test_exec_comp.py

import itertools
import unittest
import math
import os
import shutil
import tempfile

import numpy as np
from numpy.testing import assert_almost_equal
import scipy
from io import StringIO

from packaging.version import Version

try:
    from parameterized import parameterized
except ImportError:
    from openmdao.utils.assert_utils import SkipParameterized as parameterized

import openmdao.api as om
from openmdao.components.exec_comp import _expr_dict, _temporary_expr_dict
from openmdao.utils.assert_utils import assert_near_equal, assert_check_partials, assert_warning
from openmdao.utils.general_utils import env_truthy
from openmdao.utils.testing_utils import force_check_partials
from openmdao.utils.om_warnings import SetupWarning

_ufunc_test_data = {
    'min': {
        'str': 'f=min(x)',
        'check_func': np.min,
        'args': { 'f': {'val': np.zeros(6)},
                  'x': {'val': np.random.random(6)}}},
    'max': {
        'str': 'f=max(x)',
        'check_func': np.max,
        'args': { 'f': {'val': np.zeros(6)},
                  'x': {'val': np.random.random(6)}}},
    'diff': {
        'str': 'f=diff(x)',
        'check_func': np.diff,
        'args': { 'f': {'val': np.zeros(5)},
                  'x': {'val': np.random.random(6)}}},
    'abs': {
        'str': 'f=abs(x)',
        'check_func': np.abs,
        'args': { 'f': {'val': np.zeros(6)},
                  'x': {'val': np.random.random(6)}}},
    'acos': {
        'str': 'f=acos(x)',
        'check_func': np.arccos,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6) - 0.5}}},
    'arccos': {
        'str': 'f=arccos(x)',
        'check_func': np.arccos,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6) - 0.5}}},
    'arccosh': {
        'str': 'f=arccosh(x)',
        'check_func': np.arccosh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': 1.1 + np.random.random(6)}}},
    'acosh': {
        'str': 'f=acosh(x)',
        'check_func': np.arccosh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': 1.1 + np.random.random(6)}}},
    'arange': {
        'str': 'f=arange(0,10,2)',
        'check_val': np.arange(0, 10, 2),
        'args': {'f': {'val': np.zeros(5)}}},
    'arcsin': {
        'str': 'f=arcsin(x)',
        'check_func': np.arcsin,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6) - .5}}},
    'arcsinh': {
        'str': 'f=arcsinh(x)',
        'check_func': np.arcsinh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'asinh': {
        'str': 'f=asinh(x)',
        'check_func': np.arcsinh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'asin': {
        'str': 'f=asin(x)',
        'check_func': np.arcsin,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6) - .5}}},
    'arctan': {
        'str': 'f=arctan(x)',
        'check_func': np.arctan,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'arctan2': {
        'str': 'f=arctan2(y, x)',
        'check_val': np.array([-2.35619449, -0.78539816,  0.78539816,  2.35619449]),
        'args': {'f': {'val': np.zeros(4)},
                 'x': {'val': np.array([-1, +1, +1, -1])},
                 'y': {'val': np.array([-1, -1, +1, +1])}}},
    'atan': {
        'str': 'f=atan(x)',
        'check_func': np.arctan,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'cos': {
        'str': 'f=cos(x)',
        'check_func': np.cos,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'cosh': {
        'str': 'f=cosh(x)',
        'check_func': np.cosh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'dot': {
        'str': 'f=dot(x, y)',
        'check_func': np.dot,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'e': {
        'str': 'f=e',
        'check_val': np.e,
        'args': {'f': {'val': 0.0}}},
    'erf': {
        'str': 'f=erf(x)',
        'check_func': scipy.special.erf,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'erfc': {
        'str': 'f=erfc(x)',
        'check_func': scipy.special.erfc,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'exp': {
        'str': 'f=exp(x)',
        'check_func': np.exp,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'expm1': {
        'str': 'f=expm1(x)',
        'check_func': np.expm1,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'fmax': {
        'str': 'f=fmax(x, y)',
        'check_func': np.fmax,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'fmin': {
        'str': 'f=fmin(x, y)',
        'check_func': np.fmin,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'inner': {
        'str': 'f=inner(x, y)',
        'check_func': np.inner,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'isinf': {
        'str': 'f=isinf(x)',
        'check_func': np.isinf,
        'args': {'f': {'val': np.zeros(3)},
                 'x': {'val': [0, np.inf, 5.0]}}},
    'isnan': {
        'str': 'f=isnan(x)',
        'check_func': np.isnan,
        'args': {'f': {'val': np.zeros(3)},
                 'x': {'val': [0, np.nan, np.nan]}}},
    'kron': {
        'str': 'f=kron(x, y)',
        'check_func': np.kron,
        'args': {'f': {'val': np.zeros(36)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'linspace': {
        'str': 'f=linspace(0,10,50)',
        'check_val': np.linspace(0, 10, 50),
        'args': {'f': {'val': np.zeros(50)}}},
    'log': {
        'str': 'f=log(x)',
        'check_func': np.log,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6) + 0.1}}},
    'log10': {
        'str': 'f=log10(x)',
        'check_func': np.log10,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6) + 0.1}}},
    'log1p': {
        'str': 'f=log1p(x)',
        'check_func': np.log1p,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'matmul': {
        'str': 'f=matmul(x, y)',
        'check_func': np.matmul,
        'args': {'f': {'val': np.zeros((3, 1))},
                 'x': {'val': np.random.random((3, 3))},
                 'y': {'val': np.random.random((3, 1))}}},
    'maximum': {
        'str': 'f=maximum(x, y)',
        'check_func': np.maximum,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'minimum': {
        'str': 'f=minimum(x, y)',
        'check_func': np.minimum,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'ones': {
        'str': 'f=ones(21)',
        'check_val': np.ones(21),
         'args': {'f': {'val': np.zeros(21)}}},
    'outer': {
        'str': 'f=outer(x, y)',
        'check_func': np.outer,
        'args': {'f': {'val': np.zeros((6, 6))},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6)}}},
    'pi': {
        'str': 'f=pi',
        'check_val': np.pi,
        'args': {'f': {'val': 0.0}}},
    'power': {
        'str': 'f=power(x, y)',
        'check_func': np.power,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)},
                 'y': {'val': np.random.random(6) + 1.0}}},
    'prod': {
        'str': 'f=prod(x)',
        'check_func': np.prod,
        'args': {'f': {'val': 0.0},
                 'x': {'val': np.random.random(6)}}},
    'sin': {
        'str': 'f=sin(x)',
        'check_func': np.sin,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'sinh': {
        'str': 'f=sinh(x)',
        'check_func': np.sinh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'sum': {
        'str': 'f=sum(x)',
        'check_func': np.sum,
        'args': {'f': {'val': 0.0},
                 'x': {'val': np.random.random(6)}}},
    'tan': {
        'str': 'f=tan(x)',
        'check_func': np.tan,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'tanh': {
        'str': 'f=tanh(x)',
        'check_func': np.tanh,
        'args': {'f': {'val': np.zeros(6)},
                 'x': {'val': np.random.random(6)}}},
    'tensordot': {
        'str': 'f=tensordot(x, y)',
        'check_func': np.tensordot,
        'args': {'f': {'val': 0.0},
                 'x': {'val': np.random.random((6, 6))},
                 'y': {'val': np.random.random((6, 6))}}},
    'zeros': {
        'str': 'f=zeros(21)',
        'check_val': np.zeros(21),
        'args': {'f': {'val': np.zeros(21)}}},
}


class TestExecComp(unittest.TestCase):

    def test_missing_partial_warn(self):
        p = om.Problem()
        model = p.model
        comp = om.ExecComp('z=3.0*x + 2.5*y')
        model.add_subsystem('comp', comp)
        comp.declare_partials('z', 'x', method='fd')
        p.setup()
        with assert_warning(UserWarning, "'comp' <class ExecComp>: The following partial derivatives have not been declared so they are assumed to be zero: ['z' wrt 'y']."):
            p.final_setup()

    def test_colon_vars(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('y=foo:bar+1.'))
        with self.assertRaises(Exception) as context:
            prob.setup()
        self.assertEqual(str(context.exception),
                         "'C1' <class ExecComp>: failed to compile expression 'y=foo:bar+1.'.")

