A[i, j] == (a[i-j+m-1] if (0 <= (i-j+m-1) < m) else 0)

    This corresponds to a matrix whose rows are the subset of those from
    the 'full' case where all the coefficients in `a` are contained in the
    row.  For input ``[x, y, z]``, this array looks like::

        [z, y, x, 0, 0, ..., 0, 0, 0]
        [0, z, y, x, 0, ..., 0, 0, 0]
        [0, 0, z, y, x, ..., 0, 0, 0]
        ...
        [0, 0, 0, 0, 0, ..., x, 0, 0]
        [0, 0, 0, 0, 0, ..., y, x, 0]
        [0, 0, 0, 0, 0, ..., z, y, x]

    In the 'same' mode, the entries of `A` are given by::

        d = (m - 1) // 2
        A[i, j] == (a[i-j+d] if (0 <= (i-j+d) < m) else 0)

    The typical application of the 'same' mode is when one has a signal of
    length `n` (with `n` greater than ``len(a)``), and the desired output
    is a filtered signal that is still of length `n`.

    For input ``[x, y, z]``, this array looks like::

        [y, x, 0, 0, ..., 0, 0, 0]
        [z, y, x, 0, ..., 0, 0, 0]
        [0, z, y, x, ..., 0, 0, 0]
        [0, 0, z, y, ..., 0, 0, 0]
        ...
        [0, 0, 0, 0, ..., y, x, 0]
        [0, 0, 0, 0, ..., z, y, x]
        [0, 0, 0, 0, ..., 0, z, y]

    .. versionadded:: 1.5.0

    References
    ----------
    .. [1] "Convolution", https://en.wikipedia.org/wiki/Convolution

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.linalg import convolution_matrix
    >>> A = convolution_matrix([-1, 4, -2], 5, mode='same')
    >>> A
    array([[ 4, -1,  0,  0,  0],
           [-2,  4, -1,  0,  0],
           [ 0, -2,  4, -1,  0],
           [ 0,  0, -2,  4, -1],
           [ 0,  0,  0, -2,  4]])

    Compare multiplication by `A` with the use of `numpy.convolve`.

    >>> x = np.array([1, 2, 0, -3, 0.5])
    >>> A @ x
    array([  2. ,   6. ,  -1. , -12.5,   8. ])

    Verify that ``A @ x`` produced the same result as applying the
    convolution function.

    >>> np.convolve([-1, 4, -2], x, mode='same')
    array([  2. ,   6. ,  -1. , -12.5,   8. ])

    For comparison to the case ``mode='same'`` shown above, here are the
    matrices produced by ``mode='full'`` and ``mode='valid'`` for the
    same coefficients and size.

    >>> convolution_matrix([-1, 4, -2], 5, mode='full')
    array([[-1,  0,  0,  0,  0],
           [ 4, -1,  0,  0,  0],
           [-2,  4, -1,  0,  0],
           [ 0, -2,  4, -1,  0],
           [ 0,  0, -2,  4, -1],
           [ 0,  0,  0, -2,  4],
           [ 0,  0,  0,  0, -2]])

    >>> convolution_matrix([-1, 4, -2], 5, mode='valid')
    array([[-2,  4, -1,  0,  0],
           [ 0, -2,  4, -1,  0],
           [ 0,  0, -2,  4, -1]])
    r