在Python中使用Lambert函数时的NaN值

我试图用Python中的Lambert函数来解决一个问题；然而，当使用天篷时，我得到了一个NaN响应。我的方程式如下：

from scipy.special import lambertw

y=8.21016005323e+158

gama = -339.375260893

x = lambertw(y) + gama

print x

当我在Matlab中执行相同的代码时，我得到了x=20.6524的值，这就是我要寻找的结果

我不确定NaN值是由什么引起的，但我怀疑这可能与我对y的巨大价值有关。有没有办法让Python来处理这个问题并给出正确的结果

谢谢

scipy.show_config()

   umfpack_info:
  NOT AVAILABLE
lapack_opt_info:
    libraries = ['mkl_lapack95_lp64', 'mkl_core_dll', 'mkl_intel_lp64_dll', 'mkl_intel_thread_dll']
    library_dirs = ['C:\\Users\\vagrant\\src\\master-env\\libs']
    define_macros = [('SCIPY_MKL_H', None)]
    include_dirs = ['C:\\Users\\vagrant\\src\\master-env\\include']
blas_opt_info:
    libraries = ['mkl_core_dll', 'mkl_intel_lp64_dll', 'mkl_intel_thread_dll']
    library_dirs = ['C:\\Users\\vagrant\\src\\master-env\\libs']
    define_macros = [('SCIPY_MKL_H', None)]
    include_dirs = ['C:\\Users\\vagrant\\src\\master-env\\include']
openblas_info:
  NOT AVAILABLE
lapack_mkl_info:
    libraries = ['mkl_lapack95_lp64', 'mkl_core_dll', 'mkl_intel_lp64_dll', 'mkl_intel_thread_dll']
    library_dirs = ['C:\\Users\\vagrant\\src\\master-env\\libs']
    define_macros = [('SCIPY_MKL_H', None)]
    include_dirs = ['C:\\Users\\vagrant\\src\\master-env\\include']
blas_mkl_info:
    libraries = ['mkl_core_dll', 'mkl_intel_lp64_dll', 'mkl_intel_thread_dll']
    library_dirs = ['C:\\Users\\vagrant\\src\\master-env\\libs']
    define_macros = [('SCIPY_MKL_H', None)]
    include_dirs = ['C:\\Users\\vagrant\\src\\master-env\\include']
mkl_info:
    libraries = ['mkl_core_dll', 'mkl_intel_lp64_dll', 'mkl_intel_thread_dll']
    library_dirs = ['C:\\Users\\vagrant\\src\\master-env\\libs']
    define_macros = [('SCIPY_MKL_H', None)]
    include_dirs = ['C:\\Users\\vagrant\\src\\master-env\\include']

---

使用scipy版本0.14.0：

In [130]: import scipy

In [131]: scipy.__version__
Out[132]: '0.14.0.dev-371b4ff'

In [146]: scipy.show_config()
umfpack_info:
  NOT AVAILABLE
atlas_threads_info:
    libraries = ['lapack', 'ptf77blas', 'ptcblas', 'atlas']
    library_dirs = ['/usr/lib/atlas-base/atlas', '/usr/lib/atlas-base']
    define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
    language = f77
    include_dirs = ['/usr/include/atlas']
blas_opt_info:
    libraries = ['ptf77blas', 'ptcblas', 'atlas']
    library_dirs = ['/usr/lib/atlas-base']
    define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
    language = c
    include_dirs = ['/usr/include/atlas']
atlas_blas_threads_info:
    libraries = ['ptf77blas', 'ptcblas', 'atlas']
    library_dirs = ['/usr/lib/atlas-base']
    define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
    language = c
    include_dirs = ['/usr/include/atlas']
openblas_info:
  NOT AVAILABLE
lapack_opt_info:
    libraries = ['lapack', 'ptf77blas', 'ptcblas', 'atlas']
    library_dirs = ['/usr/lib/atlas-base/atlas', '/usr/lib/atlas-base']
    define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
    language = f77
    include_dirs = ['/usr/include/atlas']
lapack_mkl_info:
  NOT AVAILABLE
blas_mkl_info:
  NOT AVAILABLE
mkl_info:
  NOT AVAILABLE

