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Python sympy.erfi函数代码示例

原作者: [db:作者] 来自: [db:来源] 收藏 邀请

本文整理汇总了Python中sympy.erfi函数的典型用法代码示例。如果您正苦于以下问题：Python erfi函数的具体用法？Python erfi怎么用？Python erfi使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。



在下文中一共展示了erfi函数的12个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。

示例1: test_erf2

def test_erf2():

    assert erf2(0, 0) == S.Zero
    assert erf2(x, x) == S.Zero
    assert erf2(nan, 0) == nan

    assert erf2(-oo,  y) ==  erf(y) + 1
    assert erf2( oo,  y) ==  erf(y) - 1
    assert erf2(  x, oo) ==  1 - erf(x)
    assert erf2(  x,-oo) == -1 - erf(x)
    assert erf2(x, erf2inv(x, y)) == y

    assert erf2(-x, -y) == -erf2(x,y)
    assert erf2(-x,  y) == erf(y) + erf(x)
    assert erf2( x, -y) == -erf(y) - erf(x)
    assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels)
    assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc)
    assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper)
    assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg)
    assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
    assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint)

    assert erf2(I, 0).is_real is False
    assert erf2(0, 0).is_real is True

    assert expand_func(erf(x) + erf2(x, y)) == erf(y)

    assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))

    assert erf2(x, y).rewrite('erf')  == erf(y) - erf(x)
    assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y)
    assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y))

    raises(ArgumentIndexError, lambda: erfi(x).fdiff(3))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:34，代码来源:test_error_functions.py


示例2: test_manualintegrate_special

def test_manualintegrate_special():
    f, F = 4*exp(-x**2/3), 2*sqrt(3)*sqrt(pi)*erf(sqrt(3)*x/3)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = 3*exp(4*x**2), 3*sqrt(pi)*erfi(2*x)/4
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = x**(S(1)/3)*exp(-x/8), -16*uppergamma(S(4)/3, x/8)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = exp(2*x)/x, Ei(2*x)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = exp(1 + 2*x - x**2), sqrt(pi)*exp(2)*erf(x - 1)/2
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f = sin(x**2 + 4*x + 1)
    F = (sqrt(2)*sqrt(pi)*(-sin(3)*fresnelc(sqrt(2)*(2*x + 4)/(2*sqrt(pi))) +
        cos(3)*fresnels(sqrt(2)*(2*x + 4)/(2*sqrt(pi))))/2)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = cos(4*x**2), sqrt(2)*sqrt(pi)*fresnelc(2*sqrt(2)*x/sqrt(pi))/4
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = sin(3*x + 2)/x, sin(2)*Ci(3*x) + cos(2)*Si(3*x)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = sinh(3*x - 2)/x, -sinh(2)*Chi(3*x) + cosh(2)*Shi(3*x)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = 5*cos(2*x - 3)/x, 5*cos(3)*Ci(2*x) + 5*sin(3)*Si(2*x)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = cosh(x/2)/x, Chi(x/2)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = cos(x**2)/x, Ci(x**2)/2
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = 1/log(2*x + 1), li(2*x + 1)/2
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = polylog(2, 5*x)/x, polylog(3, 5*x)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = 5/sqrt(3 - 2*sin(x)**2), 5*sqrt(3)*elliptic_f(x, S(2)/3)/3
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
    f, F = sqrt(4 + 9*sin(x)**2), 2*elliptic_e(x, -S(9)/4)
    assert manualintegrate(f, x) == F and F.diff(x).equals(f)
开发者ID:gamechanger98，项目名称:sympy，代码行数:35，代码来源:test_manual.py


示例3: test_issue_4890

def test_issue_4890():
    z = Symbol('z', positive=True)
    assert integrate(exp(-log(x)**2), x) == \
        sqrt(pi)*exp(S(1)/4)*erf(log(x)-S(1)/2)/2
    assert integrate(exp(log(x)**2), x) == \
        sqrt(pi)*exp(-S(1)/4)*erfi(log(x)+S(1)/2)/2
    assert integrate(exp(-z*log(x)**2), x) == \
        sqrt(pi)*exp(1/(4*z))*erf(sqrt(z)*log(x) - 1/(2*sqrt(z)))/(2*sqrt(z))
开发者ID:baoqchau，项目名称:sympy，代码行数:8，代码来源:test_integrals.py


