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require 'test_helper'
class DerivTest < GSL::TestCase
def setup
@f = [GSL::Function.alloc { |x| Math.exp(x) }]
@df = [GSL::Function.alloc { |x| Math.exp(x) }]
@f << GSL::Function.alloc { |x|
x >= 0.0 ? x * Math.sqrt(x) : 0.0
}
@df << GSL::Function.alloc { |x|
x >= 0.0 ? 1.5 * Math.sqrt(x) : 0.0
}
@f << GSL::Function.alloc { |x|
x != 0.0 ? Math.sin(1.0 / x) : 0.0
}
@df << GSL::Function.alloc { |x|
x != 0.0 ? -Math.cos(1.0 / x) / (x * x) : 0.0
}
@f << GSL::Function.alloc { |x| Math.exp(-x * x) }
@df << GSL::Function.alloc { |x| -2.0 * x * Math.exp(-x * x) }
@f << GSL::Function.alloc { |x| x * x }
@df << GSL::Function.alloc { |x| 2.0 * x }
@f << GSL::Function.alloc { |x| 1.0 / x }
@df << GSL::Function.alloc { |x| -1.0 / (x * x) }
end
{
'exp(x)' => 1.0,
'x^(3/2)' => 0.1,
'sin(1/x)' => 0.45,
'exp(-x^2)' => 0.5,
'x^2' => 0.0,
'1/x' => 10.0
}.each_with_index { |(f, x), i|
%w[central forward backward].each { |deriv|
define_method("test_#{deriv}_#{i}") {
_test_deriv(deriv, @f[i], @df[i], x, "#{f}, x=#{x}, #{deriv} deriv")
}
}
}
def _test_deriv(deriv, f, df, x, desc)
expected, h = df.eval(x), 1e-4
result, abserr = f.send("deriv_#{deriv}", x, h)
assert_abs result, expected, GSL.MIN(h, expected.abs) + GSL::DBL_EPSILON, desc
if abserr < (diff = (result - expected).abs)
assert_factor abserr, (result - expected).abs, 2, desc + ' error estimate'
else
zero = result == expected || expected.zero?
assert_abs abserr, zero ? 0.0 : diff, zero ? 1e-6 : 1e6 * diff, desc + ' abserr'
end
end
end
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