The transduction. and reflection coefficients of SPUDTs are usually determined by optimization methods. Some methods need gradients or the difference vectors of IDT's P matrix in order to calculate the corresponding quantities of the error function. The difference vector is defined by the change of the P matrix due to finitely large steps of the coefficients. When a gradient component is calculated numerically, solely one coefficient of solely one cell is changed. Nevertheless, the P matrices of all cells are calculated for the changed case, requiring unneeded computing time. The purpose of the present paper is to show that P matrix gradients can be attributed without differential approximation. Therefore, the method described is not only applicable for the calculation of gradients but also of difference vectors. The P matrix is transferred to stackable matrices and vectors. Solely the gradient component of the P matrix of the cell the coefficients of which are changed is calculated. By this method, the components of the difference vector can be obtained, too. The time for optimization can substantially be reduced.