Пример #1
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class ViewSolver:
    def __init__(self, view, app):
        self.app = app
        self.view = view

        self.left_side = Var("left_side")
        self.right_side = Var("right_side")
        self.top = Var("top")
        self.bottom = Var("bottom")
        self._solver = Solver()

        self.constraints = [
            self.left_side == 0,
            self.top == 0,
            self.right_side == self.app.columns,
            self.bottom == self.app.rows,
        ]

        for c in self.constraints:
            self._solver.addConstraint(c)

        self._solver.updateVariables()

    def repr(self):
        return (f"[[{self.left_side.value()},{self.top.value()}],"
                f"[{self.right_side.value()},{self.bottom.value()}]]")
Пример #2
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def test_solver_creation():
    """Test initializing a solver.

    """
    s = Solver()
    assert isinstance(s, Solver)

    with pytest.raises(TypeError):
        Solver(Variable())
def test_basic_solver():
    s = Solver()
    x0 = Variable('x0')
    x1 = Variable('x1')
    s.addConstraint(x0 >= 0)
    s.addConstraint(x1 >= 0)
    s.updateVariables()

    assert x0.value() == 0.0
    assert x1.value() == 0.0
Пример #4
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def add_linear_containment(solver: kiwisolver.Solver, env: Dict[str, kiwisolver.Variable], parent: IView[NT]) -> None:
    pl, pr = kiwi_lookup(parent.left_anchor, env), kiwi_lookup(parent.right_anchor, env)
    pt, pb = kiwi_lookup(parent.top_anchor, env), kiwi_lookup(parent.bottom_anchor, env)
    for child in parent.children:
        cl, cr = kiwi_lookup(child.left_anchor, env), kiwi_lookup(child.right_anchor, env)
        ct, cb = kiwi_lookup(child.top_anchor, env), kiwi_lookup(child.bottom_anchor, env)

        solver.addConstraint((cl >= pl) | 'required')
        solver.addConstraint((cr <= pr) | 'required')
        solver.addConstraint((ct >= pt) | 'required')
        solver.addConstraint((cb <= pb) | 'required')
Пример #5
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def test_solving_under_constrained_system():
    """Test solving an under constrained system.

    """
    s = Solver()
    v = Variable('foo')
    c = 2 * v + 1 >= 0
    s.addEditVariable(v, 'weak')
    s.addConstraint(c)
    s.suggestValue(v, 10)
    s.updateVariables()

    assert c.expression().value() == 21
    assert c.expression().terms()[0].value() == 20
    assert c.expression().terms()[0].variable().value() == 10
Пример #6
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def test_solving_under_constrained_system():
    """Test solving an under constrained system.

    """
    s = Solver()
    v = Variable('foo')
    c = 2*v + 1 >= 0
    s.addEditVariable(v, 'weak')
    s.addConstraint(c)
    s.suggestValue(v, 10)
    s.updateVariables()

    assert c.expression().value() == 21
    assert c.expression().terms()[0].value() == 20
    assert c.expression().terms()[0].variable().value() == 10
Пример #7
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    def __init__(self, view, app):
        self.app = app
        self.view = view

        self.left_side = Var("left_side")
        self.right_side = Var("right_side")
        self.top = Var("top")
        self.bottom = Var("bottom")
        self._solver = Solver()

        self.constraints = [
            self.left_side == 0,
            self.top == 0,
            self.right_side == self.app.columns,
            self.bottom == self.app.rows,
        ]

        for c in self.constraints:
            self._solver.addConstraint(c)

        self._solver.updateVariables()
Пример #8
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    def __init__(self, spacing=6, **kwargs):
        """Create solver and basic grid parameters."""
        self._next_cell = [0, 0]  # row, col
        self._cells = {}
        self._grid_widgets = {}
        self.spacing = spacing
        self._n_added = 0
        self._default_class = ViewBox  # what to add when __getitem__ is used
        self._solver = Solver()
        self._need_solver_recreate = True

        # width and height of the Rect used to place child widgets
        self._var_w = Variable("w_rect")
        self._var_h = Variable("h_rect")

        self._width_grid = None
        self._height_grid = None

        # self._height_stay = None
        # self._width_stay = None

        Widget.__init__(self, **kwargs)
def test_basic_solver():
    s = Solver()
    x0 = Variable('x0')
    x1 = Variable('x1')
    s.addConstraint(x0 >= 0)
    s.addConstraint(x1 >= 0)
    s.updateVariables()

    assert x0.value() == 0.0
    assert x1.value() == 0.0
Пример #10
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def add_linear_axioms(solver: kiwisolver.Solver, targets: List[IView[NT]], env: Dict[str, kiwisolver.Variable]) -> None:
    for box in targets:
        strength = 'required'

        for anchor in box.anchors:
            kiwivar = kiwi_lookup(anchor, env)
            solver.addConstraint((kiwivar <= 10000.0) | 'weak')
            solver.addConstraint((kiwivar >= 0.0) | strength)

        w, h = kiwi_lookup(box.width_anchor, env), kiwi_lookup(box.height_anchor, env)
        l, r = kiwi_lookup(box.left_anchor, env), kiwi_lookup(box.right_anchor, env)
        b, t = kiwi_lookup(box.bottom_anchor, env), kiwi_lookup(box.top_anchor, env)
        c_x = kiwi_lookup(box.center_x_anchor, env)
        c_y = kiwi_lookup(box.center_y_anchor, env)

