def tips(molID, isoID, temp):
  """
  Evaluate the partition function for the given isotope(s) at the given
  temperature(s).  This is a wrapper of ctips.tips.

  Parameters:
  -----------
  molID: Scalar or iterable
     The molecular ID as given by HITRAN 2012.
  isoID: Scalar or iterable
     The isotope ID (AFGL) as given by HITRAN 2012.
  temp:  Scalar or iterable
     Temperature a which to evaluate the partition function.

  Notes:
  ------
  - The molID and isoID are casted into an integer ndarray data types.
  - The temp is casted into a double ndarray data type.
  - If the arguments have different sizes, the code resizes them to
    a same size, unless they have incompatible sizes.
  """
  # Check scalar vs iterable, turn into iterable:
  if isscalar(molID):
    molID = [molID]
  if isscalar(isoID):
    isoID = [isoID]
  if isscalar(temp):
    temp = [temp]

  # Turn them numpy arrays:
  molID = np.asarray(molID, np.int)
  isoID = np.asarray(isoID, np.int)
  temp  = np.asarray(temp,  np.double)

  # Set them to the same size:
  if len(isoID) != len(temp):
    if   len(isoID) == 1:
      isoID = np.repeat(isoID, len(temp))
    elif len(temp)  == 1:
      temp  = np.repeat(temp,  len(isoID))
    else:
      sys.exit(0)

  if len(molID) != len(isoID):
    if len(molID) != 1:
      sys.exit(0)
    molID = np.repeat(molID, len(isoID))

  return ct.tips(molID, isoID, temp)

 def __mul__(self, other):
     if isinstance(other, (N.ndarray, list, tuple)) :
         # This promotes 1-D vectors to row vectors
         return N.dot(self, asmatrix(other))
     if isscalar(other) or not hasattr(other, '__rmul__') :
         return N.dot(self, other)
     return NotImplemented

    def __getitem__(self, index):
        self._getitem = True

        try:
            out = N.ndarray.__getitem__(self, index)
        finally:
            self._getitem = False

        if not isinstance(out, N.ndarray):
            return out

        if out.ndim == 0:
            return out[()]
        if out.ndim == 1:
            sh = out.shape[0]
            # Determine when we should have a column array
            try:
                n = len(index)
            except:
                n = 0
            if n > 1 and isscalar(index[1]):
                out.shape = (sh, 1)
            else:
                out.shape = (1, sh)
        return out

def apply_along_axis(func1d,axis,arr,*args):
    """ Execute func1d(arr[i],*args) where func1d takes 1-D arrays
        and arr is an N-d array.  i varies so as to apply the function
        along the given axis for each 1-d subarray in arr.
    """
    arr = asarray(arr)
    nd = arr.ndim
    if axis < 0:
        axis += nd
    if (axis >= nd):
        raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
            % (axis,nd))
    ind = [0]*(nd-1)
    i = zeros(nd,'O')
    indlist = range(nd)
    indlist.remove(axis)
    i[axis] = slice(None,None)
    outshape = asarray(arr.shape).take(indlist)
    i.put(indlist, ind)
    res = func1d(arr[tuple(i.tolist())],*args)
    #  if res is a number, then we have a smaller output array
    if isscalar(res):
        outarr = zeros(outshape,asarray(res).dtype)
        outarr[tuple(ind)] = res
        Ntot = product(outshape)
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= outshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            i.put(indlist,ind)
            res = func1d(arr[tuple(i.tolist())],*args)
            outarr[tuple(ind)] = res
            k += 1
        return outarr
    else:
        Ntot = product(outshape)
        holdshape = outshape
        outshape = list(arr.shape)
        outshape[axis] = len(res)
        outarr = zeros(outshape,asarray(res).dtype)
        outarr[tuple(i.tolist())] = res
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= holdshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            i.put(indlist, ind)
            res = func1d(arr[tuple(i.tolist())],*args)
            outarr[tuple(i.tolist())] = res
            k += 1
        return outarr

 def __rmul__(self, other):
     # ! NumPy's matrix __rmul__ uses an apparently a restrictive
     # dot() function that cannot handle the multiplication of a
     # scalar and of a matrix containing objects (when the
     # arguments are given in this order).  We go around this
     # limitation:
     if numeric.isscalar(other):
         return numeric.dot(self, other)
     else:
         return numeric.dot(other, self)  # The order is important

 def __mul__(self, other):
     if self.shape == (1,1):
         # extract scalars from singleton matrices (self)
         return N.dot(self.flat[0], other)
     if isinstance(other, N.ndarray) and other.shape == (1,1):
         # extract scalars from singleton matrices (other)
         return N.dot(self, other.flat[0])
     if isinstance(other, (N.ndarray, list, tuple)) :
         # This promotes 1-D vectors to row vectors
         return N.dot(self, asmatrix(other))
     if isscalar(other) or not hasattr(other, '__rmul__') :
         return N.dot(self, other)
     return NotImplemented

def apply_along_axis(func1d,axis,arr,*args):
    """
    Apply a function to 1-D slices along the given axis.

