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require File.expand_path(File.dirname(__FILE__)+"/spec_helper.rb")
describe Integration do
it "should respond integration based on ruby methods" do
a=lambda {|x| x**2}
# Integration over [1,2]=x^3/3=7/3
methods=[:rectangle,:trapezoid, :simpson, :adaptive_quadrature, :romberg]
methods.each do |m|
Integration.integrate(1,2,{:method=>m,:tolerance=>1e-7},&a).should be_within(1e-6).of(7/3.0)
end
end
it "should return a correct value for a complex integration with ruby methods" do
normal_pdf=lambda {|x| (1/Math.sqrt(2*Math::PI))*Math.exp(-(x**2/2))}
Integration.integrate(0,1,{:tolerance=>1e-12,:method=>:simpson},&normal_pdf).should be_within(1e-11).of(0.341344746068)
Integration.integrate(0,1,{:tolerance=>1e-12,:method=>:adaptive_quadrature},&normal_pdf).should be_within(1e-11).of(0.341344746068)
end
it "should return a correct value for a complex integration with gsl methods" do
if Integration.has_gsl?
normal_pdf=lambda {|x| (1/Math.sqrt(2*Math::PI))*Math.exp(-(x**2/2))}
Integration.integrate(0,1,{:tolerance=>1e-12,:method=>:qng},&normal_pdf).should be_within(1e-11).of(0.341344746068)
Integration.integrate(0,1,{:tolerance=>1e-12,:method=>:qag},&normal_pdf).should be_within(1e-11).of(0.341344746068)
else
pending("GSL not available")
end
end
it "should return correct integration for infinity bounds" do
if Integration.has_gsl?
normal_pdf=lambda {|x| (1/Math.sqrt(2*Math::PI))*Math.exp(-(x**2/2))}
Integration.integrate(Integration::MInfinity, Integration::Infinity,{:tolerance=>1e-10}, &normal_pdf).should be_within(1e-09).of(1)
else
pending("GSL not available")
end
end
it "should return correct integration for infinity lower bound" do
if Integration.has_gsl?
normal_pdf=lambda {|x| (1/Math.sqrt(2*Math::PI))*Math.exp(-(x**2/2))}
Integration.integrate(Integration::MInfinity, 0 , {:tolerance=>1e-10}, &normal_pdf).should be_within(1e-09).of(0.5)
else
pending("GSL not available")
end
end
it "should return correct integration for infinity upper bound" do
if Integration.has_gsl?
normal_pdf=lambda {|x| (1/Math.sqrt(2*Math::PI))*Math.exp(-(x**2/2))}
Integration.integrate(0,Integration::Infinity,{:tolerance=>1e-10}, &normal_pdf).should be_within(1e-09).of(0.5)
else
pending("GSL not available")
end
end
it "should raise an error if a ruby methods is called with infinite bounds" do
normal_pdf=lambda {|x| (1/Math.sqrt(2*Math::PI))*Math.exp(-(x**2/2))}
lambda {Integration.integrate(0,Integration::Infinity,{:method=>:simpson}, &normal_pdf).should be_within(1e-09).of(0.5)}.should raise_exception()
end
end
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