def test_var_div_var(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(x / y) self.assertLessEqual( np.abs(f.eval_d().real / (-.44755270475041560619657805305047592426404601827) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-.13600253041648890000441351713180233327939034617) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-.44755270475041560619657805305047592426404601827") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-.13600253041648890000441351713180233327939034617") - 1), tol_mp)
def test_arith_mpfr(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol self.assertLessEqual(mp.abs((x + y) - mp.Float("0.37")), tol) self.assertLessEqual(mp.abs((z - y) - mp.Float("5.0095")), tol) self.assertLessEqual(mp.abs((z * y) - mp.Float("-4.437070")), tol) self.assertLessEqual( mp.abs((y / x) - mp.Float("-.91252955082742316784869976359338061")), tol) self.assertLessEqual( mp.abs((x**y) - mp.Float("0.0038223124228935822000384505727705508")), tol) self.assertLessEqual(mp.abs((-z) - mp.Float("-1.1495")), tol) # result = mp.Float(x) result += y self.assertLessEqual(mp.abs(result - mp.Float("0.37")), tol) result = mp.Float(z) result -= y self.assertLessEqual(mp.abs(result - mp.Float("5.0095")), tol) result = mp.Float(z) result *= y self.assertLessEqual(mp.abs(result - mp.Float("-4.437070")), tol) result = mp.Float(y) result /= x self.assertLessEqual( mp.abs(result - mp.Float("-.91252955082742316784869976359338061")), tol)
def compute_values(tol, pred, tr, td): tr.tracking_tolerance(tol) tr.predictor(pred) start_time = pybertini.multiprec.Complex("1") eg_boundary = pybertini.multiprec.Complex("0.1") midpath_points = [None]*td.num_start_points() overall_code = pybertini.tracking.SuccessCode.Success speed_start = time.time() target_tol_multiplier = 10 same_point_tol = target_tol_multiplier * tol for ii in range(td.num_start_points()): #print("Tracking path {}...".format(ii)) midpath_points[ii] = pybertini.multiprec.Vector() code = tr.track_path(result=midpath_points[ii], start_time=start_time, end_time=eg_boundary, start_point=td.start_point_mp(ii)) if code != pybertini.tracking.SuccessCode.Success: overall_code = pybertini.tracking.SuccessCode.Failure from pybertini.multiprec import abs for ii in range(td.num_start_points()): for jj in range(ii + 1, td.num_start_points()): if abs((midpath_points[ii] - midpath_points[jj]).norm()) < same_point_tol: overall_code = pybertini.tracking.SuccessCode.Failure #print("encountered a path crossing") return time.time() - speed_start, overall_code
def test_plus(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(x + y + a) self.assertLessEqual(np.abs(f.eval_d().real / (5.53) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.118) - 1), tol_d) # self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("5.53") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-1.118") - 1), tol_mp) # f = Function(x + Float("3.87")) self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d) # f = Function(x + mpfr_complex("3.87", "-2.1")) self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.89) - 1), tol_d) # self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("1.44") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-1.89") - 1), tol_mp) # f = Function(x + (-5)) self.assertLessEqual(np.abs(f.eval_d().real / (-7.43) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("-7.43") - 1), tol_mp) self.assertLessEqual(mp.abs(f.eval_mp().imag / mpfr_float("0.21") - 1), tol_mp) # f = Function(x) f += y f += a self.assertLessEqual(np.abs(f.eval_d().real / (5.53) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.118) - 1), tol_d) # self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("5.53") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-1.118") - 1), tol_mp) # f = Function(x) f += Float("3.87") self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
def test_var_times_var(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(x * y * z) self.assertLessEqual(np.abs(f.eval_d().real / (77.7616926) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-28.8346602) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("77.7616926") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-28.8346602") - 1), tol_mp)
