Python mp.log方法代码示例

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def _compute_delta(log_moments, eps):
  """Compute delta for given log_moments and eps.

  Args:
    log_moments: the log moments of privacy loss, in the form of pairs
      of (moment_order, log_moment)
    eps: the target epsilon.
  Returns:
    delta
  """
  min_delta = 1.0
  for moment_order, log_moment in log_moments:
    if moment_order == 0:
      continue
    if math.isinf(log_moment) or math.isnan(log_moment):
      sys.stderr.write("The %d-th order is inf or Nan\n" % moment_order)
      continue
    if log_moment < moment_order * eps:
      min_delta = min(min_delta,
                      math.exp(log_moment - moment_order * eps))
  return min_delta 

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def _compute_eps(log_moments, delta):
  """Compute epsilon for given log_moments and delta.

  Args:
    log_moments: the log moments of privacy loss, in the form of pairs
      of (moment_order, log_moment)
    delta: the target delta.
  Returns:
    epsilon
  """
  min_eps = float("inf")
  for moment_order, log_moment in log_moments:
    if moment_order == 0:
      continue
    if math.isinf(log_moment) or math.isnan(log_moment):
      sys.stderr.write("The %d-th order is inf or Nan\n" % moment_order)
      continue
    min_eps = min(min_eps, (log_moment - math.log(delta)) / moment_order)
  return min_eps 

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def compute_b(sigma, q, lmbd, verbose=False):
  mu0, _, mu = distributions(sigma, q)

  b_lambda_fn = lambda z: mu0(z) * np.power(cropped_ratio(mu0(z), mu(z)), lmbd)
  b_lambda = integral_inf(b_lambda_fn)
  m = sigma ** 2 * (np.log((2. - q) / (1. - q)) + 1. / (2 * sigma ** 2))

  b_fn = lambda z: (np.power(mu0(z) / mu(z), lmbd) -
                    np.power(mu(-z) / mu0(z), lmbd))
  if verbose:
    print "M =", m
    print "f(-M) = {} f(M) = {}".format(b_fn(-m), b_fn(m))
    assert b_fn(-m) < 0 and b_fn(m) < 0

  b_lambda_int1_fn = lambda z: (mu0(z) *
                                np.power(cropped_ratio(mu0(z), mu(z)), lmbd))
  b_lambda_int2_fn = lambda z: (mu0(z) *
                                np.power(cropped_ratio(mu(z), mu0(z)), lmbd))
  b_int1 = integral_bounded(b_lambda_int1_fn, -m, m)
  b_int2 = integral_bounded(b_lambda_int2_fn, -m, m)

  a_lambda_m1 = compute_a(sigma, q, lmbd - 1)
  b_bound = a_lambda_m1 + b_int1 - b_int2

  if verbose:
    print "B: by numerical integration", b_lambda
    print "B must be no more than     ", b_bound
  print b_lambda, b_bound
  return _to_np_float64(b_lambda)


###########################
# MULTIPRECISION ROUTINES #
########################### 

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def compute_b_mp(sigma, q, lmbd, verbose=False):
  lmbd_int = int(math.ceil(lmbd))
  if lmbd_int == 0:
    return 1.0

  mu0, _, mu = distributions_mp(sigma, q)

  b_lambda_fn = lambda z: mu0(z) * (mu0(z) / mu(z)) ** lmbd_int
  b_lambda = integral_inf_mp(b_lambda_fn)

  m = sigma ** 2 * (mp.log((2 - q) / (1 - q)) + 1 / (2 * (sigma ** 2)))
  b_fn = lambda z: ((mu0(z) / mu(z)) ** lmbd_int -
                    (mu(-z) / mu0(z)) ** lmbd_int)
  if verbose:
    print "M =", m
    print "f(-M) = {} f(M) = {}".format(b_fn(-m), b_fn(m))
    assert b_fn(-m) < 0 and b_fn(m) < 0

  b_lambda_int1_fn = lambda z: mu0(z) * (mu0(z) / mu(z)) ** lmbd_int
  b_lambda_int2_fn = lambda z: mu0(z) * (mu(z) / mu0(z)) ** lmbd_int
  b_int1 = integral_bounded_mp(b_lambda_int1_fn, -m, m)
  b_int2 = integral_bounded_mp(b_lambda_int2_fn, -m, m)

  a_lambda_m1 = compute_a_mp(sigma, q, lmbd - 1)
  b_bound = a_lambda_m1 + b_int1 - b_int2

  if verbose:
    print "B by numerical integration", b_lambda
    print "B must be no more than    ", b_bound
  assert b_lambda < b_bound + 1e-5
  return _to_np_float64(b_lambda) 

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def compute_log_moment(q, sigma, steps, lmbd, verify=False, verbose=False):
  """Compute the log moment of Gaussian mechanism for given parameters.

