本文整理汇总了Python中sympy.lowergamma函数的典型用法代码示例。如果您正苦于以下问题:Python lowergamma函数的具体用法?Python lowergamma怎么用?Python lowergamma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lowergamma函数的20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_branch_bug
def test_branch_bug():
assert hyperexpand(hyper((-S(1)/3, S(1)/2), (S(2)/3, S(3)/2), -z)) == \
-z**S('1/3')*lowergamma(exp_polar(I*pi)/3, z)/5 \
+ sqrt(pi)*erf(sqrt(z))/(5*sqrt(z))
assert hyperexpand(meijerg([S(7)/6, 1], [], [S(2)/3], [S(1)/6, 0], z)) == \
2*z**S('2/3')*(2*sqrt(pi)*erf(sqrt(z))/sqrt(z) - 2*lowergamma(
S(2)/3, z)/z**S('2/3'))*gamma(S(2)/3)/gamma(S(5)/3)
开发者ID:vprusso,项目名称:sympy,代码行数:7,代码来源:test_hyperexpand.py
示例2: test_hyper
def test_hyper():
for x in sorted(exparg):
test("erf", x, N(sp.erf(x)))
for x in sorted(exparg):
test("erfc", x, N(sp.erfc(x)))
gamarg = FiniteSet(*(x+S(1)/12 for x in exparg))
betarg = ProductSet(gamarg, gamarg)
for x in sorted(gamarg):
test("lgamma", x, N(sp.log(abs(sp.gamma(x)))))
for x in sorted(gamarg):
test("gamma", x, N(sp.gamma(x)))
for x, y in sorted(betarg, key=lambda (x, y): (y, x)):
test("beta", x, y, N(sp.beta(x, y)))
pgamarg = FiniteSet(S(1)/12, S(1)/3, S(3)/2, 5)
pgamargp = ProductSet(gamarg & Interval(0, oo, True), pgamarg)
for a, x in sorted(pgamargp):
test("pgamma", a, x, N(sp.lowergamma(a, x)))
for a, x in sorted(pgamargp):
test("pgammac", a, x, N(sp.uppergamma(a, x)))
for a, x in sorted(pgamargp):
test("pgammar", a, x, N(sp.lowergamma(a, x)/sp.gamma(a)))
for a, x in sorted(pgamargp):
test("pgammarc", a, x, N(sp.uppergamma(a, x)/sp.gamma(a)))
for a, x in sorted(pgamargp):
test("ipgammarc", a, N(sp.uppergamma(a, x)/sp.gamma(a)), x)
pbetargp = [(a, b, x) for a, b, x in ProductSet(betarg, pgamarg)
if a > 0 and b > 0 and x < 1]
pbetargp.sort(key=lambda (a, b, x): (b, a, x))
for a, b, x in pbetargp:
test("pbeta", a, b, x, mp.betainc(mpf(a), mpf(b), x2=mpf(x)))
for a, b, x in pbetargp:
test("pbetar", a, b, x, mp.betainc(mpf(a), mpf(b), x2=mpf(x),
regularized=True))
for a, b, x in pbetargp:
test("ipbetar", a, b, mp.betainc(mpf(a), mpf(b), x2=mpf(x),
regularized=True), x)
for x in sorted(posarg):
test("j0", x, N(sp.besselj(0, x)))
for x in sorted(posarg):
test("j1", x, N(sp.besselj(1, x)))
for x in sorted(posarg-FiniteSet(0)):
test("y0", x, N(sp.bessely(0, x)))
for x in sorted(posarg-FiniteSet(0)):
test("y1", x, N(sp.bessely(1, x)))
开发者ID:zholos,项目名称:qml,代码行数:48,代码来源:libm.py
示例3: test_uppergamma
def test_uppergamma():
from sympy import meijerg, exp_polar, I, expint
assert uppergamma(4, 0) == 6
assert uppergamma(x, y).diff(y) == -y**(x-1)*exp(-y)
assert td(uppergamma(randcplx(), y), y)
assert uppergamma(x, y).diff(x) == \
uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
assert td(uppergamma(x, randcplx()), x)
assert uppergamma(S.Half, x) == sqrt(pi)*(1 - erf(sqrt(x)))
assert not uppergamma(S.Half - 3, x).has(uppergamma)
assert not uppergamma(S.Half + 3, x).has(uppergamma)
assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
assert tn(uppergamma(S.Half + 3, x, evaluate=False),
uppergamma(S.Half + 3, x), x)
assert tn(uppergamma(S.Half - 3, x, evaluate=False),
uppergamma(S.Half - 3, x), x)
assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y)
assert tn_branch(-3, uppergamma)
assert tn_branch(-4, uppergamma)
assert tn_branch(S(1)/3, uppergamma)
assert tn_branch(pi, uppergamma)
assert uppergamma(3, exp_polar(4*pi*I)*x) == uppergamma(3, x)
assert uppergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*uppergamma(y, x*exp_polar(pi*I)) + gamma(y)*(1-exp(4*pi*I*y))
assert uppergamma(-2, exp_polar(5*pi*I)*x) == \
uppergamma(-2, x*exp_polar(I*pi)) - 2*pi*I
assert uppergamma(-2, x) == expint(3, x)/x**2
assert uppergamma(x, y).rewrite(expint) == y**x*expint(-x + 1, y)
开发者ID:BDGLunde,项目名称:sympy,代码行数:32,代码来源:test_gamma_functions.py
示例4: test_hyperexpand_bases
def test_hyperexpand_bases():
assert (
