qr.py 文件源码

def qr_fast_givens(A):
    '''
    QR factorization via fast givens transformation
    '''
    m = A.shape[0]
    n = A.shape[1]
    d = np.ones(m)
    for j in range(n):
        for i in range(m-1, j, -1):
            alpha, beta, ty = givens.fast_givens(A[i-1:i+1, j], d[i-1:i+1])
            if ty == 1:
                A[i-1:i+1, j:n+1] = np.array([[beta, 1],
                                              [1, alpha]]).dot(A[i-1:i+1, j:n+1])
            else:
                A[i-1:i+1, j:n+1] = np.array([[1, alpha],
                                              [beta, 1]]).dot(A[i-1:i+1, j:n+1])

    return A

# least square using QR (A must be full column rank)