        # print('adding axioms for', w, h, l, r, b, t, c_x, c_y)

        solver.addConstraint((w == (r - l)) | strength)
        solver.addConstraint((h == (b - t)) | strength)
        solver.addConstraint((c_x == (l + r) / 2.0) | strength)
        solver.addConstraint((c_y == (t + b) / 2.0) | strength)
Пример #11
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def test_solving_with_strength():
    """Test solving a system with unstatisfiable non-required constraint.

    """
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addConstraint(v1 + v2 == 0)
    s.addConstraint(v1 == 10)
    s.addConstraint((v2 >= 0) | 'weak')
    s.updateVariables()
    assert v1.value() == 10 and v2.value() == -10

    s.reset()

    s.addConstraint(v1 + v2 == 0)
    s.addConstraint((v1 >= 10) | 'medium')
    s.addConstraint((v2 == 2) | 'strong')
    s.updateVariables()
    assert v1.value() == -2 and v2.value() == 2
Пример #12
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#------------------------------------------------------------------------------
# Copyright (c) 2019, Nucleic Development Team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file LICENSE, distributed with this software.
#------------------------------------------------------------------------------
"""Time updating an EditVariable in a set of constraints typical of enaml use.

"""
import perf
from kiwisolver import Variable, Solver, strength

solver = Solver()

# Create custom strength
mmedium = strength.create(0, 1, 0, 1.25)
smedium = strength.create(0, 100, 0)

# Create the variable
left = Variable('left')
height = Variable('height')
top = Variable('top')
width = Variable('width')
contents_top = Variable('contents_top')
contents_bottom = Variable('contents_bottom')
contents_left = Variable('contents_left')
contents_right = Variable('contents_right')
midline = Variable('midline')
ctleft = Variable('ctleft')
ctheight = Variable('ctheight')
Пример #13
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def test_solving_with_strength():
    """Test solving a system with unstatisfiable non-required constraint.

    """
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addConstraint(v1 + v2 == 0)
    s.addConstraint(v1 == 10)
    s.addConstraint((v2 >= 0) | 'weak')
    s.updateVariables()
    assert v1.value() == 10 and v2.value() == -10

    s.reset()

    s.addConstraint(v1 + v2 == 0)
    s.addConstraint((v1 >= 10) | 'medium')
    s.addConstraint((v2 == 2) | 'strong')
    s.updateVariables()
    assert v1.value() == -2 and v2.value() == 2
Пример #14
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def test_dumping_solver(capsys):
    """Test dumping the solver internal to stdout.

    """
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addEditVariable(v2, 'weak')
    s.addConstraint(v1 + v2 == 0)
    s.addConstraint((v2 <= -1))
    s.addConstraint((v2 >= 0) | 'weak')
    s.updateVariables()
    try:
        s.addConstraint((v2 >= 1))
    except Exception:
        pass

    # Print the solver state
    s.dump()

    state = s.dumps()
    for header in ('Objective', 'Tableau', 'Infeasible', 'Variables',
                   'Edit Variables', 'Constraints'):
        assert header in state
Пример #15
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    def _constrain(self, max_length: int):
        """
        Internal method that constrains the Segment to a maximum length using kiwisolver.

        DO NOT CALL THIS DIRECTLY!
        """
        solver = Solver()

        # First add the hard constraints
        for constraint in self.hard_constraints:
            solver.addConstraint(constraint)

        # Want it to be exactly equal to the minimum of the max_length and
        # underlying number of tokens. This makes sure the constraint solver
        # doesn't try to short change and find a solution that uses less than
        # the available length.
        solver.addConstraint(
            sum(self.length_variables) == min(max_length, self.num_tokens))

        # Then add the medium constraints
        for constraint in self.strong_constraints:
            solver.addConstraint(constraint)

        # Finally add the strong constraints
        for constraint in self.strong_constraints:
            solver.addConstraint(constraint)

        solver.updateVariables()
def test_solver():
    s = Solver()
    x0 = Variable('x0')
    x1 = Variable('x1')
    s.addConstraint(x0 >= 0)
    s.addConstraint(x1 >= 0)
    s.addConstraint(x1 == x0)
    s.updateVariables()

    assert x0.value() == 0.0
    assert x1.value() == 0.0

    with edit_context(s, [x1]):
        s.suggestValue(x1, 1.0)
        s.updateVariables()
        assert x0.value() == 1.0
        assert x1.value() == 1.0
Пример #17
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def test_managing_constraints():
    """Test adding/removing constraints.