hyperexpand(hyper([2], [a], z))
== a + z ** (-a + 1) * (-a ** 2 + 3 * a + z * (a - 1) - 2) * exp(z) * lowergamma(a - 1, z) - 1
)
# TODO [a+1, a-S.Half], [2*a]
assert hyperexpand(hyper([1, 2], [3], z)) == -2 / z - 2 * log(exp_polar(-I * pi) * z + 1) / z ** 2
assert hyperexpand(hyper([S.Half, 2], [S(3) / 2], z)) == -1 / (2 * z - 2) + log((sqrt(z) + 1) / (-sqrt(z) + 1)) / (
4 * sqrt(z)
)
assert hyperexpand(hyper([S(1) / 2, S(1) / 2], [S(5) / 2], z)) == (-3 * z + 3) / 4 / (z * sqrt(-z + 1)) + (
6 * z - 3
) * asin(sqrt(z)) / (4 * z ** (S(3) / 2))
assert hyperexpand(hyper([1, 2], [S(3) / 2], z)) == -1 / (2 * z - 2) - asin(sqrt(z)) / (
sqrt(z) * (2 * z - 2) * sqrt(-z + 1)
)
assert hyperexpand(hyper([-S.Half - 1, 1, 2], [S.Half, 3], z)) == sqrt(z) * (6 * z / 7 - S(6) / 5) * atanh(
sqrt(z)
) + (-30 * z ** 2 + 32 * z - 6) / 35 / z - 6 * log(-z + 1) / (35 * z ** 2)
assert hyperexpand(hyper([1 + S.Half, 1, 1], [2, 2], z)) == -4 * log(sqrt(-z + 1) / 2 + S(1) / 2) / z
# TODO hyperexpand(hyper([a], [2*a + 1], z))
# TODO [S.Half, a], [S(3)/2, a+1]
assert hyperexpand(hyper([2], [b, 1], z)) == z ** (-b / 2 + S(1) / 2) * besseli(b - 1, 2 * sqrt(z)) * gamma(
b
) + z ** (-b / 2 + 1) * besseli(b, 2 * sqrt(z)) * gamma(b)
开发者ID:kendhia,项目名称:sympy,代码行数:25,代码来源:test_hyperexpand.py
示例5: test_gamma
def test_gamma():
k = Symbol("k", positive=True)
theta = Symbol("theta", positive=True)
X = Gamma('x', k, theta)
assert density(X) == Lambda(_x,
_x**(k - 1)*theta**(-k)*exp(-_x/theta)/gamma(k))
assert cdf(X, meijerg=True) == Lambda(_z, Piecewise(
(-k*lowergamma(k, 0)/gamma(k + 1) + k*lowergamma(k, _z/theta)/gamma(k + 1), _z >= 0), (0, True)))
assert variance(X) == (-theta**2*gamma(k + 1)**2/gamma(k)**2 +
theta*theta**(-k)*theta**(k + 1)*gamma(k + 2)/gamma(k))
k, theta = symbols('k theta', real=True, bounded=True, positive=True)
X = Gamma('x', k, theta)
assert simplify(E(X)) == k*theta
# can't get things to simplify on this one so we use subs
assert variance(X).subs(k, 5) == (k*theta**2).subs(k, 5)
开发者ID:archipleago-creature,项目名称:sympy,代码行数:17,代码来源:test_continuous_rv.py
示例6: test_branch_bug
def test_branch_bug():
from sympy import powdenest, lowergamma
# TODO combsimp cannot prove that the factor is unity
assert powdenest(integrate(erf(x**3), x, meijerg=True).diff(x),
polar=True) == 2*erf(x**3)*gamma(S(2)/3)/3/gamma(S(5)/3)
assert integrate(erf(x**3), x, meijerg=True) == \
2*x*erf(x**3)*gamma(S(2)/3)/(3*gamma(S(5)/3)) \
- 2*gamma(S(2)/3)*lowergamma(S(2)/3, x**6)/(3*sqrt(pi)*gamma(S(5)/3))
开发者ID:chaffra,项目名称:sympy,代码行数:8,代码来源:test_meijerint.py
示例7: test_chi_squared
def test_chi_squared():
k = Symbol("k", integer=True)
X = ChiSquared('x', k)
assert density(X)(x) == 2**(-k/2)*x**(k/2 - 1)*exp(-x/2)/gamma(k/2)
assert cdf(X)(x) == Piecewise((lowergamma(k/2, x/2)/gamma(k/2), x >= 0), (0, True))
X = ChiSquared('x', 15)
assert cdf(X)(3) == -14873*sqrt(6)*exp(-S(3)/2)/(5005*sqrt(pi)) + erf(sqrt(6)/2)
开发者ID:cklb,项目名称:sympy,代码行数:9,代码来源:test_continuous_rv.py
示例8: test_latex_functions
def test_latex_functions():
assert latex(exp(x)) == "e^{x}"
assert latex(exp(1)+exp(2)) == "e + e^{2}"
f = Function('f')
assert latex(f(x)) == '\\operatorname{f}{\\left (x \\right )}'
beta = Function('beta')
assert latex(beta(x)) == r"\beta{\left (x \right )}"
assert latex(sin(x)) == r"\sin{\left (x \right )}"
assert latex(sin(x), fold_func_brackets=True) == r"\sin {x}"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"\sin {2 x^{2}}"
assert latex(sin(x**2), fold_func_brackets=True) == \
r"\sin {x^{2}}"
assert latex(asin(x)**2) == r"\operatorname{asin}^{2}{\left (x \right )}"
assert latex(asin(x)**2,inv_trig_style="full") == \
r"\arcsin^{2}{\left (x \right )}"
assert latex(asin(x)**2,inv_trig_style="power") == \
r"\sin^{-1}{\left (x \right )}^{2}"
assert latex(asin(x**2),inv_trig_style="power",fold_func_brackets=True) == \
r"\sin^{-1} {x^{2}}"
assert latex(factorial(k)) == r"k!"