    def test_bad_kwargs(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('y=x+1.', xx=2.0))
        with self.assertRaises(Exception) as context:
            prob.setup()
        self.assertEqual(str(context.exception),
                         "'C1' <class ExecComp>: arg 'xx' in call to ExecComp() does not refer to any variable "
                         "in the expressions ['y=x+1.']")

    def test_bad_kwargs_meta(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('y=x+1.',
                                                   x={'val': 2, 'low': 0, 'high': 10, 'units': 'ft'}))
        with self.assertRaises(Exception) as context:
            prob.setup()
        self.assertEqual(str(context.exception),
                         "'C1' <class ExecComp>: the following metadata names were not recognized for "
                         "variable 'x': ['high', 'low']")

    def test_name_collision_const(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('e=x+1.'))
        with self.assertRaises(Exception) as context:
            prob.setup()
        self.assertEqual(str(context.exception),
                         "'C1' <class ExecComp>: cannot assign to variable 'e' because it's already defined "
                         "as an internal function or constant.")

    def test_name_collision_func(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('sin=x+1.'))
        with self.assertRaises(Exception) as context:
            prob.setup()
        self.assertEqual(str(context.exception),
                         "'C1' <class ExecComp>: cannot assign to variable 'sin' because it's already defined "
                         "as an internal function or constant.")

    def test_func_as_rhs_var(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('y=sin+1.'))
        with self.assertRaises(Exception) as context:
            prob.setup()
        self.assertEqual(str(context.exception),
                         "'C1' <class ExecComp>: cannot use 'sin' as a variable because it's already defined "
                         "as an internal function or constant.")

    def test_mixed_type(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=sum(x)',
                                                        x=np.arange(10, dtype=float)))
        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 45.0, 0.00001)

    def test_simple(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=x+1.', x=2.0))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 3.0, 0.00001)

    def test_for_spaces(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y = pi * x', x=2.0))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)
        self.assertTrue('pi' not in C1._inputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 2 * math.pi, 0.00001)

    def test_units(self):
        prob = om.Problem()
        prob.model.add_subsystem('indep', om.IndepVarComp('x', 100.0, units='cm'))
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=x+z+1.',
                                                        x={'val': 2.0, 'units': 'm'},
                                                        y={'units': 'm'},
                                                        z=2.0))
        prob.model.connect('indep.x', 'C1.x')

        prob.setup()

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 4.0, 0.00001)

    def test_units_varname(self):
        prob = om.Problem()

        with self.assertRaises(TypeError) as cm:
            prob.model.add_subsystem('C1', om.ExecComp('y=x+units+1.',
                                                       x={'val': 2.0, 'units': 'm'},
                                                       y={'units': 'm'},
                                                       units=2.0))

        self.assertEqual(str(cm.exception),
                         "ExecComp: Value (2.0) of option 'units' has type 'float', "
                         "but type 'str' was expected.")

    def test_units_varname_str(self):
        prob = om.Problem()

        with self.assertRaises(ValueError) as cm:
            prob.model.add_subsystem('C1', om.ExecComp('y=x+units+1.',
                                                       x={'val': 2.0, 'units': 'm'},
                                                       y={'units': 'm'},
                                                       units='two'))

        self.assertEqual(str(cm.exception), "The units 'two' are invalid.")

    def test_units_varname_novalue(self):
        prob = om.Problem()
        prob.model.add_subsystem('indep', om.IndepVarComp('x', 100.0, units='cm'))
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=x+units+1.',
                                                        x={'val': 2.0, 'units': 'm'},
                                                        y={'units': 'm'}))
        prob.model.connect('indep.x', 'C1.x')

        with self.assertRaises(NameError) as cm:
            prob.setup()

        self.assertEqual(str(cm.exception),
                         "'C1' <class ExecComp>: cannot use variable name 'units' because it's a reserved keyword.")

    def test_common_units(self):
        # all variables in the ExecComp have the same units
        prob = om.Problem()

        prob.model.add_subsystem('indep', om.IndepVarComp('x', 100.0, units='cm'))
        prob.model.add_subsystem('comp', om.ExecComp('y=x+z+1.', units='m',
                                                     x={'val': 2.0},
                                                     z=2.0))
        prob.model.connect('indep.x', 'comp.x')

        prob.setup()
        prob.run_model()

        assert_near_equal(prob['comp.y'], 4.0, 0.00001)

    def test_common_units_no_meta(self):
        # make sure common units are assigned when no metadata is provided
        prob = om.Problem()

        prob.model.add_subsystem('indep', om.IndepVarComp('x', 2.0, units='km'))
        prob.model.add_subsystem('comp', om.ExecComp('y = x+1', units='m'))

        prob.model.connect('indep.x', 'comp.x')

        prob.setup()
        prob.run_model()

        assert_near_equal(prob['comp.y'], 2001., 0.00001)

    def test_conflicting_units(self):
        prob = om.Problem()
        prob.model.add_subsystem('indep', om.IndepVarComp('x', 100.0, units='cm'))
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=x+z+1.', units='m',
                                                        x={'val': 2.0, 'units': 'km'},
                                                        z=2.0))
        prob.model.connect('indep.x', 'C1.x')

        with self.assertRaises(RuntimeError) as cm:
            prob.setup()

        self.assertEqual(str(cm.exception),
                         "'C1' <class ExecComp>: units of 'km' have been specified for variable 'x', but "
                         "units of 'm' have been specified for the entire component.")

    def test_shape_and_value(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5',
                                                x={'shape': (5,), 'val': np.zeros(5)},
                                                y={'shape': (5,), 'val': np.zeros(5)}))

        p.setup()
        p.run_model()

        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'], return_format='array')

        assert_almost_equal(J, np.eye(5)*3., decimal=6)

    def test_conflicting_shape(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5',
                                                x={'shape': (5,), 'val': 5},
                                                y={'shape': (5,)}))

        with self.assertRaises(Exception) as context:
            p.setup()

        self.assertEqual(str(context.exception).replace('L,', ','),  # L on Windows
                         "'comp' <class ExecComp>: shape of (5,) has been specified for variable 'x', "
                         "but a value of shape (1,) has been provided.")

    def test_common_shape(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5', shape=(5,)))

        p.setup()
        p.run_model()

        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'], return_format='array')

        assert_almost_equal(J, np.eye(5)*3., decimal=6)

    def test_common_shape_with_values(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5', shape=(5,),
                                                x={'val': np.zeros(5)},
                                                y={'val': np.zeros(5)}))

        p.setup()
        p.run_model()

        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'], return_format='array')

        assert_almost_equal(J, np.eye(5)*3., decimal=6)

    def test_common_shape_conflicting_shape(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5', shape=(5,),
                                                y={'shape': (10,)}))

        with self.assertRaises(Exception) as context:
            p.setup()

        self.assertEqual(str(context.exception).replace('L,', ','),  # L on Windows
                         "'comp' <class ExecComp>: shape of (10,) has been specified for variable 'y', "
                         "but shape of (5,) has been specified for the entire component.")

    def test_common_shape_conflicting_value(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5', shape=(5,),
                                                x={'val': 5}))

        with self.assertRaises(Exception) as context:
            p.setup()

        self.assertEqual(str(context.exception).replace('1L,', '1,'),  # 1L on Windows
                         "'comp' <class ExecComp>: value of shape (1,) has been specified for variable 'x', "
                         "but shape of (5,) has been specified for the entire component.")

