Python math.copysign() Examples

def get_strategy_path_type(self, strategy_path_id, size1, current):
        """Decodes the path from the optimal strategy to its type.

        Params:
          strategy_path_id: raw path id from strategy array.
          size1: offset used to distinguish between paths in the source and
            destination trees.
          it: node indexer
          current: current subtree processed in tree decomposition phase

        Return type of the strategy path: LEFT, RIGHT, INNER"""
        # pylint: disable=no-self-use
        if math.copysign(1, strategy_path_id) == -1:
            return LEFT
        path_id = abs(strategy_path_id) - 1
        if path_id >= size1:
            path_id = path_id - size1
        if path_id == (current.pre_ltr + current.size - 1):
            return RIGHT
        return INNER 

def assertFloatsAreIdentical(self, x, y):
        """assert that floats x and y are identical, in the sense that:
        (1) both x and y are nans, or
        (2) both x and y are infinities, with the same sign, or
        (3) both x and y are zeros, with the same sign, or
        (4) x and y are both finite and nonzero, and x == y

        """
        msg = 'floats {!r} and {!r} are not identical'

        if isnan(x) or isnan(y):
            if isnan(x) and isnan(y):
                return
        elif x == y:
            if x != 0.0:
                return
            # both zero; check that signs match
            elif copysign(1.0, x) == copysign(1.0, y):
                return
            else:
                msg += ': zeros have different signs'
        self.fail(msg.format(x, y)) 

def get_cubic_root(self):
    # We have the equation x^2 D^2 + (1-x)^4 * C / h_min^2
    # where x = sqrt(mu).
    # We substitute x, which is sqrt(mu), with x = y + 1.
    # It gives y^3 + py = q
    # where p = (D^2 h_min^2)/(2*C) and q = -p.
    # We use the Vieta's substution to compute the root.
    # There is only one real solution y (which is in [0, 1] ).
    # http://mathworld.wolfram.com/VietasSubstitution.html
    # eps in the numerator is to prevent momentum = 1 in case of zero gradient
    p = (self._dist_to_opt + eps)**2 * (self._h_min + eps)**2 / 2 / (self._grad_var + eps)
    w3 = (-math.sqrt(p**2 + 4.0 / 27.0 * p**3) - p) / 2.0
    w = math.copysign(1.0, w3) * math.pow(math.fabs(w3), 1.0/3.0)
    y = w - p / 3.0 / (w + eps)
    x = y + 1

    if DEBUG:
      logging.debug("p %f, den %f", p, self._grad_var + eps)
      logging.debug("w3 %f ", w3)
      logging.debug("y %f, den %f", y, w + eps)

    return x 

def assertFloatsAreIdentical(self, x, y):
        """assert that floats x and y are identical, in the sense that:
        (1) both x and y are nans, or
        (2) both x and y are infinities, with the same sign, or
        (3) both x and y are zeros, with the same sign, or
        (4) x and y are both finite and nonzero, and x == y

        """
        msg = 'floats {!r} and {!r} are not identical'

        if isnan(x) or isnan(y):
            if isnan(x) and isnan(y):
                return
        elif x == y:
            if x != 0.0:
                return
            # both zero; check that signs match
            elif copysign(1.0, x) == copysign(1.0, y):
                return
            else:
                msg += ': zeros have different signs'
        self.fail(msg.format(x, y)) 

def test_format_testfile(self):
        """the following is borrowed from stdlib"""
        import math
        format_testfile = 'formatfloat_testcases.txt'
        with open(os.path.join(self.test_dir, format_testfile)) as testfile:
            for line in testfile:
                print line
                if line.startswith('--'):
                    continue
                line = line.strip()
                if not line:
                    continue

                lhs, rhs = map(str.strip, line.split('->'))
                fmt, arg = lhs.split()
                arg = float(arg)
                self.assertEqual(fmt % arg, rhs)
                if not math.isnan(arg) and math.copysign(1.0, arg) > 0.0:
                    print("minus")
                    self.assertEqual(fmt % -arg, '-' + rhs) 

def assertFloatsAreIdentical(self, x, y):
        """assert that floats x and y are identical, in the sense that:
        (1) both x and y are nans, or
        (2) both x and y are infinities, with the same sign, or
        (3) both x and y are zeros, with the same sign, or
        (4) x and y are both finite and nonzero, and x == y

