Python C.cos方法代码示例

# 需要导入模块: from basic import C [as 别名]
# 或者: from basic.C import cos [as 别名]
    def _eval_expand_complex(self, *args):
        if self.exp.is_Integer:
            exp = self.exp
            re, im = self.base.as_real_imag()
            if exp >= 0:
                base = re + S.ImaginaryUnit * im
            else:
                mag = re ** 2 + im ** 2
                base = re / mag - S.ImaginaryUnit * (im / mag)
                exp = -exp
            return (base ** exp).expand()
        elif self.exp.is_Rational:
            # NOTE: This is not totally correct since for x**(p/q) with
            #       x being imaginary there are actually q roots, but
            #       only a single one is returned from here.
            re, im = self.base.as_real_imag()

            r = (re ** 2 + im ** 2) ** S.Half
            t = C.atan2(im, re)

            rp, tp = r ** self.exp, t * self.exp

            return rp * C.cos(tp) + rp * C.sin(tp) * S.ImaginaryUnit
        else:
            return C.re(self) + S.ImaginaryUnit * C.im(self)

# 需要导入模块: from basic import C [as 别名]
# 或者: from basic.C import cos [as 别名]
    def as_real_imag(self, deep=True, **hints):
        from sympy.core.symbol import symbols
        from sympy.polys.polytools import poly
        from sympy.core.function import expand_multinomial
        if self.exp.is_Integer:
            exp = self.exp
            re, im = self.base.as_real_imag(deep=deep)
            a, b = symbols('a, b', dummy=True)
            if exp >= 0:
                if re.is_Number and im.is_Number:
                    # We can be more efficient in this case
                    expr = expand_multinomial(self.base**exp)
                    return expr.as_real_imag()

                expr = poly((a + b)**exp) # a = re, b = im; expr = (a + b*I)**exp
            else:
                mag = re**2 + im**2
                re, im = re/mag, -im/mag
                if re.is_Number and im.is_Number:
                    # We can be more efficient in this case
                    expr = expand_multinomial((re + im*S.ImaginaryUnit)**-exp)
                    return expr.as_real_imag()

                expr = poly((a + b)**-exp)

            # Terms with even b powers will be real
            r = [i for i in expr.terms() if not i[0][1] % 2]
            re_part = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
            # Terms odd b powers will be imaginary
            r = [i for i in expr.terms() if i[0][1] % 4 == 1]
            im_part1 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
            r = [i for i in expr.terms() if i[0][1] % 4 == 3]
            im_part3 = Add(*[cc*a**a*b**bb for (aa, bb), cc in r])

            return (re_part.subs({a: re, b: S.ImaginaryUnit*im}),
            im_part1.subs({a: re, b: im}) + im_part3.subs({a: re, b: -im}))

        elif self.exp.is_Rational:
            # NOTE: This is not totally correct since for x**(p/q) with
            #       x being imaginary there are actually q roots, but
            #       only a single one is returned from here.
            re, im = self.base.as_real_imag(deep=deep)

            r = (re**2 + im**2)**S.Half
            t = C.atan2(im, re)

            rp, tp = r**self.exp, t*self.exp

            return (rp*C.cos(tp), rp*C.sin(tp))
        else:

            if deep:
                hints['complex'] = False
                return (C.re(self.expand(deep, complex=False)),
                C.im(self. expand(deep, **hints)))
            else:
                return (C.re(self), C.im(self))

# 需要导入模块: from basic import C [as 别名]
# 或者: from basic.C import cos [as 别名]
def do_integral(expr, prec, options):
    func = expr.args[0]
    x, (xlow, xhigh) = expr.args[1][0]
    orig = mp.prec

    oldmaxprec = options.get('maxprec', DEFAULT_MAXPREC)
    options['maxprec'] = min(oldmaxprec, 2*prec)

    try:
        mp.prec = prec+5
        xlow = as_mpmath(xlow, prec+15, options)
        xhigh = as_mpmath(xhigh, prec+15, options)

        # Integration is like summation, and we can phone home from
        # the integrand function to update accuracy summation style
        # Note that this accuracy is inaccurate, since it fails
        # to account for the variable quadrature weights,
        # but it is better than nothing

        have_part = [False, False]
        max_real_term = [MINUS_INF]
        max_imag_term = [MINUS_INF]

        def f(t):
            re, im, re_acc, im_acc = evalf(func, mp.prec, {'subs':{x:t}})

            have_part[0] = re or have_part[0]
            have_part[1] = im or have_part[1]

            max_real_term[0] = max(max_real_term[0], fastlog(re))
            max_imag_term[0] = max(max_imag_term[0], fastlog(im))

            if im:
                return mpc(re or fzero, im)
            return mpf(re or fzero)

        if options.get('quad') == 'osc':
            A = C.Wild('A', exclude=[x])
            B = C.Wild('B', exclude=[x])
            D = C.Wild('D')
            m = func.match(C.cos(A*x+B)*D)
            if not m:
                m = func.match(C.sin(A*x+B)*D)
            if not m:
                raise ValueError("An integrand of the form sin(A*x+B)*f(x) "
                  "or cos(A*x+B)*f(x) is required for oscillatory quadrature")
            period = as_mpmath(2*S.Pi/m[A], prec+15, options)
            result = quadosc(f, [xlow, xhigh], period=period)
            # XXX: quadosc does not do error detection yet
            quadrature_error = MINUS_INF
        else:
            result, quadrature_error = quadts(f, [xlow, xhigh], error=1)
            quadrature_error = fastlog(quadrature_error._mpf_)

    finally:
        options['maxprec'] = oldmaxprec
        mp.prec = orig

    if have_part[0]:
        re = result.real._mpf_
        if re == fzero:
            re = mpf_shift(fone, min(-prec,-max_real_term[0],-quadrature_error))
            re_acc = -1
        else:
            re_acc = -max(max_real_term[0]-fastlog(re)-prec, quadrature_error)
    else:
        re, re_acc = None, None

    if have_part[1]:
        im = result.imag._mpf_
        if im == fzero:
            im = mpf_shift(fone, min(-prec,-max_imag_term[0],-quadrature_error))
            im_acc = -1
        else:
            im_acc = -max(max_imag_term[0]-fastlog(im)-prec, quadrature_error)
    else:
        im, im_acc = None, None

    result = re, im, re_acc, im_acc
    return result