numpy.polynomial.legendre.legfromroots¶

polynomial.legendre.legfromroots(roots)[源代码]¶

生成具有给定根的勒让德级数。

函数返回多项式的系数

System Message: WARNING/2 (P（x）=（x-r_0） * (x - r_1) * …*（X-RYN），)

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以勒让德形式，其中 r_n 是否在中指定了根 roots . 如果一个零有多重性n，那么它必须出现在 roots n次。例如，如果2是重数3的根，而3是重数2的根，那么 roots 看起来像 [2, 2, 2，3, 3] . 根可以以任何顺序出现。

如果返回系数为 c 然后

System Message: WARNING/2 (P（x）=C_0+C_1 * L_1(x) + ... + c_n * Lnn（x）)

对于勒让德形式的Monic多项式，最后一项的系数一般不是1。

参数

rootsarray_like: 包含根的序列。

返回

out恩达雷: 一维系数数组。如果所有的根都是真的那么 out 是一个实数数组，如果某些根是复杂的，则 out 即使结果中的所有系数都是真实的，也是复杂的（参见下面的示例）。

参见

numpy.polynomial.polynomial.polyfromroots
numpy.polynomial.chebyshev.chebfromroots
numpy.polynomial.laguerre.lagfromroots
numpy.polynomial.hermite.hermfromroots
numpy.polynomial.hermite_e.hermefromroots

实例

>>> import numpy.polynomial.legendre as L
>>> L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis
array([ 0. , -0.4,  0. ,  0.4])
>>> j = complex(0,1)
>>> L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis
array([ 1.33333333+0.j,  0.00000000+0.j,  0.66666667+0.j]) # may vary

numpy.polynomial.legendre.legint numpy.polynomial.legendre.legroots