def test_power_rule(self): x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b; tol_d = self.tol_d; tol_mp = self.tol_mp; # f = x**2 + y**3; df = f.differentiate(); # self.assertLessEqual(np.abs(df.eval_d(x).real / (-4.86)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(x).imag / (0.42)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(x).real / mpfr_float("-4.86")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(x).imag / mpfr_float("0.42")-1), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(y).real / (58.9860)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(y).imag / (-56.3376)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(y).real / mpfr_float("58.9860")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(y).imag / mpfr_float("-56.3376")-1), tol_mp)
def test_I_construct(self): x_d = self.x_d y_d = self.y_d z_d = self.z_d p_d = self.p_d tol_d = self.tol_d x_mp = self.x_mp y_mp = self.y_mp z_mp = self.z_mp p_mp = self.p_mp tol_mp = self.tol_mp y = make_i() # self.assertLessEqual(np.abs(y.eval_d().real - (0)), tol_d) self.assertLessEqual(np.abs(y.eval_d().imag / (1.0) - 1), tol_d) # self.assertLessEqual(mp.abs(y.eval_mp().real - mpfr_float("0")), tol_mp) self.assertLessEqual(mp.abs(y.eval_mp().imag / mpfr_float("1.0") - 1), tol_mp)
def test_change_prec(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol mp.default_precision(45) tol = mp.Float("1e-37") t = mp.Complex("-2.43", ".21") t = t**(-2) self.assertLessEqual( mp.abs( t.real - mp.Float("0.16560329111110602501494676510297183141930819429")), tol) self.assertLessEqual( mp.abs(t.imag - mp.Float( "0.028838165251841866149715852522538399390278791818")), tol) mp.default_precision(30) tol = mp.Float("1e-27")
def test_sum_rule(self): x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b; tol_d = self.tol_d; tol_mp = self.tol_mp; # f = x+y+a; df = f.differentiate(); # self.assertLessEqual(np.abs(df.eval_d(x).real/(1.0)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(x).imag-0), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(x).real/mpfr_float("1.0")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(x).imag-mpfr_float("0")), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(y).real/(1.0)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(y).imag-0), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(y).real/mpfr_float("1.0")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(y).imag-mpfr_float("0")), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(z).real-0), tol_d) self.assertLessEqual(np.abs(df.eval_d(z).imag-0), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(z).real-mpfr_float("0.0")), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(z).imag-mpfr_float("0")), tol_mp)
def test_trancendental(self): x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b; tol_d = self.tol_d; tol_mp = self.tol_mp; # f = sin(x*y) + exp(z*y) - log(x*x); df = f.differentiate(); # self.assertLessEqual(np.abs(df.eval_d(x).real / (-17.648420086229721902138620795382021306411662490)-1), 9e-13) self.assertLessEqual(np.abs(df.eval_d(x).imag / (-803.11883403426275105632833868183320319093878729)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(x).real / mpfr_float("-17.648420086229721902138620795382021306411662490")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(x).imag / mpfr_float("-803.11883403426275105632833868183320319093878729")-1), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(y).real / (-100.97157179433748763552280062599971478593963953)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(y).imag / (361.98093991820979266721712882115615553425318528)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(y).real / mpfr_float("-100.97157179433748763552280062599971478593963953")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(y).imag / mpfr_float("361.98093991820979266721712882115615553425318528")-1), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(z).real / (-2.1642907643013779167501866500194314960002972412e-14)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(z).imag / (2.1105887207247540399884720817624768568595288922e-14)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(z).real / mpfr_float("-2.1642907643013779167501866500194314960002972412e-14")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(z).imag / mpfr_float("2.1105887207247540399884720817624768568595288922e-14")-1), tol_mp)