    """
    s = Solver()
    v = Variable('foo')
    v2 = Variable('bar')
    c1 = v >= 1
    c2 = v <= 0
    c3 = ((v2 >= 1) and (v2 <= 0))

    with pytest.raises(TypeError):
        s.hasConstraint(object())
    with pytest.raises(TypeError):
        s.addConstraint(object())
    with pytest.raises(TypeError):
        s.removeConstraint(object())

    assert not s.hasConstraint(c1)
    s.addConstraint(c1)
    assert s.hasConstraint(c1)
    with pytest.raises(DuplicateConstraint):
        s.addConstraint(c1)
    with pytest.raises(UnknownConstraint):
        s.removeConstraint(c2)
    with pytest.raises(UnsatisfiableConstraint):
        s.addConstraint(c2)
    # XXX need to find how to get an invalid symbol from choose subject
    # with pytest.raises(UnsatisfiableConstraint):
    #     s.addConstraint(c3)
    s.removeConstraint(c1)
    assert not s.hasConstraint(c1)

    s.addConstraint(c2)
    assert s.hasConstraint(c2)
    s.reset()
    assert not s.hasConstraint(c2)
Пример #18
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def test_managing_edit_variable():
    """Test adding/removing edit variables.

    """
    s = Solver()
    v1 = Variable('foo')
    v2 = Variable('bar')

    with pytest.raises(TypeError):
        s.hasEditVariable(object())
    with pytest.raises(TypeError):
        s.addEditVariable(object(), 'weak')
    with pytest.raises(TypeError):
        s.removeEditVariable(object())
    with pytest.raises(TypeError):
        s.suggestValue(object(), 10)

    assert not s.hasEditVariable(v1)
    s.addEditVariable(v1, 'weak')
    assert s.hasEditVariable(v1)
    with pytest.raises(DuplicateEditVariable):
        s.addEditVariable(v1, 'medium')
    with pytest.raises(UnknownEditVariable):
        s.removeEditVariable(v2)
    s.removeEditVariable(v1)
    assert not s.hasEditVariable(v1)

    with pytest.raises(BadRequiredStrength):
        s.addEditVariable(v1, 'required')

    s.addEditVariable(v2, 'strong')
    assert s.hasEditVariable(v2)
    with pytest.raises(UnknownEditVariable):
        s.suggestValue(v1, 10)

    s.reset()
    assert not s.hasEditVariable(v2)
Пример #19
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def test_managing_constraints():
    """Test adding/removing constraints.

    """
    s = Solver()
    v = Variable('foo')
    c1 = v >= 1
    c2 = v <= 0

    with pytest.raises(TypeError):
        s.hasConstraint(object())
    with pytest.raises(TypeError):
        s.addConstraint(object())
    with pytest.raises(TypeError):
        s.removeConstraint(object())

    assert not s.hasConstraint(c1)
    s.addConstraint(c1)
    assert s.hasConstraint(c1)
    with pytest.raises(DuplicateConstraint):
        s.addConstraint(c1)
    with pytest.raises(UnknownConstraint):
        s.removeConstraint(c2)
    with pytest.raises(UnsatisfiableConstraint):
        s.addConstraint(c2)
    s.removeConstraint(c1)
    assert not s.hasConstraint(c1)

    s.addConstraint(c2)
    assert s.hasConstraint(c2)
    s.reset()
    assert not s.hasConstraint(c2)
Пример #20
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def test_dumping_solver(capsys):
    """Test dumping the solver internal to stdout.

    """
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addConstraint(v1 + v2 == 0)
    s.addConstraint(v1 == 10)
    s.addConstraint((v2 >= 0) | 'weak')
    s.updateVariables()

    s.dump()
Пример #21
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def test_suggesting_values_for_edit_variables():
    """Test suggesting values in different situations.

    """
    # Suggest value for an edit variable entering a weak equality
    s = Solver()
    v1 = Variable('foo')

    s.addEditVariable(v1, 'medium')
    s.addConstraint((v1 == 1) | 'weak')
    s.suggestValue(v1, 2)
    s.updateVariables()
    assert v1.value() == 2

    # Suggest a value for an edit variable entering multiple solver rows
    s.reset()
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addEditVariable(v2, 'weak')
    s.addConstraint(v1 + v2 == 0)
    s.addConstraint((v2 <= -1))
    s.addConstraint((v2 >= 0) | 'weak')
    s.suggestValue(v2, 0)
    s.updateVariables()
    assert v2.value() <= -1
Пример #22
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def test_managing_constraints():
    """Test adding/removing constraints.