    Execute `func1d(a, *args)` where `func1d` operates on 1-D arrays and `a`
    is a 1-D slice of `arr` along `axis`.

    Parameters
    ----------
    func1d : function
        This function should accept 1-D arrays. It is applied to 1-D
        slices of `arr` along the specified axis.
    axis : integer
        Axis along which `arr` is sliced.
    arr : ndarray
        Input array.
    args : any
        Additional arguments to `func1d`.

    Returns
    -------
    apply_along_axis : ndarray
        The output array. The shape of `outarr` is identical to the shape of
        `arr`, except along the `axis` dimension, where the length of `outarr`
        is equal to the size of the return value of `func1d`.  If `func1d`
        returns a scalar `outarr` will have one fewer dimensions than `arr`.

    See Also
    --------
    apply_over_axes : Apply a function repeatedly over multiple axes.

    Examples
    --------
    >>> def my_func(a):
    ...     \"\"\"Average first and last element of a 1-D array\"\"\"
    ...     return (a[0] + a[-1]) * 0.5
    >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
    >>> np.apply_along_axis(my_func, 0, b)
    array([ 4.,  5.,  6.])
    >>> np.apply_along_axis(my_func, 1, b)
    array([ 2.,  5.,  8.])

    For a function that doesn't return a scalar, the number of dimensions in
    `outarr` is the same as `arr`.

    >>> def new_func(a):
    ...     \"\"\"Divide elements of a by 2.\"\"\"
    ...     return a * 0.5
    >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
    >>> np.apply_along_axis(new_func, 0, b)
    array([[ 0.5,  1. ,  1.5],
           [ 2. ,  2.5,  3. ],
           [ 3.5,  4. ,  4.5]])

    """
    arr = asarray(arr)
    nd = arr.ndim
    if axis < 0:
        axis += nd
    if (axis >= nd):
        raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
            % (axis,nd))
    ind = [0]*(nd-1)
    i = zeros(nd,'O')
    indlist = list(range(nd))
    indlist.remove(axis)
    i[axis] = slice(None,None)
    outshape = asarray(arr.shape).take(indlist)
    i.put(indlist, ind)
    res = func1d(arr[tuple(i.tolist())],*args)
    #  if res is a number, then we have a smaller output array
    if isscalar(res):
        outarr = zeros(outshape,asarray(res).dtype)
        outarr[tuple(ind)] = res
        Ntot = product(outshape)
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= outshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            i.put(indlist,ind)
            res = func1d(arr[tuple(i.tolist())],*args)
            outarr[tuple(ind)] = res
            k += 1
        return outarr
    else:
        Ntot = product(outshape)
        holdshape = outshape
        outshape = list(arr.shape)
        outshape[axis] = len(res)
        outarr = zeros(outshape,asarray(res).dtype)
        outarr[tuple(i.tolist())] = res
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
#.........这里部分代码省略.........

