python – 用numpy旋转网格

2023年6月18日 322次阅读

我想要生成一个坐标已旋转的网格.我必须在双循环中进行旋转,我确信有更好的方法来矢量化它.代码如下：

# Define the range for x and y in the unrotated matrix
xspan = linspace(-2*pi, 2*pi, 101)
yspan = linspace(-2*pi, 2*pi, 101)

# Generate a meshgrid and rotate it by RotRad radians.
def DoRotation(xspan, yspan, RotRad=0):

    # Clockwise, 2D rotation matrix
    RotMatrix = np.array([  [np.cos(RotRad),  np.sin(RotRad)],
                            [-np.sin(RotRad), np.cos(RotRad)]])
    print RotMatrix

    # This makes two 2D arrays which are the x and y coordinates for each point.
    x, y = meshgrid(xspan,yspan)

    # After rotating, I'll have another two 2D arrays with the same shapes.
    xrot = zeros(x.shape)
    yrot = zeros(y.shape)

    # Dot the rotation matrix against each coordinate from the meshgrids.
    # I BELIEVE THERE IS A BETTER WAY THAN THIS DOUBLE LOOP!!!
    # I BELIEVE THERE IS A BETTER WAY THAN THIS DOUBLE LOOP!!!
    # I BELIEVE THERE IS A BETTER WAY THAN THIS DOUBLE LOOP!!!
    # I BELIEVE THERE IS A BETTER WAY THAN THIS DOUBLE LOOP!!!
    # I BELIEVE THERE IS A BETTER WAY THAN THIS DOUBLE LOOP!!!
    # I BELIEVE THERE IS A BETTER WAY THAN THIS DOUBLE LOOP!!!
    for i in range(len(xspan)):
        for j in range(len(yspan)):
            xrot[i,j], yrot[i,j] = dot(RotMatrix, array([x[i,j], y[i,j]]))

    # Now the matrix is rotated
    return xrot, yrot

# Pick some arbitrary function and plot it (no rotation)
x, y = DoRotation(xspan, yspan, 0)
z = sin(x)+cos(y)
imshow(z)

# And now with 0.3 radian rotation so you can see that it works.
x, y = DoRotation(xspan, yspan, 0.3)
z = sin(x)+cos(y)
figure()
imshow(z)

在两个网格物体上写一个双循环似乎很愚蠢.那里的一个巫师有一个想法如何矢量化这个？

最佳答案 爱因斯坦求和(
np.einsum)对于这种事情非常快. 1001×1001我得到97毫秒.

def DoRotation(xspan, yspan, RotRad=0):
    """Generate a meshgrid and rotate it by RotRad radians."""

    # Clockwise, 2D rotation matrix
    RotMatrix = np.array([[np.cos(RotRad),  np.sin(RotRad)],
                          [-np.sin(RotRad), np.cos(RotRad)]])

    x, y = np.meshgrid(xspan, yspan)
    return np.einsum('ji, mni -> jmn', RotMatrix, np.dstack([x, y]))
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