    """
    s = Solver()
    v = Variable('foo')
    c1 = v >= 1
    c2 = v <= 0

    with pytest.raises(TypeError):
        s.hasConstraint(object())
    with pytest.raises(TypeError):
        s.addConstraint(object())
    with pytest.raises(TypeError):
        s.removeConstraint(object())

    assert not s.hasConstraint(c1)
    s.addConstraint(c1)
    assert s.hasConstraint(c1)
    with pytest.raises(DuplicateConstraint):
        s.addConstraint(c1)
    with pytest.raises(UnknownConstraint):
        s.removeConstraint(c2)
    with pytest.raises(UnsatisfiableConstraint):
        s.addConstraint(c2)
    s.removeConstraint(c1)
    assert not s.hasConstraint(c1)

    s.addConstraint(c2)
    assert s.hasConstraint(c2)
    s.reset()
    assert not s.hasConstraint(c2)
Пример #23
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def test_managing_constraints():
    """Test adding/removing constraints.

    """
    s = Solver()
    v = Variable('foo')
    v2 = Variable('bar')
    c1 = v >= 1
    c2 = v <= 0
    c3 = ((v2 >= 1) and (v2 <= 0))

    with pytest.raises(TypeError):
        s.hasConstraint(object())
    with pytest.raises(TypeError):
        s.addConstraint(object())
    with pytest.raises(TypeError):
        s.removeConstraint(object())

    assert not s.hasConstraint(c1)
    s.addConstraint(c1)
    assert s.hasConstraint(c1)
    with pytest.raises(DuplicateConstraint):
        s.addConstraint(c1)
    with pytest.raises(UnknownConstraint):
        s.removeConstraint(c2)
    with pytest.raises(UnsatisfiableConstraint):
        s.addConstraint(c2)
    # XXX need to find how to get an invalid symbol from choose subject
    # with pytest.raises(UnsatisfiableConstraint):
    #     s.addConstraint(c3)
    s.removeConstraint(c1)
    assert not s.hasConstraint(c1)

    s.addConstraint(c2)
    assert s.hasConstraint(c2)
    s.reset()
    assert not s.hasConstraint(c2)
Пример #24
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def test_suggesting_values_for_edit_variables():
    """Test suggesting values in different situations.

    """
    # Suggest value for an edit variable entering a weak equality
    s = Solver()
    v1 = Variable('foo')

    s.addEditVariable(v1, 'medium')
    s.addConstraint((v1 == 1) | 'weak')
    s.suggestValue(v1, 2)
    s.updateVariables()
    assert v1.value() == 2

    # Suggest a value for an edit variable entering multiple solver rows
    s.reset()
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addEditVariable(v2, 'weak')
    s.addConstraint(v1 + v2 == 0)
    s.addConstraint((v2 <= -1))
    s.addConstraint((v2 >= 0) | 'weak')
    s.suggestValue(v2, 0)
    s.updateVariables()
    assert v2.value() <= -1
Пример #25
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def test_handling_infeasible_constraints():
    """Test that we properly handle infeasible constraints.

    We use the example of the cassowary paper to generate an infeasible
    situation after updating an edit variable which causes the solver to use
    the dual optimization.

    """
    xm = Variable('xm')
    xl = Variable('xl')
    xr = Variable('xr')
    s = Solver()

    s.addEditVariable(xm, 'strong')
    s.addEditVariable(xl, 'weak')
    s.addEditVariable(xr, 'weak')
    s.addConstraint(2 * xm == xl + xr)
    s.addConstraint(xl + 20 <= xr)
    s.addConstraint(xl >= -10)
    s.addConstraint(xr <= 100)

    s.suggestValue(xm, 40)
    s.suggestValue(xr, 50)
    s.suggestValue(xl, 30)

    # First update causing a normal update.
    s.suggestValue(xm, 60)

    # Create an infeasible condition triggering a dual optimization
    s.suggestValue(xm, 90)
    s.updateVariables()
    assert xl.value() + xr.value() == 2 * xm.value()
    assert xl.value() == 80
    assert xr.value() == 100
Пример #26
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def test_dumping_solver(capsys):
    """Test dumping the solver internal to stdout.

    """
    v1 = Variable('foo')
    v2 = Variable('bar')
    s = Solver()

    s.addEditVariable(v2, 'weak')
    s.addConstraint(v1 + v2 == 0)
    s.addConstraint((v2 <= -1))
    s.addConstraint((v2 >= 0) | 'weak')
    s.updateVariables()
    try:
        s.addConstraint((v2 >= 1))
    except Exception:
        pass

    # Print the solver state
    s.dump()

    state = s.dumps()
    for header in ('Objective', 'Tableau', 'Infeasible', 'Variables',
                   'Edit Variables', 'Constraints'):
        assert header in state
Пример #27
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def test_managing_edit_variable():
    """Test adding/removing edit variables.

