Object
Returns a set of ranges stepped exponentially from min to
max by powers of base. Eg:
bench_exp(2, 16, 2) # => [2, 4, 8, 16]
# File minitest/benchmark.rb, line 26
def self.bench_exp min, max, base = 10
min = (Math.log10(min) / Math.log10(base)).to_i
max = (Math.log10(max) / Math.log10(base)).to_i
(min..max).map { |m| base ** m }.to_a
end
Returns a set of ranges stepped linearly from min to
max by step. Eg:
bench_linear(20, 40, 10) # => [20, 30, 40]
# File minitest/benchmark.rb, line 39
def self.bench_linear min, max, step = 10
(min..max).step(step).to_a
rescue LocalJumpError # 1.8.6
r = []; (min..max).step(step) { |n| r << n }; r
end
Specifies the ranges used for benchmarking for that class. Defaults to exponential growth from 1 to 10k by powers of 10. Override if you need different ranges for your benchmarks.
See also: ::bench_exp and ::bench_linear.
# File minitest/benchmark.rb, line 67
def self.bench_range
bench_exp 1, 10_000
end
Runs the given work, gathering the times of each run. Range
and times are then passed to a given validation proc. Outputs
the benchmark name and times in tab-separated format, making it easy to
paste into a spreadsheet for graphing or further analysis.
Ranges are specified by ::bench_range.
Eg:
def bench_algorithm validation = proc { |x, y| ... } assert_performance validation do |n| @obj.algorithm(n) end end
# File minitest/benchmark.rb, line 89
def assert_performance validation, &work
range = self.class.bench_range
io.print "#{__name__}"
times = []
range.each do |x|
GC.start
t0 = Time.now
instance_exec(x, &work)
t = Time.now - t0
io.print "\t%9.6f" % t
times << t
end
io.puts
validation[range, times]
end
Runs the given work and asserts that the times gathered fit to
match a constant rate (eg, linear slope == 0) within a given
threshold. Note: because we’re testing for a slope of 0, R^2
is not a good determining factor for the fit, so the threshold is applied
against the slope itself. As such, you probably want to tighten it from the
default.
See www.graphpad.com/curvefit/goodness_of_fit.htm for more details.
Fit is calculated by fit_linear.
Ranges are specified by ::bench_range.
Eg:
def bench_algorithm assert_performance_constant 0.9999 do |n| @obj.algorithm(n) end end
# File minitest/benchmark.rb, line 133
def assert_performance_constant threshold = 0.99, &work
validation = proc do |range, times|
a, b, rr = fit_linear range, times
assert_in_delta 0, b, 1 - threshold
[a, b, rr]
end
assert_performance validation, &work
end
Runs the given work and asserts that the times gathered fit to
match a exponential curve within a given error threshold.
Fit is calculated by fit_exponential.
Ranges are specified by ::bench_range.
Eg:
def bench_algorithm assert_performance_exponential 0.9999 do |n| @obj.algorithm(n) end end
# File minitest/benchmark.rb, line 159
def assert_performance_exponential threshold = 0.99, &work
assert_performance validation_for_fit(:exponential, threshold), &work
end
Runs the given work and asserts that the times gathered fit to
match a straight line within a given error threshold.
Fit is calculated by fit_linear.
Ranges are specified by ::bench_range.
Eg:
def bench_algorithm assert_performance_linear 0.9999 do |n| @obj.algorithm(n) end end
# File minitest/benchmark.rb, line 199
def assert_performance_linear threshold = 0.99, &work
assert_performance validation_for_fit(:linear, threshold), &work
end
Runs the given work and asserts that the times gathered fit to
match a logarithmic curve within a given error threshold.
Fit is calculated by fit_logarithmic.
Ranges are specified by ::bench_range.
Eg:
def bench_algorithm assert_performance_logarithmic 0.9999 do |n| @obj.algorithm(n) end end
# File minitest/benchmark.rb, line 179
def assert_performance_logarithmic threshold = 0.99, &work
assert_performance validation_for_fit(:logarithmic, threshold), &work
end
Runs the given work and asserts that the times gathered curve
fit to match a power curve within a given error threshold.
Fit is calculated by fit_power.
Ranges are specified by ::bench_range.
