Python numeric.nonzero函数代码示例

def roots(p):
    """ Return the roots of the polynomial coefficients in p.

        The values in the rank-1 array p are coefficients of a polynomial.
        If the length of p is n+1 then the polynomial is
        p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
    """
    # If input is scalar, this makes it an array
    p = atleast_1d(p)
    if len(p.shape) != 1:
        raise ValueError,"Input must be a rank-1 array."

    # find non-zero array entries
    non_zero = NX.nonzero(NX.ravel(p))[0]

    # Return an empty array if polynomial is all zeros
    if len(non_zero) == 0:
        return NX.array([])

    # find the number of trailing zeros -- this is the number of roots at 0.
    trailing_zeros = len(p) - non_zero[-1] - 1

    # strip leading and trailing zeros
    p = p[int(non_zero[0]):int(non_zero[-1])+1]

    # casting: if incoming array isn't floating point, make it floating point.
    if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
        p = p.astype(float)

    N = len(p)
    if N > 1:
        # build companion matrix and find its eigenvalues (the roots)
        A = diag(NX.ones((N-2,), p.dtype), -1)
        A[0, :] = -p[1:] / p[0]
        roots = _eigvals(A)
    else:
        roots = NX.array([])

    # tack any zeros onto the back of the array
    roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
    return roots

def roots(p):
    """
    Return the roots of a polynomial with coefficients given in p.

    The values in the rank-1 array `p` are coefficients of a polynomial.
    If the length of `p` is n+1 then the polynomial is described by::

      p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]

    Parameters
    ----------
    p : array_like
        Rank-1 array of polynomial coefficients.

    Returns
    -------
    out : ndarray
        An array containing the complex roots of the polynomial.

    Raises
    ------
    ValueError :
        When `p` cannot be converted to a rank-1 array.

    See also
    --------
    poly : Find the coefficients of a polynomial with a given sequence
           of roots.
    polyval : Evaluate a polynomial at a point.
    polyfit : Least squares polynomial fit.
    poly1d : A one-dimensional polynomial class.

    Notes
    -----
    The algorithm relies on computing the eigenvalues of the
    companion matrix [1]_.

    References
    ----------
    .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*.  Cambridge, UK:
        Cambridge University Press, 1999, pp. 146-7.

    Examples
    --------
    >>> coeff = [3.2, 2, 1]
    >>> np.roots(coeff)
    array([-0.3125+0.46351241j, -0.3125-0.46351241j])

    """
    # If input is scalar, this makes it an array
    p = atleast_1d(p)
    if len(p.shape) != 1:
        raise ValueError("Input must be a rank-1 array.")

    # find non-zero array entries
    non_zero = NX.nonzero(NX.ravel(p))[0]

    # Return an empty array if polynomial is all zeros
    if len(non_zero) == 0:
        return NX.array([])

    # find the number of trailing zeros -- this is the number of roots at 0.
    trailing_zeros = len(p) - non_zero[-1] - 1

    # strip leading and trailing zeros
    p = p[int(non_zero[0]):int(non_zero[-1])+1]

    # casting: if incoming array isn't floating point, make it floating point.
    if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
        p = p.astype(float)

    N = len(p)
    if N > 1:
        # build companion matrix and find its eigenvalues (the roots)
        A = diag(NX.ones((N-2,), p.dtype), -1)
        A[0, :] = -p[1:] / p[0]
        roots = eigvals(A)
    else:
        roots = NX.array([])

    # tack any zeros onto the back of the array
    roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
    return roots

def triu_indices(n, k=0, m=None):
    """
    Return the indices for the upper-triangle of an (n, m) array.

    Parameters
    ----------
    n : int
        The size of the arrays for which the returned indices will
        be valid.
    k : int, optional
        Diagonal offset (see `triu` for details).
    m : int, optional
        .. versionadded:: 1.9.0

        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.


    Returns
    -------
    inds : tuple, shape(2) of ndarrays, shape(`n`)
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.  Can be used
        to slice a ndarray of shape(`n`, `n`).