assert latex(factorial(-k)) == r"\left(- k\right)!"
assert latex(factorial2(k)) == r"k!!"
assert latex(factorial2(-k)) == r"\left(- k\right)!!"
assert latex(binomial(2,k)) == r"{\binom{2}{k}}"
assert latex(FallingFactorial(3,k)) == r"{\left(3\right)}_{\left(k\right)}"
assert latex(RisingFactorial(3,k)) == r"{\left(3\right)}^{\left(k\right)}"
assert latex(floor(x)) == r"\lfloor{x}\rfloor"
assert latex(ceiling(x)) == r"\lceil{x}\rceil"
assert latex(Abs(x)) == r"\lvert{x}\rvert"
assert latex(re(x)) == r"\Re{x}"
assert latex(re(x+y)) == r"\Re {\left (x + y \right )}"
assert latex(im(x)) == r"\Im{x}"
assert latex(conjugate(x)) == r"\overline{x}"
assert latex(gamma(x)) == r"\Gamma\left(x\right)"
assert latex(Order(x)) == r"\mathcal{O}\left(x\right)"
assert latex(lowergamma(x, y)) == r'\gamma\left(x, y\right)'
assert latex(uppergamma(x, y)) == r'\Gamma\left(x, y\right)'
assert latex(cot(x)) == r'\cot{\left (x \right )}'
assert latex(coth(x)) == r'\coth{\left (x \right )}'
assert latex(re(x)) == r'\Re{x}'
assert latex(im(x)) == r'\Im{x}'
assert latex(root(x,y)) == r'x^{\frac{1}{y}}'
assert latex(arg(x)) == r'\arg{\left (x \right )}'
assert latex(zeta(x)) == r'\zeta{\left (x \right )}'
开发者ID:songuke,项目名称:sympy,代码行数:55,代码来源:test_latex.py
示例9: test_uppergamma
def test_uppergamma():
from sympy import meijerg
assert uppergamma(4, 0) == 6
assert uppergamma(x, y).diff(y) == -y**(x-1)*exp(-y)
assert td(uppergamma(randcplx(), y), y)
assert uppergamma(x, y).diff(x) == \
uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
assert td(uppergamma(x, randcplx()), x)
assert uppergamma(S.Half, x) == sqrt(pi)*(1 - erf(sqrt(x)))
assert not uppergamma(S.Half - 3, x).has(uppergamma)
assert not uppergamma(S.Half + 3, x).has(uppergamma)
assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
assert tn(uppergamma(S.Half + 3, x, evaluate=False),
uppergamma(S.Half + 3, x), x)
assert tn(uppergamma(S.Half - 3, x, evaluate=False),
uppergamma(S.Half - 3, x), x)
assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y)
开发者ID:101man,项目名称:sympy,代码行数:19,代码来源:test_gamma_functions.py
示例10: test_uppergamma
def test_uppergamma():
from sympy import meijerg, exp_polar, I, expint
assert uppergamma(4, 0) == 6
assert uppergamma(x, y).diff(y) == -y**(x - 1)*exp(-y)
assert td(uppergamma(randcplx(), y), y)
assert uppergamma(x, y).diff(x) == \
uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
assert td(uppergamma(x, randcplx()), x)
assert uppergamma(S.Half, x) == sqrt(pi)*erfc(sqrt(x))
assert not uppergamma(S.Half - 3, x).has(uppergamma)
assert not uppergamma(S.Half + 3, x).has(uppergamma)
assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
assert tn(uppergamma(S.Half + 3, x, evaluate=False),
uppergamma(S.Half + 3, x), x)
assert tn(uppergamma(S.Half - 3, x, evaluate=False),
uppergamma(S.Half - 3, x), x)
assert tn_branch(-3, uppergamma)
assert tn_branch(-4, uppergamma)
assert tn_branch(S(1)/3, uppergamma)
assert tn_branch(pi, uppergamma)
assert uppergamma(3, exp_polar(4*pi*I)*x) == uppergamma(3, x)
assert uppergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*uppergamma(y, x*exp_polar(pi*I)) + \
gamma(y)*(1 - exp(4*pi*I*y))
assert uppergamma(-2, exp_polar(5*pi*I)*x) == \
uppergamma(-2, x*exp_polar(I*pi)) - 2*pi*I
assert uppergamma(-2, x) == expint(3, x)/x**2
assert conjugate(uppergamma(x, y)) == uppergamma(conjugate(x), conjugate(y))
assert conjugate(uppergamma(x, 0)) == gamma(conjugate(x))
assert conjugate(uppergamma(x, -oo)) == conjugate(uppergamma(x, -oo))
assert uppergamma(x, y).rewrite(expint) == y**x*expint(-x + 1, y)
assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y)
assert uppergamma(70, 6) == 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320*exp(-6)
assert (uppergamma(S(77) / 2, 6) - uppergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
assert (uppergamma(-S(77) / 2, 6) - uppergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
开发者ID:carstimon,项目名称:sympy,代码行数:41,代码来源:test_gamma_functions.py
示例11: test_hyperexpand_bases
def test_hyperexpand_bases():
