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require 'test_helper'
class SumTest < GSL::TestCase
N = 50
def setup
@t = GSL::Vector.alloc(N)
N.times { |n| @t[n] = 1.0 / (n + 1.0) ** 2 }
end
def _fill_vector(x = 1.0)
@t[0] = x
1.upto(N - 1) { |n| @t[n] = yield n, @t[n - 1] }
end
def _test_sum(expected, desc)
sum_accel, _ = GSL::Sum::Levin_utrunc.alloc(N).accel(@t)
assert_rel sum_accel, expected, 1e-8, 'trunc result, %s' % desc
sum_accel, err_est, = GSL::Sum::Levin_u.alloc(N).accel(@t)
assert_rel sum_accel, expected, 1e-8, 'full result, %s' % desc
sd_est = -Math.log10(err_est / sum_accel.abs)
sd_actual = -Math.log10(GSL::DBL_EPSILON + ((sum_accel - expected) / expected).abs)
refute sd_est > sd_actual + 1.0,
'full significant digits, %s (%g vs %g)' % [desc, sd_est, sd_actual]
end
def test_zeta_2
_test_sum(GSL::M_PI ** 2 / 6.0, 'zeta(2)')
end
def test_exp_10(x = 10.0)
_fill_vector { |n, t| t * (x / n) }
_test_sum(Math.exp(x), 'exp(%d)' % x)
end
def test_exp_neg_10
test_exp_10(-10.0)
end
def test_log(x = 0.5)
_fill_vector(x) { |n, t| t * (x * n) / (n + 1.0) }
_test_sum(-Math.log(1 - x), "-log(#{1 - x})")
end
def test_log2
test_log(-1.0)
end
def test_asymptotic_series
m = GSL::M_PI ** 2
_fill_vector(3.0 / m) { |n, t| -t * (4.0 * (n + 1.0) - 1.0) / m }
_test_sum(0.192594048773, 'asymptotic series')
end
def test_eulers_constant
_fill_vector { |n, _| 1 / (n + 1.0) + Math.log(n / (n + 1.0)) }
_test_sum(0.5772156649015328606065120900824, "Euler's constant")
end
def test_eta
N.times { |n| @t[n] = (n % 2 == 1 ? -1 : 1) * 1.0 / GSL.sqrt(n + 1.0) }
_test_sum(0.6048986434216305, 'eta(1/2)')
end
end
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