Eg:
def bench_algorithm assert_performance_power 0.9999 do |x| @obj.algorithm end end
# File minitest/benchmark.rb, line 219
def assert_performance_power threshold = 0.99, &work
assert_performance validation_for_fit(:power, threshold), &work
end
Takes an array of x/y pairs and calculates the general R^2 value.
See: en.wikipedia.org/wiki/Coefficient_of_determination
# File minitest/benchmark.rb, line 228
def fit_error xys
y_bar = sigma(xys) { |x, y| y } / xys.size.to_f
ss_tot = sigma(xys) { |x, y| (y - y_bar) ** 2 }
ss_err = sigma(xys) { |x, y| (yield(x) - y) ** 2 }
1 - (ss_err / ss_tot)
end
To fit a functional form: y = ae^(bx).
Takes x and y values and returns [a, b, r^2].
See: mathworld.wolfram.com/LeastSquaresFittingExponential.html
# File minitest/benchmark.rb, line 243
def fit_exponential xs, ys
n = xs.size
xys = xs.zip(ys)
sxlny = sigma(xys) { |x,y| x * Math.log(y) }
slny = sigma(xys) { |x,y| Math.log(y) }
sx2 = sigma(xys) { |x,y| x * x }
sx = sigma xs
c = n * sx2 - sx ** 2
a = (slny * sx2 - sx * sxlny) / c
b = ( n * sxlny - sx * slny ) / c
return Math.exp(a), b, fit_error(xys) { |x| Math.exp(a + b * x) }
end
Fits the functional form: a + bx.
Takes x and y values and returns [a, b, r^2].
See: mathworld.wolfram.com/LeastSquaresFitting.html
# File minitest/benchmark.rb, line 288
def fit_linear xs, ys
n = xs.size
xys = xs.zip(ys)
sx = sigma xs
sy = sigma ys
sx2 = sigma(xs) { |x| x ** 2 }
sxy = sigma(xys) { |x,y| x * y }
c = n * sx2 - sx**2
a = (sy * sx2 - sx * sxy) / c
b = ( n * sxy - sx * sy ) / c
return a, b, fit_error(xys) { |x| a + b * x }
end
To fit a functional form: y = a + b*ln(x).
Takes x and y values and returns [a, b, r^2].
See: mathworld.wolfram.com/LeastSquaresFittingLogarithmic.html
# File minitest/benchmark.rb, line 265
def fit_logarithmic xs, ys
n = xs.size
xys = xs.zip(ys)
slnx2 = sigma(xys) { |x,y| Math.log(x) ** 2 }
slnx = sigma(xys) { |x,y| Math.log(x) }
sylnx = sigma(xys) { |x,y| y * Math.log(x) }
sy = sigma(xys) { |x,y| y }
c = n * slnx2 - slnx ** 2
b = ( n * sylnx - sy * slnx ) / c
a = (sy - b * slnx) / n
return a, b, fit_error(xys) { |x| a + b * Math.log(x) }
end
To fit a functional form: y = ax^b.
Takes x and y values and returns [a, b, r^2].
See: mathworld.wolfram.com/LeastSquaresFittingPowerLaw.html
# File minitest/benchmark.rb, line 310
def fit_power xs, ys
n = xs.size
xys = xs.zip(ys)
slnxlny = sigma(xys) { |x, y| Math.log(x) * Math.log(y) }
slnx = sigma(xs) { |x | Math.log(x) }
slny = sigma(ys) { | y| Math.log(y) }
slnx2 = sigma(xs) { |x | Math.log(x) ** 2 }
b = (n * slnxlny - slnx * slny) / (n * slnx2 - slnx ** 2);
a = (slny - b * slnx) / n
return Math.exp(a), b, fit_error(xys) { |x| (Math.exp(a) * (x ** b)) }
end
Enumerates over enum mapping block if given,
returning the sum of the result. Eg:
sigma([1, 2, 3]) # => 1 + 2 + 3 => 7 sigma([1, 2, 3]) { |n| n ** 2 } # => 1 + 4 + 9 => 14
# File minitest/benchmark.rb, line 331
def sigma enum, &block
enum = enum.map(&block) if block
enum.inject { |sum, n| sum + n }
end
Returns a proc that calls the specified fit method and asserts that the error is within a tolerable threshold.
# File minitest/benchmark.rb, line 340
def validation_for_fit msg, threshold
proc do |range, times|
a, b, rr = send "fit_#{msg}", range, times
assert_operator rr, :>=, threshold
[a, b, rr]
end
end
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