    def test_math(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=sin(x)', x=2.0))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], math.sin(2.0), 0.00001)

    def test_np(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp(['y1=sin(x)', 'y2=np.cos(x)'], x=2.0))
        prob.setup()

        with self.assertRaises(Exception) as context:
          prob.run_model()

        self.assertEqual(str(context.exception),
            "'C1' <class ExecComp>: Error occurred evaluating 'y2=np.cos(x)':\n"
            "    ExecComp supports a subset of numpy functions directly, without the 'np' prefix.\n"
            "    'cos' is supported (See the documentation).")

    def test_numpy(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('y=numpy.sin(x)', x=2.0))
        prob.setup()

        with self.assertRaises(Exception) as context:
          prob.run_model()

        self.assertEqual(str(context.exception),
            "'C1' <class ExecComp>: Error occurred evaluating 'y=numpy.sin(x)':\n"
            "    ExecComp supports a subset of numpy functions directly, without the 'numpy' prefix.\n"
            "    'sin' is supported (See the documentation).")

    def test_numpy_fft(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('y=numpy.fft(x)', x=2.0))
        prob.setup()

        with self.assertRaises(Exception) as context:
          prob.run_model()

        self.assertEqual(str(context.exception),
            "'C1' <class ExecComp>: Error occurred evaluating 'y=numpy.fft(x)':\n"
            "    ExecComp supports a subset of numpy functions directly, without the 'numpy' prefix.\n"
            "    'fft' is not supported (See the documentation).")

    def test_array(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=x[1]',
                                                        x=np.array([1., 2., 3.]),
                                                        y=0.0))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 2.0, 0.00001)

    def test_array_lhs(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp(['y[0]=x[1]', 'y[1]=x[0]'],
                                                        x=np.array([1., 2., 3.]),
                                                        y=np.array([0., 0.])))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], np.array([2., 1.]), 0.00001)

    def test_simple_array_model(self):
        prob = om.Problem()
        prob.model.add_subsystem('comp', om.ExecComp(['y[0]=2.0*x[0]+7.0*x[1]',
                                                      'y[1]=5.0*x[0]-3.0*x[1]'],
                                                     x=np.zeros([2]), y=np.zeros([2])))

        prob.setup()
        prob.set_solver_print(level=0)
        prob.run_model()

        data = force_check_partials(prob, out_stream=None)

        assert_check_partials(data, atol=1e-5, rtol=1e-5)

    def test_simple_array_model2(self):
        prob = om.Problem()
        prob.model.add_subsystem('comp', om.ExecComp('y = mat.dot(x)',
                                                     x=np.zeros((2,)), y=np.zeros((2,)),
                                                     mat=np.array([[2., 7.], [5., -3.]])))

        prob.setup()
        prob.set_solver_print(level=0)
        prob.run_model()

        data = force_check_partials(prob, out_stream=None)

        assert_check_partials(data, atol=1e-5, rtol=1e-5)

    def test_complex_step(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp(['y=2.0*x+1.'], x=2.0))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('x' in C1._inputs)
        self.assertTrue('y' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 5.0, 0.00001)

        C1._linearize()

        assert_near_equal(C1._jacobian[('y', 'x')], [[2.0]], 0.00001)

    def test_complex_step2(self):
        prob = om.Problem(om.Group())
        prob.model.add_subsystem('comp', om.ExecComp('y=x*x + x*2.0', x=2.0))
        prob.set_solver_print(level=0)

        prob.setup(check=False, mode='fwd')
        prob.run_model()

        J = prob.compute_totals(['comp.y'], ['comp.x'], return_format='flat_dict')
        assert_near_equal(J['comp.y', 'comp.x'], np.array([[6.0]]), 0.00001)

        prob.setup(check=False, mode='rev')
        prob.run_model()

        J = prob.compute_totals(['comp.y'], ['comp.x'], return_format='flat_dict')
        assert_near_equal(J['comp.y', 'comp.x'], np.array([[6.0]]), 0.00001)

    def test_abs_complex_step(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=2.0*abs(x)', x=-2.0))

        prob.setup()
        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], 4.0, 0.00001)

        # any positive C1.x should give a 2.0 derivative for dy/dx
        C1._inputs['x'] = 1.0e-10
        C1._linearize()
        assert_near_equal(C1._jacobian['y', 'x'], [[2.0]], 0.00001)

        C1._inputs['x'] = -3.0
        C1._linearize()
        assert_near_equal(C1._jacobian['y', 'x'], [[-2.0]], 0.00001)

        C1._inputs['x'] = 0.0
        C1._linearize()
        assert_near_equal(C1._jacobian['y', 'x'], [[2.0]], 0.00001)

    def test_arctan_complex_step(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('z=2.0*arctan2(y, x)', x=np.array([1+2j]), y=1))

        prob.setup()
        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['z'], np.array([1.57079633]), 1e-8)

    def test_abs_array_complex_step(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=2.0*abs(x)',
                                                        x=np.ones(3)*-2.0, y=np.zeros(3)))

        prob.setup()
        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['y'], np.ones(3)*4.0, 0.00001)

        # any positive C1.x should give a 2.0 derivative for dy/dx
        C1._inputs['x'] = np.ones(3)*1.0e-10
        C1._linearize()
        assert_near_equal(C1._jacobian['y', 'x'], np.eye(3)*2.0, 0.00001)

        C1._inputs['x'] = np.ones(3)*-3.0
        C1._linearize()
        assert_near_equal(C1._jacobian['y', 'x'], np.eye(3)*-2.0, 0.00001)

        C1._inputs['x'] = np.zeros(3)
        C1._linearize()
        assert_near_equal(C1._jacobian['y', 'x'], np.eye(3)*2.0, 0.00001)

        C1._inputs['x'] = np.array([1.5, -0.6, 2.4])
        C1._linearize()
        expect = np.zeros((3, 3))
        expect[0, 0] = 2.0
        expect[1, 1] = -2.0
        expect[2, 2] = 2.0

        assert_near_equal(C1._jacobian['y', 'x'], expect, 0.00001)

    def test_has_diag_partials_error(self):
        p = om.Problem()
        model = p.model

        mat = np.arange(15).reshape((3,5))
        model.add_subsystem('comp', om.ExecComp('y=A.dot(x)', has_diag_partials=True, A=mat,
                                                x=np.ones(5), y=np.ones(3)))

        p.setup()

        with self.assertRaises(Exception) as context:
            p.final_setup()

        self.assertEqual(str(context.exception),
                         "'comp' <class ExecComp>: has_diag_partials is True but partial(y, A) is not square (shape=(3, 15)).")

    def test_has_diag_partials(self):
        # Really check to see that the has_diag_partials argument had its intended effect

        # run with has_diag_partials=False
        p = om.Problem()
        model = p.model
        comp = om.ExecComp('y=3.0*x + 2.5', has_diag_partials=False, x=np.ones(5), y=np.ones(5))
        model.add_subsystem('comp', comp)
        p.setup()

        self.assertEqual(len(comp._declared_partials_patterns), 0)

        # run with has_diag_partials=True
        p = om.Problem()
        model = p.model
        comp = om.ExecComp('y=3.0*x + 2.5', has_diag_partials=True, x=np.ones(5), y=np.ones(5))
        model.add_subsystem('comp', comp)
        p.setup()
        p.final_setup()

        declared_partials = comp._declared_partials_patterns[('y','x')]
        self.assertTrue('rows' in declared_partials )
        self.assertListEqual([0,1,2,3,4], list( comp._declared_partials_patterns[('y','x')]['rows']))
        self.assertTrue('cols' in declared_partials )
        self.assertListEqual([0,1,2,3,4], list( comp._declared_partials_patterns[('y','x')]['cols']))

    def test_exec_comp_deriv_sparsity(self):
        # Check to make sure that when an ExecComp has more than one
        # expression that only the partials that are needed are declared and computed