def test_prod_rule(self): x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b; tol_d = self.tol_d; tol_mp = self.tol_mp; # f = x**2*y**4 - a*x*y*z**2; df = f.differentiate(); # self.assertLessEqual(np.abs(df.eval_d(x).real / (-559.28968169592)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(x).imag / (3577.05276993648)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(x).real / mpfr_float("-559.28968169592")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(x).imag / mpfr_float("3577.05276993648")-1), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(y).real / (1161.85042980828)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(y).imag / (-3157.24325320476)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(y).real / mpfr_float("1161.85042980828")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(y).imag / mpfr_float("-3157.24325320476")-1), tol_mp) # df.reset() self.assertLessEqual(np.abs(df.eval_d(z).real / (-520.5265859088)-1), tol_d) self.assertLessEqual(np.abs(df.eval_d(z).imag / (84.7479679056)-1), tol_d) # self.assertLessEqual(mp.abs(df.eval_mp(z).real / mpfr_float("-520.5265859088")-1), tol_mp) self.assertLessEqual(mp.abs(df.eval_mp(z).imag / mpfr_float("84.7479679056")-1), tol_mp)
def test_Pi_construct(self): x_d = self.x_d y_d = self.y_d z_d = self.z_d p_d = self.p_d tol_d = self.tol_d x_mp = self.x_mp y_mp = self.y_mp z_mp = self.z_mp p_mp = self.p_mp tol_mp = self.tol_mp x = Pi() y = make_pi() # self.assertLessEqual( np.abs(x.eval_d().real / (3.1415926535897932384626433832795028841971693994) - 1), tol_d) self.assertLessEqual(np.abs(x.eval_d().imag - (0)), tol_d) # self.assertLessEqual( mp.abs(x.eval_mp().real / mpfr_float( "3.1415926535897932384626433832795028841971693994") - 1), tol_mp) self.assertLessEqual(mp.abs(x.eval_mp().imag - mpfr_float("0")), tol_mp) # self.assertLessEqual( np.abs(y.eval_d().real / (3.1415926535897932384626433832795028841971693994) - 1), tol_d) self.assertLessEqual(np.abs(y.eval_d().imag - (0)), tol_d) # self.assertLessEqual( mp.abs(y.eval_mp().real / mpfr_float( "3.1415926535897932384626433832795028841971693994") - 1), tol_mp) self.assertLessEqual(mp.abs(y.eval_mp().imag - mpfr_float("0")), tol_mp)
def test_Float_eval(self): x_d = self.x_d y_d = self.y_d z_d = self.z_d p_d = self.p_d tol_d = self.tol_d x_mp = self.x_mp y_mp = self.y_mp z_mp = self.z_mp p_mp = self.p_mp tol_mp = self.tol_mp x = Float(x_mp) y = Float(y_mp) z = Float(z_mp) # self.assertLessEqual(np.abs(x.eval_d().real / (-2.43) - 1), tol_d) self.assertLessEqual(np.abs(x.eval_d().imag / (.21) - 1), tol_d) # self.assertLessEqual(mp.abs(y.eval_mp().real / mpfr_float("4.84") - 1), tol_mp) self.assertLessEqual( mp.abs(y.eval_mp().imag / mpfr_float("-1.94") - 1), tol_mp)
def test_num_times_var(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(a * x * b * y) # self.assertLessEqual(np.abs(f.eval_d().real / (3.4011196056) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-110.9953448712) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("3.4011196056") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-110.9953448712") - 1), tol_mp)
def test_E_construct(self): x_d = self.x_d y_d = self.y_d z_d = self.z_d p_d = self.p_d tol_d = self.tol_d x_mp = self.x_mp y_mp = self.y_mp z_mp = self.z_mp p_mp = self.p_mp tol_mp = self.tol_mp x = E() y = make_e() # self.assertLessEqual( np.abs(x.eval_d().real / (2.7182818284590452353602874713526624977572470937) - 1), tol_d) self.assertLessEqual(np.abs(x.eval_d().imag - (0)), tol_d) # self.assertLessEqual( mp.abs(x.eval_mp().real - mpfr_float( "2.7182818284590452353602874713526624977572470937")), tol_mp) self.assertLessEqual(mp.abs(x.eval_mp().imag - mpfr_float("0")), tol_mp) # self.assertLessEqual( np.abs(y.eval_d().real / (2.7182818284590452353602874713526624977572470937) - 1), tol_d) self.assertLessEqual(np.abs(y.eval_d().imag - (0)), tol_d) # self.assertLessEqual( mp.abs(y.eval_mp().real / mpfr_float( "2.7182818284590452353602874713526624977572470937") - 1), tol_mp) self.assertLessEqual(mp.abs(y.eval_mp().imag - mpfr_float("0")), tol_mp)