示例4: fdiff

        def fdiff(self, argindex):
            r, mu, sigma, lamda = self.args
            # if mu=0 and sigma=1, then this is
            # just the inverse standard erf so return erfi
            if mu == 0 and sigma == 1:
                return sympy.diff(sympy.erfi(r), self.args[argindex-1])

            tmp = sympy.symbols("tmp", real=True, finite=True)
            z_s = GaussianMixtureCDF(tmp, mu, sigma, lamda)
            inv_diff = sympy.diff(z_s, self.args[argindex-1])
            return sympy.simplify(1/inv_diff.subs(tmp, self))
开发者ID:Simon-Coetzee，项目名称:idr，代码行数:11，代码来源:symbolic.py


示例5: test_erf

def test_erf():
    assert erf(nan) == nan

    assert erf(oo) == 1
    assert erf(-oo) == -1

    assert erf(0) == 0

    assert erf(I*oo) == oo*I
    assert erf(-I*oo) == -oo*I

    assert erf(-2) == -erf(2)
    assert erf(-x*y) == -erf(x*y)
    assert erf(-x - y) == -erf(x + y)

    assert erf(erfinv(x)) == x
    assert erf(erfcinv(x)) == 1 - x
    assert erf(erf2inv(0, x)) == x
    assert erf(erf2inv(0, erf(erfcinv(1 - erf(erfinv(x)))))) == x

    assert erf(I).is_real is False
    assert erf(0).is_real is True

    assert conjugate(erf(z)) == erf(conjugate(z))

    assert erf(x).as_leading_term(x) == 2*x/sqrt(pi)
    assert erf(1/x).as_leading_term(x) == erf(1/x)

    assert erf(z).rewrite('uppergamma') == sqrt(z**2)*(1 - erfc(sqrt(z**2)))/z
    assert erf(z).rewrite('erfc') == S.One - erfc(z)
    assert erf(z).rewrite('erfi') == -I*erfi(I*z)
    assert erf(z).rewrite('fresnels') == (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
        I*fresnels(z*(1 - I)/sqrt(pi)))
    assert erf(z).rewrite('fresnelc') == (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
        I*fresnels(z*(1 - I)/sqrt(pi)))
    assert erf(z).rewrite('hyper') == 2*z*hyper([S.Half], [3*S.Half], -z**2)/sqrt(pi)
    assert erf(z).rewrite('meijerg') == z*meijerg([S.Half], [], [0], [-S.Half], z**2)/sqrt(pi)
    assert erf(z).rewrite('expint') == sqrt(z**2)/z - z*expint(S.Half, z**2)/sqrt(S.Pi)

    assert limit(exp(x)*exp(x**2)*(erf(x + 1/exp(x)) - erf(x)), x, oo) == \
        2/sqrt(pi)
    assert limit((1 - erf(z))*exp(z**2)*z, z, oo) == 1/sqrt(pi)
    assert limit((1 - erf(x))*exp(x**2)*sqrt(pi)*x, x, oo) == 1
    assert limit(((1 - erf(x))*exp(x**2)*sqrt(pi)*x - 1)*2*x**2, x, oo) == -1

    assert erf(x).as_real_imag() == \
        ((erf(re(x) - I*re(x)*Abs(im(x))/Abs(re(x)))/2 +
         erf(re(x) + I*re(x)*Abs(im(x))/Abs(re(x)))/2,
         I*(erf(re(x) - I*re(x)*Abs(im(x))/Abs(re(x))) -
         erf(re(x) + I*re(x)*Abs(im(x))/Abs(re(x)))) *
         re(x)*Abs(im(x))/(2*im(x)*Abs(re(x)))))

    raises(ArgumentIndexError, lambda: erf(x).fdiff(2))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:53，代码来源:test_error_functions.py


