Beispiel #1
0
def triu(m, k=0):
    """ returns the elements on and above the k-th diagonal of m.  k=0 is the
        main diagonal, k > 0 is above and k < 0 is below the main diagonal.
    """
    m = asanyarray(m)
    out = multiply((1-tri(m.shape[0], m.shape[1], k-1, int)),m)
    return out
def diff(a, n=1, axis=-1, skip=1):
    if n == 0:
        return a
    if n < 0:
        raise ValueError(
                "order must be non-negative but got " + repr(n))

    a = asanyarray(a)
    nd = len(a.shape)
    # print 'nd', nd
    slice1 = [slice(None)]*nd
    # print '1st slice1', slice1
    slice2 = [slice(None)]*nd
    # print '1st slice2', slice2
    slice1[axis] = slice(skip, None)
    # print '2nd slice1', slice1
    slice2[axis] = slice(None, -skip)
    # print '2nd slice2', slice2
    slice1 = tuple(slice1)
    # print '3rd slice1', slice1
    slice2 = tuple(slice2)
    # print '3rd slice2', slice2
    if n > 1:
        # print 'n>1: a[slice1] = ', a[slice1]
        # print 'n>1: a[slice2] = ', a[slice2]
        # print 'n>1: a[slice1]-a[slice2] = ', a[slice1]-a[slice2]
        return diff(a[slice1]-a[slice2], n-1, axis=axis)
    else:
        # print 'n <= 1: a[slice1] = ', a[slice1]
        # print 'n <= 1: a[slice2] = ', a[slice2]
        # print 'n <= 1: a[slice1]-a[slice2] = ', a[slice1]-a[slice2]
        return a[slice1]-a[slice2]
def log2(x, y=None):
    """
    Return the base 2 logarithm of the input array, element-wise.

    Parameters
    ----------
    x : array_like
      Input array.
    y : array_like
      Optional output array with the same shape as `x`.

    Returns
    -------
    y : ndarray
      The logarithm to the base 2 of `x` element-wise.
      NaNs are returned where `x` is negative.

    See Also
    --------
    log, log1p, log10

    Examples
    --------
    >>> np.log2([-1, 2, 4])
    array([ NaN,   1.,   2.])

    """
    x = nx.asanyarray(x)
    if y is None:
        y = nx.log(x)
    else:
        nx.log(x, y)
    y /= _log2
    return y
def triu(m, k=0):
    """
    Upper triangle of an array.

    Return a copy of a matrix with the elements below the `k`-th diagonal
    zeroed.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

    Examples
    --------
    >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 0,  8,  9],
           [ 0,  0, 12]])

    """
    m = asanyarray(m)
    mask = tri(*m.shape[-2:], k=k-1, dtype=bool)

    return where(mask, zeros(1, m.dtype), m)
Beispiel #5
0
def kron(a,b):
    """kronecker product of a and b

    Kronecker product of two arrays is block array
    [[ a[ 0 ,0]*b, a[ 0 ,1]*b, ... , a[ 0 ,n-1]*b  ],
     [ ...                                   ...   ],
     [ a[m-1,0]*b, a[m-1,1]*b, ... , a[m-1,n-1]*b  ]]
    """
    wrapper = get_array_wrap(a, b)
    b = asanyarray(b)
    a = array(a,copy=False,subok=True,ndmin=b.ndim)
    ndb, nda = b.ndim, a.ndim
    if (nda == 0 or ndb == 0):
        return _nx.multiply(a,b)
    as_ = a.shape
    bs = b.shape
    if not a.flags.contiguous:
        a = reshape(a, as_)
    if not b.flags.contiguous:
        b = reshape(b, bs)
    nd = ndb
    if (ndb != nda):
        if (ndb > nda):
            as_ = (1,)*(ndb-nda) + as_
        else:
            bs = (1,)*(nda-ndb) + bs
            nd = nda
    result = outer(a,b).reshape(as_+bs)
    axis = nd-1
    for _ in xrange(nd):
        result = concatenate(result, axis=axis)
    if wrapper is not None:
        result = wrapper(result)
    return result
Beispiel #6
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def imag(val):
    """
    Return the imaginary part of the elements of the array.

    Parameters
    ----------
    val : array_like
        Input array.

    Returns
    -------
    out : ndarray
        Output array. If `val` is real, the type of `val` is used for the
        output.  If `val` has complex elements, the returned type is float.

    See Also
    --------
    real, angle, real_if_close

    Examples
    --------
    >>> a = np.array([1+2j, 3+4j, 5+6j])
    >>> a.imag
    array([ 2.,  4.,  6.])
    >>> a.imag = np.array([8, 10, 12])
    >>> a
    array([ 1. +8.j,  3.+10.j,  5.+12.j])

    """
    return asanyarray(val).imag
Beispiel #7
0
def real(val):
    """
    Return the real part of the elements of the array.

    Parameters
    ----------
    val : array_like
        Input array.

    Returns
    -------
    out : ndarray
        Output array. If `val` is real, the type of `val` is used for the
        output.  If `val` has complex elements, the returned type is float.

    See Also
    --------
    real_if_close, imag, angle

    Examples
    --------
    >>> a = np.array([1+2j, 3+4j, 5+6j])
    >>> a.real
    array([ 1.,  3.,  5.])
    >>> a.real = 9
    >>> a
    array([ 9.+2.j,  9.+4.j,  9.+6.j])
    >>> a.real = np.array([9, 8, 7])
    >>> a
    array([ 9.+2.j,  8.+4.j,  7.+6.j])

    """
    return asanyarray(val).real
def _mean(a, axis=None, dtype=None, out=None, keepdims=False):
    arr = asanyarray(a)

    is_float16_result = False
    rcount = _count_reduce_items(arr, axis)
    # Make this warning show up first
    if rcount == 0:
        warnings.warn("Mean of empty slice.", RuntimeWarning, stacklevel=2)

    # Cast bool, unsigned int, and int to float64 by default
    if dtype is None:
        if issubclass(arr.dtype.type, (nt.integer, nt.bool_)):
            dtype = mu.dtype('f8')
        elif issubclass(arr.dtype.type, nt.float16):
            dtype = mu.dtype('f4')
            is_float16_result = True

    ret = umr_sum(arr, axis, dtype, out, keepdims)
    if isinstance(ret, mu.ndarray):
        ret = um.true_divide(
                ret, rcount, out=ret, casting='unsafe', subok=False)
        if is_float16_result and out is None:
            ret = arr.dtype.type(ret)
    elif hasattr(ret, 'dtype'):
        if is_float16_result:
            ret = arr.dtype.type(ret / rcount)
        else:
            ret = ret.dtype.type(ret / rcount)
    else:
        ret = ret / rcount

    return ret
Beispiel #9
0
def tril(m, k=0):
    """
    Lower triangle of an array.

