MATLAB Online now has themes, including a dark theme (which is my preference). We will have to wait for a future release for themes to be supported on desktop MATLAB.

I recall that @nhigham was asking for this. Currently @MATLAB Online only at the moment though. Desktop MATLAB isn’t there yet

— Mike Croucher (@walkingrandomly) March 11, 2022

One can now write qr(A,'econ') instead of qr(A,0) and gsvd(A,B,'econ') instead of gsvd(A,B) for the “economy size” decompositions. This is useful as the 'econ' form is more descriptive. The svd function already supported the 'econ' argument. The economy-size QR factorization is sometimes called the thin QR factorization.

The round function, which rounds to the nearest integer, now breaks ties by rounding away from zero by default and has several other tie-breaking options (albeit not stochastic rounding). See a sequence of four blog posts on this topic by Cleve Moler starting with this one from February 2021.

The null (nullspace) and orth (orthonormal basis for the range) functions now accept a tolerance as a second argument, and any singular values less than that tolerance are treated as zero. The default tolerance is max(size(A)) * eps(norm(A)). This change brings the two functions into line with rank, which already accepted the tolerance. If you are working in double precision (the MATLAB default) and your matrix has inherent errors of order (for example), you might set the tolerance to , since singular values smaller than this are indistinguishable from zero.

The unit testing framework can now generate docx, html, and pdf reports after test execution, by using the function generatePDFReport in the latter case. This is useful for keeping a record of test results and for printing them. We use unit testing in Anymatrix and have now added an option to return the results in a variable so that the user can call one of these new functions.

Previously, if you wanted to check whether a matrix had all finite values you would need to use a construction such as all(all(isfinite(A))) or all(isfinite(A),'all'). The new allfinite function does this in one go: allfinite(A) returns true or false according as all the elements of A are finite or not, and it works for arrays of any dimension.

Similarly, anynan and anymissing check for NaNs or missing values. A missing value is a NaN for numerical arrays, but is indicated in other ways for other data types.

The new pagemldivide, pagemrdivide, and pageinv functions solve linear equations and calculate matrix inverses using pages of -dimensional arrays, while tensorprod calculates tensor products (inner products, outer products, or a combination of the two) between two -dimensional arrays.

The append option of the exportgraphics function now supports the GIF format, enabling one to create animated GIFs (previously only multipage PDF files were supported). The key command is exportgraphics(gca,file_name,"Append",true). There are other ways of creating animated GIFs in MATLAB, but this one is particularly easy. Here is an example M-file (based on cheb3plot in MATLAB Guide) with its output below.

%CHEB_GIF  Animated GIF of Chebyshev polynomials.
%   Based on cheb3plot in MATLAB Guide.
x = linspace(-1,1,1500)';
p = 49
Y = ones(length(x),p);

Y(:,2) = x;
for k = 3:p
  Y(:,k) = 2*x.*Y(:,k-1) - Y(:,k-2);
end

delete cheby_animated.gif
a = get(groot,'defaultAxesColorOrder'); m = length(a);

for j = 1:p-1 % length(k)
    plot(x,Y(:,j),'LineWidth',1.5,'color',a(1+mod(j-1,m),:));
    xlim([-1 1]), ylim([-1 1])  % Must freeze axes.
    title(sprintf('%2.0f', j),'FontWeight','normal')
    exportgraphics(gca,"cheby_animated.gif","Append",true)
end

The matrices built into Anymatrix are organized in seven groups.

• contest: the CONTEST toolbox of adjacency metrices from random network models (Taylor and D. J. Higham, 2009).
• core: miscellaneous matrices.
• gallery: matrices from the MATLAB gallery.
• hadamard: a large collection of Hadamard matrices (mostly from a collection of Sloane) and complex Hadamard matrices.
• matlab: other MATLAB matrices (not in gallery).
• nessie: matrices from real-life networks (Taylor and D. J. Higham, 2009).
• regtools: matrices from regularization problems (Hansen, 2007).

Every matrix has a unique identifier group_name/matrix_name, where matrix_name is the name of the function that implements the matrix.

