The worst bottleneck for the numerical analysis, is the looping over spins. For the nmerical models, a propagator that will evolve the magnetization is calculated. This is the matrix exponential of the matrix R that contains all the contributions to the evolution, i.e. relaxation, exchange and chemical shift evolution. The shape of R, can be (7, 7) or (9,9). Finding the matrix exponential is done over looping of spins, and spectrometer frequencies. NS and NM. If NS is 100, and NM is 2, maybe R, could get packed to: (100, 2, 7, 7) The matrix exponential is: # The eigenvalue decomposition. W, V = eig(A) # Calculate the exact exponential. eA = dot(dot(V, diag(exp(W))), inv(V)) But according to: http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html This should be possible for an array of matrixes. ##### Compute the eigenvalues and right eigenvectors of a square array. Parameters : a : (..., M, M) array Matrices for which the eigenvalues and right eigenvectors will be computed Returns : w : (..., M) array The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be always be of complex type. When a is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs v : (..., M, M) array The normalized (unit “length”) eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i]. Raises : LinAlgError If the eigenvalue computation does not converge. ------- Broadcasting rules apply, see the numpy.linalg documentation for details. This is implemented using the _geev LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. The number w is an eigenvalue of a if there exists a vector v such that dot(a,v) = w * v. Thus, the arrays a, w, and v satisfy the equations dot(a[:,:], v[:,i]) = w[i] * v[:,i] for i \in \{0,...,M-1\}. ------ #### R is: R = rcpmg_3d(R1A=r10a, R1B=r10b, R2A=R2A_si_mi, R2B=R2B_si_mi, pA=pA, pB=pB, dw=dw_si_mi, k_AB=k_AB, k_BA=k_BA) So that would need a new way to expand this, since we have R20 and dw as specific for spin and frequency. Troels Emtekær Linnet