Access MATLAB Functions and Workspace Data in C Charts

Stateflow^® charts in Simulink^® models have an action language property that defines the syntax for state and transition actions. An icon in the lower-left corner of the chart canvas indicates the action language for the chart.

MATLAB^® as the action language.
C as the action language.

In charts that use C as the action language, you can call built-in MATLAB functions and access MATLAB workspace variables by using the ml namespace operator or the ml function.

Caution

Because MATLAB functions are not available in a target environment, do not use the ml namespace operator and the ml function if you plan to build a code generation target.

`ml` Namespace Operator

For C charts, the ml namespace operator uses standard dot (.) notation to reference MATLAB variables and functions. For example, the statement a = ml.x returns the value of the MATLAB workspace variable x to the Stateflow data a.

For functions, the syntax is as follows:

[return_val1,return_val2,...] = ml.function_name(arg1,arg2,...)

For example, the statement [a, b, c] = ml.function(x, y) passes the return values from the MATLAB function function to the Stateflow data a, b, and c.

If the MATLAB function you call does not require arguments, you must still include the parentheses. If you omit the parentheses, Stateflow software interprets the function name as a workspace variable, which, when not found, generates a run-time error during simulation.

Examples

In these examples, x, y, and z are workspace variables and d1 and d2 are Stateflow data:

a = ml.sin(ml.x)
In this example, the MATLAB function sin evaluates the sine of x, which is then assigned to Stateflow data variable a. However, because x is a workspace variable, you must use the namespace operator to access it. Hence, ml.x is used instead of just x.
a = ml.sin(d1)
In this example, the MATLAB function sin evaluates the sine of d1, which is assigned to Stateflow data variable a. Because d1 is Stateflow data, you can access it directly.
ml.x = d1*d2/ml.y
The result of the expression is assigned to x. If x does not exist prior to simulation, it is automatically created in the MATLAB workspace.
ml.v[5][6][7] = ml.f(ml.x[1][3],ml.y[3])
The workspace variables x and y are arrays. x[1][3] is the (1,3) element of the two-dimensional array variable x. y[3] is the third element of the one-dimensional array variable y
The value returned by the call to f is assigned to element (5,6,7) of the workspace array, v. If v does not exist prior to simulation, it is automatically created in the MATLAB workspace.

`ml` Function

For C charts, you can use the ml function to specify calls to MATLAB functions. The format for the ml function call uses this notation:

ml(evalString,arg1,arg2,...);

evalString is an expression that is evaluated in the MATLAB workspace. It contains a MATLAB command (or a set of commands, each separated by a semicolon) to execute along with format specifiers (%g, %f, %d, etc.) that provide formatted substitution of the other arguments (arg1, arg2, etc.) into evalString.

The format specifiers used in ml functions are the same as those used in the C functions printf and sprintf. The ml function call is equivalent to calling the MATLAB eval function with the ml namespace operator if the arguments arg1, arg2,... are restricted to scalars or literals in the following command:

ml.eval(ml.sprintf(evalString,arg1,arg2,...))

Format specifiers used in the ml function must either match the data types of the arguments or the arguments must be of types that can be promoted to the type represented by the format specifier.

Stateflow software assumes scalar return values from ml namespace operator and ml function calls when they are used as arguments in this context. For more information, see How Charts Infer the Return Size for ml Expressions.

Examples

In these examples, x is a MATLAB workspace variable, and d1 and d2 are Stateflow data:

a = ml("sin(x)")
In this example, the ml function calls the MATLAB function sin to evaluate the sine of x in the MATLAB workspace. The result is then assigned to Stateflow data object a. Because x is a workspace variable, and sin(x) is evaluated in the MATLAB workspace, you enter it directly as the string "sin(x)".
sfmat_44 = ml("rand(4)")
In this example, a square 4-by-4 matrix of random numbers between 0 and 1 is returned and assigned to the Stateflow data object sf_mat44. you must define this data object as a 4-by-4 array before simulation. Otherwise, a size mismatch error occurs during run-time.
a = ml("sin(%f)",d1)
In this example, the MATLAB function sin evaluates the sine of d1 in the MATLAB workspace and assigns the result to Stateflow data object a. Because d1 is Stateflow data, its value is inserted in the string argument "sin(%f)" using the format expression %f. If d1 = 1.5, the expression evaluated in the MATLAB workspace is sin(1.5).
a = ml("f(%g,x,%f)",d1,d2)
In this example, the expression is the evalString shown in the preceding format statement. Stateflow data d1 and d2 are inserted into the expression "f(%g,x,%f)" by using the format specifiers %g and %f, respectively.