In the rest of this post we introduce the toolbox through a few examples.

We first find what symmetric positive definite matrices with integer entries are available.

>> anymatrix('properties','integer and positive definite')
ans =
  7×1 cell array
    {'core/beta'     }
    {'core/wilson'   }
    {'gallery/gcdmat'}
    {'gallery/minij' }
    {'gallery/moler' }
    {'gallery/pei'   }
    {'matlab/pascal' }

Three of the seven groups built into Anymatrix—core, gallery, and matlab—contain such matrices. We check the properties of the core/beta matrix. Here, 'p' is short for 'properties'.

>> anymatrix('core/beta','p')
ans =
  12×1 cell array
    {'built-in'            }
    {'infinitely divisible'}
    {'integer'             }
    {'nonnegative'         }
    {'positive'            }
    {'positive definite'   }
    {'real'                }
    {'scalable'            }
    {'square'              }
    {'symmetric'           }
    {'totally nonnegative' }
    {'totally positive'    }

Infinitely divisibility of a symmetric positive semidefinite is the property that is positive semidefinite for all , where is the Hadamard power. We verify this property for and by checking that the eigenvalues are nonnegative:

>> A = anymatrix('core/beta',4)
A =
     1     2     3     4
     2     6    12    20
     3    12    30    60
     4    20    60   140

> eig(A.^(1/10))
ans =
   3.9036e-05
   3.1806e-03
   1.4173e-01
   5.0955e+00

The search on properties returns results across all the groups. If we want to restrict to a particular group we can use the contains command (one of the powerful MATLAB string-handling functions) to narrow the results. In the next example we find all the Hankel matrices built into MATLAB, that is, contained in the gallery and matlab groups.

>> m = anymatrix('p','hankel')
m =
  5×1 cell array
    {'core/dembo9'    }
    {'gallery/ipjfact'}
    {'gallery/ris'    }
    {'matlab/hankel'  }
    {'regtools/ursell'}
>> m = m(contains(m,{'gallery','matlab'}))
m =
  3×1 cell array
    {'gallery/ipjfact'}
    {'gallery/ris'    }
    {'matlab/hankel'  }

Anymatrix makes it possible to run tests over all or a subset of the matrices in the collection. This is not easy to do with the MATLAB gallery. The following code computes the minimum of the ratio over all the matrices, with default input arguments and size if the dimension is variable. This ratio is known to lie between and . We note several features of the code.

• By checking the built-in property, we only include matrices from the built-in groups (as opposed to any remote groups that have been downloaded).
• The input arguments to some of the matrices are of a special form not respected by our general-purpose code, so the try construct handles the errors generated in these cases.
• Some of the matrices are stored in the sparse format, so we make sure that the matrices are in the full format before taking the -norm.

mats = anymatrix('all'); % All matrix IDs.
rng(1), k = 1;
n = 64; % Size of the scalable matrices.
for i = 1:length(mats)
    ID = mats{i};
    props = anymatrix(ID,'p');
    if ~contains(props, {'built-in'}), continue, end 
    try
        if ismember('scalable',props);
            A = anymatrix(ID,n);
        else
            A = anymatrix(ID);
        end
        A = full(A);  % Convert sparse matrices to full.
        [mm,nn] = size(A);
        if max(mm,nn) > 1 && max(mm,nn) <= 1e3
           fprintf('%s: (%g,%g)\n', ID, size(A,1), size(A,2))
           A = A/norm(A,1); % Normalize to avoid overflow.
           r = norm(A)/sqrt(norm(A,1)*norm(A,inf));
           ratio(k) = r; k = k+1;
        end
    catch
        fprintf('Skipping %s\n', ID)
    end    
end    
fprintf('Min(ratio) = %9.2e\n', min(ratio))

The output is, with [...] denoting omitted lines,

contest/erdrey: (64,64)
contest/geo: (64,64)
[...]
regtools/ursell: (64,64)
regtools/wing: (64,64)
Min(ratio) =  1.25e-01

The core group contains some matrices with optimality properties. For example, core/triminsval01 is the unique matrix having the minimal smallest singular value over all nonsingular binary upper triangular matrices.

