使用python计算向量投影 [英] using python to calculate Vector Projection

问题描述

是否有更简单的命令来计算矢量投影? 我改为使用以下内容:

Is there an easier command to compute vector projection? I am instead using the following:

x = np.array([ 3, -4,  0])
y = np.array([10,  5, -6])
z=float(np.dot(x, y))
z1=float(np.dot(x, x))
z2=np.sqrt(z1)
z3=(z/z2**2)
x*z3

推荐答案

也许这就是您真正想要的:

Maybe this is what you really want:

np.dot(x, y) / np.linalg.norm(y)

这应该使向量x投影到向量y上-参见 https://en .wikipedia.org/wiki/Vector_projection .另外，如果要计算y在x上的投影，则在上式的分母(norm)中用x替换y.

This should give the projection of vector x onto vector y - see https://en.wikipedia.org/wiki/Vector_projection. Alternatively, if you want to compute the projection of y onto x, then replace y with x in the denominator (norm) of the above equation.

正如@VaidAbhishek所评论的那样，以上公式用于 scalar 投影.为了获得 vector 投影，将标量投影乘以单位矢量，然后在投影第一矢量的方向上将其乘以单位矢量.然后可以将该公式修改为:

As @VaidAbhishek commented, the above formula is for the scalar projection. To obtain vector projection multiply scalar projection by a unit vector in the direction of the vector onto which the first vector is projected. The formula then can be modified as:

y * np.dot(x, y) / np.dot(y, y)

，用于x在y上的矢量投影.

for the vector projection of x onto y.

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