        """
        msg = 'floats {!r} and {!r} are not identical'

        if isnan(x) or isnan(y):
            if isnan(x) and isnan(y):
                return
        elif x == y:
            if x != 0.0:
                return
            # both zero; check that signs match
            elif copysign(1.0, x) == copysign(1.0, y):
                return
            else:
                msg += ': zeros have different signs'
        self.fail(msg.format(x, y)) 

def get_boundaries_intersections(self, z, d, trust_radius):
        """
        Solve the scalar quadratic equation ||z + t d|| == trust_radius.
        This is like a line-sphere intersection.
        Return the two values of t, sorted from low to high.
        """
        a = np.dot(d, d)
        b = 2 * np.dot(z, d)
        c = np.dot(z, z) - trust_radius**2
        sqrt_discriminant = math.sqrt(b*b - 4*a*c)

        # The following calculation is mathematically
        # equivalent to:
        # ta = (-b - sqrt_discriminant) / (2*a)
        # tb = (-b + sqrt_discriminant) / (2*a)
        # but produce smaller round off errors.
        # Look at Matrix Computation p.97
        # for a better justification.
        aux = b + math.copysign(sqrt_discriminant, b)
        ta = -aux / (2*a)
        tb = -2*c / aux
        return sorted([ta, tb]) 

def get_boundaries_intersections(self, z, d, trust_radius):
        """
        Solve the scalar quadratic equation ||z + t d|| == trust_radius.
        This is like a line-sphere intersection.
        Return the two values of t, sorted from low to high.
        """
        a = np.dot(d, d)
        b = 2 * np.dot(z, d)
        c = np.dot(z, z) - trust_radius**2
        sqrt_discriminant = math.sqrt(b*b - 4*a*c)

        # The following calculation is mathematically
        # equivalent to:
        # ta = (-b - sqrt_discriminant) / (2*a)
        # tb = (-b + sqrt_discriminant) / (2*a)
        # but produce smaller round off errors.
        # Look at Matrix Computation p.97
        # for a better justification.
        aux = b + math.copysign(sqrt_discriminant, b)
        ta = -aux / (2*a)
        tb = -2*c / aux
        return sorted([ta, tb]) 

def _sign(x):
    return int(copysign(1, x))

# vim:ts=4:sw=4:et 

def sign(x):
    return copysign(1, x) 

def sign(x):
    return copysign(1, x) 

def _givens_to_1(self, aii, ajj, aij):
        """Computes a 2x2 Givens matrix to put 1's on the diagonal for the input matrix.

        The input matrix is a 2x2 symmetric matrix M = [ aii aij ; aij ajj ].

        The output matrix g is a 2x2 anti-symmetric matrix of the form [ c s ; -s c ];
        the elements c and s are returned.

        Applying the output matrix to the input matrix (as b=g.T M g)
        results in a matrix with bii=1, provided tr(M) - det(M) >= 1
        and floating point issues do not occur. Otherwise, some other
        valid rotation is returned. When tr(M)==2, also bjj=1.

        """
        aiid = aii - 1.
        ajjd = ajj - 1.

        if ajjd == 0:
            # ajj==1, so swap aii and ajj to avoid division by zero
            return 0., 1.

        dd = math.sqrt(max(aij**2 - aiid*ajjd, 0))

        # The choice of t should be chosen to avoid cancellation [1]
        t = (aij + math.copysign(dd, aij)) / ajjd
        c = 1. / math.sqrt(1. + t*t)
        if c == 0:
            # Underflow
            s = 1.0
        else:
            s = c*t
        return c, s 

def _compute_offset(self):
        locs = self.locs
        if locs is None or not len(locs):
            self.offset = 0
            return
        # Restrict to visible ticks.
        vmin, vmax = sorted(self.axis.get_view_interval())
        locs = np.asarray(locs)
        locs = locs[(vmin <= locs) & (locs <= vmax)]
        if not len(locs):
            self.offset = 0
            return
        lmin, lmax = locs.min(), locs.max()
        # Only use offset if there are at least two ticks and every tick has
        # the same sign.
        if lmin == lmax or lmin <= 0 <= lmax:
            self.offset = 0
            return
        # min, max comparing absolute values (we want division to round towards
        # zero so we work on absolute values).
        abs_min, abs_max = sorted([abs(float(lmin)), abs(float(lmax))])
        sign = math.copysign(1, lmin)
        # What is the smallest power of ten such that abs_min and abs_max are
        # equal up to that precision?
        # Note: Internally using oom instead of 10 ** oom avoids some numerical
        # accuracy issues.
        oom_max = np.ceil(math.log10(abs_max))
        oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
                       if abs_min // 10 ** oom != abs_max // 10 ** oom)
        if (abs_max - abs_min) / 10 ** oom <= 1e-2:
            # Handle the case of straddling a multiple of a large power of ten
            # (relative to the span).
            # What is the smallest power of ten such that abs_min and abs_max
            # are no more than 1 apart at that precision?
            oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
                           if abs_max // 10 ** oom - abs_min // 10 ** oom > 1)
        # Only use offset if it saves at least _offset_threshold digits.
        n = self._offset_threshold - 1
        self.offset = (sign * (abs_max // 10 ** oom) * 10 ** oom
                       if abs_max // 10 ** oom >= 10**n
                       else 0) 

