numpy.polynomial.legendre.legvander3d¶

polynomial.legendre.legvander3d(x, y, z, deg)[源代码]¶

给定度数的伪范德蒙矩阵。

返回度的伪范德蒙矩阵 deg 和采样点 (x, y, z) .如果 l, m, n 给定的度数是多少 x, y, z ，则伪范德蒙矩阵定义为

System Message: WARNING/2 (V […，（m+1）（n+1）i+（n+1）j+k] ＝Li i（x） *L_j(y)* LYK（Z），)

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Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} LaTeX Warning: Command \textellipsis invalid in math mode on input line 14. ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. 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Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...i（x） *L_j(y)* LYK（Z），\end{split} [1] (./math.aux) ) (see the transcript file for additional information) Output written on math.dvi (1 page, 472 bytes). Transcript written on math.log.

在哪里？ 0 <= i <= l ， 0 <= j <= m 和 0 <= j <= n . 主要指标 V 索引点 (x, y, z) 最后一个索引编码勒让德多项式的度数。

如果 V = legvander3d(x, y, z, [xdeg, ydeg, zdeg]) ，然后是 V 对应于三维系数数组的元素 c 按顺序排列的形状（xdeg+1、ydeg+1、zdeg+1）

System Message: WARNING/2 (C_000，C_001，C_002，…，C_010，C_011，C_012，…)

和 np.dot(V, c.flat) 和 legval3d(x, y, z, c) 在环形交叉路口也一样。这种等效性对于最小二乘拟合和大量相同度数和采样点的三维勒让德级数的计算都是有用的。

参数

x，y，zarray_like: 点坐标数组，所有形状相同。根据元素是否复杂，数据类型将转换为float64或complex128。标量转换为一维数组。
deg英特列表: 窗体的最大度数列表 [x_deg, y_deg, z_deg] .

返回

vander3d恩达雷: 返回矩阵的形状为 x.shape + (order,) 在哪里 $order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)$ . 数据类型将与转换后的类型相同 x ， y 和 z .

参见

legvander, legvander3d, legval2d, legval3d

笔记

1.7.0 新版功能.

numpy.polynomial.legendre.legvander2d numpy.polynomial.legendre.leggauss