assert hyperexpand(hyper([2], [a], z)) == \
a + z**(-a + 1)*(-a**2 + 3*a + z*(a - 1) - 2)*exp(z)*lowergamma(a - 1, z) - 1
# TODO [a+1, a-S.Half], [2*a]
assert hyperexpand(hyper([1, 2], [3], z)) == -2/z - 2*log(-z + 1)/z**2
assert hyperexpand(hyper([S.Half, 2], [S(3)/2], z)) == \
-1/(2*z - 2) + log((z**(S(1)/2) + 1)/(-z**(S(1)/2) + 1))/(4*z**(S(1)/2))
assert hyperexpand(hyper([S(1)/2, S(1)/2], [S(5)/2], z)) == \
(-3*z + 3)/(4*z*(-z + 1)**(S(1)/2)) \
+ (6*z - 3)*asin(z**(S(1)/2))/(4*z**(S(3)/2))
assert hyperexpand(hyper([1, 2], [S(3)/2], z)) == -1/(2*z - 2) \
- asin(z**(S(1)/2))/(z**(S(1)/2)*(2*z - 2)*(-z + 1)**(S(1)/2))
assert hyperexpand(hyper([-S.Half - 1, 1, 2], [S.Half, 3], z)) == \
z**(S(1)/2)*(6*z/7 - S(6)/5)*atanh(z**(S(1)/2)) \
+ (-30*z**2 + 32*z - 6)/(35*z) - 6*log(-z + 1)/(35*z**2)
assert hyperexpand(hyper([1+S.Half, 1, 1], [2, 2], z)) == \
-4*log((-z + 1)**(S(1)/2)/2 + S(1)/2)/z
# TODO hyperexpand(hyper([a], [2*a + 1], z))
# TODO [S.Half, a], [S(3)/2, a+1]
assert hyperexpand(hyper([2], [b, 1], z)) == \
z**(-b/2 + S(1)/2)*besseli(b - 1, 2*z**(S(1)/2))*gamma(b) \
+ z**(-b/2 + 1)*besseli(b, 2*z**(S(1)/2))*gamma(b)
开发者ID:TeddyBoomer,项目名称:wxgeometrie,代码行数:22,代码来源:test_hyperexpand.py
示例12: test_latex_functions
def test_latex_functions():
assert latex(exp(x)) == "e^{x}"
assert latex(exp(1)+exp(2)) == "e + e^{2}"
f = Function('f')
assert latex(f(x)) == '\\operatorname{f}\\left(x\\right)'
beta = Function('beta')
assert latex(beta(x)) == r"\operatorname{beta}\left(x\right)"
assert latex(sin(x)) == r"\operatorname{sin}\left(x\right)"
assert latex(sin(x), fold_func_brackets=True) == r"\operatorname{sin}x"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"\operatorname{sin}2 x^{2}"
assert latex(sin(x**2), fold_func_brackets=True) == \
r"\operatorname{sin}x^{2}"
assert latex(asin(x)**2) == r"\operatorname{asin}^{2}\left(x\right)"
assert latex(asin(x)**2,inv_trig_style="full") == \
r"\operatorname{arcsin}^{2}\left(x\right)"
assert latex(asin(x)**2,inv_trig_style="power") == \
r"\operatorname{sin}^{-1}\left(x\right)^{2}"
assert latex(asin(x**2),inv_trig_style="power",fold_func_brackets=True) == \
r"\operatorname{sin}^{-1}x^{2}"
assert latex(factorial(k)) == r"k!"
assert latex(factorial(-k)) == r"\left(- k\right)!"
assert latex(floor(x)) == r"\lfloor{x}\rfloor"
assert latex(ceiling(x)) == r"\lceil{x}\rceil"
assert latex(Abs(x)) == r"\lvert{x}\rvert"
assert latex(re(x)) == r"\Re{x}"
assert latex(im(x)) == r"\Im{x}"
assert latex(conjugate(x)) == r"\overline{x}"
assert latex(gamma(x)) == r"\operatorname{\Gamma}\left(x\right)"
assert latex(Order(x)) == r"\operatorname{\mathcal{O}}\left(x\right)"
assert latex(lowergamma(x, y)) == r'\operatorname{\gamma}\left(x, y\right)'
assert latex(uppergamma(x, y)) == r'\operatorname{\Gamma}\left(x, y\right)'
开发者ID:qmattpap,项目名称:sympy,代码行数:38,代码来源:test_latex.py
示例13: test_latex_functions
def test_latex_functions():
assert latex(exp(x)) == "e^{x}"
assert latex(exp(1) + exp(2)) == "e + e^{2}"
f = Function("f")
assert latex(f(x)) == "\\operatorname{f}{\\left (x \\right )}"
beta = Function("beta")
assert latex(beta(x)) == r"\beta{\left (x \right )}"
assert latex(sin(x)) == r"\sin{\left (x \right )}"
assert latex(sin(x), fold_func_brackets=True) == r"\sin {x}"
assert latex(sin(2 * x ** 2), fold_func_brackets=True) == r"\sin {2 x^{2}}"
assert latex(sin(x ** 2), fold_func_brackets=True) == r"\sin {x^{2}}"
assert latex(asin(x) ** 2) == r"\operatorname{asin}^{2}{\left (x \right )}"
assert latex(asin(x) ** 2, inv_trig_style="full") == r"\arcsin^{2}{\left (x \right )}"
assert latex(asin(x) ** 2, inv_trig_style="power") == r"\sin^{-1}{\left (x \right )}^{2}"
assert latex(asin(x ** 2), inv_trig_style="power", fold_func_brackets=True) == r"\sin^{-1} {x^{2}}"
assert latex(factorial(k)) == r"k!"
assert latex(factorial(-k)) == r"\left(- k\right)!"
assert latex(subfactorial(k)) == r"!k"
assert latex(subfactorial(-k)) == r"!\left(- k\right)"
assert latex(factorial2(k)) == r"k!!"
assert latex(factorial2(-k)) == r"\left(- k\right)!!"