        # with has_diag_partials set to the default of False and just scalars
        p = om.Problem()
        model = p.model
        comp = om.ExecComp(['y1=2.0*x1+1.', 'y2=3.0*x2-1.'],x1=1.0, x2=2.0)
        model.add_subsystem('comp', comp)
        p.setup()
        p.final_setup()

        ## make sure only the partials that are needed are declared
        declared_partials = comp._declared_partials_patterns
        self.assertListEqual( sorted([('y1', 'x1'), ('y2', 'x2') ]),
                              sorted(declared_partials.keys()))

        p.run_model()

        # make sure only what is needed was computed
        subjacs_info = comp._jacobian._subjacs_info
        self.assertListEqual(sorted([('comp.y1', 'comp.x1'), ('comp.y2', 'comp.x2'),
                                     ('comp.y1', 'comp.y1'),('comp.y2', 'comp.y2')]),
                             sorted(subjacs_info.keys()))

        # make sure the result of compute_partials is correct
        J = p.compute_totals(of=['comp.y1'], wrt=['comp.x1'], return_format='array')
        self.assertEqual(2.0, J)
        J = p.compute_totals(of=['comp.y2'], wrt=['comp.x2'], return_format='array')
        self.assertEqual(3.0, J)

        # make sure this works with arrays and when has_diag_partials is the default of False
        p = om.Problem()
        model = p.model
        comp = om.ExecComp(['y1=2.0*x1+1.', 'y2=3.0*x2-1.'],
                           x1=np.ones(5), y1=np.ones(5), x2=np.ones(5), y2=np.ones(5))
        model.add_subsystem('comp', comp)
        p.setup()
        p.final_setup()

        declared_partials = comp._declared_partials_patterns
        self.assertListEqual( sorted([('y1', 'x1'), ('y2', 'x2') ]),
                              sorted(declared_partials.keys()))

        p.run_model()
        J = p.compute_totals(of=['comp.y1'], wrt=['comp.x1'], return_format='array')
        self.assertTrue(np.all(2.0*np.identity(5) == J))
        J = p.compute_totals(of=['comp.y2'], wrt=['comp.x2'], return_format='array')
        self.assertTrue(np.all(3.0*np.identity(5) == J))

        # with has_diag_partials True to make sure that still works with arrays
        p = om.Problem()
        model = p.model
        comp = om.ExecComp(['y1=2.0*x1+1.', 'y2=3.0*x2-1.'], has_diag_partials=True,
                           x1=np.ones(5), y1=np.ones(5), x2=np.ones(5), y2=np.ones(5) )
        model.add_subsystem('comp', comp)
        p.setup()
        p.final_setup()

        declared_partials = comp._declared_partials_patterns
        self.assertListEqual( sorted([('y1', 'x1'), ('y2', 'x2') ]),
                              sorted(declared_partials.keys()))
        self.assertTrue('cols' in declared_partials[('y1', 'x1')] )
        self.assertTrue('rows' in declared_partials[('y1', 'x1')] )
        self.assertTrue('cols' in declared_partials[('y2', 'x2')] )
        self.assertTrue('rows' in declared_partials[('y2', 'x2')] )
        self.assertListEqual([0,1,2,3,4], list( comp._declared_partials_patterns[('y1','x1')]['rows']))
        self.assertListEqual([0,1,2,3,4], list( comp._declared_partials_patterns[('y1','x1')]['cols']))
        self.assertListEqual([0,1,2,3,4], list( comp._declared_partials_patterns[('y2','x2')]['rows']))
        self.assertListEqual([0,1,2,3,4], list( comp._declared_partials_patterns[('y2','x2')]['cols']))

        p.run_model()

        J = p.compute_totals(of=['comp.y1'], wrt=['comp.x1'], return_format='array')
        self.assertTrue(np.all(2.0*np.identity(5) == J))
        J = p.compute_totals(of=['comp.y2'], wrt=['comp.x2'], return_format='array')
        self.assertTrue(np.all(3.0*np.identity(5) == J))

    def test_has_diag_partials_shape_only(self):
        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5', has_diag_partials=True,
                                                x={'shape': (5,)}, y={'shape': (5,)}))

        p.setup()
        p.run_model()

        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'], return_format='array')

        assert_almost_equal(J, np.eye(5)*3., decimal=6)

    def test_tags(self):
        prob = om.Problem(model=om.Group())
        C1 = prob.model.add_subsystem('C1', om.ExecComp('y=x+z+1.',
                                                        x={'val': 1.0, 'units': 'm', 'tags': 'tagx'},
                                                        y={'units': 'm', 'tags': ['tagy','tagq']},
                                                        z={'val': 2.0, 'tags': 'tagz'}))

        prob.setup(check=False)

        prob.set_solver_print(level=0)
        prob.run_model()

        # Inputs no tags
        inputs = prob.model.list_inputs(val=False, prom_name=False, out_stream=None)
        self.assertEqual(sorted(inputs), [
            ('C1.x', {}),
            ('C1.z', {}),
        ])

        # Inputs with tags
        inputs = prob.model.list_inputs(val=False, prom_name=False, out_stream=None, tags="tagx")
        self.assertEqual(sorted(inputs), [
            ('C1.x', {}),
        ])

        # Inputs with multiple tags
        inputs = prob.model.list_inputs(val=False, prom_name=False, out_stream=None, tags=["tagx", "tagz"])
        self.assertEqual(sorted(inputs), [
            ('C1.x', {}),
            ('C1.z', {}),
        ])

        # Inputs with tag that does not match
        inputs = prob.model.list_inputs(val=False, prom_name=False, out_stream=None, tags="tag_wrong")
        self.assertEqual(sorted(inputs), [])

        # Outputs no tags
        outputs = prob.model.list_outputs(val=False, prom_name=False, out_stream=None)
        self.assertEqual(sorted(outputs), [
            ('C1.y', {}),
        ])

        # Outputs with tags
        outputs = prob.model.list_outputs(val=False, prom_name=False, out_stream=None, tags="tagy")
        self.assertEqual(sorted(outputs), [
            ('C1.y', {}),
        ])

        # Outputs with multiple tags
        outputs = prob.model.list_outputs(val=False, prom_name=False, out_stream=None, tags=["tagy", "tagx"])
        self.assertEqual(sorted(outputs), [
            ('C1.y', {}),
        ])

        # Outputs with tag that does not match
        outputs = prob.model.list_outputs(val=False, prom_name=False, out_stream=None, tags="tag_wrong")
        self.assertEqual(sorted(outputs), [])

    def test_feature_has_diag_partials(self):

        p = om.Problem()
        model = p.model

        model.add_subsystem('comp', om.ExecComp('y=3.0*x + 2.5',
                                                has_diag_partials=True,
                                                x=np.ones(5), y=np.ones(5)))

        p.setup()

        p.set_val('comp.x', np.ones(5))

        p.run_model()

        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'], return_format='array')

        assert_almost_equal(J, np.eye(5)*3., decimal=6)

    def test_feature_multi_output(self):

        prob = om.Problem()
        model = prob.model

        model.add_subsystem('comp', om.ExecComp(['y1=x+1.', 'y2=x-1.']), promotes=['x'])

        prob.setup()

        prob.set_val('x', 2.0)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(prob.get_val('comp.y1'), 3.0, 0.00001)
        assert_near_equal(prob.get_val('comp.y2'), 1.0, 0.00001)

    def test_feature_multi_output2(self):
        # verify that expressions can have multiple LHS variables.

        prob = om.Problem()
        model = prob.model

        model.add_subsystem('comp', om.ExecComp(['y1, y2 = x+1., x-1.']), promotes=['x'])

        prob.setup()

        prob.set_val('x', 2.0)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(prob.get_val('comp.y1'), 3.0, 0.00001)
        assert_near_equal(prob.get_val('comp.y2'), 1.0, 0.00001)

    def test_feature_array(self):

        prob = om.Problem()
        model = prob.model

        model.add_subsystem('comp', om.ExecComp('y=x[1]',
                                                x=np.array([1., 2., 3.]),
                                                y=0.0))

        prob.setup()

