What’s New in MATLAB R2021a?

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).