示例6: test_issue_3940

def test_issue_3940():
    a, b, c, d = symbols('a:d', positive=True, finite=True)
    assert integrate(exp(-x**2 + I*c*x), x) == \
        -sqrt(pi)*exp(-c**2/4)*erf(I*c/2 - x)/2
    assert integrate(exp(a*x**2 + b*x + c), x) == \
        sqrt(pi)*exp(c)*exp(-b**2/(4*a))*erfi(sqrt(a)*x + b/(2*sqrt(a)))/(2*sqrt(a))

    from sympy import expand_mul
    from sympy.abc import k
    assert expand_mul(integrate(exp(-x**2)*exp(I*k*x), (x, -oo, oo))) == \
        sqrt(pi)*exp(-k**2/4)
    a, d = symbols('a d', positive=True)
    assert expand_mul(integrate(exp(-a*x**2 + 2*d*x), (x, -oo, oo))) == \
        sqrt(pi)*exp(d**2/a)/sqrt(a)
开发者ID:baoqchau，项目名称:sympy，代码行数:14，代码来源:test_integrals.py


示例7: test_erfc

def test_erfc():
    assert erfc(nan) == nan

    assert erfc(oo) == 0
    assert erfc(-oo) == 2

    assert erfc(0) == 1

    assert erfc(I*oo) == -oo*I
    assert erfc(-I*oo) == oo*I

    assert erfc(-x) == S(2) - erfc(x)
    assert erfc(erfcinv(x)) == x

    assert erfc(I).is_real is False
    assert erfc(0).is_real is True

    assert conjugate(erfc(z)) == erfc(conjugate(z))

    assert erfc(x).as_leading_term(x) == S.One
    assert erfc(1/x).as_leading_term(x) == erfc(1/x)

    assert erfc(z).rewrite('erf') == 1 - erf(z)
    assert erfc(z).rewrite('erfi') == 1 + I*erfi(I*z)
    assert erfc(z).rewrite('fresnels') == 1 - (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
        I*fresnels(z*(1 - I)/sqrt(pi)))
    assert erfc(z).rewrite('fresnelc') == 1 - (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) -
        I*fresnels(z*(1 - I)/sqrt(pi)))
    assert erfc(z).rewrite('hyper') == 1 - 2*z*hyper([S.Half], [3*S.Half], -z**2)/sqrt(pi)
    assert erfc(z).rewrite('meijerg') == 1 - z*meijerg([S.Half], [], [0], [-S.Half], z**2)/sqrt(pi)
    assert erfc(z).rewrite('uppergamma') == 1 - sqrt(z**2)*(1 - erfc(sqrt(z**2)))/z
    assert erfc(z).rewrite('expint') == S.One - sqrt(z**2)/z + z*expint(S.Half, z**2)/sqrt(S.Pi)
    assert expand_func(erf(x) + erfc(x)) == S.One

    assert erfc(x).as_real_imag() == \
        ((erfc(re(x) - I*re(x)*Abs(im(x))/Abs(re(x)))/2 +
         erfc(re(x) + I*re(x)*Abs(im(x))/Abs(re(x)))/2,
         I*(erfc(re(x) - I*re(x)*Abs(im(x))/Abs(re(x))) -
         erfc(re(x) + I*re(x)*Abs(im(x))/Abs(re(x)))) *
         re(x)*Abs(im(x))/(2*im(x)*Abs(re(x)))))

    raises(ArgumentIndexError, lambda: erfc(x).fdiff(2))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:42，代码来源:test_error_functions.py


示例8: _create_table

def _create_table(table):
    """
    Creates the look-up table. For a similar implementation
    see meijerint._create_lookup_table.
    """

    def add(formula, annihilator, arg, x0=0, y0=[]):
        """
        Adds a formula in the dictionary
        """
        table.setdefault(_mytype(formula, x_1), []).append((formula,
            HolonomicFunction(annihilator, arg, x0, y0)))

    R = QQ.old_poly_ring(x_1)
    _, Dx = DifferentialOperators(R, 'Dx')

    from sympy import (sin, cos, exp, log, erf, sqrt, pi,
        sinh, cosh, sinc, erfc, Si, Ci, Shi, erfi)

    # add some basic functions
    add(sin(x_1), Dx**2 + 1, x_1, 0, [0, 1])
    add(cos(x_1), Dx**2 + 1, x_1, 0, [1, 0])
    add(exp(x_1), Dx - 1, x_1, 0, 1)
    add(log(x_1), Dx + x_1*Dx**2, x_1, 1, [0, 1])

    add(erf(x_1), 2*x_1*Dx + Dx**2, x_1, 0, [0, 2/sqrt(pi)])
    add(erfc(x_1), 2*x_1*Dx + Dx**2, x_1, 0, [1, -2/sqrt(pi)])
    add(erfi(x_1), -2*x_1*Dx + Dx**2, x_1, 0, [0, 2/sqrt(pi)])

    add(sinh(x_1), Dx**2 - 1, x_1, 0, [0, 1])
    add(cosh(x_1), Dx**2 - 1, x_1, 0, [1, 0])

    add(sinc(x_1), x_1 + 2*Dx + x_1*Dx**2, x_1)

    add(Si(x_1), x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1)
    add(Ci(x_1), x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1)

    add(Shi(x_1), -x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1)
开发者ID:AlexanderKulka，项目名称:sympy，代码行数:38，代码来源:holonomic.py