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(prob.get_val('comp.y'), 2.0, 0.00001)

    def test_feature_math(self):

        prob = om.Problem()
        model = prob.model

        model.add_subsystem('comp', om.ExecComp('z = sin(x)**2 + cos(y)**2'))

        prob.setup()

        prob.set_val('comp.x', np.pi/2.0)
        prob.set_val('comp.y', np.pi/2.0)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(prob.get_val('comp.z'), 1.0, 0.00001)

    def test_feature_numpy(self):

        prob = om.Problem()
        model = prob.model

        model.add_subsystem('comp', om.ExecComp('y=sum(x)', x=np.array([1., 2., 3.])))

        prob.setup()

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(prob['comp.y'], 6.0, 0.00001)

    def test_feature_metadata(self):

        prob = om.Problem()
        model = prob.model

        model.add_subsystem('comp', om.ExecComp('z=x+y',
                                                x={'val': 0.0, 'units': 'inch'},
                                                y={'val': 0.0, 'units': 'inch'},
                                                z={'val': 0.0, 'units': 'inch'}))

        prob.setup()

        prob.set_val('comp.x', 12.0, units='inch')
        prob.set_val('comp.y', 1.0, units='ft')

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(prob.get_val('comp.z'), 24.0, 0.00001)

    def test_feature_options(self):

        model = om.Group()

        xcomp = model.add_subsystem('comp', om.ExecComp('y=2*x', shape=(2,)))

        xcomp.options['units'] = 'm'

        prob = om.Problem(model)
        prob.setup()

        prob.set_val('comp.x', [100., 200.], units='cm')

        prob.run_model()

        assert_near_equal(prob.get_val('comp.y'), [2., 4.], 0.00001)

    def test_list_outputs_resids_tol(self):
        prob = om.Problem()
        model = prob.model

        model.add_subsystem(
            "quad_1",
            om.ExecComp(
                "y = a * x ** 2 + b * x + c",
                a={"val": 2.0},
                b={"val": 5.0},
                c={"val": 3.0},
                x={"shape": (2,)},
                y={"shape": (2,)},
            ),
        )

        balance = model.add_subsystem("balance", om.BalanceComp())
        balance.add_balance("x_1", val=np.array([1, -1]), rhs_val=np.array([0., 0.]))
        model.connect("balance.x_1", "quad_1.x")
        model.connect("quad_1.y", "balance.lhs:x_1")

        prob.model.linear_solver = om.ScipyKrylov()
        prob.model.nonlinear_solver = om.NewtonSolver(solve_subsystems=False, maxiter=100, iprint=2)

        prob.setup()
        prob.model.nonlinear_solver.options["maxiter"] = 0
        prob.run_model()

        stream = StringIO()
        outputs = prob.model.list_outputs(residuals=True, residuals_tol=1e-5, out_stream=stream)

        text = stream.getvalue()
        self.assertTrue("balance" in text)
        self.assertTrue("x_1" in text)

    def test_add_expr(self):
        p = om.Problem()

        excomp = om.ExecComp('y=x',
                             x={'val' : 3.0, 'units' : 'mm'},
                             y={'shape' : (1, ), 'units' : 'cm'})

        excomp.add_expr('z = 2.9*x',
                        z={'shape' : (1, ), 'units' : 's'})

        p.model.add_subsystem('comp', excomp, promotes=['*'])
        p.setup()
        p.run_model()

        assert_almost_equal(p.get_val('z'), 8.7, 1e-8)
        assert_almost_equal(p.get_val('y'), 3.0, 1e-8)

    def test_add_expr_bare(self):
        p = om.Problem()

        excomp = om.ExecComp()

        excomp.add_expr('z = 2.9*x',
                        x={'val' : 3.0, 'units' : 'mm'},
                        z={'shape' : (1, ), 'units' : 's'})

        p.model.add_subsystem('comp', excomp, promotes=['*'])
        p.setup()
        p.run_model()

        assert_almost_equal(p.get_val('z'), 8.7, 1e-8)

    def test_add_expr_configure(self):

        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp('y=x',
                                     x={'val' : 3.0, 'units' : 'mm'},
                                     y={'shape' : (1, ), 'units' : 'cm'})

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                self.excomp.add_expr('z = 2.9*x',
                                     z={'shape' : (1, ), 'units' : 's'})


        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()
        p.run_model()

        assert_almost_equal(p.get_val('z'), 8.7, 1e-8)
        assert_almost_equal(p.get_val('y'), 3.0, 1e-8)

    def test_add_expr_configure_no_shape_or_val(self):

        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp('x_constraint=x',
                                     x_constraint={'units': None},
                                     x={'units': 's'})

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                self.excomp.add_expr('y_constraint = y',
                                     y_constraint={'units': None},
                                     y={'units': 's'})

        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()
        p.set_val('x', 3.0)
        p.set_val('y', 4.0)
        p.run_model()

        assert_almost_equal(p.get_val('x_constraint'), 3.0)
        assert_almost_equal(p.get_val('y_constraint'), 4.0)

    def test_no_expressions_until_configure(self):

        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp()

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                self.excomp.add_expr('y_constraint = y**2',
                                     y_constraint={'units': None},
                                     y={'units': 's'})

        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()
        p.set_val('y', 4.0)
        p.run_model()

        assert_almost_equal(p.get_val('y_constraint'), 16.0)

    def test_no_expressions(self):

        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp()

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                pass

        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()
        p.run_model()

    def test_add_expr_configure_delay_defaults(self):

        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp('y=x',
                                     y={'shape' : (1, ), 'units' : 'cm'})

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                self.excomp.add_expr('z = 2.9*x',
                                     x={'val' : 3.0, 'units' : 'mm'},
                                     z={'shape' : (1, ), 'units' : 's'})


        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()
        p.run_model()

        assert_almost_equal(p.get_val('z'), 8.7, 1e-8)
        assert_almost_equal(p.get_val('y'), 3.0, 1e-8)

    def test_add_expr_errors(self):
        p = om.Problem()

        excomp = om.ExecComp('y=x',
                             x={'val' : 3.0, 'units' : 'mm'},
                             y={'shape' : (1, ), 'units' : 'cm'})

        with self.assertRaises(NameError) as cm:
            excomp.add_expr('z = 2.9*x',
                            x={'val' : 3.0, 'units' : 'cm'},
                            z={'shape' : (1, ), 'units' : 's'})

        self.assertEqual(cm.exception.args[0],
                         "Defaults for 'x' have already been defined in a previous "
                         "expression.")

        with self.assertRaises(TypeError) as cm:
            excomp.add_expr(p)

        self.assertEqual(cm.exception.args[0],
                         "Argument 'expr' must be of type 'str', but type 'Problem' was found.")

        excomp.add_expr('y = 2.9*x')
        p.model.add_subsystem('zzz', excomp)
        with self.assertRaises(RuntimeError) as cm:
            p.setup()

        self.assertEqual(cm.exception.args[0],
                         "'zzz' <class ExecComp>: The output 'y' has already been defined by an expression.")

    def test_feature_add_expr(self):

        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp('y=x',
                                     x={'val' : 3.0, 'units' : 'mm'},
                                     y={'shape' : (1, ), 'units' : 'cm'})

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                self.excomp.add_expr('z = 2.9*x',
                                     z={'shape' : (1, ), 'units' : 's'})

        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()
        p.run_model()

        assert_almost_equal(p.get_val('z'), 8.7, 1e-8)
        assert_almost_equal(p.get_val('y'), 3.0, 1e-8)

    def test_val_type(self):
        class ConfigGroup(om.Group):
            def setup(self):
                excomp = om.ExecComp('y=x',
                                     x={'val': 3.0, 'units': 'mm'},
                                     y={'shape': (1,), 'units': 'cm'})

                self.add_subsystem('excomp', excomp, promotes=['*'])

            def configure(self):
                self.excomp.add_expr('z = 2.9*x',
                                     z={'shape': (1,), 'units': 's'})

        p = om.Problem()
        p.model.add_subsystem('sub', ConfigGroup(), promotes=['*'])
        p.setup()