    """
    s = Solver()
    v1 = Variable('foo')
    v2 = Variable('bar')

    with pytest.raises(TypeError):
        s.hasEditVariable(object())
    with pytest.raises(TypeError):
        s.addEditVariable(object(), 'weak')
    with pytest.raises(TypeError):
        s.removeEditVariable(object())
    with pytest.raises(TypeError):
        s.suggestValue(object(), 10)

    assert not s.hasEditVariable(v1)
    s.addEditVariable(v1, 'weak')
    assert s.hasEditVariable(v1)
    with pytest.raises(DuplicateEditVariable):
        s.addEditVariable(v1, 'medium')
    with pytest.raises(UnknownEditVariable):
        s.removeEditVariable(v2)
    s.removeEditVariable(v1)
    assert not s.hasEditVariable(v1)

    with pytest.raises(BadRequiredStrength):
        s.addEditVariable(v1, 'required')

    s.addEditVariable(v2, 'strong')
    assert s.hasEditVariable(v2)
    with pytest.raises(UnknownEditVariable):
        s.suggestValue(v1, 10)

    s.reset()
    assert not s.hasEditVariable(v2)
Пример #28
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def test_handling_infeasible_constraints():
    """Test that we properly handle infeasible constraints.

    We use the example of the cassowary paper to generate an infeasible
    situation after updating an edit variable which causes the solver to use
    the dual optimization.

    """
    xm = Variable('xm')
    xl = Variable('xl')
    xr = Variable('xr')
    s = Solver()

    s.addEditVariable(xm, 'strong')
    s.addEditVariable(xl, 'weak')
    s.addEditVariable(xr, 'weak')
    s.addConstraint(2*xm == xl + xr)
    s.addConstraint(xl + 20 <= xr)
    s.addConstraint(xl >= -10)
    s.addConstraint(xr <= 100)

    s.suggestValue(xm, 40)
    s.suggestValue(xr, 50)
    s.suggestValue(xl, 30)

    # First update causing a normal update.
    s.suggestValue(xm, 60)

    # Create an infeasible condition triggering a dual optimization
    s.suggestValue(xm, 90)
    s.updateVariables()
    assert xl.value() + xr.value() == 2*xm.value()
    assert xl.value() == 80
    assert xr.value() == 100
def test_solver():
    s = Solver()
    x0 = Variable('x0')
    x1 = Variable('x1')
    s.addConstraint(x0 >= 0)
    s.addConstraint(x1 >= 0)
    s.addConstraint(x1 == x0)
    s.updateVariables()

    assert x0.value() == 0.0
    assert x1.value() == 0.0

    with edit_context(s, [x1]):
        s.suggestValue(x1, 1.0)
        s.updateVariables()
        assert x0.value() == 1.0
        assert x1.value() == 1.0
Пример #30
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class Grid(Widget):
    """Widget for proportionally dividing its internal area into a grid.

    This widget will automatically set the position and size of child widgets
    according to provided constraints.

    Parameters
    ----------
    spacing : int
        Spacing between widgets.
    **kwargs : dict
        Keyword arguments to pass to `Widget`.
    """
    def __init__(self, spacing=6, **kwargs):
        """Create solver and basic grid parameters."""
        self._next_cell = [0, 0]  # row, col
        self._cells = {}
        self._grid_widgets = {}
        self.spacing = spacing
        self._n_added = 0
        self._default_class = ViewBox  # what to add when __getitem__ is used
        self._solver = Solver()
        self._need_solver_recreate = True

        # width and height of the Rect used to place child widgets
        self._var_w = Variable("w_rect")
        self._var_h = Variable("h_rect")

        self._width_grid = None
        self._height_grid = None

        # self._height_stay = None
        # self._width_stay = None

        Widget.__init__(self, **kwargs)