>> A = anymatrix('core/triminsval01',8)
A =
     1     1     0     1     0     1     0     1
     0     1     1     0     1     0     1     0
     0     0     1     1     0     1     0     1
     0     0     0     1     1     0     1     0
     0     0     0     0     1     1     0     1
     0     0     0     0     0     1     1     0
     0     0     0     0     0     0     1     1
     0     0     0     0     0     0     0     1
>> min(svd(A))
ans =
   4.7385e-02
>> inv(A)
ans =
     1    -1     1    -2     3    -5     8   -13
     0     1    -1     1    -2     3    -5     8
     0     0     1    -1     1    -2     3    -5
     0     0     0     1    -1     1    -2     3
     0     0     0     0     1    -1     1    -2
     0     0     0     0     0     1    -1     1
     0     0     0     0     0     0     1    -1
     0     0     0     0     0     0     0     1

Notice the appearance of Fibonacci numbers in the inverse.

The following groups of matrices can be added to Anymatrix. We hope that other groups will be made available by users in the future.

• https://github.com/higham/matrices-correlation-invalid: invalid correlation matrices. These are matrices that are intended to be correlation matrices but for various reasons relating to their construction have a negative eigenvalue and so are not positive semidefinite.
• https://github.com/higham/hpl-ai-matrix: a parametrized matrix designed by Fasi and Higham for use in the HPL-AI Mixed Precision Benchmark.
• https://github.com/Xiaobo-Liu/matrices-mp-cosm: a collection of MATLAB functions that generate the matrices used by Higham and Liu in testing multiprecision algorithms for computing the matrix cosine.
• https://github.com/mfasi/randsvdfast-matlab: a function randsvdfast by Fasi and Higham that provides similar functionality to anymatrix('gallery/randsvd') but uses a faster algorithm.

To incorporate the matrices in the first of these repositories as a group named corrinv we can use the 'groups' command ('g' for short) as follows.

>> anymatrix('g','corrinv','higham/matrices-correlation-invalid');
Cloning into '[...]/corrinv/private'...
[...]
Anymatrix remote group cloned.

Now we can access matrices in the corrinv group.

>> anymatrix('corrinv/tec03','h')
 tec03    Invalid correlation matrix from stress testing.
    tec03 is a 4-by-4 invalid correlation matrix from stress testing.

>> C = anymatrix('corrinv/tec03')
C =
   1.0000e+00  -5.5000e-01  -1.5000e-01  -1.0000e-01
  -5.5000e-01   1.0000e+00   9.0000e-01   9.0000e-01
  -1.5000e-01   9.0000e-01   1.0000e+00   9.0000e-01
  -1.0000e-01   9.0000e-01   9.0000e-01   1.0000e+00

>> eig(C)
ans =
  -2.7759e-02
   1.0000e-01
   1.0137e+00
   2.9140e+00

The MATLAB suite of solvers for ordinary differential equations previously contained 8 solvers, including 3 Runge-Kutta solvers: ode23, ode23tb, and ode45. The suite has been augmented with two new high-order Runge-Kutta solvers: ode78 uses 7th and 8th order Runge-Kutta formulas and ode89 uses 8th and 9th order Runge-Kutta formulas.

The documentation says that

• ode78 and ode89 may be more efficient than ode45 on non-stiff problems that are smooth except possibly for a few isolated discontinuities.
• ode89 may be more efficient than ode78 on very smooth problems, when integrating over long time intervals, or when tolerances are tight.
• ode78 and ode89 may not be as fast or as accurate as ode45 in single precision.

The MATLAB mpower function is called by an exponentiation A^z when A is a matrix and z is a real or complex scalar. For the meaning of such arbitrary matrix powers see What Is a Fractional Matrix Power?

Previously, mpower used a diagonalization of A. For a matrix that is not diagonalizable, or is close to being not diagonalizaable, the results could be inaccurate. In R2021b a Schur–Padé algorithm, which employs a Schur decomposition in conjunction with Padé approximation, is used that works for all matrices. The difference in accuracy between the old and new versions of mpower is clearly demonstrated by computing the square root of a 2-by-2 Jordan block (a difficult case because it is defective).