`ml` Expressions

For C charts, you can mix ml namespace operator and ml function expressions along with Stateflow data in larger expressions. The following example squares the sine and cosine of an angle in workspace variable X and adds them:

a = ml.power(ml.sin(ml.X),2) + ml("power(cos(X),2)")

The first operand uses the ml namespace operator to call the sin function. Its argument is ml.X, since X is in the MATLAB workspace. The second operand uses the ml function. Because X is in the workspace, it appears in the evalString expression as X. The squaring of each operand is performed with the MATLAB power function, which takes two arguments: the value to square, and the power value, 2.

Expressions using the ml namespace operator and the ml function can be used as arguments for ml namespace operator and ml function expressions. The following example nests ml expressions at three different levels:

a = ml.power(ml.sin(ml.X + ml("cos(Y)")),2)

In composing your ml expressions, follow the levels of precedence set out in Binary Operations. Use parentheses around power expressions with the ^ operator when you use them in conjunction with other arithmetic operators.

Stateflow software checks expressions for data size mismatches in your actions when you update or simulate the model. Because the return values for ml expressions are not known until run time, Stateflow software must infer the size of their return values. For more information, see How Charts Infer the Return Size for ml Expressions.

Which `ml` Should I Use?

In most cases, the notation of the ml namespace operator is more straightforward. However, using the ml function call does offer a few advantages:

Use the ml function to dynamically construct workspace variables.
The following flow chart creates four new MATLAB matrices:
The for loop creates four new matrix variables in the MATLAB workspace. The default transition initializes the Stateflow counter i to 0, while the transition segment between the top two junctions increments it by 1. If i is less than 5, the transition segment back to the top junction evaluates the ml function call ml("A%d = rand(%d)",i,i) for the current value of i. When i is greater than or equal to 5, the transition segment between the bottom two junctions occurs and execution stops.
The transition executes the following MATLAB commands, which create a workspace scalar (A1) and three matrices (A2, A3, A4):
```
A1 = rand(1)
A2 = rand(2)
A3 = rand(3)
A4 = rand(4)
```
Use the ml function with full MATLAB notation.
You cannot use full MATLAB notation with the ml namespace operator, as the following example shows:
```
ml.A = ml.magic(4);
B = ml("A + A'");
```
This example sets the workspace variable A to a magic 4-by-4 matrix using the ml namespace operator. Stateflow data B is then set to the addition of A and its transpose matrix, A', which produces a symmetric matrix. Because the ml namespace operator cannot evaluate the expression A', the ml function is used instead. However, you can call the MATLAB function transpose with the ml namespace operator in the following equivalent expression:
```
ml.A = ml.magic(4);
B = ml.A + ml.transpose(ml.A)
```
As another example, you cannot use arguments with cell arrays or subscript expressions involving colons with the ml namespace operator. However, these can be included in an ml function call.

`ml` Data Type

Stateflow data of type ml is typed internally with the MATLAB type mxArray for C charts. You can assign (store) any type of data available in the Stateflow hierarchy to a data of type ml. These types include any data type defined in the Stateflow hierarchy or returned from the MATLAB workspace with the ml namespace operator or ml function.

Rules for Using `ml` Data Type

These rules apply to Stateflow data of type ml:

You can initialize ml data from the MATLAB workspace just like other data in the Stateflow hierarchy (see Initialize Data from the MATLAB Base Workspace).
Any numerical scalar or array of ml data in the Stateflow hierarchy can participate in any kind of unary operation and any kind of binary operation with any other data in the hierarchy.
If ml data participates in any numerical operation with other data, the size of the ml data must be inferred from the context in which it is used, just as return data from the ml namespace operator and ml function are. For more information, see How Charts Infer the Return Size for ml Expressions.
You cannot define ml data with the scope Constant.
This option is disabled in the Data properties dialog box and in the Model Explorer for Stateflow data of type ml.
You can use ml data to build a simulation target but not to build an embeddable code generation target.
If data of type ml contains an array, you can access the elements of the array via indexing with these rules:
1. You can index only arrays with numerical elements.
2. You can index numerical arrays only by their dimension.
  In other words, you can access only one-dimensional arrays by a single index value. You cannot access a multidimensional array with a single index value.
3. The first index value for each dimension of an array is 1, and not 0, as in C language arrays.
In the examples that follow, mldata is a Stateflow data of type ml, ws_num_array is a 2-by-2 MATLAB workspace array with numerical values, and ws_str_array is a 2-by-2 MATLAB workspace array with character vector values.
```
mldata = ml.ws_num_array; /* OK */
n21 = mldata[2][1]; /* OK for numerical data of type ml */
n21 = mldata[3]; /* NOT OK for 2-by-2 array data */
mldata = ml.ws_str_array; /* OK */
s21 = mldata[2][1]; /* NOT OK for character vector data of type ml*/
```
ml data cannot have a scope outside a C chart; that is, you cannot define the scope of ml data as Input from Simulink or Output to Simulink.