assert latex(binomial(2, k)) == r"{\binom{2}{k}}"
assert latex(FallingFactorial(3, k)) == r"{\left(3\right)}_{\left(k\right)}"
assert latex(RisingFactorial(3, k)) == r"{\left(3\right)}^{\left(k\right)}"
assert latex(floor(x)) == r"\lfloor{x}\rfloor"
assert latex(ceiling(x)) == r"\lceil{x}\rceil"
assert latex(Min(x, 2, x ** 3)) == r"\min\left(2, x, x^{3}\right)"
assert latex(Min(x, y) ** 2) == r"\min\left(x, y\right)^{2}"
assert latex(Max(x, 2, x ** 3)) == r"\max\left(2, x, x^{3}\right)"
assert latex(Max(x, y) ** 2) == r"\max\left(x, y\right)^{2}"
assert latex(Abs(x)) == r"\lvert{x}\rvert"
assert latex(re(x)) == r"\Re{x}"
assert latex(re(x + y)) == r"\Re{x} + \Re{y}"
assert latex(im(x)) == r"\Im{x}"
assert latex(conjugate(x)) == r"\overline{x}"
assert latex(gamma(x)) == r"\Gamma\left(x\right)"
assert latex(Order(x)) == r"\mathcal{O}\left(x\right)"
assert latex(lowergamma(x, y)) == r"\gamma\left(x, y\right)"
assert latex(uppergamma(x, y)) == r"\Gamma\left(x, y\right)"
assert latex(cot(x)) == r"\cot{\left (x \right )}"
assert latex(coth(x)) == r"\coth{\left (x \right )}"
assert latex(re(x)) == r"\Re{x}"
assert latex(im(x)) == r"\Im{x}"
assert latex(root(x, y)) == r"x^{\frac{1}{y}}"
assert latex(arg(x)) == r"\arg{\left (x \right )}"
assert latex(zeta(x)) == r"\zeta\left(x\right)"
assert latex(zeta(x)) == r"\zeta\left(x\right)"
assert latex(zeta(x) ** 2) == r"\zeta^{2}\left(x\right)"
assert latex(zeta(x, y)) == r"\zeta\left(x, y\right)"
assert latex(zeta(x, y) ** 2) == r"\zeta^{2}\left(x, y\right)"
assert latex(dirichlet_eta(x)) == r"\eta\left(x\right)"
assert latex(dirichlet_eta(x) ** 2) == r"\eta^{2}\left(x\right)"
assert latex(polylog(x, y)) == r"\operatorname{Li}_{x}\left(y\right)"
assert latex(polylog(x, y) ** 2) == r"\operatorname{Li}_{x}^{2}\left(y\right)"
assert latex(lerchphi(x, y, n)) == r"\Phi\left(x, y, n\right)"
assert latex(lerchphi(x, y, n) ** 2) == r"\Phi^{2}\left(x, y, n\right)"
assert latex(Ei(x)) == r"\operatorname{Ei}{\left (x \right )}"
assert latex(Ei(x) ** 2) == r"\operatorname{Ei}^{2}{\left (x \right )}"
assert latex(expint(x, y) ** 2) == r"\operatorname{E}_{x}^{2}\left(y\right)"
assert latex(Shi(x) ** 2) == r"\operatorname{Shi}^{2}{\left (x \right )}"
assert latex(Si(x) ** 2) == r"\operatorname{Si}^{2}{\left (x \right )}"
assert latex(Ci(x) ** 2) == r"\operatorname{Ci}^{2}{\left (x \right )}"
assert latex(Chi(x) ** 2) == r"\operatorname{Chi}^{2}{\left (x \right )}"
assert latex(jacobi(n, a, b, x)) == r"P_{n}^{\left(a,b\right)}\left(x\right)"
assert latex(jacobi(n, a, b, x) ** 2) == r"\left(P_{n}^{\left(a,b\right)}\left(x\right)\right)^{2}"
assert latex(gegenbauer(n, a, x)) == r"C_{n}^{\left(a\right)}\left(x\right)"
assert latex(gegenbauer(n, a, x) ** 2) == r"\left(C_{n}^{\left(a\right)}\left(x\right)\right)^{2}"
assert latex(chebyshevt(n, x)) == r"T_{n}\left(x\right)"
assert latex(chebyshevt(n, x) ** 2) == r"\left(T_{n}\left(x\right)\right)^{2}"
assert latex(chebyshevu(n, x)) == r"U_{n}\left(x\right)"
assert latex(chebyshevu(n, x) ** 2) == r"\left(U_{n}\left(x\right)\right)^{2}"
assert latex(legendre(n, x)) == r"P_{n}\left(x\right)"
assert latex(legendre(n, x) ** 2) == r"\left(P_{n}\left(x\right)\right)^{2}"
assert latex(assoc_legendre(n, a, x)) == r"P_{n}^{\left(a\right)}\left(x\right)"
assert latex(assoc_legendre(n, a, x) ** 2) == r"\left(P_{n}^{\left(a\right)}\left(x\right)\right)^{2}"
assert latex(laguerre(n, x)) == r"L_{n}\left(x\right)"
assert latex(laguerre(n, x) ** 2) == r"\left(L_{n}\left(x\right)\right)^{2}"
assert latex(assoc_laguerre(n, a, x)) == r"L_{n}^{\left(a\right)}\left(x\right)"
assert latex(assoc_laguerre(n, a, x) ** 2) == r"\left(L_{n}^{\left(a\right)}\left(x\right)\right)^{2}"
assert latex(hermite(n, x)) == r"H_{n}\left(x\right)"
assert latex(hermite(n, x) ** 2) == r"\left(H_{n}\left(x\right)\right)^{2}"
# Test latex printing of function names with "_"
assert latex(polar_lift(0)) == r"\operatorname{polar\_lift}{\left (0 \right )}"
assert latex(polar_lift(0) ** 3) == r"\operatorname{polar\_lift}^{3}{\left (0 \right )}"
开发者ID:kushal124,项目名称:sympy,代码行数:99,代码来源:test_latex.py
示例14: test_prob
def test_prob():