def apply_along_axis(func1d,axis,arr,*args,**kwargs):
    """ Execute func1d(arr[i],*args) where func1d takes 1-D arrays
        and arr is an N-d array.  i varies so as to apply the function
        along the given axis for each 1-d subarray in arr.
    """
    arr = core.array(arr, copy=False, subok=True)
    nd = arr.ndim
    if axis < 0:
        axis += nd
    if (axis >= nd):
        raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
            % (axis,nd))
    ind = [0]*(nd-1)
    i = numeric.zeros(nd,'O')
    indlist = range(nd)
    indlist.remove(axis)
    i[axis] = slice(None,None)
    outshape = numeric.asarray(arr.shape).take(indlist)
    i.put(indlist, ind)
    j = i.copy()
    res = func1d(arr[tuple(i.tolist())],*args,**kwargs)
    #  if res is a number, then we have a smaller output array
    asscalar = numeric.isscalar(res)
    if not asscalar:
        try:
            len(res)
        except TypeError:
            asscalar = True
    # Note: we shouldn't set the dtype of the output from the first result...
    #...so we force the type to object, and build a list of dtypes
    #...we'll just take the largest, to avoid some downcasting
    dtypes = []
    if asscalar:
        dtypes.append(numeric.asarray(res).dtype)
        outarr = zeros(outshape, object_)
        outarr[tuple(ind)] = res
        Ntot = numeric.product(outshape)
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= outshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            i.put(indlist,ind)
            res = func1d(arr[tuple(i.tolist())],*args,**kwargs)
            outarr[tuple(ind)] = res
            dtypes.append(asarray(res).dtype)
            k += 1
    else:
        res = core.array(res, copy=False, subok=True)
        j = i.copy()
        j[axis] = ([slice(None,None)] * res.ndim)
        j.put(indlist, ind)
        Ntot = numeric.product(outshape)
        holdshape = outshape
        outshape = list(arr.shape)
        outshape[axis] = res.shape
        dtypes.append(asarray(res).dtype)
        outshape = flatten_inplace(outshape)
        outarr = zeros(outshape, object_)
        outarr[tuple(flatten_inplace(j.tolist()))] = res
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= holdshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            i.put(indlist, ind)
            j.put(indlist, ind)
            res = func1d(arr[tuple(i.tolist())],*args,**kwargs)
            outarr[tuple(flatten_inplace(j.tolist()))] = res
            dtypes.append(asarray(res).dtype)
            k += 1
    max_dtypes = numeric.dtype(numeric.asarray(dtypes).max())
    if not hasattr(arr, '_mask'):
        result = numeric.asarray(outarr, dtype=max_dtypes)
    else:
        result = core.asarray(outarr, dtype=max_dtypes)
        result.fill_value = core.default_fill_value(result)
    return result

def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
    """histogramdd(sample, bins=10, range=None, normed=False, weights=None)

    Return the N-dimensional histogram of the sample.

    Parameters:

        sample : sequence or array
            A sequence containing N arrays or an NxM array. Input data.

        bins : sequence or scalar
            A sequence of edge arrays, a sequence of bin counts, or a scalar
            which is the bin count for all dimensions. Default is 10.

        range : sequence
            A sequence of lower and upper bin edges. Default is [min, max].

        normed : boolean
            If False, return the number of samples in each bin, if True,
            returns the density.

        weights : array
            Array of weights.  The weights are normed only if normed is True.
            Should the sum of the weights not equal N, the total bin count will
            not be equal to the number of samples.

    Returns:

        hist : array
            Histogram array.

        edges : list
            List of arrays defining the lower bin edges.

    SeeAlso:

        histogram

    Example

        >>> x = random.randn(100,3)
        >>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))

    """

    try:
        # Sample is an ND-array.
        N, D = sample.shape
    except (AttributeError, ValueError):
        # Sample is a sequence of 1D arrays.
        sample = atleast_2d(sample).T
        N, D = sample.shape

    nbin = empty(D, int)
    edges = D*[None]
    dedges = D*[None]
    if weights is not None:
        weights = asarray(weights)

    try:
        M = len(bins)
        if M != D:
            raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
    except TypeError:
        bins = D*[bins]

    # Select range for each dimension
    # Used only if number of bins is given.
    if range is None:
        smin = atleast_1d(array(sample.min(0), float))
        smax = atleast_1d(array(sample.max(0), float))
    else:
        smin = zeros(D)
        smax = zeros(D)
        for i in arange(D):
            smin[i], smax[i] = range[i]

    # Make sure the bins have a finite width.
    for i in arange(len(smin)):
        if smin[i] == smax[i]:
            smin[i] = smin[i] - .5
            smax[i] = smax[i] + .5

    # Create edge arrays
    for i in arange(D):
        if isscalar(bins[i]):
            nbin[i] = bins[i] + 2 # +2 for outlier bins
            edges[i] = linspace(smin[i], smax[i], nbin[i]-1)
        else:
            edges[i] = asarray(bins[i], float)
            nbin[i] = len(edges[i])+1  # +1 for outlier bins
        dedges[i] = diff(edges[i])

    nbin =  asarray(nbin)

    # Compute the bin number each sample falls into.
    Ncount = {}
    for i in arange(D):
        Ncount[i] = digitize(sample[:,i], edges[i])

#.........这里部分代码省略.........