MATLAB Release Notes

Mathematics Features

Evaluation of Solutions to Differential Equation Problems

A new function, `deval`, enables you to evaluate the solution of a differential equation problem at a vector of points from the interval in which the problem was solved. `deval` uses, as input, the output structure `sol` of an initial value problem solver (`ode45`, `ode23`, `ode113`, `ode15s`, `ode23s`, `ode23t`, `ode23tb`) or the boundary value problem solver (`bvp4c)`. A new ODE solver syntax returns the structure `sol`.

These functions are now based on Qhull:

• `delaunay` -- two-dimensional Delaunay triangulation
• `convhull` -- two-dimensional convex hull

These functions call `delaunay` and therefore are now indirectly based on Qhull:

• `voronoi` -- two-dimensional Voronoi diagrams
• `griddata` -- data gridding and surface fitting

These functions are in addition to the Qhull-based functions introduced in MATLAB 6.0 (Release 12.0): `convhulln`, `delaunay3`, `delaunayn`, `griddata3`, `griddatan`, and `voronoin`.

Math Function Summary Tables

This section summarizes

 Note    See Upgrading from an Earlier Release for information about obsolete functions.

 Function Purpose `deval` Evaluate the solution of a differential equation problem using the output of `ode45`, `ode23`, `ode113`, `ode15s`, `ode23s`, `ode23t`, `ode23tb`, or `bvp4c`. `erfcinv` Inverse complementary error function. `tetramesh` Tetrahedron mesh plot for use with `delaunayn`. `triplot` 2-D triangular plot for use with `delaunay`.

 Function Enhancement/Change `bvpinit` New syntax `solinit = bvpinit(sol,[anew bnew])` extrapolates a solution `sol` as an initial guess for solving a BVP on an extended interval. It can copy parameters from the previous iteration or let the user to provide new ones. For more information, see Boundary Value Problems for ODEs in the MATLAB documentation. `bvpset` New `Vectorized` option lets you pass to the solver `bvp4c` an array of column vectors. This allows `bvp4c` to reduce the number of function evaluations, and may significantly reduce solution time. For more information see Boundary Value Problems for ODEs in the MATLAB documentation. `convhull` New syntax `[K,a] = convhull(x,y)` returns the area `a` of the convex hull. `convhulln` New syntax `[K,v] = convhulln(X)` returns the volume `v` of the convex hull. `numel` New syntax `n = numel(A, varargin)` returns the number of subscripted elements, `n`, in `A(index1,index2,...,indexn)`, where `varargin` is a cell array whose elements are `index1`, `index2`, `...`, `indexn`. `ode45, ode23, ode113, ode15s, ode23s, ode23t, ode23tb` New syntax `sol = ``solver``(odefun,[t0 tf],y0...)` returns a structure that you can use with the new function `deval` to evaluate the solution at any point on the interval `[t0,tf]`. `polyeig` New syntax `e = polyeig(A0,A1,..,Ap)` returns only the eigenvalues of the specified eigenvalue problem. Use [`X,e] = polyeig(A0,A1,...Ap)` if you also want the eigenvectors. This capability is available in MATLAB 6.0 (Release 12.0). `ppval` New syntax `ppval(xx,pp)` transposes the input arguments to enable you to use `ppval` with function functions. `qz` New syntax `[AA,BB,Q,Z,V,W] = qz(A,B)` returns `W`, the left generalized eigenvectors of `A` and `B`. `reshape` New syntax `reshape(A,...,[],...)` calculates the length of the dimension specified by the placeholder `[]`. `svd` Can now return only the first two outputs, `U` and `S`, where `S` is a diagonal matrix of the same dimension as the input argument `X`, and `U` is a unitary matrix.

 Development Environment Features Programming and Data Types Features