def test_Variable_eval(self): x_d = self.x_d y_d = self.y_d z_d = self.z_d p_d = self.p_d tol_d = self.tol_d x_mp = self.x_mp y_mp = self.y_mp z_mp = self.z_mp p_mp = self.p_mp tol_mp = self.tol_mp x = Variable("x") y = Variable("y") x.set_current_value(x_d) x.set_current_value(x_mp) # self.assertLessEqual(np.abs(x.eval_d().real / (-2.43) - 1), tol_d) self.assertLessEqual(np.abs(x.eval_d().imag / (.21) - 1), tol_d) # self.assertLessEqual( mp.abs(x.eval_mp().real / mpfr_float("-2.43") - 1), tol_mp) self.assertLessEqual(mp.abs(x.eval_mp().imag / mpfr_float(".21") - 1), tol_mp)
def test_change_prec(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol mp.default_precision(40) tol = mp.Float("1e-37") t = mp.Float("4.23") self.assertLessEqual( mp.abs(t**(-2) - mp.Float( "0.055888089689206333238323580861682566828183245868")), tol) mp.default_precision(30) tol = mp.Float("1e-27")
def test_Float_funcs(self): x_d = self.x_d y_d = self.y_d z_d = self.z_d p_d = self.p_d tol_d = self.tol_d x_mp = self.x_mp y_mp = self.y_mp z_mp = self.z_mp p_mp = self.p_mp tol_mp = self.tol_mp x = Float(x_mp) y = Float(y_mp) z = Float(z_mp) # self.assertEqual(x.degree(), 0) d = y.differentiate() self.assertLessEqual(mp.abs(d.eval_mp().real - mpfr_float("0")), tol_mp) self.assertLessEqual(mp.abs(d.eval_mp().imag - mpfr_float("0")), tol_mp) self.assertTrue(y.is_homogeneous()) self.assertTrue(y.is_polynomial())
def test_sub(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(x - y - a) self.assertLessEqual(np.abs(f.eval_d().real / (-10.39) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (1.538) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("-10.39") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("1.538") - 1), tol_mp) # f = Function(y - Float("3.87")) self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d) # f = Function(y - Float("3.87", "0")) self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d) # # f = Function(y - mpfr_complex("3.87", "-2.1")) self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (0.16) - 1), tol_d) # self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("0.97") - 1), tol_mp) self.assertLessEqual(mp.abs(f.eval_mp().imag / mpfr_float("0.16") - 1), tol_mp) # f = Function(y - (-5)) self.assertLessEqual(np.abs(f.eval_d().real / (9.84) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d) # f = Function(x) f -= y f -= a self.assertLessEqual(np.abs(f.eval_d().real / (-10.39) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (1.538) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("-10.39") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("1.538") - 1), tol_mp) # f = Function(y) f -= Float("3.87") self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
def test_misc_funcs(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol # res = mp.norm(x) self.assertLessEqual(mp.abs(res - mp.Float("5.949")), tol) res = mp.abs2(x) self.assertLessEqual(mp.abs(res - mp.Float("5.949")), tol) res = mp.conj(x) self.assertLessEqual(mp.abs(res.real - x.real), tol) self.assertLessEqual(mp.abs(res.imag - (-x.imag)), tol) res = mp.polar(mp.Float("3.21"), mp.Float("-5.62")) self.assertLessEqual( mp.abs( res.real - mp.Float("2.5295931897050156212406076422629449344206513531")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("1.9761726378527774897831544771425943545375239972")), tol) res = mp.arg(y) self.assertLessEqual( mp.abs( res - mp.Float("-.38121862770417378405072154507774424569831993182")), tol) res = mp.inverse(z) self.assertLessEqual( mp.abs(res.real - mp.Float( "-0.15238180880075963272315628064317633672297417498")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "0.017189984912554828938368401412062021935878722517")), tol)
