Python mpmath.log方法代码示例

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_boxcox(self):

        def mp_boxcox(x, lmbda):
            x = mpmath.mp.mpf(x)
            lmbda = mpmath.mp.mpf(lmbda)
            if lmbda == 0:
                return mpmath.mp.log(x)
            else:
                return mpmath.mp.powm1(x, lmbda) / lmbda

        assert_mpmath_equal(sc.boxcox,
                            exception_to_nan(mp_boxcox),
                            [Arg(a=0, inclusive_a=False), Arg()],
                            n=200,
                            dps=60,
                            rtol=1e-13) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath 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: import mpmath [as 别名]
# 或者: from mpmath 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: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def eta(lam):
    """Function from DLMF 8.12.1 shifted to be centered at 0."""
    if lam > 0:
        return mp.sqrt(2*(lam - mp.log(lam + 1)))
    elif lam < 0:
        return -mp.sqrt(2*(lam - mp.log(lam + 1)))
    else:
        return 0 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_beta():
    np.random.seed(1234)

    b = np.r_[np.logspace(-200, 200, 4),
              np.logspace(-10, 10, 4),
              np.logspace(-1, 1, 4),
              np.arange(-10, 11, 1),
              np.arange(-10, 11, 1) + 0.5,
              -1, -2.3, -3, -100.3, -10003.4]
    a = b

    ab = np.array(np.broadcast_arrays(a[:,None], b[None,:])).reshape(2, -1).T

    old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
    try:
        mpmath.mp.dps = 400

        assert_func_equal(sc.beta,
                          lambda a, b: float(mpmath.beta(a, b)),
                          ab,
                          vectorized=False,
                          rtol=1e-10,
                          ignore_inf_sign=True)

        assert_func_equal(
            sc.betaln,
            lambda a, b: float(mpmath.log(abs(mpmath.beta(a, b)))),
            ab,
            vectorized=False,
            rtol=1e-10)
    finally:
        mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec


#------------------------------------------------------------------------------
# Machinery for systematic tests
#------------------------------------------------------------------------------ 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_log(self):
        with mp.workdps(30):
            logcoeffs = mp.taylor(lambda x: mp.log(1 + x), 0, 10)
            expcoeffs = mp.taylor(lambda x: mp.exp(x) - 1, 0, 10)
            invlogcoeffs = lagrange_inversion(logcoeffs)
            mp_assert_allclose(invlogcoeffs, expcoeffs) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_beta():
    np.random.seed(1234)

    b = np.r_[np.logspace(-200, 200, 4),
              np.logspace(-10, 10, 4),
              np.logspace(-1, 1, 4),
              np.arange(-10, 11, 1),
              np.arange(-10, 11, 1) + 0.5,
              -1, -2.3, -3, -100.3, -10003.4]
    a = b

    ab = np.array(np.broadcast_arrays(a[:,None], b[None,:])).reshape(2, -1).T

    old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
    try:
        mpmath.mp.dps = 400

        assert_func_equal(sc.beta,
                          lambda a, b: float(mpmath.beta(a, b)),
                          ab,
                          vectorized=False,
                          rtol=1e-10,
                          ignore_inf_sign=True)

        assert_func_equal(
            sc.betaln,
            lambda a, b: float(mpmath.log(abs(mpmath.beta(a, b)))),
            ab,
            vectorized=False,
            rtol=1e-10)
    finally:
        mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec


# ------------------------------------------------------------------------------
# loggamma
# ------------------------------------------------------------------------------ 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_exprel(self):
        assert_mpmath_equal(sc.exprel,
                            lambda x: mpmath.expm1(x)/x if x != 0 else mpmath.mpf('1.0'),
                            [Arg(a=-np.log(np.finfo(np.double).max), b=np.log(np.finfo(np.double).max))])
        assert_mpmath_equal(sc.exprel,
                            lambda x: mpmath.expm1(x)/x if x != 0 else mpmath.mpf('1.0'),
                            np.array([1e-12, 1e-24, 0, 1e12, 1e24, np.inf]), rtol=1e-11)
        assert_(np.isinf(sc.exprel(np.inf)))
        assert_(sc.exprel(-np.inf) == 0) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_log1p_complex(self):
        assert_mpmath_equal(sc.log1p,
                            lambda x: mpmath.log(x+1),
                            [ComplexArg()], dps=60) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_log_ndtr(self):
        assert_mpmath_equal(sc.log_ndtr,
                            exception_to_nan(lambda z: mpmath.log(mpmath.ncdf(z))),
                            [Arg()], n=600, dps=300) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_log_ndtr_complex(self):
        assert_mpmath_equal(sc.log_ndtr,
                            exception_to_nan(lambda z: mpmath.log(mpmath.erfc(-z/np.sqrt(2.))/2.)),
                            [ComplexArg(a=complex(-10000, -100),
                                        b=complex(10000, 100))], n=200, dps=300) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_gammaln(self):
        # The real part of loggamma is log(|gamma(z)|).
        def f(z):
            return mpmath.loggamma(z).real

        assert_mpmath_equal(sc.gammaln, exception_to_nan(f), [Arg()]) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath import log [as 别名]
def test_lgam1p(self):
        def param_filter(x):
            # Filter the poles
            return np.where((np.floor(x) == x) & (x <= 0), False, True)

        def mp_lgam1p(z):
            # The real part of loggamma is log(|gamma(z)|)
            return mpmath.loggamma(1 + z).real

        assert_mpmath_equal(_lgam1p,
                            mp_lgam1p,
                            [Arg()], rtol=1e-13, dps=100,
                            param_filter=param_filter) 

# 需要导入模块: import mpmath [as 别名]
# 或者: from mpmath 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: import mpmath [as 别名]
# 或者: from mpmath 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)