        # check that 'val' has been saved as a numpy array (see issue #2415)
        abs2meta = p.model._var_abs2meta
        for typ in ['input', 'output']:
            for abs_name in abs2meta[typ]:
                val = abs2meta[typ][abs_name]['val']
                if not isinstance(val, np.ndarray):
                    self.fail(f"The {typ} variable '{abs_name}' has a value of {val} "
                              f"with type {type(val)}, but it should be a numpy array.")


    def test_constants_simple(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('x = a + b', a={'val': 6, 'constant':True}))

        prob.setup()
        prob.final_setup()

        self.assertFalse('a' in C1._inputs)
        self.assertTrue('b' in C1._inputs)
        self.assertTrue('x' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['x'], 7.0, 0.00001)

    def test_constants_val_not_given(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('x = a + b', a={'constant':True}))

        with self.assertRaises(RuntimeError) as cm:
            prob.setup()
            self.assertEqual(str(cm.exception), "C1' <class ExecComp>: arg 'a' in call to ExecComp() is a constant but no value is given")

    def test_constants_units_given(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('x = a + b', a={'constant':True, 'val': 6, 'units': 'ft'}))

        expected_warning_msg = "'C1' <class ExecComp>: arg 'a' in call to " \
                               "ExecComp() is a constant. The units will be ignored"
        with assert_warning(SetupWarning, expected_warning_msg):
            prob.setup()

    def test_constants_shape_given(self):
        prob = om.Problem()
        prob.model.add_subsystem('C1', om.ExecComp('x = a + b', a={'constant':True, 'val': 6, 'shape': (1,)}))

        expected_warning_msg = "'C1' <class ExecComp>: arg 'a' in call to " \
                               "ExecComp() is a constant. The shape will be ignored"
        with assert_warning(SetupWarning, expected_warning_msg):
            prob.setup()

    def test_constants_set_constant_false(self):
        prob = om.Problem()
        C1 = prob.model.add_subsystem('C1', om.ExecComp('x = a + b', a={'val': 6, 'constant':False}))

        prob.setup()

        # Conclude setup but don't run model.
        prob.final_setup()

        self.assertTrue('a' in C1._inputs)
        self.assertTrue('b' in C1._inputs)
        self.assertTrue('x' in C1._outputs)

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(C1._outputs['x'], 7.0, 0.00001)

    def test_constants_multiple_equations(self):
        prob = om.Problem()
        model = prob.model
        comp = om.ExecComp(['y1=2.0*x1+a', 'y2=3.0*x2-a'], x1=1.0, x2=2.0, a={'val': 6, 'constant':True})
        model.add_subsystem('comp', comp)
        prob.setup()
        prob.run_model()

        assert_near_equal(comp._outputs['y1'], 8.0, 0.00001)
        assert_near_equal(comp._outputs['y2'], 0.0, 0.00001)

    def test_constants_arrays(self):
        prob = om.Problem()
        model = prob.model

        comp = model.add_subsystem('comp', om.ExecComp('y=x+a',
                                                       y={'shape': (3,), 'val': np.zeros(3)},
                                                       x=np.array([1., 2., 3.]),
                                                       a={ 'val': np.array([1., 2., 3.]), 'constant':True}))

        prob.setup()

        prob.set_solver_print(level=0)
        prob.run_model()

        assert_near_equal(comp._outputs['y'], 2.0 * np.array([1., 2., 3.]), 0.00001)


class TestFunctionRegistration(unittest.TestCase):

    # These 2 tests don't run normally unless you run testflo with a -m "featuretest_*"
    # I don't want to include them in our normal tests because they don't contain
    # the _temporary_expr_dict contextmanager (to avoid user confusion)
    # which keeps the contents of the ExecComp _expr_dict clean
    def featuretest_register_simple(self):

        om.ExecComp.register("myfunc", lambda x: x * x, complex_safe=True)
        p = om.Problem()
        comp = p.model.add_subsystem("comp", om.ExecComp("y = 2 * myfunc(x)"))

        p.setup()
        p.run_model()
        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'])
        assert_near_equal(J['comp.y', 'comp.x'][0][0], 4., 1e-10)

    def featuretest_register_simple_unsafe(self):

        # the following function isn't really complex unsafe, but we'll call it unsafe anyway
        # for demonstration purposes
        om.ExecComp.register("unsafe", lambda x: x * x, complex_safe=False)
        p = om.Problem()
        comp = p.model.add_subsystem("comp", om.ExecComp("y = 2 * unsafe(x)"))

        # because our function is complex unsafe, we must declare that the partials
        # with respect to 'x' use 'fd' instead of 'cs'
        comp.declare_partials('*', 'x', method='fd')

        p.setup()
        p.run_model()
        J = p.compute_totals(of=['comp.y'], wrt=['comp.x'])
        assert_near_equal(J['comp.y', 'comp.x'][0][0], 4., 1e-5)

    def test_register_simple(self):
        with _temporary_expr_dict():
            om.ExecComp.register('area', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)'))
            p.setup()
            p['comp.x'] = 3.
            p.run_model()
            self.assertEqual(p['comp.area_square'], 9.)
            J = p.compute_totals(of=['comp.area_square'], wrt=['comp.x'])
            self.assertEqual(J['comp.area_square', 'comp.x'], 6.)

    def test_register_simple_arr(self):
        with _temporary_expr_dict():
            size = 5
            om.ExecComp.register('area', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size))
            p.setup()
            p['comp.x'] = x = np.arange(1, size+1, dtype=float)
            p.run_model()
            assert_near_equal(p['comp.area_square'], x * x, 1e-11)
            J = p.compute_totals(of=['comp.area_square'], wrt=['comp.x'])
            assert_near_equal(J['comp.area_square', 'comp.x'], np.eye(size) * x * 2., 1e-11)

    def test_register_check_partials_not_safe(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('area', lambda x: x**2, complex_safe=False)
            p = om.Problem()
            comp = p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size))
            comp.declare_partials('*', '*', method='fd')
            p.setup()
            p['comp.x'] = 3.
            p.run_model()
            assert_near_equal(p['comp.area_square'], np.ones(size) * 9., 1e-6)

            data = force_check_partials(p, out_stream=None, step=1e-7)
            self.assertEqual(list(data), ['comp'])

    def test_register_check_partials_not_safe_err(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('area', lambda x: x**2, complex_safe=False)
            p = om.Problem()
            comp = p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size))
            p.setup()
            p['comp.x'] = 3.
            # calling run_model should NOT raise an exception
            p.run_model()
            assert_near_equal(p['comp.area_square'], np.ones(size) * 9., 1e-6)

            with self.assertRaises(Exception) as cm:
                data = force_check_partials(p, out_stream=None)
            self.assertEqual(cm.exception.args[0],
                             "'comp' <class ExecComp>: expression contains functions ['area'] that are not complex safe. To fix this, call declare_partials('*', ['x'], method='fd') on this component prior to setup.")

    def test_register_check_partials_not_safe_mult_expr(self):
        with _temporary_expr_dict():
            size = 5
            om.ExecComp.register('unsafe', lambda x: x**2, complex_safe=False)
            om.ExecComp.register('safe', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            comp = p.model.add_subsystem('comp', om.ExecComp(['out1 = unsafe(x) * z',
                                                              'out2 = safe(y) + z'], shape=size))
            rows = cols = np.arange(size)
            comp.declare_partials('out1', ['x', 'z'], rows=rows, cols=cols, method='fd')
            comp.declare_partials('out2', ['y'], rows=rows, cols=cols, method='cs')
            comp.declare_partials('out2', ['z'], rows=rows, cols=cols, method='fd')
            p.setup()
            xx = np.arange(1, size + 1, dtype=float)
            p['comp.x'] = x = xx * 3.
            p['comp.y'] = y = xx * 4.
            p['comp.z'] = z = xx * 5.
            p.run_model()
            assert_near_equal(p['comp.out1'], x * x * z, 1e-10)
            assert_near_equal(p['comp.out2'], y * y + z, 1e-10)