Place Holder for Workspace Data

Both the ml namespace operator and the ml function can access data directly in the MATLAB workspace and return it to a C chart. However, maintaining data in the MATLAB workspace can present Stateflow users with conflicts with other data already resident in the workspace. Consequently, with the ml data type, you can maintain ml data in a chart and use it for MATLAB computations in C charts.

As an example, in the following statements, mldata1 and mldata2 are Stateflow data of type ml:

mldata1 = ml.rand(3);
mldata2 = ml.transpose(mldata1);

In the first line of this example, mldata1 receives the return value of the MATLAB function rand, which, in this case, returns a 3-by-3 array of random numbers. Note that mldata1 is not specified as an array or sized in any way. It can receive any MATLAB workspace data or the return of any MATLAB function because it is defined as a Stateflow data of type ml.

In the second line of the example, mldata2, also of Stateflow data type ml, receives the transpose matrix of the matrix in mldata1. It is assigned the return value of the MATLAB function transpose in which mldata1 is the argument.

Note the differences in notation if the preceding example were to use MATLAB workspace data (wsdata1 and wsdata2) instead of Stateflow ml data to hold the generated matrices:

ml.wsdata1 = ml.rand(3);
ml.wsdata2 = ml.transpose(ml.wsdata1);

In this case, each workspace data must be accessed through the ml namespace operator.

How Charts Infer the Return Size for `ml` Expressions

In C charts, Stateflow expressions using the ml namespace operator and the ml function evaluate in the MATLAB workspace at run time. The actual size of the data returned from the following expression types is known only at run time:

MATLAB workspace data or functions using the ml namespace operator or the ml function call
For example, the size of the return values from the expressions ml.var, ml.func(), or ml(evalString, arg1, arg2,...), where var is a MATLAB workspace variable and func is a MATLAB function, cannot be known until run-time.
Stateflow data of type ml
Graphical functions that return Stateflow data of type ml

When these expressions appear in actions, Stateflow code generation creates temporary data to hold intermediate returns for evaluation of the full expression of which they are a part. Because the size of these return values is unknown until run time, Stateflow software must employ context rules to infer the sizes for creation of the temporary data.

During run time, if the actual returned value from one of these commands differs from the inferred size of the temporary variable that stores it, a size mismatch error appears. To prevent run-time errors, use the following guidelines to write actions with MATLAB commands or ml data:

Guideline		Example
Return sizes of MATLAB commands or data in an expression must match return sizes of peer expressions.		In the expression `ml.func() * (x + ml.y)`, if `x` is a 3-by-2 matrix, then `ml.func()` and `ml.y` are also assumed to evaluate to 3-by-2 matrices. If either returns a value of different size (other than a scalar), an error results during run-time.
Expressions that return a scalar never produce an error. You can combine matrices and scalars in larger expressions because MATLAB commands use scalar expansion.		In the expression `ml.x + y`, if `y` is a 3-by-2 matrix and `ml.x` returns a scalar, the resulting value is the result of adding the scalar value of `ml.x` to every member of `y` to produce a matrix with the size of `y`, that is, a 3-by-2 matrix. The same rule applies to subtraction (`-`), multiplication (`*`), division (`/`), and any other binary operations.
MATLAB commands or Stateflow data of type `ml` can be members of these independent levels of expression, for which resolution of return size is necessary:	Arguments The expression for each function argument is a larger expression for which the return size of MATLAB commands or Stateflow data of type `ml` must be determined.	In the expression `z + func(x + ml.y)`, the size of `ml.y` is independent of the size of `z`, because `ml.y` is used at the function argument level. However, the return size for `func(x + ml.y)` must match the size of `z`, because they are both at the same expression level.
	Array indices The expression for an array index is an independent level of expression that must be scalar in size.	In the expression `x + array[y]`, the size of `y` is independent of the size of `x` because `y` and `x` are at different levels of expression. Also, `y` must be a scalar.
The return size for an indexed array element access must be a scalar.		The expression `x[1][1]`, where `x` is a 3-by-2 array, must evaluate to a scalar.
MATLAB command or data elements used in an expression for the input argument of a MATLAB function called through the `ml` namespace operator are resolved for size. This resolution uses the rule for peer expressions (preceding rule 1) for the expression itself, because no size definition prototype is available.		In the function call `ml.func(x + ml.y)`, if `x` is a 3-by-2 array, `ml.y` must return a 3-by-2 array or a scalar.
MATLAB command or data elements used for the input argument for a graphical function in an expression are resolved for size by the function prototype.		If the graphical function `gfunc` has the prototype `gfunc(arg1)`, where `arg1` is a 2-by-3 Stateflow data array, the calling expression, `gfunc(ml.y + x)`, requires that both `ml.y` and `x` evaluate to 2-by-3 arrays (or scalars) during run-time.
`ml` function calls can take only scalar or character vector literal arguments. Any MATLAB command or data that specifies an argument for the `ml` function must return a scalar value.		In the expression `a = ml("sin(x)")`, the `ml` function calls the MATLAB function `sin` to evaluate the sine of `x` in the MATLAB workspace. Stateflow data variable `a` stores that result.
In an assignment, the size of the right-hand expression must match the size of the left-hand expression, with one exception. If the left-hand expression is a single MATLAB variable, such as `ml.x`, or Stateflow data of type `ml`, the right-hand expression determines the sizes of both expressions.		In the expression `s = ml.func(x)`, where `x` is a 3-by-2 matrix and `s` is scalar Stateflow data, `ml.func(x)` must return a scalar to match the left-hand expression, `s`. However, in the expression `ml.y = x + s`, where `x` is a 3-by-2 data array and `s` is scalar, the left-hand expression, workspace variable `y`, is assigned the size of a 3-by-2 array to match the size of the right-hand expression, `x+s`, a 3-by-2 array.
In an assignment, Stateflow column vectors on the left-hand side are compatible with MATLAB row or column vectors of the same size on the right-hand side. A matrix you define with a row dimension of 1 is considered a row vector. A matrix you define with one dimension or with a column dimension of 1 is considered a column vector.		In the expression `s = ml.func()`, where `ml.func()` returns a 1-by-3 matrix, if `s` is a vector of size `3`, the assignment is valid.
If you cannot resolve the return size of MATLAB command or data elements in a larger expression by any of the preceding rules, they are assumed to return scalar values.		In the expression `ml.x = ml.y + ml.z`, none of the preceding rules can be used to infer a common size among `ml.x`, `ml.y`, and `ml.z`. In this case, both `ml.y` and `ml.z` are assumed to return scalar values. Even if `ml.y` and `ml.z` return matching sizes at run-time, if they return nonscalar values, a size mismatch error results.
The preceding rules for resolving the size of member MATLAB commands or Stateflow data of type `ml` in a larger expression apply only to cases in which numeric values are expected for that member. For nonnumeric returns, a run-time error results. Note Member MATLAB commands or data of type `ml` in a larger expression are limited to numeric values (scalar or array) only if they participate in numeric expressions.		The expression `x + ml.str`, where `ml.str` is a character vector workspace variable, produces a run-time error stating that `ml.str` is not a numeric type.

Special cases exist, in which no size checking occurs to resolve the size of MATLAB command or data expressions that are part of larger expressions. Use of the following expressions does not require enforcement of size checking at run-time:

ml.var
ml.func()
ml(evalString, arg1, arg2,...)
Stateflow data of type ml
Graphical function returning a Stateflow data of type ml

In these cases, assignment of a return to the left-hand side of an assignment statement or a function argument occurs without checking for a size mismatch between the two:

An assignment in which the left-hand side is a MATLAB workspace variable
For example, in the expression ml.x = ml.y, ml.y is a MATLAB workspace variable of any size and type (structure, cell array, character vector, and so on).
An assignment in which the left-hand side is a data of type ml
For example, in the expression m_x = ml.func(), m_x is a Stateflow data of type ml.
Input arguments of a MATLAB function
For example, in the expression ml.func(m_x, ml.x, gfunc()), m_x is a Stateflow data of type ml, ml.x is a MATLAB workspace variable of any size and type, and gfunc() is a Stateflow graphical function that returns a Stateflow data of type ml. Although size checking does not occur for the input type, if the passed-in data is not of the expected type, an error results from the function call ml.func().
Arguments for a graphical function that are specified as Stateflow data of type ml in its prototype statement
Note
If you replace the inputs in the preceding cases with non-MATLAB numeric Stateflow data, conversion to an ml type occurs.