    See also
    --------
    tril_indices : similar function, for lower-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    triu, tril

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    Compute two different sets of indices to access 4x4 arrays, one for the
    upper triangular part starting at the main diagonal, and one starting two
    diagonals further right:

    >>> iu1 = np.triu_indices(4)
    >>> iu2 = np.triu_indices(4, 2)

    Here is how they can be used with a sample array:

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Both for indexing:

    >>> a[iu1]
    array([ 0,  1,  2,  3,  5,  6,  7, 10, 11, 15])

    And for assigning values:

    >>> a[iu1] = -1
    >>> a
    array([[-1, -1, -1, -1],
           [ 4, -1, -1, -1],
           [ 8,  9, -1, -1],
           [12, 13, 14, -1]])

    These cover only a small part of the whole array (two diagonals right
    of the main one):

    >>> a[iu2] = -10
    >>> a
    array([[ -1,  -1, -10, -10],
           [  4,  -1,  -1, -10],
           [  8,   9,  -1,  -1],
           [ 12,  13,  14,  -1]])

    """
    return nonzero(~tri(n, m, k=k-1, dtype=bool))

def mask_indices(n, mask_func, k=0):
    """
    Return the indices to access (n, n) arrays, given a masking function.

    Assume `mask_func` is a function that, for a square array a of size
    ``(n, n)`` with a possible offset argument `k`, when called as
    ``mask_func(a, k)`` returns a new array with zeros in certain locations
    (functions like `triu` or `tril` do precisely this). Then this function
    returns the indices where the non-zero values would be located.

    Parameters
    ----------
    n : int
        The returned indices will be valid to access arrays of shape (n, n).
    mask_func : callable
        A function whose call signature is similar to that of `triu`, `tril`.
        That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.
        `k` is an optional argument to the function.
    k : scalar
        An optional argument which is passed through to `mask_func`. Functions
        like `triu`, `tril` take a second argument that is interpreted as an
        offset.

    Returns
    -------
    indices : tuple of arrays.
        The `n` arrays of indices corresponding to the locations where
        ``mask_func(np.ones((n, n)), k)`` is True.

    See Also
    --------
    triu, tril, triu_indices, tril_indices

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    These are the indices that would allow you to access the upper triangular
    part of any 3x3 array:

    >>> iu = np.mask_indices(3, np.triu)

    For example, if `a` is a 3x3 array:

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

    An offset can be passed also to the masking function.  This gets us the
    indices starting on the first diagonal right of the main one:

    >>> iu1 = np.mask_indices(3, np.triu, 1)

    with which we now extract only three elements:

    >>> a[iu1]
    array([1, 2, 5])

    """
    m = ones((n, n), int)
    a = mask_func(m, k)
    return nonzero(a != 0)

def roots(p):
    """
    Return the roots of a polynomial with coefficients given in p.

    The values in the rank-1 array `p` are coefficients of a polynomial.
    If the length of `p` is n+1 then the polynomial is described by
    p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]

    Parameters
    ----------
    p : array_like of shape(M,)
        Rank-1 array of polynomial co-efficients.

    Returns
    -------
    out : ndarray
        An array containing the complex roots of the polynomial.

    Raises
    ------
    ValueError:
        When `p` cannot be converted to a rank-1 array.

    Examples
    --------

    >>> coeff = [3.2, 2, 1]
    >>> print np.roots(coeff)
    [-0.3125+0.46351241j -0.3125-0.46351241j]

    """
    # If input is scalar, this makes it an array
    p = atleast_1d(p)
    if len(p.shape) != 1:
        raise ValueError,"Input must be a rank-1 array."

    # find non-zero array entries
    non_zero = NX.nonzero(NX.ravel(p))[0]

    # Return an empty array if polynomial is all zeros
    if len(non_zero) == 0:
        return NX.array([])

    # find the number of trailing zeros -- this is the number of roots at 0.
    trailing_zeros = len(p) - non_zero[-1] - 1

    # strip leading and trailing zeros
    p = p[int(non_zero[0]):int(non_zero[-1])+1]

    # casting: if incoming array isn't floating point, make it floating point.
    if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
        p = p.astype(float)

    N = len(p)
    if N > 1:
        # build companion matrix and find its eigenvalues (the roots)
        A = diag(NX.ones((N-2,), p.dtype), -1)
        A[0, :] = -p[1:] / p[0]
        roots = eigvals(A)
    else:
        roots = NX.array([])

    # tack any zeros onto the back of the array
    roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
    return roots