            J = p.compute_totals(of=['comp.out1', 'comp.out2'], wrt=['comp.x', 'comp.y', 'comp.z'])
            assert_near_equal(J['comp.out1', 'comp.x'], np.eye(size) * 2. * x * z, 1e-6)
            assert_near_equal(J['comp.out1', 'comp.y'], np.zeros((size, size)), 1e-6)
            assert_near_equal(J['comp.out1', 'comp.z'], np.eye(size) * x**2, 1e-6)
            assert_near_equal(J['comp.out2', 'comp.x'], np.zeros((size, size)), 1e-11)
            assert_near_equal(J['comp.out2', 'comp.y'], np.eye(size) * 2. * y, 1e-11)
            assert_near_equal(J['comp.out2', 'comp.z'], np.eye(size), 1e-6)

            data = force_check_partials(p, out_stream=None, step=1e-7)
            self.assertEqual(list(data), ['comp'])

    def test_register_check_partials_not_safe_mult_expr_err(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('unsafe', lambda x: x**2, complex_safe=False)
            om.ExecComp.register('safe', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            comp = p.model.add_subsystem('comp', om.ExecComp(['out1 = unsafe(x) * z',
                                                              'out2 = safe(y) + z'], shape=size))
            comp.declare_partials('*', ['x'], method='fd')
            p.setup()
            p['comp.x'] = 3.
            p['comp.y'] = 4.
            p['comp.z'] = 5.
            p.run_model()
            assert_near_equal(p['comp.out1'], np.ones(size) * 45., 1e-6)
            assert_near_equal(p['comp.out2'], np.ones(size) * 21., 1e-6)

            with self.assertRaises(Exception) as cm:
                data = force_check_partials(p, out_stream=None, step=1e-7)
            self.assertEqual(cm.exception.args[0],
                             "'comp' <class ExecComp>: expression contains functions ['unsafe'] that are not complex safe. To fix this, call declare_partials('*', ['z'], method='fd') on this component prior to setup.")

    def test_register_check_partials_safe(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('area', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size))
            p.setup()
            p['comp.x'] = 3.
            p.run_model()
            assert_near_equal(p['comp.area_square'], np.ones(size) * 9., 1e-11)

            data = force_check_partials(p, out_stream=None)
            self.assertEqual(list(data), ['comp'])

    def test_register_simple_arr_manual_partials_cs(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('area', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            comp = p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size))
            comp.declare_partials('area_square', 'x', method='cs')
            p.setup()
            p['comp.x'] = 3.
            p.run_model()
            assert_near_equal(p['comp.area_square'], np.ones(size) * 9., 1e-11)
            J = p.compute_totals(of=['comp.area_square'], wrt=['comp.x'])
            assert_near_equal(J['comp.area_square', 'comp.x'], np.eye(size) * 6., 1e-11)

    def test_register_simple_arr_manual_partials_fd(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('area', lambda x: x**2, complex_safe=False)
            p = om.Problem()
            comp = p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size))
            comp.declare_partials('area_square', 'x', method='fd')
            p.setup()
            p['comp.x'] = 3.
            p.run_model()
            assert_near_equal(p['comp.area_square'], np.ones(size) * 9., 1e-6)
            J = p.compute_totals(of=['comp.area_square'], wrt=['comp.x'])
            assert_near_equal(J['comp.area_square', 'comp.x'], np.eye(size) * 6., 1e-6)

    def test_register_simple_arr_diag(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('area', lambda x: x**2, complex_safe=True)
            p = om.Problem()
            p.model.add_subsystem('comp', om.ExecComp('area_square = area(x)', shape=size, has_diag_partials=True))
            p.setup()
            p['comp.x'] = 3.
            p.run_model()
            assert_near_equal(p['comp.area_square'], np.ones(size) * 9., 1e-11)
            J = p.compute_totals(of=['comp.area_square'], wrt=['comp.x'])
            assert_near_equal(J['comp.area_square', 'comp.x'], np.eye(size) * 6., 1e-11)

            # verify diagonal subjac
            self.assertTrue(np.all(p.model.comp._subjacs_info['comp.area_square', 'comp.x']['rows'] == np.arange(size)))
            self.assertTrue(np.all(p.model.comp._subjacs_info['comp.area_square', 'comp.x']['cols'] == np.arange(size)))

    def test_register_shape_by_conn(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('part', lambda x: x[2:], complex_safe=True)
            p = om.Problem()
            p.model.add_subsystem('indeps', om.IndepVarComp('x', np.ones(size)))
            p.model.add_subsystem('comp', om.ExecComp('y = part(x) * 3.', shape_by_conn=True))
            p.model.add_subsystem('sink', om.ExecComp('y=x', shape=size-2))
            p.model.connect("indeps.x", "comp.x")
            p.model.connect("comp.y", "sink.x")
            p.setup()
            p['indeps.x'] = 3.
            p.run_model()
            assert_near_equal(p['comp.x'], np.ones(size) * 3., 1e-11)
            assert_near_equal(p['comp.y'], np.ones(size-2) * 9., 1e-11)
            assert_near_equal(p['sink.y'], np.ones(size-2) * 9., 1e-11)
            J = p.compute_totals(of=['sink.y'], wrt=['indeps.x'])
            assert_near_equal(J['sink.y', 'indeps.x'], np.eye(size)[2:, :] * 3., 1e-11)

    def test_register_shape_by_conn_err(self):
        with _temporary_expr_dict():
            size = 10
            om.ExecComp.register('double', lambda x: x * 2, complex_safe=True)
            p = om.Problem()
            p.model.add_subsystem('indeps', om.IndepVarComp('x', np.ones(size)))
            p.model.add_subsystem('comp', om.ExecComp('y = double(x) * 3.', shape_by_conn=True))
            p.model.add_subsystem('sink', om.ExecComp('y=x', shape=size-2))
            p.model.connect("indeps.x", "comp.x")
            p.model.connect("comp.y", "sink.x")
            p.setup()
            p['indeps.x'] = 3.

            # if shape_by_conn results in inputs and outputs being different shapes, we can't detect if that's
            # an error or not because we don't know how the expressions evaluate, so we have to wait until
            # compute runs and just report as an error during expression evaluation.

            # have to use regex to handle differences in numpy print formats for shape
            msg = "'comp' <class ExecComp>: Error occurred evaluating 'y = double\(x\) \* 3\.':\n" \
                  "could not broadcast input array from shape \(10.*\) into shape \(8.*\)"
            with self.assertRaisesRegex(Exception, msg) as cm:
                p.run_model()

    def test_shape_by_conn_bug_has_diag_partials_bug(self):
        # this is for a bug where has_diag_partials was being ignored when shape_by_conn
        # and/or copy_shape was used.

        prob = om.Problem()

        size = 100000
        t = np.linspace(0, 1, size)

        prob.model.add_subsystem("ivc",
                                om.IndepVarComp("t", val=t),
                                promotes_outputs=["*"])

        comp1 = prob.model.add_subsystem("comp1", om.ExecComp(["x = t + 1"],
                t={"shape_by_conn":True},
                x={"shape_by_conn":True, "copy_shape":"t"},
                has_diag_partials=True), promotes=["*"])

        comp2 = prob.model.add_subsystem("comp2", om.ExecComp(["y = t + 2"],
                t={"shape":size},
                y={"copy_shape":"t"},
                has_diag_partials=True), promotes=["*"])

        comp3 = prob.model.add_subsystem("comp3", om.ExecComp(["z = t + 3"],
                t={"shape_by_conn":True},
                z={"shape":size},
                has_diag_partials=True), promotes=["*"])

        comp4 = prob.model.add_subsystem("comp4", om.ExecComp(["w = t + 4"],
                t={"shape":size},
                w={"shape":size},
                has_diag_partials=True), promotes=["*"])

        prob.setup()
        prob.final_setup()

