Linalg.py 文件源码

def solve(A,b,rtol=10**-8):
    '''
    Solve the matrix equation A*x=b by QR decomposition.

    Parameters
    ----------
    A : 2d ndarray
        The coefficient matrix.
    b : 1d ndarray
        The ordinate values.
    rtol : np.float64
        The relative tolerance of the solution.

    Returns
    -------
    1d ndarray
        The solution.

    Raises
    ------
    LinAlgError
        When no solution exists.
    '''
    assert A.ndim==2
    nrow,ncol=A.shape
    if nrow>=ncol:
        result=np.zeros(ncol,dtype=np.find_common_type([],[A.dtype,b.dtype]))
        q,r=sl.qr(A,mode='economic',check_finite=False)
        temp=q.T.dot(b)
        for i,ri in enumerate(r[::-1]):
            result[-1-i]=(temp[-1-i]-ri[ncol-i:].dot(result[ncol-i:]))/ri[-1-i]
    else:
        temp=np.zeros(nrow,dtype=np.find_common_type([],[A.dtype,b.dtype]))
        q,r=sl.qr(dagger(A),mode='economic',check_finite=False)
        for i,ri in enumerate(dagger(r)):
            temp[i]=(b[i]-ri[:i].dot(temp[:i]))/ri[i]
        result=q.dot(temp)
    if not np.allclose(A.dot(result),b,rtol=rtol):
        raise sl.LinAlgError('solve error: no solution.')
    return result