% R2021a
>> A = [1 1; 0 1], X = A^(0.5), residual = A - X^2
A =
     1     1
     0     1
X =
     1     0
     0     1
residual =
     0     1
     0     0

% R2021b
>> A = [1 1; 0 1], X = A^(0.5), residual = A - X^2
A =
     1     1
     0     1
X =
   1.0000e+00   5.0000e-01
            0   1.0000e+00
residual =
     0     0
     0     0

The new function pagesvd computes the singular value decomposition (SVD) of pages of nD arrays. A page is a 2D slice (i.e., a matrix) formed by taking all the elements in the first two dimensions and fixing the later subscripts. Related functions include pagemtimes for matrix multiplication abd pagetranspose for transposition, both introduced in R2020b. Better performance can be expected from these page functions than from explicit looping over the pages, especially for small-sized pages.

Several improvements have been introduced to the MATLAB Editor. Ones that caught my eye are the ability to edit rectangular areas of text, automatic completion of block endings and delimiters, wrapping of comments, and changing the case of selected text. I do all my editing in Emacs, using the MATLAB major mode, and these sorts of things are either available or can be added by customization. However, these are great additions for MATLAB Editor users.

In function calls that accept “name, value” pairs, separated by a comma, the values can now be specified with an equals sign. Example:

x = linspace(0,2*pi,100); y = tan(x);

% Existing syntax
plot(x,y,'Color','red','LineWidth',2)
plot(x,y,"Color","red","LineWidth",2)

% New syntax
plot(x,y,Color = "red",LineWidth = 2)
lw = 2; plot(x,y,Color = "red",LineWidth = lw) 

Note that the string can be given as a character vector in single quotes or as a string array in double quotes (string arrays were introduced in R2016b).

There are some limitations, including that all name=value arguments must appear after any comma separated pairs and after any positional arguments (arguments that must be passed to a function in a specific order).

For skew-symmetric and skew-Hermitian matrices, the eig function now guarantees that the matrix of eigenvectors is unitary (to machine precision) and that the computed eigenvalues are pure imaginary. The code

rng(2); n = 5; A = gallery('randsvd',n,-1e3,2); A = 1i*A; 
[V,D] = eig(A); 
unitary_test = norm(V'*V-eye(n),1)
norm_real_part = norm(real(D),1)

produces

% R2020b
unitary_test =
   9.6705e-01
norm_real_part =
   8.3267e-17

% R2021a
unitary_test =
   1.9498e-15
norm_real_part =
     0

For this matrix MATLAB R2020b produces an eigenvector matrix that is far from being unitary and eigenvalues with a nonzero (but tiny) real part, whereas MATLAB R2021a produces real eigenvalues and eigenvectors that are unitary to machine precision.

Among the reported performance improvements are faster matrix multiplication for large sparse matrices (based on the use of the GraphBLAS: see here and here) and faster solution of multiple right-hand systems with a sparse coefficient matrix, both resulting from added support for multithreading.

An interesting addition to the Symbolic Math Toolbox is the symmatrix class, which represents a symbolic matrix. An example of usage is

>> A = symmatrix('A',[2 2]); B = symmatrix('B',[2 2]); whos A B
  Name      Size            Bytes  Class        Attributes

  A         2x2                 8  symmatrix              
  B         2x2                 8  symmatrix              

>> X = A*B, Y = symmatrix2sym(X), whos X Y
X =
A*B
Y =
[A1_1*B1_1 + A1_2*B2_1, A1_1*B1_2 + A1_2*B2_2]
[A2_1*B1_1 + A2_2*B2_1, A2_1*B1_2 + A2_2*B2_2]
  Name      Size            Bytes  Class        Attributes

  X         2x2                 8  symmatrix              
  Y         2x2                 8  sym    

The range of functions that can be applied to a symmatrix is as follows:

>> methods symmatrix

Methods for class symmatrix:

adjoint         horzcat         mldivide        symmatrix       
cat             isempty         mpower          symmatrix2sym   
conj            isequal         mrdivide        tan             
cos             isequaln        mtimes          times           
ctranspose      kron            norm            trace           
det             latex           plus            transpose       
diff            ldivide         power           uminus          
disp            length          pretty          uplus           
display         log             rdivide         vertcat         
eq              matlabFunction  sin             
exp             minus           size            

Static methods:

empty         

In order to invert A*B in this example, or find its eigenvalues, use inv(Y) or eig(Y).