def emit(name, iname, cdf, args, no_small=False):
V = []
for arg in sorted(args):
y = cdf(*arg)
if isinstance(y, mpf):
e = sp.nsimplify(y, rational=True)
if e.is_Rational and e.q <= 1000 and \
mp.almosteq(mp.mpf(e), y, 1e-25):
y = e
else:
y = N(y)
V.append(arg + (y,))
for v in V:
if name:
test(name, *v)
for v in V:
if iname and (not no_small or 1/1000 <= v[-1] <= 999/1000):
test(iname, *(v[:-2] + v[:-3:-1]))
x = sp.Symbol("x")
emit("ncdf", "nicdf",
sp.Lambda(x, st.cdf(st.Normal("X", 0, 1))(x)), zip(exparg))
# using cdf() for anything more complex is too slow
df = FiniteSet(1, S(3)/2, 2, S(5)/2, 5, 25)
emit("c2cdf", "c2icdf",
lambda k, x: sp.lowergamma(k/2, x/2)/sp.gamma(k/2),
ProductSet(df, posarg), no_small=True)
dfint = df & sp.fancysets.Naturals()
def cdf(k, x):
k, x = map(mpf, (k, x))
return .5 + .5*mp.sign(x)*mp.betainc(k/2, .5, x1=1/(1+x**2/k),
regularized=True)
emit("stcdf", "sticdf", cdf, ProductSet(dfint, exparg))
def cdf(d1, d2, x):
d1, d2, x = map(mpf, (d1, d2, x))
return mp.betainc(d1/2, d2/2, x2=x/(x+d2/d1), regularized=True)
emit("fcdf", "ficdf", cdf, ProductSet(dfint, dfint, posarg))
kth = ProductSet(sp.ImageSet(lambda x: x/5, df),
posarg - FiniteSet(0))
emit("gcdf", "gicdf",
lambda k, th, x: sp.lowergamma(k, x/th)/sp.gamma(k),
ProductSet(kth, posarg), no_small=True)
karg = FiniteSet(0, 1, 2, 5, 10, 15, 40)
knparg = [(k, n, p) for k, n, p
in ProductSet(karg, karg, posarg & Interval(0, 1, True, True))
if k <= n and n > 0]
def cdf(k, n, p):
return st.P(st.Binomial("X", n, p) <= k)
emit("bncdf", "bnicdf", cdf, knparg, no_small=True)
def cdf(k, lamda):
return sp.uppergamma(k+1, lamda)/sp.gamma(k+1)
emit("pscdf", "psicdf", cdf,
ProductSet(karg, posarg + karg - FiniteSet(0)), no_small=True)
x, i = sp.symbols("x i")
def smcdf(n, e):
return 1-sp.Sum(sp.binomial(n, i)*e*(e+i/n)**(i-1)*(1-e-i/n)**(n-i),
(i, 0, sp.floor(n*(1-e)))).doit()
kcdf = sp.Lambda(x,
sp.sqrt(2*pi)/x*sp.Sum(sp.exp(-pi**2/8*(2*i-1)**2/x**2), (i, 1, oo)))
smarg = ProductSet(karg - FiniteSet(0), posarg & Interval(0, 1, True, True))
karg = FiniteSet(S(1)/100, S(1)/10) + (posarg & Interval(S(1)/4, oo, True))
for n, e in sorted(smarg):
test("smcdf", n, e, N(smcdf(n, e)))
prec("1e-10")
for x in sorted(karg):
test("kcdf", x, N(kcdf(x)))
prec("1e-9")
for n, e in sorted(smarg):
p = smcdf(n, e)
if p < S(9)/10:
test("smicdf", n, N(p), e)
prec("1e-6")
for x in sorted(karg):
p = kcdf(x)
if N(p) > S(10)**-8:
test("kicdf", N(p), x)
开发者ID:zholos,项目名称:qml,代码行数:86,代码来源:libm.py
示例15: test_lowergamma
def test_lowergamma():
from sympy import meijerg, exp_polar, I, expint
assert lowergamma(x, y).diff(y) == y**(x - 1)*exp(-y)
assert td(lowergamma(randcplx(), y), y)
assert td(lowergamma(x, randcplx()), x)
assert lowergamma(x, y).diff(x) == \
gamma(x)*polygamma(0, x) - uppergamma(x, y)*log(y) \
- meijerg([], [1, 1], [0, 0, x], [], y)
assert lowergamma(S.Half, x) == sqrt(pi)*erf(sqrt(x))
assert not lowergamma(S.Half - 3, x).has(lowergamma)
assert not lowergamma(S.Half + 3, x).has(lowergamma)
assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
assert tn(lowergamma(S.Half + 3, x, evaluate=False),
lowergamma(S.Half + 3, x), x)
assert tn(lowergamma(S.Half - 3, x, evaluate=False),
lowergamma(S.Half - 3, x), x)
assert tn_branch(-3, lowergamma)
assert tn_branch(-4, lowergamma)
assert tn_branch(S(1)/3, lowergamma)
assert tn_branch(pi, lowergamma)
assert lowergamma(3, exp_polar(4*pi*I)*x) == lowergamma(3, x)
assert lowergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*lowergamma(y, x*exp_polar(pi*I))
assert lowergamma(-2, exp_polar(5*pi*I)*x) == \
lowergamma(-2, x*exp_polar(I*pi)) + 2*pi*I
assert conjugate(lowergamma(x, y)) == lowergamma(conjugate(x), conjugate(y))
assert conjugate(lowergamma(x, 0)) == conjugate(lowergamma(x, 0))
assert conjugate(lowergamma(x, -oo)) == conjugate(lowergamma(x, -oo))
assert lowergamma(
x, y).rewrite(expint) == -y**x*expint(-x + 1, y) + gamma(x)
k = Symbol('k', integer=True)
assert lowergamma(
k, y).rewrite(expint) == -y**k*expint(-k + 1, y) + gamma(k)
k = Symbol('k', integer=True, positive=False)
assert lowergamma(k, y).rewrite(expint) == lowergamma(k, y)
assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y)
开发者ID:A-turing-machine,项目名称:sympy,代码行数:40,代码来源:test_gamma_functions.py
示例16: test_lowergamma
def test_lowergamma():
from sympy import meijerg, exp_polar, I
assert lowergamma(x, y).diff(y) == y**(x-1)*exp(-y)
assert td(lowergamma(randcplx(), y), y)
assert lowergamma(x, y).diff(x) == \
gamma(x)*polygamma(0, x) - uppergamma(x, y)*log(y) \
+ meijerg([], [1, 1], [0, 0, x], [], y)
assert lowergamma(S.Half, x) == sqrt(pi)*erf(sqrt(x))
assert not lowergamma(S.Half - 3, x).has(lowergamma)
assert not lowergamma(S.Half + 3, x).has(lowergamma)
assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
assert tn(lowergamma(S.Half + 3, x, evaluate=False),
lowergamma(S.Half + 3, x), x)
assert tn(lowergamma(S.Half - 3, x, evaluate=False),
lowergamma(S.Half - 3, x), x)
assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y)
assert tn_branch(-3, lowergamma)
assert tn_branch(-4, lowergamma)
assert tn_branch(S(1)/3, lowergamma)
assert tn_branch(pi, lowergamma)
assert lowergamma(3, exp_polar(4*pi*I)*x) == lowergamma(3, x)
assert lowergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*lowergamma(y, x*exp_polar(pi*I))
assert lowergamma(-2, exp_polar(5*pi*I)*x) == \
lowergamma(-2, x*exp_polar(I*pi)) + 2*pi*I
开发者ID:Kimay,项目名称:sympy,代码行数:28,代码来源:test_gamma_functions.py
示例17: test_latex_functions
def test_latex_functions():
assert latex(exp(x)) == "e^{x}"
assert latex(exp(1) + exp(2)) == "e + e^{2}"
f = Function('f')
assert latex(f(x)) == r'f{\left (x \right )}'
assert latex(f) == r'f'
g = Function('g')
assert latex(g(x, y)) == r'g{\left (x,y \right )}'
assert latex(g) == r'g'
h = Function('h')
assert latex(h(x, y, z)) == r'h{\left (x,y,z \right )}'
assert latex(h) == r'h'
Li = Function('Li')
assert latex(Li) == r'\operatorname{Li}'
assert latex(Li(x)) == r'\operatorname{Li}{\left (x \right )}'
beta = Function('beta')
# not to be confused with the beta function
assert latex(beta(x)) == r"\beta{\left (x \right )}"
assert latex(beta) == r"\beta"
assert latex(sin(x)) == r"\sin{\left (x \right )}"
assert latex(sin(x), fold_func_brackets=True) == r"\sin {x}"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"\sin {2 x^{2}}"
assert latex(sin(x**2), fold_func_brackets=True) == \
r"\sin {x^{2}}"
assert latex(asin(x)**2) == r"\operatorname{asin}^{2}{\left (x \right )}"
assert latex(asin(x)**2, inv_trig_style="full") == \
r"\arcsin^{2}{\left (x \right )}"
assert latex(asin(x)**2, inv_trig_style="power") == \
r"\sin^{-1}{\left (x \right )}^{2}"
assert latex(asin(x**2), inv_trig_style="power",
fold_func_brackets=True) == \
r"\sin^{-1} {x^{2}}"
assert latex(factorial(k)) == r"k!"
assert latex(factorial(-k)) == r"\left(- k\right)!"
assert latex(subfactorial(k)) == r"!k"
assert latex(subfactorial(-k)) == r"!\left(- k\right)"
assert latex(factorial2(k)) == r"k!!"
assert latex(factorial2(-k)) == r"\left(- k\right)!!"
assert latex(binomial(2, k)) == r"{\binom{2}{k}}"
assert latex(
FallingFactorial(3, k)) == r"{\left(3\right)}_{\left(k\right)}"
assert latex(RisingFactorial(3, k)) == r"{\left(3\right)}^{\left(k\right)}"
assert latex(floor(x)) == r"\lfloor{x}\rfloor"
assert latex(ceiling(x)) == r"\lceil{x}\rceil"
assert latex(Min(x, 2, x**3)) == r"\min\left(2, x, x^{3}\right)"
assert latex(Min(x, y)**2) == r"\min\left(x, y\right)^{2}"
assert latex(Max(x, 2, x**3)) == r"\max\left(2, x, x^{3}\right)"
assert latex(Max(x, y)**2) == r"\max\left(x, y\right)^{2}"
assert latex(Abs(x)) == r"\left\lvert{x}\right\rvert"
assert latex(re(x)) == r"\Re{x}"
assert latex(re(x + y)) == r"\Re{x} + \Re{y}"
assert latex(im(x)) == r"\Im{x}"
assert latex(conjugate(x)) == r"\overline{x}"
assert latex(gamma(x)) == r"\Gamma\left(x\right)"
assert latex(Order(x)) == r"\mathcal{O}\left(x\right)"
assert latex(lowergamma(x, y)) == r'\gamma\left(x, y\right)'
assert latex(uppergamma(x, y)) == r'\Gamma\left(x, y\right)'
assert latex(cot(x)) == r'\cot{\left (x \right )}'
assert latex(coth(x)) == r'\coth{\left (x \right )}'
assert latex(re(x)) == r'\Re{x}'
assert latex(im(x)) == r'\Im{x}'
assert latex(root(x, y)) == r'x^{\frac{1}{y}}'
assert latex(arg(x)) == r'\arg{\left (x \right )}'
