示例：三次样条插值

使用 lspline、pspline 和 cspline 函数可构建三次样条 (分段多项式)，并在数据点之间进行插值。

1. 定义矩阵。

2. 使用函数 csort 对数据进行排序，以使 Cu 的第二列按升序排列。

应用于样条函数的 x 值必须按升序排列。

3. 创建包含 x 和 y 的矢量。

4. 使用函数 cspline 创建三次样条矢量，然后使用函数 interp 获取插值。

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5. 使用函数 lspline 创建线性样条矢量，然后使用函数 interp 获取插值。

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6. 使用函数 pspline 创建抛物线样条矢量，然后使用函数 interp 获取插值。

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7. 绘制原始数据点和三次样条图像。

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8. 放大前两个数据点。

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除端点外，这三个样条函数所生成的结果相同。

9. 计算插值线性样条矢量的二阶导数，并证明其在端点处等于 0。

10. 计算插值抛物线样条的二阶导数，并证明其在端点处等于下一最近点的值。

◦ 计算第一个点和第二个点处的二阶导数，并证明它们相等。

◦ 计算倒数第二个点和最后一个点处的二阶导数，并证明它们相等。

您可以使用样条拟合的导数来求解插值曲线的极大值和极小值、斜率以及其他特征。