require 'spec_helper'

describe Dydx::Integrand do
  before { reset }

  it 'ex1' do
    f(x, y) <= x * y
    integrand = S(f(x, y), dx)
    expect(integrand.function).to eq(f(x, y))
    expect(integrand.var).to eq(x)
    expect { integrand[4, 3] }.to raise_error(ArgumentError)
  end

  it 'ex2' do
    f(x) <= x * x
    expect(S(f(x), dx)[0, 1]).to eq(0.33333333)
  end

  it 'ex3' do
    f(x) <= sin(x)
    expect(S(f(x), dx)[0, pi / 2]).to eq(1.0)
  end

  it 'ex4' do
    f(x) <= cos(x)
    expect(S(f(x), dx)[0, pi]).to eq(0.0)
  end

  it 'ex5' do
    f(x) <= log(x)
    expect(S(f(x), dx)[0, 1]).to eq(-oo)
  end

  it 'ex6' do
    f(x) <= e ** -x ** 2
    expect(f(0)).to eq(1)
    expect(f(1)).to eq(1.0 / Math::E)
    expect(f(1000)).to eq(0)
    expect(S(f(x), dx)[-1000, 1000, 3000]).to eq(1.77239273)
  end

  it 'ex7' do
    f(x) <= (1.0 / ( 2.0 * Math::PI ) ** 0.5) * e ** (- x ** 2 / 2)
    expect(S(f(x), dx)[-1000, 1000]).to eq(1.0)
  end

  it 'ex8' do
    f(x) <= (1.0 / ( 2.0 * Math::PI ) ** 0.5) * e ** (- x ** 2 / 2)
    expect(S(f(x), dx)[-oo, oo]).to eq(1.0)
  end

  it 'ex9' do
    expect(S(log(x), dx)[0, 1]).to eq(-oo)
  end
end