    Return a copy of an array with elements above the `k`-th diagonal zeroed.

    Parameters
    ----------
    m : array_like, shape (M, N)
        Input array.
    k : int, optional
        Diagonal above which to zero elements.  `k = 0` (the default) is the
        main diagonal, `k < 0` is below it and `k > 0` is above.

    Returns
    -------
    tril : ndarray, shape (M, N)
        Lower triangle of `m`, of same shape and data-type as `m`.

    See Also
    --------
    triu : same thing, only for the upper triangle

    Examples
    --------
    >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 0,  0,  0],
           [ 4,  0,  0],
           [ 7,  8,  0],
           [10, 11, 12]])

    """
    m = asanyarray(m)
    out = multiply(tri(m.shape[0], m.shape[1], k=k, dtype=m.dtype),m)
    return out
Beispiel #10
0
def triu(m, k=0):
    """
    Upper triangle of an array.

    Return a copy of a matrix with the elements below the `k`-th diagonal
    zeroed.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

    Examples
    --------
    >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 0,  8,  9],
           [ 0,  0, 12]])

    """
    m = asanyarray(m)
    out = multiply((1 - tri(m.shape[0], m.shape[1], k - 1, dtype=m.dtype)), m)
    return out
Beispiel #11
0
def tril(m, k=0):
    """ returns the elements on and below the k-th diagonal of m.  k=0 is the
        main diagonal, k > 0 is above and k < 0 is below the main diagonal.
    """
    m = asanyarray(m)
    out = multiply(tri(m.shape[0], m.shape[1], k=k, dtype=int),m)
    return out
Beispiel #12
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def iscomplex(x):
    """
    Returns a bool array, where True if input element is complex.

    What is tested is whether the input has a non-zero imaginary part, not if
    the input type is complex.

    Parameters
    ----------
    x : array_like
        Input array.

    Returns
    -------
    out : ndarray of bools
        Output array.

    See Also
    --------
    isreal
    iscomplexobj : Return True if x is a complex type or an array of complex
                   numbers.

    Examples
    --------
    >>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j])
    array([ True, False, False, False, False,  True])

    """
    ax = asanyarray(x)
    if issubclass(ax.dtype.type, _nx.complexfloating):
        return ax.imag != 0
    res = zeros(ax.shape, bool)
    return res[()]   # convert to scalar if needed
Beispiel #13
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def _var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
    arr = asanyarray(a)

    rcount = _count_reduce_items(arr, axis)
    # Make this warning show up on top.
    if ddof >= rcount:
        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning,
                      stacklevel=2)

    # Cast bool, unsigned int, and int to float64 by default
    if dtype is None and issubclass(arr.dtype.type, (nt.integer, nt.bool_)):
        dtype = mu.dtype('f8')

    # Compute the mean.
    # Note that if dtype is not of inexact type then arraymean will
    # not be either.
    arrmean = umr_sum(arr, axis, dtype, keepdims=True)
    if isinstance(arrmean, mu.ndarray):
        arrmean = um.true_divide(
                arrmean, rcount, out=arrmean, casting='unsafe', subok=False)
    else:
        arrmean = arrmean.dtype.type(arrmean / rcount)

    # Compute sum of squared deviations from mean
    # Note that x may not be inexact and that we need it to be an array,
    # not a scalar.
    x = asanyarray(arr - arrmean)
    if issubclass(arr.dtype.type, (nt.floating, nt.integer)):
        x = um.multiply(x, x, out=x)
    else:
        x = um.multiply(x, um.conjugate(x), out=x).real

    ret = umr_sum(x, axis, dtype, out, keepdims)

    # Compute degrees of freedom and make sure it is not negative.
    rcount = max([rcount - ddof, 0])

    # divide by degrees of freedom
    if isinstance(ret, mu.ndarray):
        ret = um.true_divide(
                ret, rcount, out=ret, casting='unsafe', subok=False)
    elif hasattr(ret, 'dtype'):
        ret = ret.dtype.type(ret / rcount)
    else:
        ret = ret / rcount

    return ret
Beispiel #14
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def flipud(m):
    """ returns an array with the columns preserved and rows flipped in
        the up/down direction.  Works on the first dimension of m.
    """
    m = asanyarray(m)
    if m.ndim < 1:
        raise ValueError, "Input must be >= 1-d."
    return m[::-1,...]
Beispiel #15
0
def fliplr(m):
    """ returns an array m with the rows preserved and columns flipped
        in the left/right direction.  Works on the first two dimensions of m.
    """
    m = asanyarray(m)
    if m.ndim < 2:
        raise ValueError, "Input must be >= 2-d."
    return m[:, ::-1]
def stack(arrays, axis=0):
    """
    Join a sequence of arrays along a new axis.
    The `axis` parameter specifies the index of the new axis in the dimensions
    of the result. For example, if ``axis=0`` it will be the first dimension
    and if ``axis=-1`` it will be the last dimension.
    .. versionadded:: 1.10.0
    Parameters
    ----------
    arrays : sequence of array_like
        Each array must have the same shape.
    axis : int, optional
        The axis in the result array along which the input arrays are stacked.
    Returns
    -------
    stacked : ndarray
        The stacked array has one more dimension than the input arrays.
    See Also
    --------
    concatenate : Join a sequence of arrays along an existing axis.
    split : Split array into a list of multiple sub-arrays of equal size.
    Examples
    --------
    >>> arrays = [np.random.randn(3, 4) for _ in range(10)]
    >>> np.stack(arrays, axis=0).shape
    (10, 3, 4)
    >>> np.stack(arrays, axis=1).shape
    (3, 10, 4)
    >>> np.stack(arrays, axis=2).shape
    (3, 4, 10)
    >>> a = np.array([1, 2, 3])
    >>> b = np.array([2, 3, 4])
    >>> np.stack((a, b))
    array([[1, 2, 3],
           [2, 3, 4]])
    >>> np.stack((a, b), axis=-1)
    array([[1, 2],
           [2, 3],
           [3, 4]])
    """
    arrays = [asanyarray(arr) for arr in arrays]
    if not arrays:
        raise ValueError('need at least one array to stack')