def scale_range(vmin, vmax, n=1, threshold=100):
    dv = abs(vmax - vmin)  # > 0 as nonsingular is called before.
    meanv = (vmax + vmin) / 2
    if abs(meanv) / dv < threshold:
        offset = 0
    else:
        offset = math.copysign(10 ** (math.log10(abs(meanv)) // 1), meanv)
    scale = 10 ** (math.log10(dv / n) // 1)
    return scale, offset 

def get_cubic_root(self):
    # We have the equation x^2 D^2 + (1-x)^4 * C / h_min^2
    # where x = sqrt(mu).
    # We substitute x, which is sqrt(mu), with x = y + 1.
    # It gives y^3 + py = q
    # where p = (D^2 h_min^2)/(2*C) and q = -p.
    # We use the Vieta's substution to compute the root.
    # There is only one real solution y (which is in [0, 1] ).
    # http://mathworld.wolfram.com/VietasSubstitution.html
    # eps in the numerator is to prevent momentum = 1 in case of zero gradient
    if np.isnan(self._dist_to_opt.cpu()) or np.isnan(self._h_min.cpu()) or np.isnan(self._grad_var) \
      or np.isinf(self._dist_to_opt.cpu()) or np.isinf(self._h_min.cpu()) or np.isinf(self._grad_var):
      logging.warning("Input to cubic solver has invalid nan/inf value!")
      raise Exception("Input to cubic solver has invalid nan/inf value!")

    p = (self._dist_to_opt + eps)**2 * (self._h_min + eps)**2 / 2 / (self._grad_var + eps)
    w3 = (-math.sqrt(p**2 + 4.0 / 27.0 * p**3) - p) / 2.0
    w = math.copysign(1.0, w3) * math.pow(math.fabs(w3), 1.0/3.0)
    y = w - p / 3.0 / (w + eps)
    x = y + 1

    if self._verbose:
      logging.debug("p %f, denominator %f", p, self._grad_var + eps)
      logging.debug("w3 %f ", w3)
      logging.debug("y %f, denominator %f", y, w + eps)

    if np.isnan(x.cpu()) or np.isinf(x.cpu()):
      logging.warning("Output from cubic is invalid nan/inf value!")
      raise Exception("Output from cubic is invalid nan/inf value!")

    return x.item() 

def _py2_round(x):
    # The polyline algorithm uses Python 2's way of rounding
    return int(math.copysign(math.floor(math.fabs(x) + 0.5), x)) 

def intersect_trust_region(x, s, Delta):
    """Find the intersection of a line with the boundary of a trust region.
    
    This function solves the quadratic equation with respect to t
    ||(x + s*t)||**2 = Delta**2.
    
    Returns
    -------
    t_neg, t_pos : tuple of float
        Negative and positive roots.
    
    Raises
    ------
    ValueError
        If `s` is zero or `x` is not within the trust region.
    """
    a = np.dot(s, s)
    if a == 0:
        raise ValueError("`s` is zero.")

    b = np.dot(x, s)

    c = np.dot(x, x) - Delta**2
    if c > 0:
        raise ValueError("`x` is not within the trust region.")

    d = np.sqrt(b*b - a*c)  # Root from one fourth of the discriminant.