def test_trancendentals(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol self.assertLessEqual( mp.abs((mp.exp(x)) - mp.Float("68.717232173846461408252914213396109")), tol) self.assertLessEqual( mp.abs((mp.log(z)) - mp.Float("0.13932706522109918666170810230684295")), tol) self.assertLessEqual( mp.abs((mp.sqrt(z)) - mp.Float("1.0721473779289860297522254519889560")), tol) # self.assertLessEqual( mp.abs((mp.sin(x)) - mp.Float("-.88588921129660245121088859729926237")), tol) self.assertLessEqual( mp.abs((mp.cos(y)) - mp.Float("-.75285494656729525719980460936483635")), tol) self.assertLessEqual( mp.abs((mp.tan(z)) - mp.Float("2.2315038042849919118711153687209483")), tol) # self.assertLessEqual( mp.abs((mp.asin(p)) - mp.Float("0.34691689752716170922069696210451452")), tol) self.assertLessEqual( mp.abs((mp.acos(p)) - mp.Float("1.2238794292677349100106247295352369")), tol) self.assertLessEqual( mp.abs((mp.atan(z)) - mp.Float("0.85483739856328448882289109284144652")), tol) # self.assertLessEqual( mp.abs((mp.sinh(x)) - mp.Float("34.351339891649022639414777866662100")), tol) self.assertLessEqual( mp.abs((mp.cosh(y)) - mp.Float("23.743209684188284295743755381842167")), tol) self.assertLessEqual( mp.abs((mp.tanh(z)) - mp.Float("0.81758837109637920976170104688035086")), tol)
def test_arith_mp_float(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol a = mp.Float("3.12") b = mp.Float("-5.92") res = mp.Complex(x + a) self.assertLessEqual(mp.abs(res.real - mp.Float("0.69")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("0.21")), tol) res = mp.Complex(y - b) self.assertLessEqual(mp.abs(res.real - mp.Float("10.76")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.94")), tol) res = mp.Complex(a + x) self.assertLessEqual(mp.abs(res.real - mp.Float("0.69")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("0.21")), tol) res = mp.Complex(b - y) self.assertLessEqual(mp.abs(res.real - mp.Float("-10.76")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("1.94")), tol) res = mp.Complex(z * a) self.assertLessEqual(mp.abs(res.real - mp.Float("-20.2176")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-2.28072")), tol) res = mp.Complex(a * z) self.assertLessEqual(mp.abs(res.real - mp.Float("-20.2176")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-2.28072")), tol) res = mp.Complex(y / b) self.assertLessEqual( mp.abs( res.real - mp.Float("-.81756756756756756756756756756756756756756756757")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float(".3277027027027027027027027027027027027027027027")), tol) res = mp.Complex(b / y) self.assertLessEqual( mp.abs( res.real - mp.Float("-1.0538301972842157915642975887484736586585850264")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("-.42240301296102864372618539714298324334662292381")), tol) res = mp.Complex(x**a) self.assertLessEqual( mp.abs( res.real - mp.Float("-16.054376621961088182387920766649714821973863952")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("-1.7411284591111236754359685247799914985638458821")), tol) # # # res = mp.Complex(x) res += a self.assertLessEqual(mp.abs(res.real - mp.Float("0.69")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("0.21")), tol) res = mp.Complex(y) res -= b self.assertLessEqual(mp.abs(res.real - mp.Float("10.76")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.94")), tol) res = mp.Complex(z) res *= a self.assertLessEqual(mp.abs(res.real - mp.Float("-20.2176")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-2.28072")), tol) res = mp.Complex(y) res /= b self.assertLessEqual( mp.abs( res.real - mp.Float("-.81756756756756756756756756756756756756756756757")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float(".3277027027027027027027027027027027027027027027")), tol) # res = mp.Complex(x**4) self.assertLessEqual(mp.abs(res.real - mp.Float("33.30735228")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-11.96306496")), tol) # res = mp.Complex(-z) self.assertLessEqual(mp.abs(res.real - mp.Float("6.48")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float(".731")), tol)