        # all subjac values should be size == size from above instead of (size, size)
        self.assertEqual(comp1._subjacs_info[('comp1.x', 'comp1.t')]['val'].size, size)
        self.assertEqual(comp2._subjacs_info[('comp2.y', 'comp2.t')]['val'].size, size)
        self.assertEqual(comp3._subjacs_info[('comp3.z', 'comp3.t')]['val'].size, size)
        self.assertEqual(comp4._subjacs_info[('comp4.w', 'comp4.t')]['val'].size, size)

    def test_register_err_keyword(self):
        with _temporary_expr_dict():
            with self.assertRaises(Exception) as cm:
                om.ExecComp.register('shape', lambda x: x, complex_safe=True)
            self.assertEqual(cm.exception.args[0], "ExecComp: cannot register name 'shape' because "
                             "it's a reserved keyword.")

    def test_register_err_not_callable(self):
        with _temporary_expr_dict():
            with self.assertRaises(Exception) as cm:
                om.ExecComp.register('foo', 99, complex_safe=True)
            self.assertEqual(cm.exception.args[0], "ExecComp: 'foo' passed to register() of type 'int' is not callable.")

    def test_register_err_dup(self):
        with _temporary_expr_dict():
            with self.assertRaises(Exception) as cm:
                om.ExecComp.register('exp', lambda x: x, complex_safe=True)
            self.assertEqual(cm.exception.args[0], "ExecComp: 'exp' has already been registered.")


_MASK = np.array(
    [[1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1],
    [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1],
    [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1],
    [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0],
    [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0],
    [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1],
    [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1],
    [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0],
    [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0],
    [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0],
    [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]]
)


def setup_sparsity(mask):
    sparsity = np.random.random(mask.shape) + 1e-5
    return sparsity * mask



class TestFunctionRegistrationColoring(unittest.TestCase):
    def setUp(self):
        np.random.seed(11)
        self.startdir = os.getcwd()
        self.tempdir = tempfile.mkdtemp(prefix=self.__class__.__name__ + '_')
        os.chdir(self.tempdir)

    def tearDown(self):
        os.chdir(self.startdir)
        try:
            shutil.rmtree(self.tempdir)
        except OSError:
            pass

    def test_manual_coloring(self):
        with _temporary_expr_dict():

            prob = om.Problem(coloring_dir=self.tempdir)
            model = prob.model

            sparsity = setup_sparsity(_MASK)

            def mydot(x):
                return sparsity.dot(x)

            om.ExecComp.register('mydot', mydot, complex_safe=True)

            comp = model.add_subsystem('comp', om.ExecComp('y=mydot(x)',
                                                            x=np.ones(sparsity.shape[1]),
                                                            y=np.ones(sparsity.shape[0])))
            comp.declare_coloring('x', method='cs')

            prob.setup(mode='fwd')
            prob.set_solver_print(level=0)
            prob.run_model()

            J = prob.compute_totals('comp.y', 'comp.x')

            assert_near_equal(J['comp.y', 'comp.x'], sparsity)

            self.assertTrue(np.all(comp._coloring_info['coloring'].get_dense_sparsity() == _MASK))

    def test_auto_coloring(self):
        with _temporary_expr_dict():

            prob = om.Problem(coloring_dir=self.tempdir)
            model = prob.model

            sparsity = setup_sparsity(_MASK)

            def mydot(x):
                return sparsity.dot(x)

            om.ExecComp.register('mydot', mydot, complex_safe=True)

            comp = model.add_subsystem('comp', om.ExecComp('y=mydot(x)',
                                                            x=np.ones(sparsity.shape[1]),
                                                            y=np.ones(sparsity.shape[0])))
            prob.setup(mode='fwd')
            prob.set_solver_print(level=0)
            prob.run_model()

            J = prob.compute_totals('comp.y', 'comp.x')

            assert_near_equal(J['comp.y', 'comp.x'], sparsity)

            self.assertTrue(np.all(comp._coloring_info['coloring'].get_dense_sparsity() == _MASK))


class TestExecCompParameterized(unittest.TestCase):

    @parameterized.expand(itertools.product([
      func_name for func_name in _expr_dict if func_name not in ('np', 'numpy', '__builtins__')
    ]), name_func=lambda f, n, p: 'test_exec_comp_value_' + '_'.join(a for a in p.args))
    def test_exec_comp_value(self, f):
        test_data = _ufunc_test_data[f]

        prob = om.Problem()
        model = prob.model

        if len(test_data['args']) > 1:
            ivc = model.add_subsystem(name='ivc', subsys=om.IndepVarComp())
            for arg_name, arg_value in test_data['args'].items():
                if arg_name == 'f':
                    continue
                ivc.add_output(name=arg_name, val=arg_value['val'])
                model.connect('ivc.{0}'.format(arg_name), 'comp.{0}'.format(arg_name))

        model.add_subsystem('comp', om.ExecComp(test_data['str'], **test_data['args']),
                            promotes_outputs=['f'])
        prob.setup()

        if 'error' in test_data:
            err, msg = test_data['error']
            with self.assertRaises(err) as cm:
                prob.run_model()
            self.assertTrue(msg in str(cm.exception))
            return
        elif 'warning' in test_data:
            with assert_warning(*test_data['warning']):
                prob.run_model()
        else:
            prob.run_model()

        if 'check_func' in test_data:
            check_args = []
            try:
                check_args.append(test_data['args']['x']['val'])
            except Exception:
                pass
            try:
                check_args.append(test_data['args']['y']['val'])
            except Exception:
                pass
            check_args = tuple(check_args)

            expected = test_data['check_func'](*check_args)
        else:
            expected = test_data['check_val']
        np.testing.assert_almost_equal(prob['f'], expected)

        if 'check_val' not in test_data:
            try:
                force_check_partials(prob, out_stream=None)
            except TypeError as e:
                print(f, 'does not support complex-step differentiation')

    @parameterized.expand(itertools.product([
      func_name for func_name in _expr_dict if func_name not in ('np', 'numpy', '__builtins__')
    ]), name_func=lambda f, n, p: 'test_exec_comp_jac_' + '_'.join(a for a in p.args))
    def test_exec_comp_jac(self, f):
        test_data = _ufunc_test_data[f]

        prob = om.Problem()
        model = prob.model

        if len(test_data['args']) > 1:
            ivc = model.add_subsystem(name='ivc', subsys=om.IndepVarComp())
            for arg_name, arg_value in test_data['args'].items():
                if arg_name == 'f':
                    continue
                ivc.add_output(name=arg_name, val=arg_value['val'])
                model.connect('ivc.{0}'.format(arg_name),
                              '{0}_comp.{1}'.format(f, arg_name))

        model.add_subsystem('{0}_comp'.format(f),
                            om.ExecComp(test_data['str'], **test_data['args']),
                            promotes_outputs=['f'])
        prob.setup()

        if 'error' in test_data:
            err, msg = test_data['error']
            with self.assertRaises(err) as cm:
                prob.run_model()
            self.assertTrue(msg in str(cm.exception))
            return
        elif 'warning' in test_data:
            with assert_warning(*test_data['warning']):
                prob.run_model()
        else:
            prob.run_model()

        if 'check_val' not in test_data:
            cpd = force_check_partials(prob, out_stream=None)

            for comp in cpd:
                for (var, wrt) in cpd[comp]:
                    np.testing.assert_almost_equal(cpd[comp][var, wrt]['abs error'][0], 0, decimal=4,
                                                   verbose=True, err_msg=f"{test_data['args']=}")


if __name__ == "__main__":
    unittest.main()