  Args:
    q: the sampling ratio.
    sigma: the noise sigma.
    steps: the number of steps.
    lmbd: the moment order.
    verify: if False, only compute the symbolic version. If True, computes
      both symbolic and numerical solutions and verifies the results match.
    verbose: if True, print out debug information.
  Returns:
    the log moment with type np.float64, could be np.inf.
  """
  moment = compute_a(sigma, q, lmbd, verbose=verbose)
  if verify:
    mp.dps = 50
    moment_a_mp = compute_a_mp(sigma, q, lmbd, verbose=verbose)
    moment_b_mp = compute_b_mp(sigma, q, lmbd, verbose=verbose)
    np.testing.assert_allclose(moment, moment_a_mp, rtol=1e-10)
    if not np.isinf(moment_a_mp):
      # The following test fails for (1, np.inf)!
      np.testing.assert_array_less(moment_b_mp, moment_a_mp)
  if np.isinf(moment):
    return np.inf
  else:
    return np.log(moment) * steps 

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def compute_b(sigma, q, lmbd, verbose=False):
  mu0, _, mu = distributions(sigma, q)

  b_lambda_fn = lambda z: mu0(z) * np.power(cropped_ratio(mu0(z), mu(z)), lmbd)
  b_lambda = integral_inf(b_lambda_fn)
  m = sigma ** 2 * (np.log((2. - q) / (1. - q)) + 1. / (2 * sigma ** 2))

  b_fn = lambda z: (np.power(mu0(z) / mu(z), lmbd) -
                    np.power(mu(-z) / mu0(z), lmbd))
  if verbose:
    print("M =", m)
    print("f(-M) = {} f(M) = {}".format(b_fn(-m), b_fn(m)))
    assert b_fn(-m) < 0 and b_fn(m) < 0

  b_lambda_int1_fn = lambda z: (mu0(z) *
                                np.power(cropped_ratio(mu0(z), mu(z)), lmbd))
  b_lambda_int2_fn = lambda z: (mu0(z) *
                                np.power(cropped_ratio(mu(z), mu0(z)), lmbd))
  b_int1 = integral_bounded(b_lambda_int1_fn, -m, m)
  b_int2 = integral_bounded(b_lambda_int2_fn, -m, m)

  a_lambda_m1 = compute_a(sigma, q, lmbd - 1)
  b_bound = a_lambda_m1 + b_int1 - b_int2

  if verbose:
    print("B: by numerical integration", b_lambda)
    print("B must be no more than     ", b_bound)
  print(b_lambda, b_bound)
  return _to_np_float64(b_lambda)


###########################
# MULTIPRECISION ROUTINES #
########################### 

# 需要导入模块: from sympy.mpmath import mp [as 别名]
# 或者: from sympy.mpmath.mp import log [as 别名]
def compute_b_mp(sigma, q, lmbd, verbose=False):
  lmbd_int = int(math.ceil(lmbd))
  if lmbd_int == 0:
    return 1.0

  mu0, _, mu = distributions_mp(sigma, q)

  b_lambda_fn = lambda z: mu0(z) * (mu0(z) / mu(z)) ** lmbd_int
  b_lambda = integral_inf_mp(b_lambda_fn)

  m = sigma ** 2 * (mp.log((2 - q) / (1 - q)) + 1 / (2 * (sigma ** 2)))
  b_fn = lambda z: ((mu0(z) / mu(z)) ** lmbd_int -
                    (mu(-z) / mu0(z)) ** lmbd_int)
  if verbose:
    print("M =", m)
    print("f(-M) = {} f(M) = {}".format(b_fn(-m), b_fn(m)))
    assert b_fn(-m) < 0 and b_fn(m) < 0

  b_lambda_int1_fn = lambda z: mu0(z) * (mu0(z) / mu(z)) ** lmbd_int
  b_lambda_int2_fn = lambda z: mu0(z) * (mu(z) / mu0(z)) ** lmbd_int
  b_int1 = integral_bounded_mp(b_lambda_int1_fn, -m, m)
  b_int2 = integral_bounded_mp(b_lambda_int2_fn, -m, m)

  a_lambda_m1 = compute_a_mp(sigma, q, lmbd - 1)
  b_bound = a_lambda_m1 + b_int1 - b_int2

  if verbose:
    print("B by numerical integration", b_lambda)
    print("B must be no more than    ", b_bound)
  assert b_lambda < b_bound + 1e-5
  return _to_np_float64(b_lambda)