Code Generation for Complex Data
Restrictions When Defining Complex Variables
For code generation, you must set the complexity of variables at the time of
assignment. Assign a complex constant to the variable or use the
complex function. For
x = 5 + 6i; % x is a complex number by assignment. y = complex(5,6); % y is the complex number 5 + 6i.
After assignment, you cannot change the complexity of a variable. Code
generation for the following function fails because
x(k) = 3 +
4i changes the complexity of
function x = test1( ) x = zeros(3,3); % x is real for k = 1:numel(x) x(k) = 3 + 4i; end end
To resolve this issue, assign a complex constant to
function x = test1( ) x = zeros(3,3)+ 0i; %x is complex for k = 1:numel(x) x(k) = 3 + 4i; end end
Code Generation for Complex Data with Zero-Valued Imaginary Parts
For code generation, complex data that has all zero-valued imaginary parts remains complex. This data does not become real. This behavior has the following implications:
In some cases, results from functions that sort complex data by absolute value can differ from the MATLAB® results. See Functions That Sort Complex Values by Absolute Value.
For functions that require that complex inputs are sorted by absolute value, complex inputs with zero-valued imaginary parts must be sorted by absolute value. These functions include
Functions That Sort Complex Values by Absolute Value
Functions that sort complex values by absolute value include
max. These functions sort
complex numbers by absolute value even when the imaginary parts are zero. In
general, sorting the absolute values produces a different result than sorting
the real parts. Therefore, when inputs to these functions are complex with
zero-valued imaginary parts in generated code, but real in MATLAB, the generated code can produce different results than MATLAB. In the following examples, the input to
is real in MATLAB, but complex with zero-valued imaginary parts in the generated code:
Results of Expressions That Have Complex Operands
In general, expressions that contain one or more complex operands produce a complex result in generated code, even if the value of the result is zero. Consider the following line of code:
z = x + y;
Suppose that at run time,
x has the value
y has the value
3i. In MATLAB, this code produces the real result
z = 4.
During code generation, the types for
y are known, but their values are not known. Because
either or both operands in this expression are complex,
defined as a complex variable requiring storage for a real and an imaginary
z equals the complex result
4 + 0i
in generated code, not
4, as in MATLAB code.
Exceptions to this behavior are:
Functions that take complex arguments but produce real results return real values.
y = real(x); % y is the real part of the complex number x. y = imag(x); % y is the real-valued imaginary part of x. y = isreal(x); % y is false (0) for a complex number x.
Functions that take real arguments but produce complex results return complex values.
z = complex(x,y); % z is a complex number for a real x and y.
Results of Complex Multiplication with Nonfinite Values
When an operand of a complex multiplication contains a nonfinite value, the generated code might produce a different result than the result that MATLAB produces. The difference is due to the way that code generation defines complex multiplication. For code generation:
Multiplication of a complex value by a complex value (a + bi) (c + di) is defined as (ac - bd) + (ad + bc)i. The complete calculation is performed, even when a real or an imaginary part is zero.
Multiplication of a real value by a complex value c(a + bi) is defined as ca + cbi .