    def __getitem__(self, idxs):
        """Return an item or create it if the location is available."""
        if not isinstance(idxs, tuple):
            idxs = (idxs, )
        if len(idxs) == 1:
            idxs = idxs + (slice(0, 1, None), )
        elif len(idxs) != 2:
            raise ValueError('Incorrect index: %s' % (idxs, ))
        lims = np.empty((2, 2), int)
        for ii, idx in enumerate(idxs):
            if isinstance(idx, int):
                idx = slice(idx, idx + 1, None)
            if not isinstance(idx, slice):
                raise ValueError('indices must be slices or integers, not %s' %
                                 (type(idx), ))
            if idx.step is not None and idx.step != 1:
                raise ValueError('step must be one or None, not %s' % idx.step)
            start = 0 if idx.start is None else idx.start
            end = self.grid_size[ii] if idx.stop is None else idx.stop
            lims[ii] = [start, end]
        layout = self.layout_array
        existing = layout[lims[0, 0]:lims[0, 1], lims[1, 0]:lims[1, 1]] + 1
        if existing.any():
            existing = set(list(existing.ravel()))
            ii = list(existing)[0] - 1
            if len(existing) != 1 or (
                (layout == ii).sum() != np.prod(np.diff(lims))):
                raise ValueError('Cannot add widget (collision)')
            return self._grid_widgets[ii][-1]
        spans = np.diff(lims)[:, 0]
        item = self.add_widget(self._default_class(),
                               row=lims[0, 0],
                               col=lims[1, 0],
                               row_span=spans[0],
                               col_span=spans[1])
        return item

    def add_widget(self,
                   widget=None,
                   row=None,
                   col=None,
                   row_span=1,
                   col_span=1,
                   **kwargs):
        """Add a new widget to this grid.

        This will cause other widgets in the grid to be resized to make room
        for the new widget. Can be used to replace a widget as well.

        Parameters
        ----------
        widget : Widget | None
            The Widget to add. New widget is constructed if widget is None.
        row : int
            The row in which to add the widget (0 is the topmost row)
        col : int
            The column in which to add the widget (0 is the leftmost column)
        row_span : int
            The number of rows to be occupied by this widget. Default is 1.
        col_span : int
            The number of columns to be occupied by this widget. Default is 1.
        **kwargs : dict
            parameters sent to the new Widget that is constructed if
            widget is None

        Notes
        -----
        The widget's parent is automatically set to this grid, and all other
        parent(s) are removed.
        """
        if row is None:
            row = self._next_cell[0]
        if col is None:
            col = self._next_cell[1]

        if widget is None:
            widget = Widget(**kwargs)
        else:
            if kwargs:
                raise ValueError("cannot send kwargs if widget is given")

        _row = self._cells.setdefault(row, {})
        _row[col] = widget
        self._grid_widgets[self._n_added] = (row, col, row_span, col_span,
                                             widget)
        self._n_added += 1
        widget.parent = self

        self._next_cell = [row, col + col_span]

        widget._var_w = Variable("w-(row: %s | col: %s)" % (row, col))
        widget._var_h = Variable("h-(row: %s | col: %s)" % (row, col))

        # update stretch based on colspan/rowspan
        # usually, if you make something consume more grids or columns,
        # you also want it to actually *take it up*, ratio wise.
        # otherwise, it will never *use* the extra rows and columns,
        # thereby collapsing the extras to 0.
        stretch = list(widget.stretch)
        stretch[0] = col_span if stretch[0] is None else stretch[0]
        stretch[1] = row_span if stretch[1] is None else stretch[1]
        widget.stretch = stretch

        self._need_solver_recreate = True

        return widget

    def remove_widget(self, widget):
        """Remove a widget from this grid.

        Parameters
        ----------
        widget : Widget
            The Widget to remove
        """
        self._grid_widgets = dict((key, val)
                                  for (key, val) in self._grid_widgets.items()
                                  if val[-1] != widget)

        self._need_solver_recreate = True

    def resize_widget(self, widget, row_span, col_span):
        """Resize a widget in the grid to new dimensions.

        Parameters
        ----------
        widget : Widget
            The widget to resize
        row_span : int
            The number of rows to be occupied by this widget.
        col_span : int
            The number of columns to be occupied by this widget.
        """
        row = None
        col = None

        for (r, c, _rspan, _cspan, w) in self._grid_widgets.values():
            if w == widget:
                row = r
                col = c

                break

        if row is None or col is None:
            raise ValueError("%s not found in grid" % widget)

        self.remove_widget(widget)
        self.add_widget(widget, row, col, row_span, col_span)
        self._need_solver_recreate = True

    def _prepare_draw(self, view):
        self._update_child_widget_dim()

    def add_grid(self, row=None, col=None, row_span=1, col_span=1, **kwargs):
        """
        Create a new Grid and add it as a child widget.

        Parameters
        ----------
        row : int
            The row in which to add the widget (0 is the topmost row)
        col : int
            The column in which to add the widget (0 is the leftmost column)
        row_span : int
            The number of rows to be occupied by this widget. Default is 1.
        col_span : int
            The number of columns to be occupied by this widget. Default is 1.
        **kwargs : dict
            Keyword arguments to pass to the new `Grid`.
        """
        from .grid import Grid
        grid = Grid(**kwargs)
        return self.add_widget(grid, row, col, row_span, col_span)

    def add_view(self, row=None, col=None, row_span=1, col_span=1, **kwargs):
        """
        Create a new ViewBox and add it as a child widget.

