rotation of 4D data

I have XYZ matrix of some intensity V space distribution and I need to rotate it. Values of V are placed in each voxel of XYZ matrix. Coordinate vectors are regularly spaced and known: 0...xMax, 0...yMax, 0...zMax.

I know about matrices of rotation, but if I understand correct, their application needs matices of following XYZ_ format:

XYZ_ =

x1 x2 x3 ... xMax

y1 y2 y3 ... yMax

z1 z2 z3 ... zMax

V1 V2 V3 ... VMax

It can be used too simple solution by organizing tree loops for x, y, z coordinates and shaping inside these loops this XYZ_ matrix, but it seems that should exist more clever solution. Number of voxels is in order of 10^8.

How is it possible to reshape XYZ matrix into XYZ_ one in less time consuming way and rotate it?