require 'test_helper' class ChebTest < GSL::TestCase def test_cheb tol, pi, order = 100.0 * GSL::DBL_EPSILON, GSL::M_PI, 40 cs = GSL::Cheb.alloc(order) cs.init(GSL::Function.alloc { |x| 1.0 }, -1.0, 1.0) order.times { |i| assert_abs cs.c[i], i == 0 ? 2.0 : 0.0, tol, 'c[%d] for T_0(x)' % i } cs.init(GSL::Function.alloc { |x| x }, -1.0, 1.0) order.times { |i| assert_abs cs.c[i], i == 1 ? 1.0 : 0.0, tol, 'c[%d] for T_1(x)' % i } cs.init(GSL::Function.alloc { |x| 2.0 * x * x - 1.0 }, -1.0, 1.0) order.times { |i| assert_abs cs.c[i], i == 2 ? 1.0 : 0.0, tol, 'c[%d] for T_2(x)' % i } cs.init(GSL::Function.alloc { |x| Math.sin(x) }, -pi, pi) assert_abs cs.c[0], 0.0, tol, 'c[0] for F_sin(x)' assert_abs cs.c[1], 5.69230686359506e-01, tol, 'c[1] for F_sin(x)' assert_abs cs.c[2], 0.0, tol, 'c[2] for F_sin(x)' assert_abs cs.c[3], -6.66916672405979e-01, tol, 'c[3] for F_sin(x)' assert_abs cs.c[4], 0.0, tol, 'c[4] for F_sin(x)' assert_abs cs.c[5], 1.04282368734237e-01, tol, 'c[5] for F_sin(x)' x = -pi while x < pi assert_abs cs.eval(x), Math.sin(x), tol, 'GSL::Cheb#eval, sin(%.3g)' % x x += pi / 100.0 end x = -pi while x < pi r, e = cs.eval_err(x) assert_abs r, Math.sin(x), tol, 'GSL::Cheb#eval_err, sin(%.3g)' % x assert_factor((r - Math.sin(x)).abs + GSL::DBL_EPSILON, e, 10.0, 'GSL::Cheb#eval_err, error sin(%.3g)' % x) x += pi / 100.0 end x = -pi while x < pi assert_abs cs.eval_n(25, x), Math.sin(x), tol, 'GSL::Cheb#eval_n, sin(%.3g)' % x x += pi / 100.0 end x = -pi while x < pi r, e = cs.eval_n_err(25, x) assert_abs r, Math.sin(x), tol, 'GSL::Cheb#eval_n_err, sin(%.3g)' % x assert_factor((r - Math.sin(x)).abs + GSL::DBL_EPSILON, e, 10.0, 'GSL::Cheb#eval_n_err, error sin(%.3g)' % x) x += pi / 100.0 end csd, x = cs.calc_deriv, -pi while x < pi assert_abs csd.eval(x), Math.cos(x), 1600 * tol, 'GSL::Cheb#eval, deriv sin(%.3g)' % x x += pi / 100.0 end csi, x = cs.calc_integ, -pi while x < pi assert_abs csi.eval(x), -(1 + Math.cos(x)), tol, 'GSL::Cheb#eval, integ sin(%.3g)' % x x += pi / 100.0 end end end