        Parameters
        ----------
        row : int
            The row in which to add the widget (0 is the topmost row)
        col : int
            The column in which to add the widget (0 is the leftmost column)
        row_span : int
            The number of rows to be occupied by this widget. Default is 1.
        col_span : int
            The number of columns to be occupied by this widget. Default is 1.
        **kwargs : dict
            Keyword arguments to pass to `ViewBox`.
        """
        view = ViewBox(**kwargs)
        return self.add_widget(view, row, col, row_span, col_span)

    def next_row(self):
        self._next_cell = [self._next_cell[0] + 1, 0]

    @property
    def grid_size(self):
        rvals = [
            widget[0] + widget[2] for widget in self._grid_widgets.values()
        ]
        cvals = [
            widget[1] + widget[3] for widget in self._grid_widgets.values()
        ]
        return max(rvals + [0]), max(cvals + [0])

    @property
    def layout_array(self):
        locs = -1 * np.ones(self.grid_size, int)
        for key in self._grid_widgets.keys():
            r, c, rs, cs = self._grid_widgets[key][:4]
            locs[r:r + rs, c:c + cs] = key
        return locs

    def __repr__(self):
        return (('<Grid at %s:\n' % hex(id(self))) +
                str(self.layout_array + 1) + '>')

    @staticmethod
    def _add_total_width_constraints(solver, width_grid, _var_w):
        for ws in width_grid:
            width_expr = ws[0]
            for w in ws[1:]:
                width_expr += w
            solver.addConstraint(width_expr == _var_w)

    @staticmethod
    def _add_total_height_constraints(solver, height_grid, _var_h):
        for hs in height_grid:
            height_expr = hs[0]
            for h in hs[1:]:
                height_expr += h
            solver.addConstraint(height_expr == _var_h)

    @staticmethod
    def _add_gridding_width_constraints(solver, width_grid):
        # access widths of one "y", different x
        for ws in width_grid.T:
            for w in ws[1:]:
                solver.addConstraint(ws[0] == w)

    @staticmethod
    def _add_gridding_height_constraints(solver, height_grid):
        # access heights of one "y"
        for hs in height_grid.T:
            for h in hs[1:]:
                solver.addConstraint(hs[0] == h)

    @staticmethod
    def _add_stretch_constraints(solver, width_grid, height_grid, grid_widgets,
                                 widget_grid):
        xmax = len(height_grid)
        ymax = len(width_grid)

        stretch_widths = [[] for _ in range(0, ymax)]
        stretch_heights = [[] for _ in range(0, xmax)]

        for (y, x, ys, xs, widget) in grid_widgets.values():
            for ws in width_grid[y:y + ys]:
                total_w = np.sum(ws[x:x + xs])

                for sw in stretch_widths[y:y + ys]:
                    sw.append((total_w, widget.stretch[0]))

            for hs in height_grid[x:x + xs]:
                total_h = np.sum(hs[y:y + ys])

                for sh in stretch_heights[x:x + xs]:
                    sh.append((total_h, widget.stretch[1]))

        for (x, xs) in enumerate(widget_grid):
            for (y, widget) in enumerate(xs):
                if widget is None:
                    stretch_widths[y].append((width_grid[y][x], 1))
                    stretch_heights[x].append((height_grid[x][y], 1))

        for sws in stretch_widths:
            if len(sws) <= 1:
                continue

            comparator = sws[0][0] / sws[0][1]

            for (stretch_term, stretch_val) in sws[1:]:
                solver.addConstraint((comparator == stretch_term / stretch_val)
                                     | 'weak')

        for sws in stretch_heights:
            if len(sws) <= 1:
                continue

            comparator = sws[0][0] / sws[0][1]

            for (stretch_term, stretch_val) in sws[1:]:
                solver.addConstraint((comparator == stretch_term / stretch_val)
                                     | 'weak')

    @staticmethod
    def _add_widget_dim_constraints(solver, width_grid, height_grid,
                                    total_var_w, total_var_h, grid_widgets):
        assert (total_var_w is not None)
        assert (total_var_h is not None)

        for ws in width_grid:
            for w in ws:
                solver.addConstraint(w >= 0, )

        for hs in height_grid:
            for h in hs:
                solver.addConstraint(h >= 0)

        for (_, val) in grid_widgets.items():
            (y, x, ys, xs, widget) = val

            for ws in width_grid[y:y + ys]:
                total_w = np.sum(ws[x:x + xs])
                # assert(total_w is not None)
                solver.addConstraint(total_w >= widget.width_min)

                if widget.width_max is not None:
                    solver.addConstraint(total_w <= widget.width_max)
                else:
                    solver.addConstraint(total_w <= total_var_w)