---

在

lambertw

代码中有一个迭代。显然，当给出一个大的论据时，它不会收敛。（正如@unutbu的回答所示，它是否收敛似乎取决于您的配置。）

下面是一个适用于最大浮点值的（标量）正实数参数的替代方法：

import numpy as np
from scipy.optimize import fsolve


def lw(x):
    """Lambert W function, for real x >= 0."""

    def func(w, x):
        return np.log(x) - np.log(w) - w

    if x == 0:
        return 0
    if x > 2.5:
        lnx = np.log(x)
        w0 = lnx - np.log(lnx)
    elif x > 0.25:
        w0 = 0.8 * np.log(x + 1)
    else:
        w0 = x * (1.0 - x)

    return fsolve(func, w0, args=(x,))[0]

例如：

In [79]: lw(8.21016005323e+158)
Out[79]: 360.02763631519991

In [80]: np.finfo(1.0).max
Out[80]: 1.7976931348623157e+308

In [81]: lw(np.finfo(1.0).max)
Out[81]: 703.22703310477016

---

以下是我的配置：

In [87]: scipy.show_config()
atlas_threads_info:
  NOT AVAILABLE
blas_opt_info:
    extra_link_args = ['-Wl,-framework', '-Wl,Accelerate']
    extra_compile_args = ['-msse3', '-I/System/Library/Frameworks/vecLib.framework/Headers']
    define_macros = [('NO_ATLAS_INFO', 3)]
atlas_blas_threads_info:
  NOT AVAILABLE
openblas_info:
  NOT AVAILABLE
lapack_opt_info:
    extra_link_args = ['-Wl,-framework', '-Wl,Accelerate']
    extra_compile_args = ['-msse3']
    define_macros = [('NO_ATLAS_INFO', 3)]
atlas_info:
  NOT AVAILABLE
lapack_mkl_info:
  NOT AVAILABLE
blas_mkl_info:
  NOT AVAILABLE
atlas_blas_info:
  NOT AVAILABLE
mkl_info:
  NOT AVAILABLE

---

谢谢你的回答。我试过你的建议，但还是失败了。我正在使用Python和Enthow Corporation环境。当我检查scipy版本时，它返回0.13.3，这是预先包装好的Canopy（昨天安装的）。你认为树冠可能是导致这种情况的原因吗？我从scipy'0.15.0.dev-7ce6faf'中得到了

（nan+0j）

对于

lambertw（8.21016005323e+158）

。lambertw代码中有一个迭代，显然没有收敛。调用

scipy.special.errprint（True）

查看相关警告之前，请先调用

scipy.special.errprint（True）

。我刚刚尝试在单独的机器上与scipy 0.9.0一起使用，它可以正常工作fine@WarrenWeckesser我按照你的建议做了，我有三个错误；收敛太慢（未能收敛）、溢出（浮点溢出）和域错误（浮点无效值）。你知道这些是什么意思吗？@allankey:如果你和@WarrenWeckesser post

scipy.show_config（）

，那可能会很有趣。你可能想发布一篇文章。@unutbu谢谢你的帮助。我刚发帖。

In [87]: scipy.show_config()
atlas_threads_info:
  NOT AVAILABLE
blas_opt_info:
    extra_link_args = ['-Wl,-framework', '-Wl,Accelerate']
    extra_compile_args = ['-msse3', '-I/System/Library/Frameworks/vecLib.framework/Headers']
    define_macros = [('NO_ATLAS_INFO', 3)]
atlas_blas_threads_info:
  NOT AVAILABLE
openblas_info:
  NOT AVAILABLE
lapack_opt_info:
    extra_link_args = ['-Wl,-framework', '-Wl,Accelerate']
    extra_compile_args = ['-msse3']
    define_macros = [('NO_ATLAS_INFO', 3)]
atlas_info:
  NOT AVAILABLE
lapack_mkl_info:
  NOT AVAILABLE
blas_mkl_info:
  NOT AVAILABLE
atlas_blas_info:
  NOT AVAILABLE
mkl_info:
  NOT AVAILABLE