The exportgraphics function is very useful for saving to a file a tightly cropped version of a figure with the border white instead of gray. Simple usages are

exportgraphics(gca,'image.pdf')
exportgraphics(gca,'image.jpg','Resolution',200)

I have previously used the export_fig function, which is not built into MATLAB but is available from File Exchange; I think I will be using exportgraphics instead from now on.

The new svdsketch function computes the singular value decomposition (SVD) of a low rank approximation to a matrix ( and orthogonal, diagonal with nonnegative diagonal entries). It is mainly intended for use with matrices that are close to having low rank, as is the case in various applications.

This function uses a randomized algorithm that computes a sketch of the given -by- matrix , which is essentially a product , where is an orthonormal basis for the product , where is a random -by- matrix. The value of is chosen automatically to achieve , where is a tolerance that defaults to and must not be less than , where is the machine epsilon ( for double precision). The algorithm includes a power method iteration that refines the sketch before computing the SVD.

The output of the function is an SVD in which and are numerically orthogonal and the singular values in of size or larger are good approximations to singular values of , but smaller singular values in may not be good approximations to singular values of .

Here is an example. The code

n = 8; rng(1); 8; A = gallery('randsvd',n,1e8,3);
[U,S,V] = svdsketch(A,1e-3);
rel_res = norm(A-U*S*V')/norm(A)
singular_values = [svd(A) [diag(S); zeros(n-length(S),1)]]

produces the following output, with the exact singular values in the first column and the approximate ones in the second column:

rel_res =
   1.9308e-06
singular_values =
   1.0000e+00   1.0000e+00
   7.1969e-02   7.1969e-02
   5.1795e-03   5.1795e-03
   3.7276e-04   3.7276e-04
   2.6827e-05   2.6827e-05
   1.9307e-06            0
   1.3895e-07            0
   1.0000e-08            0

The approximate singular values are correct down to around , which is more than the requested. This is a difficult matrix for svdsketch because there is no clear gap in the singular values of .

The padding property of an axis puts some padding between the axis limits and the surrounding box. The code

x = linspace(0,2*pi,50); plot(x,tan(x),'linewidth',1.4)
title('Original axis')
axis padded, title('Padded axis')

produces the output

The default colormap changed from jet (the rainbow color map) to parula in R2014b (with a tweak in R2017a), because parula is more perceptually uniform and maintains information when printed in monochrome. The new turbo colormap is a more perceptually uniform version of jet, as these examples show. Notice that turbo has a longer transition through the greens and yellows. If you can’t give up on jet, use turbo instead.

Turbo:

Jet:

Parula:

The new pagemtimes function performs matrix multiplication on pages of -dimensional arrays, while pagetranspose and pagectranspose carry out the transpose and conjugate transpose, respectively, on pages of -dimensional arrays.

Both releases report significantly improved speed of certain functions, including some of the ODE solvers.

A call to chop has the form chop(X,options), where the structure options spceifies how to round the elements of the real array X to a lower precision arithmetic. X should be a single precision or double precision array and the output will have the same type. The structure options controls various aspects of the rounding, as we now explain.

1. The arithmetic format is specified by options.format, which is one of
   • ‘b’, ‘bfloat16’: bfloat16,
   • ‘h’, ‘half’, ‘fp16’: IEEE half precision (the default),
   • ‘s’, ‘single’, ‘fp32’: IEEE single precision,
   • ‘d’, ‘double’, ‘fp64’: IEEE double precision,
   • ‘c’, ‘custom’: custom format.

