I didn’t have time earlier this year to write about the first MATLAB release of 2019, so in this post I will discuss R2019a and R2019b together. As usual in this series, I concentrate on the features most relevant to my work.

## Modified Akima Cubic Hermite Interpolation (R2019b)

A new function `makima`

computes a piecewise cubic interpolant with continuous first-order derivatives. It produces fewer undulations than the existing `spline`

function, with less flattening than `pchip`

. This form of interpolant has been an option in `interp1`

, `interp2`

, `interp3`

, `interpn`

, and `griddedInterpolant`

since R2017b and is now also a standalone function. For more details see Cleve Moler’s blog post about makima, from which the code used to generate the image above is taken.

## Linear Assignment Problem and Equilibration (R2019a)

The `matchpairs`

function solves the *linear assignment problem*, which requires each row of a matrix to be assigned to a column in such a way that the total cost of the assignments (given by the “sum of assigned elements” of the matrix) is minimized (or maximized). This problem can also be described as finding a minimum-weight matching in a weighted bipartite graph. The problem arises in sparse matrix computations.

The `equilibrate`

function take as input a matrix `A`

(dense or sparse) and returns a permutation matrix `P`

and nonsingular diagonal matrices `R`

and `C`

such that `R*P*A*C`

has diagonal entries of magnitude 1 and off-diagonal entries of magnitude at most 1. The outputs `P`

, `R`

, and `C`

are sparse. This matrix equilibration can improve conditioning and can be a useful preprocessing step both in computing incomplete LU preconditioners and in iterative solvers. See, for example, the recent paper Max-Balanced Hungarian Scalings by Hook, Pestana, Tisseur, and Hogg.

The scaling produced by `equilibrate`

is known as Hungarian scaling, and its computation involves solving a linear assignment problem.

## Function Argument Validation (R2019b)

A powerful new feature allows a function to check that its input arguments have the desired class, size, and other aspects. Previously, this could be done by calling the function `validateattributes`

with each argument in turn or by using the inputParser object (see Loren Shure’s comparison of the different approaches).

The new feature provides a more structured way of achieving the same effect. It also allows default values for arguments to be specified. Function argument validation contains many aspects and has a long help page. We just illustrate it with a simple example that should be self-explanatory.

function fav_example(a,b,f,t) arguments a (1,1) double % Double scalar. b {mustBeNumeric,mustBeReal} % Numeric type and real. f double {mustBeMember(f,[-1,0,1])} = 0 % -1, 0 (default), or 1. t string = "-" % String, with default value. end % Body of function. end

The functions `mustBeNumeric`

and `mustBeMember`

are just two of a long list of validation functions. Here is an example call:

>> a = 0; b = 2; f = 11; fav_example(a,b,f) Error using fav_example Invalid input argument at position 3. Value must be a member of ... this set: -1 0 1

One caveat is that a specification within the `arguments`

block

v (1,:) double

allows not just `1-by-n`

vectors (for any `n`

) but also `n-by-1`

vectors, because of the convention that in many situations MATLAB does not distinguish between row and column vectors.

For more extensive examples, see New with R2019b – Function Argument Validation and Spider Plots and More Argument Validation by Jiro Doke at MathWorks Blogs.

## Dot Indexing (R2019b)

One can now dot index the result of a function call. For example, consider

>> optimset('Display','iter').Display ans = 'iter'

The output of the dot call can even be indexed:

>> optimset('OutputFcn',{@outfun1,@outfun2}).OutputFcn{2} ans = function_handle with value: @outfun2

Of course, these are contrived examples, but in real codes such indexing can be useful. This syntax was not allowed in R2019a and earlier.

## Hexadecimal and Binary Values (R2019b)

One can now specify hexadecimal and binary values using the prefixes 0x or 0X for hexadecimal (with upper or lower case for A to F) and 0b or 0B for binary. By default the results have integer type.

>> 0xA ans = uint8 10 >> 0b101 ans = uint8 5

## Changes to Function Precedence Order (R2019b)

The Release Notes say “Starting in R2019b, MATLAB changes the rules for name resolution, impacting the precedence order of variables, nested functions, local functions, and external functions. The new rules simplify and standardize name resolution”. A number of examples are given where the meaning of code is different in R2019b, and they could cause an error to be generated for codes that ran without error in earlier versions. As far as I can see, though, these changes are not likely to affect well-written MATLAB code.

## Program File Size (R2019b)

Program files larger than “approximately 128 MB” will no longer open or run. This is an interesting change because I cannot imagine writing an M-file of that size. Good programming practice dictates splitting a code into separate functions and not including all of them in one program file. Presumably, some MATLAB users have produced such long files—perhaps automatically generated.

For a modern introduction and reference to MATLAB, see MATLAB Guide (third edition, 2017)

Nice and quite good job as usual.