    shapes = set(arr.shape for arr in arrays)
    if len(shapes) != 1:
        raise ValueError('all input arrays must have the same shape')

    result_ndim = arrays[0].ndim + 1
    if not -result_ndim <= axis < result_ndim:
        msg = 'axis {0} out of bounds [-{1}, {1})'.format(axis, result_ndim)
        raise IndexError(msg)
    if axis < 0:
        axis += result_ndim

    sl = (slice(None),) * axis + (_nx.newaxis,)
    expanded_arrays = [arr[sl] for arr in arrays]
    return _nx.concatenate(expanded_arrays, axis=axis)
def append(arr, values, axis=None):
    """Append to the end of an array along axis (ravel first if None)
    """
    arr = asanyarray(arr)
    if axis is None:
        if arr.ndim != 1:
            arr = arr.ravel()
        values = ravel(values)
        axis = arr.ndim-1
    return concatenate((arr, values), axis=axis)
def piecewise(x, condlist, funclist, *args, **kw):
    """Return a piecewise-defined function.

    x is the domain

    condlist is a list of boolean arrays or a single boolean array
      The length of the condition list must be n2 or n2-1 where n2
      is the length of the function list.  If len(condlist)==n2-1, then
      an 'otherwise' condition is formed by |'ing all the conditions
      and inverting.

    funclist is a list of functions to call of length (n2).
      Each function should return an array output for an array input
      Each function can take (the same set) of extra arguments and
      keyword arguments which are passed in after the function list.
      A constant may be used in funclist for a function that returns a
      constant (e.g. val  and lambda x: val are equivalent in a funclist).

    The output is the same shape and type as x and is found by
      calling the functions on the appropriate portions of x.

    Note: This is similar to choose or select, except
          the the functions are only evaluated on elements of x
          that satisfy the corresponding condition.

    The result is
           |--
           |  f1(x)  for condition1
     y = --|  f2(x)  for condition2
           |   ...
           |  fn(x)  for conditionn
           |--

    """
    x = asanyarray(x)
    n2 = len(funclist)
    if not isinstance(condlist, type([])):
        condlist = [condlist]
    n = len(condlist)
    if n == n2-1:  # compute the "otherwise" condition.
        totlist = condlist[0]
        for k in range(1, n):
            totlist |= condlist[k]
        condlist.append(~totlist)
        n += 1
    if (n != n2):
        raise ValueError, "function list and condition list must be the same"
    y = empty(x.shape, x.dtype)
    for k in range(n):
        item = funclist[k]
        if not callable(item):
            y[condlist[k]] = item
        else:
            y[condlist[k]] = item(x[condlist[k]], *args, **kw)
    return y
def iscomplex(x):
    """Return a boolean array where elements are True if that element
    is complex (has non-zero imaginary part).

    For scalars, return a boolean.
    """
    ax = asanyarray(x)
    if issubclass(ax.dtype.type, _nx.complexfloating):
        return ax.imag != 0
    res = zeros(ax.shape, bool)
    return +res  # convet to array-scalar if needed
Beispiel #20
0
def real_if_close(a, tol=100):
    """
    If complex input returns a real array if complex parts are close to zero.

    "Close to zero" is defined as `tol` * (machine epsilon of the type for
    `a`).

    Parameters
    ----------
    a : array_like
        Input array.
    tol : float
        Tolerance in machine epsilons for the complex part of the elements
        in the array.

    Returns
    -------
    out : ndarray
        If `a` is real, the type of `a` is used for the output.  If `a`
        has complex elements, the returned type is float.

    See Also
    --------
    real, imag, angle

    Notes
    -----
    Machine epsilon varies from machine to machine and between data types
    but Python floats on most platforms have a machine epsilon equal to
    2.2204460492503131e-16.  You can use 'np.finfo(np.float).eps' to print
    out the machine epsilon for floats.

    Examples
    --------
    >>> np.finfo(np.float).eps
    2.2204460492503131e-16

    >>> np.real_if_close([2.1 + 4e-14j], tol=1000)
    array([ 2.1])
    >>> np.real_if_close([2.1 + 4e-13j], tol=1000)
    array([ 2.1 +4.00000000e-13j])

    """
    a = asanyarray(a)
    if not issubclass(a.dtype.type, _nx.complexfloating):
        return a
    if tol > 1:
        from numpy.core import getlimits

        f = getlimits.finfo(a.dtype.type)
        tol = f.eps * tol
    if _nx.allclose(a.imag, 0, atol=tol):
        a = a.real
    return a
Beispiel #21
0
def fix(x, y=None):
    """
    Round to nearest integer towards zero.

    Round an array of floats element-wise to nearest integer towards zero.
    The rounded values are returned as floats.

    Parameters
    ----------
    x : array_like
        An array of floats to be rounded
    y : ndarray, optional
        Output array

    Returns
    -------
    out : ndarray of floats
        The array of rounded numbers

    See Also
    --------
    trunc, floor, ceil
    around : Round to given number of decimals

    Examples
    --------
    >>> np.fix(3.14)
    3.0
    >>> np.fix(3)
    3.0
    >>> np.fix([2.1, 2.9, -2.1, -2.9])
    array([ 2.,  2., -2., -2.])

    """
    x = nx.asanyarray(x)
    y1 = nx.floor(x)
    y2 = nx.ceil(x)
    if y is None:
        y = nx.asanyarray(y1)
    y[...] = nx.where(x >= 0, y1, y2)
    return y
Beispiel #22
0
def log2(x, y=None):
    """Returns the base 2 logarithm of x

    If y is an array, the result replaces the contents of y.
    """
    x = asanyarray(x)
    if y is None:
        y = umath.log(x)
    else:
        umath.log(x, y)
    y /= _log2
    return y
Beispiel #23
0
def flipud(m):
    """
    Flip array in the up/down direction.

    Flip the entries in each column in the up/down direction.
    Rows are preserved, but appear in a different order than before.

    Parameters
    ----------
    m : array_like
        Input array.

    Returns
    -------
    out : array_like
        A view of `m` with the rows reversed.  Since a view is
        returned, this operation is :math:`\\mathcal O(1)`.

    See Also
    --------
    fliplr : Flip array in the left/right direction.
    rot90 : Rotate array counterclockwise.