    # Computations below avoid loss of significance, see "Numerical Recipes".
    q = -(b + copysign(d, b))
    t1 = q / a
    t2 = c / q

    if t1 < t2:
        return t1, t2
    else:
        return t2, t1 

def testTanh(self):
        self.assertRaises(TypeError, math.tanh)
        self.ftest('tanh(0)', math.tanh(0), 0)
        self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
        self.ftest('tanh(inf)', math.tanh(INF), 1)
        self.ftest('tanh(-inf)', math.tanh(NINF), -1)
        self.assertTrue(math.isnan(math.tanh(NAN)))
        # check that tanh(-0.) == -0. on IEEE 754 systems
        if float.__getformat__("double").startswith("IEEE"):
            self.assertEqual(math.tanh(-0.), -0.)
            self.assertEqual(math.copysign(1., math.tanh(-0.)),
                             math.copysign(1., -0.)) 

def _sign(x):
    return int(copysign(1, x))

# vim:ts=4:sw=4:et 

def scale_range(vmin, vmax, n=1, threshold=100):
    dv = abs(vmax - vmin)  # > 0 as nonsingular is called before.
    meanv = (vmax + vmin) / 2
    if abs(meanv) / dv < threshold:
        offset = 0
    else:
        offset = math.copysign(10 ** (math.log10(abs(meanv)) // 1), meanv)
    scale = 10 ** (math.log10(dv / n) // 1)
    return scale, offset 

def _compute_offset(self):
        locs = self.locs
        # Restrict to visible ticks.
        vmin, vmax = sorted(self.axis.get_view_interval())
        locs = np.asarray(locs)
        locs = locs[(vmin <= locs) & (locs <= vmax)]
        if not len(locs):
            self.offset = 0
            return
        lmin, lmax = locs.min(), locs.max()
        # Only use offset if there are at least two ticks and every tick has
        # the same sign.
        if lmin == lmax or lmin <= 0 <= lmax:
            self.offset = 0
            return
        # min, max comparing absolute values (we want division to round towards
        # zero so we work on absolute values).
        abs_min, abs_max = sorted([abs(float(lmin)), abs(float(lmax))])
        sign = math.copysign(1, lmin)
        # What is the smallest power of ten such that abs_min and abs_max are
        # equal up to that precision?
        # Note: Internally using oom instead of 10 ** oom avoids some numerical
        # accuracy issues.
        oom_max = np.ceil(math.log10(abs_max))
        oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
                       if abs_min // 10 ** oom != abs_max // 10 ** oom)
        if (abs_max - abs_min) / 10 ** oom <= 1e-2:
            # Handle the case of straddling a multiple of a large power of ten
            # (relative to the span).
            # What is the smallest power of ten such that abs_min and abs_max
            # are no more than 1 apart at that precision?
            oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
                           if abs_max // 10 ** oom - abs_min // 10 ** oom > 1)
        # Only use offset if it saves at least _offset_threshold digits.
        n = self._offset_threshold - 1
        self.offset = (sign * (abs_max // 10 ** oom) * 10 ** oom
                       if abs_max // 10 ** oom >= 10**n
                       else 0) 

def _sign(x):
    return int(copysign(1, x))

# vim:ts=4:sw=4:et 

def _ibis_sqlite_sign(arg):
    if not arg:
        return 0
    return math.copysign(1, arg) 

def testTanh(self):
        self.assertRaises(TypeError, math.tanh)
        self.ftest('tanh(0)', math.tanh(0), 0)
        self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
        self.ftest('tanh(inf)', math.tanh(INF), 1)
        self.ftest('tanh(-inf)', math.tanh(NINF), -1)
        self.assertTrue(math.isnan(math.tanh(NAN)))
        # check that tanh(-0.) == -0. on IEEE 754 systems
        if float.__getformat__("double").startswith("IEEE"):
            self.assertEqual(math.tanh(-0.), -0.)
            self.assertEqual(math.copysign(1., math.tanh(-0.)),
                             math.copysign(1., -0.)) 

def testCopysign(self):
        self.assertEqual(math.copysign(1, 42), 1.0)
        self.assertEqual(math.copysign(0., 42), 0.0)
        self.assertEqual(math.copysign(1., -42), -1.0)
        self.assertEqual(math.copysign(3, 0.), 3.0)
        self.assertEqual(math.copysign(4., -0.), -4.0)

