MATLAB 6.1 Release Notes (MATLAB Release Notes)

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.

Additional Functions Use Qhull

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

New math functions
Functions with new or changed capabilities

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

New Math 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.

**New Math 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`.

Math Functions with New or Changed Capabilities
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.

**Math Functions with New or Changed Capabilities**
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