----
    This is an interface to the LAPACK routines dgeqrf, zgeqrf,
    dorgqr, zungqr, dgeqp3, and zgeqp3.

    If ``mode=economic``, the shapes of Q and R are (M, K) and (K, N) instead
    of (M,M) and (M,N), with ``K=min(M,N)``.

    Examples
    --------
    >>> import numpy as np
    >>> from scipy import linalg
    >>> rng = np.random.default_rng()
    >>> a = rng.standard_normal((9, 6))

    >>> q, r = linalg.qr(a)
    >>> np.allclose(a, np.dot(q, r))
    True
    >>> q.shape, r.shape
    ((9, 9), (9, 6))

    >>> r2 = linalg.qr(a, mode='r')
    >>> np.allclose(r, r2)
    True

    >>> q3, r3 = linalg.qr(a, mode='economic')
    >>> q3.shape, r3.shape
    ((9, 6), (6, 6))

    >>> q4, r4, p4 = linalg.qr(a, pivoting=True)
    >>> d = np.abs(np.diag(r4))
    >>> np.all(d[1:] <= d[:-1])
    True
    >>> np.allclose(a[:, p4], np.dot(q4, r4))
    True
    >>> q4.shape, r4.shape, p4.shape
    ((9, 9), (9, 6), (6,))

    >>> q5, r5, p5 = linalg.qr(a, mode='economic', pivoting=True)
    >>> q5.shape, r5.shape, p5.shape
    ((9, 6), (6, 6), (6,))

    )