separable():
 
 
 def test_factorable():
+    assert integrate(-asin(f(2*x)+pi), x) == -Integral(asin(pi + f(2*x)), x)
     _ode_solver_test(_get_examples_ode_sol_factorable())
 
 
@@ -601,6 +623,7 @@ def _get_examples_ode_sol_factorable():
     nth_linear_constant_coeff_undetermined_coefficients"""
 
     y = Dummy('y')
+    a0,a1,a2,a3,a4 = symbols('a0, a1, a2, a3, a4')
     return {
             'hint': "factorable",
             'func': f(x),
@@ -703,6 +726,19 @@ def _get_examples_ode_sol_factorable():
         'eq': f(x).diff(x)**2 - f(x)**3,
         'sol': [Eq(f(x), 4/(C1**2 - 2*C1*x + x**2))]
     },
+
+    # kamke ode 1.1
+    'fact_17': {
+        'eq': f(x).diff(x)-(a4*x**4 + a3*x**3 + a2*x**2 + a1*x + a0)**(-1/2),
+        'sol': [Eq(f(x), C1 + Integral(1/sqrt(a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4), x))]
+    },
+
+    # This is from issue: https://github.com/sympy/sympy/issues/9446
+    'fact_18':{
+        'eq': Eq(f(2 * x), sin(Derivative(f(x)))),
+        'sol': [Eq(f(x), C1 + pi*x - Integral(asin(f(2*x)), x)), Eq(f(x), C1 + Integral(asin(f(2*x)), x))],
+        'checkodesol_XFAIL':True
+    },
     }
     }
 
@@ -1284,6 +1320,80 @@ def _get_examples_ode_sol_separable():
     }
 
 
+def _get_examples_ode_sol_1st_exact():
+    # Type: Exact differential equation, p(x,f) + q(x,f)*f' == 0,
+    # where dp/df == dq/dx
+    '''
+    Example 7 is an exact equation that fails under the exact engine. It is caught
+    by first order homogeneous albeit with a much contorted solution.  The
+    exact engine fails because of a poorly simplified integral of q(0,y)dy,
+    where q is the function multiplying f'.  The solutions should be
+    Eq(sqrt(x**2+f(x)**2)**3+y**3, C1).  The equation below is
+    equivalent, but it is so complex that checkodesol fails, and takes a long
+    time to do so.
+    '''
+    return {
+            'hint': "1st_exact",
+            'func': f(x),
+            'examples':{
+    '1st_exact_01': {
+        'eq': sin(x)*cos(f(x)) + cos(x)*sin(f(x))*f(x).diff(x),
+        'sol': [Eq(f(x), -acos(C1/cos(x)) + 2*pi), Eq(f(x), acos(C1/cos(x)))],
+        'slow': True,
+    },
+
+    '1st_exact_02': {
+        'eq': (2*x*f(x) + 1)/f(x) + (f(x) - x)/f(x)**2*f(x).diff(x),
+        'sol': [Eq(f(x), exp(C1 - x**2 + LambertW(-x*exp(-C1 + x**2))))],
+        'XFAIL': ['lie_group'], #It shows dsolve raises an exception: List index out of range for lie_group
+        'slow': True,
+        'checkodesol_XFAIL':True
+    },
+
+    '1st_exact_03': {
+        'eq': 2*x + f(x)*cos(x) + (2*f(x) + sin(x) - sin(f(x)))*f(x).diff(x),
+        'sol': [Eq(f(x)*sin(x) + cos(f(x)) + x**2 + f(x)**2, C1)],
+        'XFAIL': ['lie_group'], #It goes into infinite loop for lie_group.
+        'slow': True,
+    },
+
+    '1st_exact_04': {
+        'eq': cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x),
+        'sol': [Eq(x*cos(f(x)) + f(x)**3/3, C1)],
+        'slow': True,
+    },
+
+    '1st_exact_05': {
+        'eq': 2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x),
+        'sol': [Eq(x**2*f(x) + f(x)**3/3, C1)],
+        'slow': True,
+        'simplify_flag':False
+    },
+
+    # This was from issue: https://github.com/sympy/sympy/issues/11290
+    '1st_exact_06': {
+        'eq': cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x),
+        'sol': [Eq(x*cos(f(x)) + f(x)**3/3, C1)],
+        'simplify_flag':False
+    },
+
+    '1st_exact_07': {
+        'eq': x*sqrt(x**2 + f(x)**2) - (x**2*f(x)/(f(x) - sqrt(x**2 + f(x)**2)))*f(x).diff(x),
+        'sol': [Eq(log(x),
+        C1 - 9*sqrt(1 + f(x)**2/x**2)*asinh(f(x)/x)/(-27*f(x)/x +
+        27*sqrt(1 + f(x)**2/x**2)) - 9*sqrt(1 + f(x)**2/x**2)*
+        log(1 - sqrt(1 + f(x)**2/x**2)*f(x)/x + 2*f(x)**2/x**2)/
+        (-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2)) +
+        9*asinh(f(x)/x)*f(x)/(x*(-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2))) +
+        9*f(x)*log(1 - sqrt(1 + f(x)**2/x**2)*f(x)/x + 2*f(x)**2/x**2)/
+        (x*(-27*f(x)/x + 27*sqrt(1 + f(x)**2/x**2))))],
+        'slow': True,
+        'dsolve_too_slow':True
+    },
+    }
+    }
+
+
 def _get_all_examples():
     all_solvers = [_get_examples_ode_sol_euler_homogeneous(),
     _get_examples_ode_sol_euler_undetermined_coeff(),
@@ -1293,6 +1403,7 @@ def _get_all_examples():
     _get_examples_ode_sol_nth_algebraic(),
     _get_examples_ode_sol_riccati(),
     _get_examples_ode_sol_1st_linear(),
+    _get_examples_ode_sol_1st_exact(),
     _get_examples_ode_sol_almost_linear(),
     _get_examples_ode_sol_nth_order_reducible(),
     _get_examples_ode_sol_nth_linear_undetermined_coefficients(),
@@ -1309,6 +1420,7 @@ def _get_all_examples():
                 'eq': solver['examples'][example]['eq'],
                 'sol': solver['examples'][example]['sol'],
                 'XFAIL': solver['examples'][example].get('XFAIL',[]),
+                'simplify_flag':solver['examples'][example].get('simplify_flag',True),
                 'checkodesol_XFAIL': solver['examples'][example].get('checkodesol_XFAIL', False),
                 'example_name': example,
             }