    Notes
    -----
    Equivalent to ``A[::-1,...]``.
    Does not require the array to be two-dimensional.

    Examples
    --------
    >>> A = np.diag([1.0, 2, 3])
    >>> A
    array([[ 1.,  0.,  0.],
           [ 0.,  2.,  0.],
           [ 0.,  0.,  3.]])
    >>> np.flipud(A)
    array([[ 0.,  0.,  3.],
           [ 0.,  2.,  0.],
           [ 1.,  0.,  0.]])

    >>> A = np.random.randn(2,3,5)
    >>> np.all(np.flipud(A)==A[::-1,...])
    True

    >>> np.flipud([1,2])
    array([2, 1])

    """
    m = asanyarray(m)
    if m.ndim < 1:
        raise ValueError("Input must be >= 1-d.")
    return m[::-1,...]
Beispiel #24
0
def rot90(m, k=1):
    """ returns the array found by rotating m by k*90
    degrees in the counterclockwise direction.  Works on the first two
    dimensions of m.
    """
    m = asanyarray(m)
    if m.ndim < 2:
        raise ValueError, "Input must >= 2-d."
    k = k % 4
    if k == 0: return m
    elif k == 1: return fliplr(m).swapaxes(0,1)
    elif k == 2: return fliplr(flipud(m))
    else: return fliplr(m.swapaxes(0,1))  # k==3
Beispiel #25
0
def rot90(m, k=1):
    """
    Rotate an array by 90 degrees in the counter-clockwise direction.

    The first two dimensions are rotated; therefore, the array must be at
    least 2-D.

    Parameters
    ----------
    m : array_like
        Array of two or more dimensions.
    k : integer
        Number of times the array is rotated by 90 degrees.

    Returns
    -------
    y : ndarray
        Rotated array.

    See Also
    --------
    fliplr : Flip an array horizontally.
    flipud : Flip an array vertically.

    Examples
    --------
    >>> m = np.array([[1,2],[3,4]], int)
    >>> m
    array([[1, 2],
           [3, 4]])
    >>> np.rot90(m)
    array([[2, 4],
           [1, 3]])
    >>> np.rot90(m, 2)
    array([[4, 3],
           [2, 1]])

    """
    m = asanyarray(m)
    if m.ndim < 2:
        raise ValueError("Input must >= 2-d.")
    k = k % 4
    if k == 0:
        return m
    elif k == 1:
        return fliplr(m).swapaxes(0,1)
    elif k == 2:
        return fliplr(flipud(m))
    else:
        # k == 3
        return fliplr(m.swapaxes(0,1))
def predict_from_smiles_conformal_median(regressor_list, smiles):
    """
    Description - Predict value of penetration (kp) from a SMILES-description'
    of a molecule using the median of multiple conformal models.
    """
    
    print('########## Predict using multiple conformal models ##############')
    
    print smiles
    
    descriptors_df = calculate_descriptors(smiles)
    Xvalues = []
    Xvalues = asanyarray(descriptors_df.iloc[:,1:])
    
    print(len(Xvalues))
   
    A = pandas.DataFrame(index = range(len(Xvalues)))
    B = pandas.DataFrame(index = range(len(Xvalues)))
    C = pandas.DataFrame(index = range(len(Xvalues)))


    index = list(xrange(len(smiles)))

    i = 0    
    for regressor in regressor_list:
        
        predicted_skin_permiabillity = regressor.predict(Xvalues, significance = 0.2)
        predicted_values = pandas.DataFrame(predicted_skin_permiabillity)

        A[i] = predicted_values[0]
        B[i] = predicted_values[1]     
        
        i +=1 
        #print(predicted_values) DEBUG

    C['median_prediction_0'] = A.median(axis=1)
    C['median_prediction_1'] = B.median(axis=1)
    C['median_prediction'] = (C['median_prediction_0'] + C['median_prediction_1'])/2
    C['median_prediction_size'] = C['median_prediction'] - C['median_prediction_0']

    #Y_pred_median_test = C['median_prediction'].dropna()
    #median_prediction_size = C['median_prediction_size'].dropna().tolist()
           
    if args.verbose:
        print('Number of conformal models used: '+ str(i))
        print('Predicted range (first entry): '+str(C['median_prediction_0'][0])+' to '+str(C['median_prediction_1'][0]))
        print('Predicted value (first entry): '+str(C['median_prediction'][0]))
        print('Predicted range (first entry): '+str(C['median_prediction_size'][0]))
    #print('Predicted range (second entry): '+str(C['median_prediction_0'][1])+' - '+str(C['median_prediction_1'][1]))

    return C
Beispiel #27
0
def fix(x, y=None):
    """ Round x to nearest integer towards zero.
    """
    x = asanyarray(x)
    if y is None:
        y = nx.floor(x)
    else:
        nx.floor(x, y)
    if x.ndim == 0:
        if (x<0):
            y += 1
    else:
        y[x<0] = y[x<0]+1
    return y
Beispiel #28
0
def fliplr(m):
    """
    Flip array in the left/right direction.

    Flip the entries in each row in the left/right direction.
    Columns are preserved, but appear in a different order than before.

    Parameters
    ----------
    m : array_like
        Input array.

    Returns
    -------
    f : ndarray
        A view of `m` with the columns reversed.  Since a view
        is returned, this operation is :math:`\\mathcal O(1)`.

    See Also
    --------
    flipud : Flip array in the up/down direction.
    rot90 : Rotate array counterclockwise.

    Notes
    -----
    Equivalent to A[:,::-1]. Does not require the array to be
    two-dimensional.

    Examples
    --------
    >>> A = np.diag([1.,2.,3.])
    >>> A
    array([[ 1.,  0.,  0.],
           [ 0.,  2.,  0.],
           [ 0.,  0.,  3.]])
    >>> np.fliplr(A)
    array([[ 0.,  0.,  1.],
           [ 0.,  2.,  0.],
           [ 3.,  0.,  0.]])

    >>> A = np.random.randn(2,3,5)
    >>> np.all(numpy.fliplr(A)==A[:,::-1,...])
    True

    """
    m = asanyarray(m)
    if m.ndim < 2:
        raise ValueError, "Input must be >= 2-d."
    return m[:, ::-1]
Beispiel #29
0
def imag(val):
    """
    Return the imaginary part of array.

    Parameters
    ----------
    val : array_like
        Input array.

    Returns
    -------
    out : ndarray, real or int
        Real part of each element, same shape as `val`.