            for hs in height_grid[x:x + xs]:
                total_h = np.sum(hs[y:y + ys])
                solver.addConstraint(total_h >= widget.height_min)

                if widget.height_max is not None:
                    solver.addConstraint(total_h <= widget.height_max)
                else:
                    solver.addConstraint(total_h <= total_var_h)

    def _recreate_solver(self):
        self._solver.reset()
        self._var_w = Variable("w_rect")
        self._var_h = Variable("h_rect")
        self._solver.addEditVariable(self._var_w, 'strong')
        self._solver.addEditVariable(self._var_h, 'strong')

        rect = self.rect.padded(self.padding + self.margin)
        ymax, xmax = self.grid_size

        self._solver.suggestValue(self._var_w, rect.width)
        self._solver.suggestValue(self._var_h, rect.height)

        self._solver.addConstraint(self._var_w >= 0)
        self._solver.addConstraint(self._var_h >= 0)

        # self._height_stay = None
        # self._width_stay = None

        # add widths
        self._width_grid = np.array([[
            Variable("width(x: %s, y: %s)" % (x, y)) for x in range(0, xmax)
        ] for y in range(0, ymax)])

        # add heights
        self._height_grid = np.array([[
            Variable("height(x: %s, y: %s" % (x, y)) for y in range(0, ymax)
        ] for x in range(0, xmax)])

        # setup stretch
        stretch_grid = np.zeros(shape=(xmax, ymax, 2), dtype=float)
        stretch_grid.fill(1)

        for (_, val) in self._grid_widgets.items():
            (y, x, ys, xs, widget) = val
            stretch_grid[x:x + xs, y:y + ys] = widget.stretch

        # even though these are REQUIRED, these should never fail
        # since they're added first, and thus the slack will "simply work".
        Grid._add_total_width_constraints(self._solver, self._width_grid,
                                          self._var_w)
        Grid._add_total_height_constraints(self._solver, self._height_grid,
                                           self._var_h)

        try:
            # these are REQUIRED constraints for width and height.
            # These are the constraints which can fail if
            # the corresponding dimension of the widget cannot be fit in the
            # grid.
            Grid._add_gridding_width_constraints(self._solver,
                                                 self._width_grid)
            Grid._add_gridding_height_constraints(self._solver,
                                                  self._height_grid)
        except UnsatisfiableConstraint:
            self._need_solver_recreate = True

        # these are WEAK constraints, so these constraints will never fail
        # with a RequiredFailure.
        Grid._add_stretch_constraints(self._solver, self._width_grid,
                                      self._height_grid, self._grid_widgets,
                                      self._widget_grid)

        Grid._add_widget_dim_constraints(self._solver, self._width_grid,
                                         self._height_grid, self._var_w,
                                         self._var_h, self._grid_widgets)

        self._solver.updateVariables()

    def _update_child_widget_dim(self):
        # think in terms of (x, y). (row, col) makes code harder to read
        ymax, xmax = self.grid_size
        if ymax <= 0 or xmax <= 0:
            return

        rect = self.rect  # .padded(self.padding + self.margin)
        if rect.width <= 0 or rect.height <= 0:
            return
        if self._need_solver_recreate:
            self._need_solver_recreate = False
            self._recreate_solver()

        # we only need to remove and add the height and width constraints of
        # the solver if they are not the same as the current value
        h_changed = abs(rect.height - self._var_h.value()) > 1e-4
        w_changed = abs(rect.width - self._var_w.value()) > 1e-4
        if h_changed:
            self._solver.suggestValue(self._var_h, rect.height)

        if w_changed:
            self._solver.suggestValue(self._var_w, rect.width)
        if h_changed or w_changed:
            self._solver.updateVariables()

        value_vectorized = np.vectorize(lambda x: x.value())

        for (_, val) in self._grid_widgets.items():
            (row, col, rspan, cspan, widget) = val

            width = np.sum(
                value_vectorized(self._width_grid[row][col:col + cspan]))
            height = np.sum(
                value_vectorized(self._height_grid[col][row:row + rspan]))
            if col == 0:
                x = 0
            else:
                x = np.sum(value_vectorized(self._width_grid[row][0:col]))

            if row == 0:
                y = 0
            else:
                y = np.sum(value_vectorized(self._height_grid[col][0:row]))

            if isinstance(widget, ViewBox):
                widget.rect = Rect(x, y, width, height)
            else:
                widget.size = (width, height)
                widget.pos = (x, y)

    @property
    def _widget_grid(self):
        ymax, xmax = self.grid_size
        widget_grid = np.array([[None for _ in range(0, ymax)]
                                for _ in range(0, xmax)])
        for (_, val) in self._grid_widgets.items():
            (y, x, ys, xs, widget) = val
            widget_grid[x:x + xs, y:y + ys] = widget

        return widget_grid