3d diag matlab code#

Using Octave, I found that after the while-loop in MinVolEllipse ends, u = X,y,z = np.dot(np.transpose(V),np.array(,y,z])) + centroidĪx = fig.add_subplot(111, projection='3d')Īx.scatter(points,points,points)Īx.plot_surface(x, y, z, cstride = 1, rstride = 1, alpha = 0.1) The corresponding test code: from mpl_toolkits.mplot3d import Axes3Dįrom mpl_3d import Pol圓DCollection M = np.diag( np.dot(np.dot(np.transpose(Q), la.inv(X)),Q)) X = np.dot(np.dot(Q, np.diag(u)), np.transpose(Q))

3d diag matlab code#

Now, here is my attempt at port this code to Python (2.7): from _future_ import division Which will produce the the covariance matrix: A = Here is some MATLAB test code: points = , I'll paste the relevant part for convenience: function = MinVolEllipse(P, tolerance)

Option to use a smooth ramp to avoid start-up transients.MATLAB code exists to find the so-called 'minimum volume enclosing ellipsoid' (e.g. Note, setting a value for the optional input 'Time' will override this value. Option to specify the multiplicative factor used to calculate t based on the time taken to propagate across the longest grid diagonal. Option to specify the time t at which the wavefield is calculated to extract the amplitude and phase. The saved variables can be used to run simulations using the C++ code. If set, after the precomputation phase, the input variables used in the time loop are saved the specified location in HDF5 format. String containing a filename (including pathname if required). Note, setting a value for the optional input 'ExpandedGridSize' will override this value. Option to set the search range used to find the expanded grid size with the smallest prime factors.

Option to specify the multiplicative factor used to calculate the minimum expanded grid size to avoid wave wrapping based on time t. Option to specify the size of the grid after expansion used to avoid wave wrapping. (one, two, or three element vector) or 'auto' Optional 'string', value pairs that may be used to modify the default computational settings. Matrix of the source phase at each grid point Matrix of the source amplitude at each grid point The Journal of the Acoustical Society of America, 143(1), 529-537. Rapid calculation of acoustic fields from arbitrary continuous-wave sources. = acousticFieldPropagator(amp_in, phase_in, dx, f0, c0) % define grid propertiesĭx = 1e-4 % % define input amplitude and phase for a line sourceĬ0 = 1500 % % compute pressure field To avoid wave wrapping, the domain size used for calculation is automatically expanded to a suitable dimension size with small prime factors.Ī simple example of computing the field from a line source in 2D is given below. This allows the acoustic pressure for all spatial positions at any time t > 0 to be calculated in a single step without numerical quadrature.

The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space as outlined in. This allows arrays of arbitrary geometry and numbers of elements to be defined. The phased array is defined in completely general form as a matrix of amplitude and phase. )ĪcousticFieldPropagator calculates the steady state field pattern (complex pressure or amplitude and phase) from an arbitrary phased array (or other acoustic source) driven by a single frequency continuous wave sinusoid in a homogeneous and lossless medium. = acousticFieldPropagator(amp_in, phase_in, dx, f0, c0. Pressure = acousticFieldPropagator(amp_in, phase_in, dx, f0, c0. Pressure = acousticFieldPropagator(amp_in, phase_in, dx, f0, c0)