    """
    return asanyarray(val).imag
def real_if_close(a,tol=100):
    """If a is a complex array, return it as a real array if the imaginary
    part is close enough to zero.

    "Close enough" is defined as tol*(machine epsilon of a's element type).
    """
    a = asanyarray(a)
    if not issubclass(a.dtype.type, _nx.complexfloating):
        return a
    if tol > 1:
        import getlimits
        f = getlimits.finfo(a.dtype.type)
        tol = f.eps * tol
    if _nx.allclose(a.imag, 0, atol=tol):
        a = a.real
    return a
def diag(v, k=0):
    """
    Extract a diagonal or construct a diagonal array.

    See the more detailed documentation for ``numpy.diagonal`` if you use this
    function to extract a diagonal and wish to write to the resulting array;
    whether it returns a copy or a view depends on what version of numpy you
    are using.

    Parameters
    ----------
    v : array_like
        If `v` is a 2-D array, return a copy of its `k`-th diagonal.
        If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th
        diagonal.
    k : int, optional
        Diagonal in question. The default is 0. Use `k>0` for diagonals
        above the main diagonal, and `k<0` for diagonals below the main
        diagonal.

    Returns
    -------
    out : ndarray
        The extracted diagonal or constructed diagonal array.

    See Also
    --------
    diagonal : Return specified diagonals.
    diagflat : Create a 2-D array with the flattened input as a diagonal.
    trace : Sum along diagonals.
    triu : Upper triangle of an array.
    tril : Lower triangle of an array.

    Examples
    --------
    >>> x = np.arange(9).reshape((3,3))
    >>> x
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])

    >>> np.diag(x)
    array([0, 4, 8])
    >>> np.diag(x, k=1)
    array([1, 5])
    >>> np.diag(x, k=-1)
    array([3, 7])

    >>> np.diag(np.diag(x))
    array([[0, 0, 0],
           [0, 4, 0],
           [0, 0, 8]])

    """
    v = asanyarray(v)
    s = v.shape
    if len(s) == 1:
        n = s[0]+abs(k)
        res = zeros((n, n), v.dtype)
        if k >= 0:
            i = k
        else:
            i = (-k) * n
        res[:n-k].flat[i::n+1] = v
        return res
    elif len(s) == 2:
        return diagonal(v, k)
    else:
        raise ValueError("Input must be 1- or 2-d.")
Beispiel #32
0
def kron(a, b):
    """
    Kronecker product of two arrays.

    Computes the Kronecker product, a composite array made of blocks of the
    second array scaled by the first.

    Parameters
    ----------
    a, b : array_like

    Returns
    -------
    out : ndarray

    See Also
    --------
    outer : The outer product

    Notes
    -----
    The function assumes that the number of dimensions of `a` and `b`
    are the same, if necessary prepending the smallest with ones.
    If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`,
    the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`.
    The elements are products of elements from `a` and `b`, organized
    explicitly by::

        kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]

    where::

        kt = it * st + jt,  t = 0,...,N

    In the common 2-D case (N=1), the block structure can be visualized::

        [[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
         [  ...                              ...   ],
         [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]


    Examples
    --------
    >>> np.kron([1,10,100], [5,6,7])
    array([  5,   6,   7,  50,  60,  70, 500, 600, 700])
    >>> np.kron([5,6,7], [1,10,100])
    array([  5,  50, 500,   6,  60, 600,   7,  70, 700])

    >>> np.kron(np.eye(2), np.ones((2,2)))
    array([[ 1.,  1.,  0.,  0.],
           [ 1.,  1.,  0.,  0.],
           [ 0.,  0.,  1.,  1.],
           [ 0.,  0.,  1.,  1.]])

    >>> a = np.arange(100).reshape((2,5,2,5))
    >>> b = np.arange(24).reshape((2,3,4))
    >>> c = np.kron(a,b)
    >>> c.shape
    (2, 10, 6, 20)
    >>> I = (1,3,0,2)
    >>> J = (0,2,1)
    >>> J1 = (0,) + J             # extend to ndim=4
    >>> S1 = (1,) + b.shape
    >>> K = tuple(np.array(I) * np.array(S1) + np.array(J1))
    >>> c[K] == a[I]*b[J]
    True

    """
    b = asanyarray(b)
    a = array(a, copy=False, subok=True, ndmin=b.ndim)
    ndb, nda = b.ndim, a.ndim
    if (nda == 0 or ndb == 0):
        return _nx.multiply(a, b)
    as_ = a.shape
    bs = b.shape
    if not a.flags.contiguous:
        a = reshape(a, as_)
    if not b.flags.contiguous:
        b = reshape(b, bs)
    nd = ndb
    if (ndb != nda):
        if (ndb > nda):
            as_ = (1,)*(ndb-nda) + as_
        else:
            bs = (1,)*(nda-ndb) + bs
            nd = nda
    result = outer(a, b).reshape(as_+bs)
    axis = nd-1
    for _ in range(nd):
        result = concatenate(result, axis=axis)
    wrapper = get_array_prepare(a, b)
    if wrapper is not None:
        result = wrapper(result)
    wrapper = get_array_wrap(a, b)
    if wrapper is not None:
        result = wrapper(result)
    return result
Beispiel #33
0
def expand_dims(a, axis):
    """
    Expand the shape of an array.

    Insert a new axis that will appear at the `axis` position in the expanded
    array shape.

    .. note:: Previous to NumPy 1.13.0, neither ``axis < -a.ndim - 1`` nor
       ``axis > a.ndim`` raised errors or put the new axis where documented.
       Those axis values are now deprecated and will raise an AxisError in the
       future.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int
        Position in the expanded axes where the new axis is placed.

    Returns
    -------
    res : ndarray
        Output array. The number of dimensions is one greater than that of
        the input array.

