Python Matrix.inv方法代码示例

# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import inv [as 别名]
def demo_symetricA_Msquare(A):
    print "\n1)Any symmetric matrix A can be written as A = M^2:\n"\
            "<= any symetric matrix A can be diagonalized as A = Q * D * Q.inv()\n"\
            "<= D is diagonal matrix with eigen values\n"\
            "   Q is eigen vectors with norm 1\n"\
            "   Q.inv() == Q.T\n"\
            "first take a look as eigen vectors:\n"
    pprint(A.eigenvects())
    print "\nthen sympy diagonalized result:\n"
    pprint(A.diagonalize())
    d = A.diagonalize()[1]
    q = A.diagonalize()[0]
    q = Matrix(q.rows, q.cols, lambda i, j: q[:,j].normalized()[i])
    print "\nthen normalized Q:\n"
    pprint(q)
    print "\nthen the transpose of Q:\n"
    pprint(q.T)
    print "\nthen the inverse of Q:\n"
    pprint(q.inv())
    print "\nthen Q * D * Q.inv():\n"
    pprint(q*d*q.inv())
    print "\nif we define a new diagonal matrix Droot:\n"
    d = d.applyfunc(lambda x: x**.5)
    pprint(d)
    print "\nthen let M = Q * Droot * Q.inv():\n"
    m = q*d*q.inv()
    pprint(m)
    print "\nthen A = M*M:\n"
    pprint(q*d*d*q.inv())

# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import inv [as 别名]
def vcv2corr(vcv):
    n = vcv.rows
    m = vcv.cols
    if n != m:
        raise ValueError('variance mattrix has to be square matrix')
    def var(i, j):
        if i == j:
            return vcv[i, j]**.5
        else:
            return 0
    D = Matrix(n, n, var)
    corr = D.inv() * vcv * D.inv()
    return corr, D

# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import inv [as 别名]
def euler101():
    #actual function that generates polynomials
    def u(n):
        return n ** 3

    order = 3  # largest polynomial order of u
    seq = [u(x) for x in range(1, order + 2)]
    A = Matrix([[1 ** 1, 1], [8 ** 1, 1]][::-1])
    b = Matrix([[x] for x in seq[:2]])
    return A.inv() * b