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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 example:

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 x.

function x = test1( )
x = zeros(3,3); % x is real
for k = 1:numel(x)
    x(k) = 3 + 4i;

To resolve this issue, assign a complex constant to x.

function x = test1( )
x = zeros(3,3)+ 0i; %x is complex
for k = 1:numel(x)
    x(k) = 3 + 4i;

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 ismember, union, intersect, setdiff, and setxor.

Functions That Sort Complex Values by Absolute Value

Functions that sort complex values by absolute value include sort, issorted, sortrows, median, min, and 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 sort is real in MATLAB, but complex with zero-valued imaginary parts in the generated code:

  •  You Pass Real Inputs to a Function Generated for Complex Inputs

  •  Input to sort Is Output from a Function That Returns Complex in 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 2 + 3i and y has the value 2 - 3i. In MATLAB, this code produces the real result z = 4. During code generation, the types for x and y are known, but their values are not known. Because either or both operands in this expression are complex, z is defined as a complex variable requiring storage for a real and an imaginary part. 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.
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