    See Also
    --------
    squeeze : The inverse operation, removing singleton dimensions
    reshape : Insert, remove, and combine dimensions, and resize existing ones
    doc.indexing, atleast_1d, atleast_2d, atleast_3d

    Examples
    --------
    >>> x = np.array([1,2])
    >>> x.shape
    (2,)

    The following is equivalent to ``x[np.newaxis,:]`` or ``x[np.newaxis]``:

    >>> y = np.expand_dims(x, axis=0)
    >>> y
    array([[1, 2]])
    >>> y.shape
    (1, 2)

    >>> y = np.expand_dims(x, axis=1)  # Equivalent to x[:,np.newaxis]
    >>> y
    array([[1],
           [2]])
    >>> y.shape
    (2, 1)

    Note that some examples may use ``None`` instead of ``np.newaxis``.  These
    are the same objects:

    >>> np.newaxis is None
    True

    """
    if isinstance(a, matrix):
        a = asarray(a)
    else:
        a = asanyarray(a)

    shape = a.shape
    if axis > a.ndim or axis < -a.ndim - 1:
        # 2017-05-17, 1.13.0
        warnings.warn(
            "Both axis > a.ndim and axis < -a.ndim - 1 are "
            "deprecated and will raise an AxisError in the future.",
            DeprecationWarning,
            stacklevel=2,
        )
    # When the deprecation period expires, delete this if block,
    if axis < 0:
        axis = axis + a.ndim + 1
    # and uncomment the following line.
    # axis = normalize_axis_index(axis, a.ndim + 1)
    return a.reshape(shape[:axis] + (1,) + shape[axis:])
Beispiel #34
0
def real(val):
    """Return the real part of val.

    Useful if val maybe a scalar or an array.
    """
    return asanyarray(val).real
Beispiel #35
0
def matrix_power(M, n):
    """
    Raise a square matrix to the (integer) power `n`.

    For positive integers `n`, the power is computed by repeated matrix
    squarings and matrix multiplications. If ``n == 0``, the identity matrix
    of the same shape as M is returned. If ``n < 0``, the inverse
    is computed and then raised to the ``abs(n)``.

    Parameters
    ----------
    M : ndarray or matrix object
        Matrix to be "powered."  Must be square, i.e. ``M.shape == (m, m)``,
        with `m` a positive integer.
    n : int
        The exponent can be any integer or long integer, positive,
        negative, or zero.

    Returns
    -------
    M**n : ndarray or matrix object
        The return value is the same shape and type as `M`;
        if the exponent is positive or zero then the type of the
        elements is the same as those of `M`. If the exponent is
        negative the elements are floating-point.

    Raises
    ------
    LinAlgError
        If the matrix is not numerically invertible.

    See Also
    --------
    matrix
        Provides an equivalent function as the exponentiation operator
        (``**``, not ``^``).

    Examples
    --------
    >>> from numpy import linalg as LA
    >>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit
    >>> LA.matrix_power(i, 3) # should = -i
    array([[ 0, -1],
           [ 1,  0]])
    >>> LA.matrix_power(np.matrix(i), 3) # matrix arg returns matrix
    matrix([[ 0, -1],
            [ 1,  0]])
    >>> LA.matrix_power(i, 0)
    array([[1, 0],
           [0, 1]])
    >>> LA.matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements
    array([[ 0.,  1.],
           [-1.,  0.]])

    Somewhat more sophisticated example

    >>> q = np.zeros((4, 4))
    >>> q[0:2, 0:2] = -i
    >>> q[2:4, 2:4] = i
    >>> q # one of the three quarternion units not equal to 1
    array([[ 0., -1.,  0.,  0.],
           [ 1.,  0.,  0.,  0.],
           [ 0.,  0.,  0.,  1.],
           [ 0.,  0., -1.,  0.]])
    >>> LA.matrix_power(q, 2) # = -np.eye(4)
    array([[-1.,  0.,  0.,  0.],
           [ 0., -1.,  0.,  0.],
           [ 0.,  0., -1.,  0.],
           [ 0.,  0.,  0., -1.]])

    """
    M = asanyarray(M)
    if len(M.shape) != 2 or M.shape[0] != M.shape[1]:
        raise ValueError("input must be a square array")
    if not issubdtype(type(n), int):
        raise TypeError("exponent must be an integer")

    from numpy.linalg import inv

    if n == 0:
        M = M.copy()
        M[:] = identity(M.shape[0])
        return M
    elif n < 0:
        M = inv(M)
        n *= -1

    result = M
    if n <= 3:
        for _ in range(n - 1):
            result = N.dot(result, M)
        return result

    # binary decomposition to reduce the number of Matrix
    # multiplications for n > 3.
    beta = binary_repr(n)
    Z, q, t = M, 0, len(beta)
    while beta[t - q - 1] == '0':
        Z = N.dot(Z, Z)
        q += 1
    result = Z
    for k in range(q + 1, t):
        Z = N.dot(Z, Z)
        if beta[t - k - 1] == '1':
            result = N.dot(result, Z)
    return result
Beispiel #36
0
def imag(val):
    """Return the imaginary part of val.

    Useful if val maybe a scalar or an array.
    """
    return asanyarray(val).imag
Beispiel #37
0
def _parse_einsum_input(operands):
    """
    A reproduction of einsum c side einsum parsing in python.

    Returns
    -------
    input_strings : str
        Parsed input strings
    output_string : str
        Parsed output string
    operands : list of array_like
        The operands to use in the numpy contraction

    Examples
    --------
    The operand list is simplified to reduce printing:

    >>> a = np.random.rand(4, 4)
    >>> b = np.random.rand(4, 4, 4)
    >>> __parse_einsum_input(('...a,...a->...', a, b))
    ('za,xza', 'xz', [a, b])

    >>> __parse_einsum_input((a, [Ellipsis, 0], b, [Ellipsis, 0]))
    ('za,xza', 'xz', [a, b])
    """

    if len(operands) == 0:
        raise ValueError("No input operands")

    if isinstance(operands[0], str):
        subscripts = operands[0].replace(" ", "")
        operands = [asanyarray(v) for v in operands[1:]]

        # Ensure all characters are valid
        for s in subscripts:
            if s in '.,->':
                continue
            if s not in einsum_symbols:
                raise ValueError("Character %s is not a valid symbol." % s)

    else:
        tmp_operands = list(operands)
        operand_list = []
        subscript_list = []
        for p in range(len(operands) // 2):
            operand_list.append(tmp_operands.pop(0))
            subscript_list.append(tmp_operands.pop(0))

        output_list = tmp_operands[-1] if len(tmp_operands) else None
        operands = [asanyarray(v) for v in operand_list]
        subscripts = ""
        last = len(subscript_list) - 1
        for num, sub in enumerate(subscript_list):
            for s in sub:
                if s is Ellipsis:
                    subscripts += "..."
                elif isinstance(s, int):
                    subscripts += einsum_symbols[s]
                else:
                    raise TypeError("For this input type lists must contain "
                                    "either int or Ellipsis")
            if num != last:
                subscripts += ","

        if output_list is not None:
            subscripts += "->"
            for s in output_list:
                if s is Ellipsis:
                    subscripts += "..."
                elif isinstance(s, int):
                    subscripts += einsum_symbols[s]
                else:
                    raise TypeError("For this input type lists must contain "
                                    "either int or Ellipsis")
    # Check for proper "->"
    if ("-" in subscripts) or (">" in subscripts):
        invalid = (subscripts.count("-") > 1) or (subscripts.count(">") > 1)
        if invalid or (subscripts.count("->") != 1):
            raise ValueError("Subscripts can only contain one '->'.")