def test_power(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(y**3) self.assertLessEqual(np.abs(f.eval_d().real / (58.732432) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-129.035608) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("58.732432") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-129.035608") - 1), tol_mp) # f = Function(pow(y, 3)) self.assertLessEqual(np.abs(f.eval_d().real / (58.732432) - 1), tol_d) self.assertLessEqual(np.abs(f.eval_d().imag / (-129.035608) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float("58.732432") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float("-129.035608") - 1), tol_mp) # f = Function(x**p) self.assertLessEqual( np.abs(f.eval_d().real / (-.35190932545709434788093164550270669097948909024) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-6.7687858345625791466707575744042177964518271087) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-.35190932545709434788093164550270669097948909024") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-6.7687858345625791466707575744042177964518271087") - 1), tol_mp) # f = Function(pow(x, p)) self.assertLessEqual( np.abs(f.eval_d().real / (-.35190932545709434788093164550270669097948909024) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-6.7687858345625791466707575744042177964518271087) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-.35190932545709434788093164550270669097948909024") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-6.7687858345625791466707575744042177964518271087") - 1), tol_mp)
def test_trans_funcs(self): x = self.x y = self.y z = self.z p = self.p a = self.a b = self.b tol_d = self.tol_d tol_mp = self.tol_mp # f = Function(sin(x)) self.assertLessEqual( np.abs(f.eval_d().real / (-.66749329633668695550441899166308616328986315948) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-.16020928942503633132090203927960650380076680938) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-.66749329633668695550441899166308616328986315948") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-.16020928942503633132090203927960650380076680938") - 1), tol_mp) # f = Function(cos(y)) self.assertLessEqual( np.abs(f.eval_d().real / (0.45194679593300564730917329070452033759984813611) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-3.3798161097977088705360399142708324234265626016) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "0.45194679593300564730917329070452033759984813611") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-3.3798161097977088705360399142708324234265626016") - 1), tol_mp) # f = Function(tan(z)) self.assertLessEqual( np.abs(f.eval_d().real / (-.11998086808607765336591715593714295443402911227) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-.63859741450762243500349270264429166927927928889) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-.11998086808607765336591715593714295443402911227") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-.63859741450762243500349270264429166927927928889") - 1), tol_mp) # f = Function(asin(x)) self.assertLessEqual( np.abs(f.eval_d().real / (-1.4763431474004472804452143435221887167393328861) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (1.5406263884278099750127157814537559611048741005) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-1.4763431474004472804452143435221887167393328861") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "1.5406263884278099750127157814537559611048741005") - 1), tol_mp) # f = Function(acos(y)) self.assertLessEqual( np.abs(f.eval_d().real / (0.38769800860408664087229892623614567735197135529) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (2.3379037587834289977359318611458042347281923566) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "0.38769800860408664087229892623614567735197135529") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "2.3379037587834289977359318611458042347281923566") - 1), tol_mp) # f = Function(atan(z)) self.assertLessEqual( np.abs(f.eval_d().real / (-1.4195347801361539102032503530226060969949192059) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-0.16801358511827150554928904776095870747673962940e-1) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-1.4195347801361539102032503530226060969949192059") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-0.16801358511827150554928904776095870747673962940e-1") - 1), tol_mp) # f = Function(exp(y)) self.assertLessEqual( np.abs(f.eval_d().real / (-45.639359208255772966298371983389382308765171859) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-117.94721623715960520658000231550940351946595854) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "-45.639359208255772966298371983389382308765171859") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-117.94721623715960520658000231550940351946595854") - 1), tol_mp) # f = Function(log(z)) self.assertLessEqual( np.abs(f.eval_d().real / (1.8750432590213669716781046977781508038070552297) - 1), tol_d) self.assertLessEqual( np.abs(f.eval_d().imag / (-3.0292589170775161726973168096174940982043177322) - 1), tol_d) # self.assertLessEqual( mp.abs(f.eval_mp().real / mpfr_float( "1.8750432590213669716781046977781508038070552297") - 1), tol_mp) self.assertLessEqual( mp.abs(f.eval_mp().imag / mpfr_float( "-3.0292589170775161726973168096174940982043177322") - 1), tol_mp)
def test_arith_mp_complex(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol # res = mp.Complex(x + y) self.assertLessEqual(mp.abs(res.real - mp.Float("2.41")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.73")), tol) res = mp.Complex(y - z) self.assertLessEqual(mp.abs(res.real - mp.Float("11.32")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.209")), tol) res = mp.Complex(y + x) self.assertLessEqual(mp.abs(res.real - mp.Float("2.41")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.73")), tol) res = mp.Complex(z - y) self.assertLessEqual(mp.abs(res.real - mp.Float("-11.32")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("1.209")), tol) res = mp.Complex(z * x) self.assertLessEqual(mp.abs(res.real - mp.Float("15.89991")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("0.41553")), tol) res = mp.Complex(x * z) self.assertLessEqual(mp.abs(res.real - mp.Float("15.89991")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float(".41553")), tol) res = mp.Complex(y / x) self.assertLessEqual( mp.abs( res.real - mp.Float("-2.0454866364094805849722642460917801311144730207")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("0.62158345940494200706001008572869389813414019163")), tol) res = mp.Complex(x / y) self.assertLessEqual( mp.abs( res.real - mp.Float("-.44755270475041560619657805305047592426404601827")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("-.13600253041648890000441351713180233327939034617")), tol) res = mp.Complex(y**z) self.assertLessEqual( mp.abs(res.real - mp.Float( "0.0000051612634484879218649489640888954160904291899461")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "0.16242051733741136410199105656393042124100116889e-4")), tol) # # # res = mp.Complex(x) res += y self.assertLessEqual(mp.abs(res.real - mp.Float("2.41")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.73")), tol) res = mp.Complex(y) res -= z self.assertLessEqual(mp.abs(res.real - mp.Float("11.32")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-1.209")), tol) res = mp.Complex(z) res *= x self.assertLessEqual(mp.abs(res.real - mp.Float("15.89991")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float(".41553")), tol) res = mp.Complex(y) res /= x self.assertLessEqual( mp.abs( res.real - mp.Float("-2.0454866364094805849722642460917801311144730207")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("0.62158345940494200706001008572869389813414019163")), tol)