        self.assertRaises(TypeError, math.copysign)
        # copysign should let us distinguish signs of zeros
        self.assertEqual(math.copysign(1., 0.), 1.)
        self.assertEqual(math.copysign(1., -0.), -1.)
        self.assertEqual(math.copysign(INF, 0.), INF)
        self.assertEqual(math.copysign(INF, -0.), NINF)
        self.assertEqual(math.copysign(NINF, 0.), INF)
        self.assertEqual(math.copysign(NINF, -0.), NINF)
        # and of infinities
        self.assertEqual(math.copysign(1., INF), 1.)
        self.assertEqual(math.copysign(1., NINF), -1.)
        self.assertEqual(math.copysign(INF, INF), INF)
        self.assertEqual(math.copysign(INF, NINF), NINF)
        self.assertEqual(math.copysign(NINF, INF), INF)
        self.assertEqual(math.copysign(NINF, NINF), NINF)
        self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
        self.assertTrue(math.isnan(math.copysign(NAN, INF)))
        self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
        self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
        # copysign(INF, NAN) may be INF or it may be NINF, since
        # we don't know whether the sign bit of NAN is set on any
        # given platform.
        self.assertTrue(math.isinf(math.copysign(INF, NAN)))
        # similarly, copysign(2., NAN) could be 2. or -2.
        self.assertEqual(abs(math.copysign(2., NAN)), 2.) 

def identical(self, x, y):
        # check that floats x and y are identical, or that both
        # are NaNs
        if isnan(x) or isnan(y):
            if isnan(x) == isnan(y):
                return
        elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)):
            return
        self.fail('%r not identical to %r' % (x, y)) 

def test_format_testfile(self):
        with open(format_testfile) as testfile:
            for line in open(format_testfile):
                if line.startswith('--'):
                    continue
                line = line.strip()
                if not line:
                    continue

                lhs, rhs = map(str.strip, line.split('->'))
                fmt, arg = lhs.split()
                arg = float(arg)
                self.assertEqual(fmt % arg, rhs)
                if not math.isnan(arg) and copysign(1.0, arg) > 0.0:
                    self.assertEqual(fmt % -arg, '-' + rhs) 

def assertEqualAndEqualSign(self, a, b):
        # fail unless a == b and a and b have the same sign bit;
        # the only difference from assertEqual is that this test
        # distinguishes -0.0 and 0.0.
        self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b))) 

def __init__(self,
                 dt,
                 asset,
                 amount,
                 stop=None,
                 limit=None,
                 filled=0,
                 commission=0,
                 id=None,
                 ):
        """
        @dt - datetime.datetime that the order was placed
        @asset - asset for the order.
        @amount - the number of shares to buy/sell
                  a positive sign indicates a buy
                  a negative sign indicates a sell
        @filled - how many shares of the order have been filled so far
        """

        self.id = self.make_id() if id is None else id
        self.dt = dt
        self.reason = None
        self.created = dt
        self.asset = asset
        self.amount = amount
        self.filled = filled
        self.commission = commission
        self._status = ORDER_STATUS.OPEN
        self.stop = stop
        self.limit = limit
        self.stop_reached = False
        self.limit_reached = False
        self.direction = math.copysign(1, self.amount)
        # just make it None as it should not be used in live trade.
        self.type = None
        self.broker_order_id = None 

def get_cubic_root(self):
        # We have the equation x^2 D^2 + (1-x)^4 * C / h_min^2
        # where x = sqrt(mu).
        # We substitute x, which is sqrt(mu), with x = y + 1.
        # It gives y^3 + py = q
        # where p = (D^2 h_min^2)/(2*C) and q = -p.
        # We use the Vieta's substution to compute the root.
        # There is only one real solution y (which is in [0, 1] ).
        # http://mathworld.wolfram.com/VietasSubstitution.html
        # eps in the numerator is to prevent momentum = 1 in case of zero gradient
        if np.isnan(self._dist_to_opt) or np.isnan(self._h_min) or np.isnan(self._grad_var) \
                or np.isinf(self._dist_to_opt) or np.isinf(self._h_min) or np.isinf(self._grad_var):
            logging.warning("Input to cubic solver has invalid nan/inf value!")
            raise Exception("Input to cubic solver has invalid nan/inf value!")

        p = (self._dist_to_opt + eps) ** 2 * (self._h_min + eps) ** 2 / 2 / (self._grad_var + eps)
        w3 = (-math.sqrt(p ** 2 + 4.0 / 27.0 * p ** 3) - p) / 2.0
        w = math.copysign(1.0, w3) * math.pow(math.fabs(w3), 1.0 / 3.0)
        y = w - p / 3.0 / (w + eps)
        x = y + 1

        if self._verbose:
            logging.debug("p %f, denominator %f", p, self._grad_var + eps)
            logging.debug("w3 %f ", w3)
            logging.debug("y %f, denominator %f", y, w + eps)

        if np.isnan(x) or np.isinf(x):
            logging.warning("Output from cubic is invalid nan/inf value!")
            raise Exception("Output from cubic is invalid nan/inf value!")

        return x