    # Parse ellipses
    if "." in subscripts:
        used = subscripts.replace(".", "").replace(",", "").replace("->", "")
        unused = list(einsum_symbols_set - set(used))
        ellipse_inds = "".join(unused)
        longest = 0

        if "->" in subscripts:
            input_tmp, output_sub = subscripts.split("->")
            split_subscripts = input_tmp.split(",")
            out_sub = True
        else:
            split_subscripts = subscripts.split(',')
            out_sub = False

        for num, sub in enumerate(split_subscripts):
            if "." in sub:
                if (sub.count(".") != 3) or (sub.count("...") != 1):
                    raise ValueError("Invalid Ellipses.")

                # Take into account numerical values
                if operands[num].shape == ():
                    ellipse_count = 0
                else:
                    ellipse_count = max(operands[num].ndim, 1)
                    ellipse_count -= (len(sub) - 3)

                if ellipse_count > longest:
                    longest = ellipse_count

                if ellipse_count < 0:
                    raise ValueError("Ellipses lengths do not match.")
                elif ellipse_count == 0:
                    split_subscripts[num] = sub.replace('...', '')
                else:
                    rep_inds = ellipse_inds[-ellipse_count:]
                    split_subscripts[num] = sub.replace('...', rep_inds)

        subscripts = ",".join(split_subscripts)
        if longest == 0:
            out_ellipse = ""
        else:
            out_ellipse = ellipse_inds[-longest:]

        if out_sub:
            subscripts += "->" + output_sub.replace("...", out_ellipse)
        else:
            # Special care for outputless ellipses
            output_subscript = ""
            tmp_subscripts = subscripts.replace(",", "")
            for s in sorted(set(tmp_subscripts)):
                if s not in (einsum_symbols):
                    raise ValueError("Character %s is not a valid symbol." % s)
                if tmp_subscripts.count(s) == 1:
                    output_subscript += s
            normal_inds = ''.join(
                sorted(set(output_subscript) - set(out_ellipse)))

            subscripts += "->" + out_ellipse + normal_inds

    # Build output string if does not exist
    if "->" in subscripts:
        input_subscripts, output_subscript = subscripts.split("->")
    else:
        input_subscripts = subscripts
        # Build output subscripts
        tmp_subscripts = subscripts.replace(",", "")
        output_subscript = ""
        for s in sorted(set(tmp_subscripts)):
            if s not in einsum_symbols:
                raise ValueError("Character %s is not a valid symbol." % s)
            if tmp_subscripts.count(s) == 1:
                output_subscript += s

    # Make sure output subscripts are in the input
    for char in output_subscript:
        if char not in input_subscripts:
            raise ValueError(
                "Output character %s did not appear in the input" % char)

    # Make sure number operands is equivalent to the number of terms
    if len(input_subscripts.split(',')) != len(operands):
        raise ValueError("Number of einsum subscripts must be equal to the "
                         "number of operands.")

    return (input_subscripts, output_subscript, operands)
Beispiel #38
0
def polyval(p, x):
    """
    Evaluate a polynomial at specific values.

    If `p` is of length N, this function returns the value:

        ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]``

    If `x` is a sequence, then `p(x)` is returned for each element of `x`.
    If `x` is another polynomial then the composite polynomial `p(x(t))`
    is returned.

    Parameters
    ----------
    p : array_like or poly1d object
       1D array of polynomial coefficients (including coefficients equal
       to zero) from highest degree to the constant term, or an
       instance of poly1d.
    x : array_like or poly1d object
       A number, an array of numbers, or an instance of poly1d, at
       which to evaluate `p`.

    Returns
    -------
    values : ndarray or poly1d
       If `x` is a poly1d instance, the result is the composition of the two
       polynomials, i.e., `x` is "substituted" in `p` and the simplified
       result is returned. In addition, the type of `x` - array_like or
       poly1d - governs the type of the output: `x` array_like => `values`
       array_like, `x` a poly1d object => `values` is also.

    See Also
    --------
    poly1d: A polynomial class.

    Notes
    -----
    Horner's scheme [1]_ is used to evaluate the polynomial. Even so,
    for polynomials of high degree the values may be inaccurate due to
    rounding errors. Use carefully.

    If `x` is a subtype of `ndarray` the return value will be of the same type.

    References
    ----------
    .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng.
       trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand
       Reinhold Co., 1985, pg. 720.

    Examples
    --------
    >>> np.polyval([3,0,1], 5)  # 3 * 5**2 + 0 * 5**1 + 1
    76
    >>> np.polyval([3,0,1], np.poly1d(5))
    poly1d([76.])
    >>> np.polyval(np.poly1d([3,0,1]), 5)
    76
    >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5))
    poly1d([76.])

    """
    p = NX.asarray(p)
    if isinstance(x, poly1d):
        y = 0
    else:
        x = NX.asanyarray(x)
        y = NX.zeros_like(x)
    for i in range(len(p)):
        y = y * x + p[i]
    return y
Beispiel #39
0
def apply_along_axis(func1d, axis, arr, *args, **kwargs):
    """
    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`.

    This is equivalent to (but faster than) the following use of `ndindex` and
    `s_`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        for ii in ndindex(Ni):
            for kk in ndindex(Nk):
                f = func1d(arr[ii + s_[:,] + kk])
                Nj = f.shape
                for jj in ndindex(Nj):
                    out[ii + jj + kk] = f[jj]

    Equivalently, eliminating the inner loop, this can be expressed as::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        for ii in ndindex(Ni):
            for kk in ndindex(Nk):
                out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])

    Parameters
    ----------
    func1d : function (M,) -> (Nj...)
        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 (Ni..., M, Nk...)
        Input array.
    args : any
        Additional arguments to `func1d`.
    kwargs : any
        Additional named arguments to `func1d`.