def test_trancendentals(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol # res = mp.exp(x) self.assertLessEqual( mp.abs(res.real - mp.Float( "0.086102743899954532232498058731947255067424332219")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "0.018352149302889219131202317785160051395400089327")), tol) res = mp.log(y) self.assertLessEqual( mp.abs( res.real - mp.Float("1.6514099178148475691128039277241118340531698491")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "-0.38121862770417378405072154507774424569831993182")), tol) res = mp.sqrt(z) self.assertLessEqual( mp.abs( res.real - mp.Float("0.14335482322754515813189359093523204816185445814")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("-2.5496177371015053245565185485769652617478797292")), tol) res = mp.sin(x) self.assertLessEqual( mp.abs(res.real - mp.Float( "-0.66749329633668695550441899166308616328986315948")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "-0.16020928942503633132090203927960650380076680938")), tol) res = mp.cos(y) self.assertLessEqual( mp.abs( res.real - mp.Float("0.45194679593300564730917329070452033759984813611")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("-3.3798161097977088705360399142708324234265626016")), tol) res = mp.tan(z) self.assertLessEqual( mp.abs(res.real - mp.Float( "-0.11998086808607765336591715593714295443402911227")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "-0.63859741450762243500349270264429166927927928889")), tol) res = mp.asin(x) self.assertLessEqual( mp.abs( res.real - mp.Float("-1.4763431474004472804452143435221887167393328861")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("1.5406263884278099750127157814537559611048741005")), tol) res = mp.acos(y) self.assertLessEqual( mp.abs( res.real - mp.Float("0.38769800860408664087229892623614567735197135529")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("2.3379037587834289977359318611458042347281923566")), tol) res = mp.atan(z) self.assertLessEqual( mp.abs( res.real - mp.Float("-1.4195347801361539102032503530226060969949192059")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "-0.016801358511827150554928904776095870747673962940")), tol) res = mp.sinh(x) self.assertLessEqual( mp.abs( res.real - mp.Float("-5.5116175435238027338707341903303682792175349461")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("1.1931117850318239903301857156967336540973461581")), tol) res = mp.cosh(y) self.assertLessEqual( mp.abs( res.real - mp.Float("-22.821106324812396153305984541517740047129741299")), tol) self.assertLessEqual( mp.abs( res.imag - mp.Float("-58.969920999917202046449299163531439999586349377")), tol) res = mp.tanh(z) self.assertLessEqual( mp.abs( res.real - mp.Float("-.99999948909538256503828034023523935671055767287")), tol) self.assertLessEqual( mp.abs(res.imag - mp.Float( "-0.0000046773288796255165542679839050497228616710086412")), tol) res = mp.square(z) self.assertLessEqual(mp.abs(res.real - mp.Float("41.456039")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("9.47376")), tol) res = mp.cube(z) self.assertLessEqual(mp.abs(res.real - mp.Float("-261.70981416")), tol) self.assertLessEqual(mp.abs(res.imag - mp.Float("-91.694329309")), tol)
def test_arith_int(self): x = self.x y = self.y z = self.z p = self.p tol = self.tol self.assertLessEqual(mp.abs((x + 8) - mp.Float("12.23")), tol) self.assertLessEqual(mp.abs((y - 2) - mp.Float("-5.86")), tol) self.assertLessEqual(mp.abs((8 + x) - mp.Float("12.23")), tol) self.assertLessEqual(mp.abs((2 - y) - mp.Float("5.86")), tol) self.assertLessEqual(mp.abs((z * 6) - mp.Float("6.897")), tol) self.assertLessEqual(mp.abs((6 * z) - mp.Float("6.897")), tol) self.assertLessEqual( mp.abs((y / 3) - mp.Float("-1.2866666666666666666666666666666667")), tol) self.assertLessEqual( mp.abs((3 / y) - mp.Float("-.77720207253886010362694300518134714")), tol) self.assertLessEqual(mp.abs((x**3) - mp.Float("75.686967")), tol) # result = mp.Float(x) result += 8 self.assertLessEqual(mp.abs(result - mp.Float("12.23")), tol) result = mp.Float(y) result -= 2 self.assertLessEqual(mp.abs(result - mp.Float("-5.86")), tol) result = mp.Float(z) result *= 6 self.assertLessEqual(mp.abs(result - mp.Float("6.897")), tol) result = mp.Float(y) result /= 3 self.assertLessEqual( mp.abs(result - mp.Float("-1.2866666666666666666666666666666667")), tol) # self.assertLessEqual(mp.abs((-z) - mp.Float("-1.1495")), tol)