示例9: test_erfi_evalf

def test_erfi_evalf():
    assert abs( erfi(Float(2.0)) - 18.5648024145756 ) < 1E-13  # XXX
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:2，代码来源:test_error_functions.py


示例10: test_erfi_series

def test_erfi_series():
    assert erfi(x).series(x, 0, 7) == 2*x/sqrt(pi) + \
        2*x**3/3/sqrt(pi) + x**5/5/sqrt(pi) + O(x**7)
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:3，代码来源:test_error_functions.py


示例11: test_erfi

def test_erfi():
    assert erfi(nan) == nan

    assert erfi(oo) == S.Infinity
    assert erfi(-oo) == S.NegativeInfinity

    assert erfi(0) == S.Zero

    assert erfi(I*oo) == I
    assert erfi(-I*oo) == -I

    assert erfi(-x) == -erfi(x)

    assert erfi(I*erfinv(x)) == I*x
    assert erfi(I*erfcinv(x)) == I*(1 - x)
    assert erfi(I*erf2inv(0, x)) == I*x

    assert erfi(I).is_real is False
    assert erfi(0).is_real is True

    assert conjugate(erfi(z)) == erfi(conjugate(z))

    assert erfi(z).rewrite('erf') == -I*erf(I*z)
    assert erfi(z).rewrite('erfc') == I*erfc(I*z) - I
    assert erfi(z).rewrite('fresnels') == (1 - I)*(fresnelc(z*(1 + I)/sqrt(pi)) -
        I*fresnels(z*(1 + I)/sqrt(pi)))
    assert erfi(z).rewrite('fresnelc') == (1 - I)*(fresnelc(z*(1 + I)/sqrt(pi)) -
        I*fresnels(z*(1 + I)/sqrt(pi)))
    assert erfi(z).rewrite('hyper') == 2*z*hyper([S.Half], [3*S.Half], z**2)/sqrt(pi)
    assert erfi(z).rewrite('meijerg') == z*meijerg([S.Half], [], [0], [-S.Half], -z**2)/sqrt(pi)
    assert erfi(z).rewrite('uppergamma') == (sqrt(-z**2)/z*(uppergamma(S.Half,
        -z**2)/sqrt(S.Pi) - S.One))
    assert erfi(z).rewrite('expint') == sqrt(-z**2)/z - z*expint(S.Half, -z**2)/sqrt(S.Pi)
    assert expand_func(erfi(I*z)) == I*erf(z)

    assert erfi(x).as_real_imag() == \
        ((erfi(re(x) - I*re(x)*Abs(im(x))/Abs(re(x)))/2 +
         erfi(re(x) + I*re(x)*Abs(im(x))/Abs(re(x)))/2,
         I*(erfi(re(x) - I*re(x)*Abs(im(x))/Abs(re(x))) -
         erfi(re(x) + I*re(x)*Abs(im(x))/Abs(re(x)))) *
         re(x)*Abs(im(x))/(2*im(x)*Abs(re(x)))))

    raises(ArgumentIndexError, lambda: erfi(x).fdiff(2))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:43，代码来源:test_error_functions.py


示例12: test_issue_841

def test_issue_841():
    a, b, c, d = symbols('a:d', positive=True, bounded=True)
    assert integrate(exp(-x**2 + I*c*x), x) == \
        -sqrt(pi)*exp(-c**2/4)*erf(I*c/2 - x)/2
    assert integrate(exp(a*x**2 + b*x + c), x) == \
        sqrt(pi)*exp(c)*exp(-b**2/(4*a))*erfi(sqrt(a)*x + b/(2*sqrt(a)))/(2*sqrt(a))
开发者ID:FedericoV，项目名称:sympy，代码行数:6，代码来源:test_integrals.py



注：本文中的sympy.erfi函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。

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