        .. versionadded:: 1.9.0


    Returns
    -------
    out : ndarray  (Ni..., Nj..., Nk...)
        The output array. The shape of `out` is identical to the shape of
        `arr`, except along the `axis` dimension. This axis is removed, and
        replaced with new dimensions equal to the shape of the return value
        of `func1d`. So if `func1d` returns a scalar `out` 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 returns a 1D array, the number of dimensions in
    `outarr` is the same as `arr`.

    >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])
    >>> np.apply_along_axis(sorted, 1, b)
    array([[1, 7, 8],
           [3, 4, 9],
           [2, 5, 6]])

    For a function that returns a higher dimensional array, those dimensions
    are inserted in place of the `axis` dimension.

    >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
    >>> np.apply_along_axis(np.diag, -1, b)
    array([[[1, 0, 0],
            [0, 2, 0],
            [0, 0, 3]],
           [[4, 0, 0],
            [0, 5, 0],
            [0, 0, 6]],
           [[7, 0, 0],
            [0, 8, 0],
            [0, 0, 9]]])
    """
    # handle negative axes
    arr = asanyarray(arr)
    nd = arr.ndim
    axis = normalize_axis_index(axis, nd)

    # arr, with the iteration axis at the end
    in_dims = list(range(nd))
    inarr_view = transpose(arr, in_dims[:axis] + in_dims[axis + 1 :] + [axis])

    # compute indices for the iteration axes, and append a trailing ellipsis to
    # prevent 0d arrays decaying to scalars, which fixes gh-8642
    inds = ndindex(inarr_view.shape[:-1])
    inds = (ind + (Ellipsis,) for ind in inds)

    # invoke the function on the first item
    try:
        ind0 = next(inds)
    except StopIteration:
        raise ValueError("Cannot apply_along_axis when any iteration dimensions are 0")
    res = asanyarray(func1d(inarr_view[ind0], *args, **kwargs))

    # build a buffer for storing evaluations of func1d.
    # remove the requested axis, and add the new ones on the end.
    # laid out so that each write is contiguous.
    # for a tuple index inds, buff[inds] = func1d(inarr_view[inds])
    buff = zeros(inarr_view.shape[:-1] + res.shape, res.dtype)

    # permutation of axes such that out = buff.transpose(buff_permute)
    buff_dims = list(range(buff.ndim))
    buff_permute = (
        buff_dims[0:axis]
        + buff_dims[buff.ndim - res.ndim : buff.ndim]
        + buff_dims[axis : buff.ndim - res.ndim]
    )

    # matrices have a nasty __array_prepare__ and __array_wrap__
    if not isinstance(res, matrix):
        buff = res.__array_prepare__(buff)

    # save the first result, then compute and save all remaining results
    buff[ind0] = res
    for ind in inds:
        buff[ind] = asanyarray(func1d(inarr_view[ind], *args, **kwargs))

    if not isinstance(res, matrix):
        # wrap the array, to preserve subclasses
        buff = res.__array_wrap__(buff)

        # finally, rotate the inserted axes back to where they belong
        return transpose(buff, buff_permute)

    else:
        # matrices have to be transposed first, because they collapse dimensions!
        out_arr = transpose(buff, buff_permute)
        return res.__array_wrap__(out_arr)
Beispiel #40
0
def apply_along_axis(func1d, axis, arr, *args, **kwargs):
    """
    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`.
    kwargs : any
        Additional named arguments to `func1d`.

        .. versionadded:: 1.9.0


    Returns
    -------
    apply_along_axis : ndarray
        The output array. The shape of `outarr` is identical to the shape of
        `arr`, except along the `axis` dimension. This axis is removed, and
        replaced with new dimensions equal to the shape of the return value
        of `func1d`. So 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 returns a 1D array, the number of dimensions in
    `outarr` is the same as `arr`.

    >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])
    >>> np.apply_along_axis(sorted, 1, b)
    array([[1, 7, 8],
           [3, 4, 9],
           [2, 5, 6]])

    For a function that returns a higher dimensional array, those dimensions
    are inserted in place of the `axis` dimension.

    >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
    >>> np.apply_along_axis(np.diag, -1, b)
    array([[[1, 0, 0],
            [0, 2, 0],
            [0, 0, 3]],

           [[4, 0, 0],
            [0, 5, 0],
            [0, 0, 6]],

           [[7, 0, 0],
            [0, 8, 0],
            [0, 0, 9]]])
    """
    # handle negative axes
    arr = asanyarray(arr)
    nd = arr.ndim
    if not (-nd <= axis < nd):
        raise IndexError('axis {0} out of bounds [-{1}, {1})'.format(axis, nd))
    if axis < 0:
        axis += nd

    # arr, with the iteration axis at the end
    in_dims = list(range(nd))
    inarr_view = transpose(arr, in_dims[:axis] + in_dims[axis+1:] + [axis])

    # compute indices for the iteration axes
    inds = ndindex(inarr_view.shape[:-1])

    # invoke the function on the first item
    ind0 = next(inds)
    res = asanyarray(func1d(inarr_view[ind0], *args, **kwargs))

    # build a buffer for storing evaluations of func1d.
    # remove the requested axis, and add the new ones on the end.
    # laid out so that each write is contiguous.
    # for a tuple index inds, buff[inds] = func1d(inarr_view[inds])
    buff = zeros(inarr_view.shape[:-1] + res.shape, res.dtype)

    # permutation of axes such that out = buff.transpose(buff_permute)
    buff_dims = list(range(buff.ndim))
    buff_permute = (
        buff_dims[0 : axis] +
        buff_dims[buff.ndim-res.ndim : buff.ndim] +
        buff_dims[axis : buff.ndim-res.ndim]
    )

    # matrices have a nasty __array_prepare__ and __array_wrap__
    if not isinstance(res, matrix):
        buff = res.__array_prepare__(buff)

    # save the first result, then compute and save all remaining results
    buff[ind0] = res
    for ind in inds:
        buff[ind] = asanyarray(func1d(inarr_view[ind], *args, **kwargs))

    if not isinstance(res, matrix):
        # wrap the array, to preserve subclasses
        buff = res.__array_wrap__(buff)

        # finally, rotate the inserted axes back to where they belong
        return transpose(buff, buff_permute)

    else:
        # matrices have to be transposed first, because they collapse dimensions!
        out_arr = transpose(buff, buff_permute)
        return res.__array_wrap__(out_arr)