   In the last case the (base 2) format is defined by options.params, which is a 2-vector [t,emax], where t is the number of bits in the significand (including the hidden bit) and emax is the maximum value of the exponent.

2. options.subnormal specifies whether subnormal numbers are supported (if they are not, subnormals are flushed to zero):
   • 0 = do not support subnormals (the default for bfloat16),
   • 1 = support subnormals (the default for fp16, fp32, and fp64).
3. The form of rounding is specified by options.round:
   • 1: round to nearest using round to even last bit to break ties (the default);
   • 2: round towards plus infinity (round up);
   • 3: round towards minus infinity (round down);
   • 4: round towards zero;
   • 5: stochastic rounding—round to the next larger or next smaller floating-point number with probability proportional to 1 minus the distance to those floating-point numbers;
   • 6: stochastic rounding—round to the next larger or next smaller floating-point number with equal probability.

   For stochastic rounding, exact floating-point numbers are not changed.

4. If options.flip = 1 (default 0) then each element of the rounded result has, with probability options.p (default 0.5), a randomly chosen bit in its significand flipped. This option is useful for simulating soft errors.
5. If options.explim = 0 (default 1) then emax (the maximal exponent) for the specified arithmetic is ignored, so overflow, underflow, or subnormal numbers will be produced only if necessary for the data type of X. This option is useful for exploring low precisions independent of range limitations.

To avoid repeatedly passing the options argument, one can issue a call chop([],options) and the subsequent calls will use the previously given options parameters. The value of options can be inspected with [~,options] = chop.

In the rest of this post we give examples of the use of chop.

The code

x = 1/3;
opt_h.format = 'h'; xh = chop(x,opt_h); err_h = (x - xh)/x
opt_b.format = 'b'; xb = chop(x,opt_b); err_b = (x - xb)/x
x = 70000;
xh = chop(x,opt_h)
xb = chop(x,opt_b)

produces the output

err_h =
2.4414e-04
err_b =
-1.9531e-03
xh =
Inf
xb =
70144

which illustrates the higher precison but smaller range of fp16 compared with bfloat16.

The code

opt.format = 'h'; x = 0.1; rng(2)
for k = 1:6
opt.round = k;
y(k) = chop(x,opt);
end
errors = y - x
diff_y = diff(y)

rounds 0.1 to fp16 using six different rounding modes. The output is

errors =
-2.4414e-05   3.6621e-05  -2.4414e-05  -2.4414e-05  -2.4414e-05
3.6621e-05
diff_y =
6.1035e-05  -6.1035e-05            0            0   6.1035e-05

Rounding maps a number to the next larger or next smaller floating-point number, so there are only two possibilties for the error, and they have opposite signs. The diff_y values are consistent with the spacing of the fp16 floating-point numbers around 0.1, which is .

The overheads of chop can be minimized by choosing a suitable implementation of a computation. Matrix multiplication provides a good example. The multiplication C = A*B of -by- matrices involves floating-point operations, each of which needs to be chopped. The following code uses only calls to chop, because it processes an outer product in a single call, taking advantage of the fact that chop can take a matrix argument.

A = rand(m,n); B = rand(n,p);
C = zeros(m,p);
for i = 1:n
C = chop(C + chop(A(:,i)*B(i,:)));
end

The recently announced NVIDIA A100 GPU supports a new floating-point format called tf32 in its tensor cores. Tf32 is a 19-bit format that has 11 bits in the significand (including the hidden bit) and 8 bits in the exponent. So it has the precision of fp16 and the range of bfloat16, effectively combining the best features of these two formats. We can simulate tf32 using the custom format of chop. The code

opt.format = 'custom';
% tf32. Significand: 10 bits plus 1 hidden, exponent: 8 bits.
t = 11; emax = 127;
opt.params = [t,emax];
x = 1/3;
xt = chop(x,opt); err_t = (x - xt)/x
x = 70000;
xt = chop(x,opt)

produces the output

err_t =
2.4414e-04
xt =
70016

The error is the same as for fp16 but the number 70000 now rounds to a finite floating-point number.

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.

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.

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.

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.

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

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 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)