assert latex(zeta(x)) == r'\zeta\left(x\right)'
assert latex(zeta(x)) == r"\zeta\left(x\right)"
assert latex(zeta(x)**2) == r"\zeta^{2}\left(x\right)"
assert latex(zeta(x, y)) == r"\zeta\left(x, y\right)"
assert latex(zeta(x, y)**2) == r"\zeta^{2}\left(x, y\right)"
assert latex(dirichlet_eta(x)) == r"\eta\left(x\right)"
assert latex(dirichlet_eta(x)**2) == r"\eta^{2}\left(x\right)"
assert latex(polylog(x, y)) == r"\operatorname{Li}_{x}\left(y\right)"
assert latex(
polylog(x, y)**2) == r"\operatorname{Li}_{x}^{2}\left(y\right)"
assert latex(lerchphi(x, y, n)) == r"\Phi\left(x, y, n\right)"
assert latex(lerchphi(x, y, n)**2) == r"\Phi^{2}\left(x, y, n\right)"
assert latex(elliptic_k(z)) == r"K\left(z\right)"
assert latex(elliptic_k(z)**2) == r"K^{2}\left(z\right)"
assert latex(elliptic_f(x, y)) == r"F\left(x\middle| y\right)"
assert latex(elliptic_f(x, y)**2) == r"F^{2}\left(x\middle| y\right)"
assert latex(elliptic_e(x, y)) == r"E\left(x\middle| y\right)"
assert latex(elliptic_e(x, y)**2) == r"E^{2}\left(x\middle| y\right)"
assert latex(elliptic_e(z)) == r"E\left(z\right)"
#.........这里部分代码省略.........
开发者ID:Ronn3y,项目名称:sympy,代码行数:101,代码来源:test_latex.py
示例18: test_lowergamma
def test_lowergamma():
from sympy import meijerg
assert lowergamma(x, y).diff(y) == y ** (x - 1) * exp(-y)
assert td(lowergamma(randcplx(), y), y)
assert lowergamma(x, y).diff(x) == gamma(x) * polygamma(0, x) - uppergamma(x, y) * log(y) + meijerg(
[], [1, 1], [0, 0, x], [], y
)
assert lowergamma(S.Half, x) == sqrt(pi) * erf(sqrt(x))
assert not lowergamma(S.Half - 3, x).has(lowergamma)
assert not lowergamma(S.Half + 3, x).has(lowergamma)
assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
assert tn(lowergamma(S.Half + 3, x, evaluate=False), lowergamma(S.Half + 3, x), x)
assert tn(lowergamma(S.Half - 3, x, evaluate=False), lowergamma(S.Half - 3, x), x)
开发者ID:hitej,项目名称:meta-core,代码行数:15,代码来源:test_gamma_functions.py
示例19: test_gammas
def test_gammas():
assert upretty(lowergamma(x, y)) == u"γ(x, y)"
assert upretty(uppergamma(x, y)) == u"Γ(x, y)"
开发者ID:lazovich,项目名称:sympy,代码行数:3,代码来源:test_pretty.py
示例20: test_meijerint
def test_meijerint():
from sympy import symbols, expand, arg
s, t, mu = symbols("s t mu", real=True)
assert integrate(
meijerg([], [], [0], [], s * t) * meijerg([], [], [mu / 2], [-mu / 2], t ** 2 / 4), (t, 0, oo)
).is_Piecewise
s = symbols("s", positive=True)
assert integrate(x ** s * meijerg([[], []], [[0], []], x), (x, 0, oo)) == gamma(s + 1)
assert integrate(x ** s * meijerg([[], []], [[0], []], x), (x, 0, oo), meijerg=True) == gamma(s + 1)
assert isinstance(integrate(x ** s * meijerg([[], []], [[0], []], x), (x, 0, oo), meijerg=False), Integral)
assert meijerint_indefinite(exp(x), x) == exp(x)
# TODO what simplifications should be done automatically?
# This tests "extra case" for antecedents_1.
a, b = symbols("a b", positive=True)
assert simplify(meijerint_definite(x ** a, x, 0, b)[0]) == b ** (a + 1) / (a + 1)
# This tests various conditions and expansions:
meijerint_definite((x + 1) ** 3 * exp(-x), x, 0, oo) == (16, True)
# Again, how about simplifications?
sigma, mu = symbols("sigma mu", positive=True)
i, c = meijerint_definite(exp(-((x - mu) / (2 * sigma)) ** 2), x, 0, oo)
assert simplify(i) == sqrt(pi) * sigma * (2 - erfc(mu / (2 * sigma)))
assert c == True
i, _ = meijerint_definite(exp(-mu * x) * exp(sigma * x), x, 0, oo)
# TODO it would be nice to test the condition
assert simplify(i) == 1 / (mu - sigma)
# Test substitutions to change limits
assert meijerint_definite(exp(x), x, -oo, 2) == (exp(2), True)
# Note: causes a NaN in _check_antecedents
assert expand(meijerint_definite(exp(x), x, 0, I)[0]) == exp(I) - 1
assert expand(meijerint_definite(exp(-x), x, 0, x)[0]) == 1 - exp(-exp(I * arg(x)) * abs(x))
# Test -oo to oo
assert meijerint_definite(exp(-x ** 2), x, -oo, oo) == (sqrt(pi), True)
assert meijerint_definite(exp(-abs(x)), x, -oo, oo) == (2, True)
assert meijerint_definite(exp(-(2 * x - 3) ** 2), x, -oo, oo) == (sqrt(pi) / 2, True)
assert meijerint_definite(exp(-abs(2 * x - 3)), x, -oo, oo) == (1, True)
assert
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