def test_specfun():
n = Symbol('n')
for f in [besselj, bessely, besseli, besselk]:
assert octave_code(f(n, x)) == f.__name__ + '(n, x)'
for f in (erfc, erfi, erf, erfinv, erfcinv, fresnelc, fresnels, gamma):
assert octave_code(f(x)) == f.__name__ + '(x)'
assert octave_code(hankel1(n, x)) == 'besselh(n, 1, x)'
assert octave_code(hankel2(n, x)) == 'besselh(n, 2, x)'
assert octave_code(airyai(x)) == 'airy(0, x)'
assert octave_code(airyaiprime(x)) == 'airy(1, x)'
assert octave_code(airybi(x)) == 'airy(2, x)'
assert octave_code(airybiprime(x)) == 'airy(3, x)'
assert octave_code(uppergamma(
n, x)) == '(gammainc(x, n, \'upper\').*gamma(n))'
assert octave_code(lowergamma(n, x)) == '(gammainc(x, n).*gamma(n))'
assert octave_code(z**lowergamma(n, x)) == 'z.^(gammainc(x, n).*gamma(n))'
assert octave_code(jn(
n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
assert octave_code(yn(
n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
assert octave_code(LambertW(x)) == 'lambertw(x)'
assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'
# Automatic rewrite
assert octave_code(Ei(x)) == 'logint(exp(x))'
assert octave_code(dirichlet_eta(x)) == '(1 - 2.^(1 - x)).*zeta(x)'
assert octave_code(
riemann_xi(x)) == 'pi.^(-x/2).*x.*(x - 1).*gamma(x/2).*zeta(x)/2'
def _generate_patterns():
"""
Generates patterns for transcendental equations.
This is lazily calculated (called) in the tsolve() function and stored in
the patterns global variable.
"""
tmp1 = f**(h - (c * g / b))
tmp2 = (-e * tmp1 / a)**(1 / d)
global patterns
patterns = [
(a * (b * x + c)**d + e, ((-(e / a))**(1 / d) - c) / b),
(b + c * exp(d * x + e), (log(-b / c) - e) / d),
(a * x + b + c * exp(d * x + e),
-b / a - LambertW(c * d * exp(e - b * d / a) / a) / d),
(b + c * f**(d * x + e), (log(-b / c) - e * log(f)) / d / log(f)),
(a * x + b + c * f**(d * x + e), -b / a -
LambertW(c * d * f**(e - b * d / a) * log(f) / a) / d / log(f)),
(b + c * log(d * x + e), (exp(-b / c) - e) / d),
(a * x + b + c * log(d * x + e),
-e / d + c / a * LambertW(a / c / d * exp(-b / c + a * e / c / d))),
(a * (b * x + c)**d + e * f**(g * x + h),
-c / b - d * LambertW(-tmp2 * g * log(f) / b / d) / g / log(f))
]
def test_specfun():
n = Symbol('n')
for f in [besselj, bessely, besseli, besselk]:
assert octave_code(f(n, x)) == f.__name__ + '(n, x)'
assert octave_code(hankel1(n, x)) == 'besselh(n, 1, x)'
assert octave_code(hankel2(n, x)) == 'besselh(n, 2, x)'
assert octave_code(airyai(x)) == 'airy(0, x)'
assert octave_code(airyaiprime(x)) == 'airy(1, x)'
assert octave_code(airybi(x)) == 'airy(2, x)'
assert octave_code(airybiprime(x)) == 'airy(3, x)'
assert octave_code(uppergamma(n, x)) == 'gammainc(x, n, \'upper\')'
assert octave_code(lowergamma(n, x)) == 'gammainc(x, n, \'lower\')'
assert octave_code(jn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
assert octave_code(yn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
assert octave_code(LambertW(x)) == 'lambertw(x)'
assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'
def test_Function():
assert mcode(f(x, y, z)) == "f[x, y, z]"
assert mcode(sin(x)**cos(x)) == "Sin[x]^Cos[x]"
assert mcode(sec(x) * acsc(x)) == "ArcCsc[x]*Sec[x]"
assert mcode(atan2(x, y)) == "ArcTan[x, y]"
assert mcode(conjugate(x)) == "Conjugate[x]"
assert mcode(Max(x, y, z) * Min(y, z)) == "Max[x, y, z]*Min[y, z]"
assert mcode(fresnelc(x)) == "FresnelC[x]"
assert mcode(fresnels(x)) == "FresnelS[x]"
assert mcode(gamma(x)) == "Gamma[x]"
assert mcode(uppergamma(x, y)) == "Gamma[x, y]"
assert mcode(polygamma(x, y)) == "PolyGamma[x, y]"
assert mcode(loggamma(x)) == "LogGamma[x]"
assert mcode(erf(x)) == "Erf[x]"
assert mcode(erfc(x)) == "Erfc[x]"
assert mcode(erfi(x)) == "Erfi[x]"
assert mcode(erf2(x, y)) == "Erf[x, y]"
assert mcode(expint(x, y)) == "ExpIntegralE[x, y]"
assert mcode(erfcinv(x)) == "InverseErfc[x]"
assert mcode(erfinv(x)) == "InverseErf[x]"
assert mcode(erf2inv(x, y)) == "InverseErf[x, y]"
assert mcode(Ei(x)) == "ExpIntegralEi[x]"
assert mcode(Ci(x)) == "CosIntegral[x]"
assert mcode(li(x)) == "LogIntegral[x]"
assert mcode(Si(x)) == "SinIntegral[x]"
assert mcode(Shi(x)) == "SinhIntegral[x]"
assert mcode(Chi(x)) == "CoshIntegral[x]"
assert mcode(beta(x, y)) == "Beta[x, y]"
assert mcode(factorial(x)) == "Factorial[x]"
assert mcode(factorial2(x)) == "Factorial2[x]"
assert mcode(subfactorial(x)) == "Subfactorial[x]"
assert mcode(FallingFactorial(x, y)) == "FactorialPower[x, y]"
assert mcode(RisingFactorial(x, y)) == "Pochhammer[x, y]"
assert mcode(catalan(x)) == "CatalanNumber[x]"
assert mcode(harmonic(x)) == "HarmonicNumber[x]"
assert mcode(harmonic(x, y)) == "HarmonicNumber[x, y]"
assert mcode(Li(x)) == "LogIntegral[x] - LogIntegral[2]"
assert mcode(LambertW(x)) == "ProductLog[x]"
assert mcode(LambertW(x, -1)) == "ProductLog[-1, x]"
assert mcode(LambertW(x, y)) == "ProductLog[y, x]"
def test_specfun():
n = Symbol("n")
for f in [besselj, bessely, besseli, besselk]:
assert octave_code(f(n, x)) == f.__name__ + "(n, x)"
for f in (erfc, erfi, erf, erfinv, erfcinv, fresnelc, fresnels, gamma):
assert octave_code(f(x)) == f.__name__ + "(x)"
assert octave_code(hankel1(n, x)) == "besselh(n, 1, x)"
assert octave_code(hankel2(n, x)) == "besselh(n, 2, x)"
assert octave_code(airyai(x)) == "airy(0, x)"
assert octave_code(airyaiprime(x)) == "airy(1, x)"
assert octave_code(airybi(x)) == "airy(2, x)"
assert octave_code(airybiprime(x)) == "airy(3, x)"
assert octave_code(uppergamma(n,
x)) == "(gammainc(x, n, 'upper').*gamma(n))"
assert octave_code(lowergamma(n, x)) == "(gammainc(x, n).*gamma(n))"
assert octave_code(z**lowergamma(n, x)) == "z.^(gammainc(x, n).*gamma(n))"
assert octave_code(jn(
n, x)) == "sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2"
assert octave_code(yn(
n, x)) == "sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2"
assert octave_code(LambertW(x)) == "lambertw(x)"
assert octave_code(LambertW(x, n)) == "lambertw(n, x)"