mapSymType

Create a symbolic expression that contains symbolic numbers using sym.

expr = sym('2') + 1i*pi

expr = $$2+\pi \hspace{0.17em}\mathrm{i}$$

Construct a function handle that computes the square of a number.

sq = @(y) y^2;

Apply the function sq to the symbolic subobject of type 'integer' in the expression expr.

X = mapSymType(expr,'integer',sq)

X = $$4+\pi \hspace{0.17em}\mathrm{i}$$

You can also apply an existing MATLAB® function, such as exp. Apply the exp function to the symbolic subobject of type 'complex' in the expression expr.

X = mapSymType(expr,'complex',@exp)

X = $$\pi \hspace{0.17em}{\mathrm{e}}^{\mathrm{i}}+2$$

Apply a symbolic function to specific subobjects in a symbolic equation.

Create a symbolic equation.

syms x t
eq = 0.5*x + sin(x) == t/4

eq = 
$$\frac{x}{2}+\sin \left(x\right)=\frac{t}{4}$$

Construct a symbolic function that multiplies an input by 2.

syms f(u)
f(u) = 2*u;

Apply the symbolic function f to the symbolic subobjects of type 'variable' in the equation eq.

X = mapSymType(eq,'variable',f)

X = 
$$x+\sin \left(2\hspace{0.17em}x\right)=\frac{t}{2}$$

The symbolic variables x and t in the equation are multiplied by 2.

You can also apply the same symbolic function that is created using symfun.

X = mapSymType(eq,'variable',symfun(2*u,u))

X = 
$$x+\sin \left(2\hspace{0.17em}x\right)=\frac{t}{2}$$

Now create an unassigned symbolic function. Apply the unassigned function to the symbolic subobjects of type 'sin' in the equation eq.

syms g(u)
X = mapSymType(eq,'sin',g)

X = 
$$\frac{x}{2}+g\left(\sin \left(x\right)\right)=\frac{t}{4}$$

Convert the largest symbolic subexpression of specific type in an expression.

Create a symbolic expression.

syms f(x) y
expr = sin(x) + f(x) - 2*y

expr = $$f\left(x\right)-2\hspace{0.17em}y+\sin \left(x\right)$$

Apply the log function to the symbolic subobject of type 'expression' in the expression expr.

X = mapSymType(expr,'expression',@log)

X = $$\log \left(f\left(x\right)-2\hspace{0.17em}y+\sin \left(x\right)\right)$$

When there are several subexpressions of type 'expression', mapSymType applies the log function to the largest subexpression.

Convert unassigned symbolic functions with specific variable dependencies in an expression.

Create a symbolic expression.

syms f(x) g(t) h(x,t) 
expr = f(x) + 2*g(t) + h(x,t)*sin(x)

expr = $$2\hspace{0.17em}g\left(t\right)+f\left(x\right)+\sin \left(x\right)\hspace{0.17em}h\left(x,t\right)$$

Construct a function handle that converts an input to a symbolic variable with name 'z'.

func = @(obj) sym('z');

Apply the conversion function func to the unassigned symbolic functions in the expression expr.

Convert the functions that depend on the exact sequence of variables [x t] using 'symfunOf'.

X = mapSymType(expr,'symfunOf',[x t],func)

X = $$2\hspace{0.17em}g\left(t\right)+f\left(x\right)+z\hspace{0.17em}\sin \left(x\right)$$

Convert the functions that have a dependency on the variable t using 'symfunDependingOn'.

X = mapSymType(expr,'symfunDependingOn',x,func)

X = $$z+2\hspace{0.17em}g\left(t\right)+z\hspace{0.17em}\sin \left(x\right)$$

Remove variable dependency of unassigned symbolic functions in a symbolic array.

Create a symbolic array consisting of multiple equations.

syms f1(t) f2(t) g1(t) g2(t)
eq = [f1(t) + f2(t) == 0, f1(t) == 2*g1(t), g1(t) == diff(g2(t))]

eq = 
$$\left(\begin{array}{ccc}{f}_1\left(t\right)+f_2\left(t\right)=0& f_1\left(t\right)=2\hspace{0.17em}{g}_1\left(t\right)& g_1\left(t\right)=\frac{\partial }{\partial t}\mathrm{ }{g}_2\left(t\right)\end{array}\right)$$

Apply the symFunType function to replace an unassigned symbolic function with a variable of the same name.

Find all functions that have a dependency on the variable t using 'symfunOf' and convert them using symFunType.

X = mapSymType(eq,'symfunOf',t,@symFunType)

X = $$\left(\begin{array}{ccc}{f}_1+f_2=0& f_1=2\hspace{0.17em}{g}_1& g_1=0\end{array}\right)$$

Create a symbolic expression. Find its inverse Laplace transform.

syms s;
G = (s+10)/(s^2+2*s+4)/(s^2-4*s+1);
expr = ilaplace(G)

expr = 
$$\frac{19\hspace{0.17em}{\mathrm{e}}^{-t}\hspace{0.17em}\left(\cos \left(\sqrt{3}\hspace{0.17em}t\right)+\frac{\sqrt{3}\hspace{0.17em}\sin \left(\sqrt{3}\hspace{0.17em}t\right)}{19}\right)}{39}-\frac{19\hspace{0.17em}{\mathrm{e}}^{2\hspace{0.17em}t}\hspace{0.17em}\left(\cosh \left(\sqrt{3}\hspace{0.17em}t\right)-\frac{18\hspace{0.17em}\sqrt{3}\hspace{0.17em}\sinh \left(\sqrt{3}\hspace{0.17em}t\right)}{19}\right)}{39}$$

The result is in terms of the exp, sin, cos, sinh, and cosh functions.

Rewrite sinh and cosh in the result as exp. Use mapSymType to apply the rewrite function to subexpressions that contain sinh or cosh.

expr = mapSymType(expr,"sinh|cosh",@(subexpr) rewrite(subexpr,"exp"))

expr = 
$$\frac{19\hspace{0.17em}{\mathrm{e}}^{-t}\hspace{0.17em}\left(\cos \left(\sqrt{3}\hspace{0.17em}t\right)+\frac{\sqrt{3}\hspace{0.17em}\sin \left(\sqrt{3}\hspace{0.17em}t\right)}{19}\right)}{39}-\frac{19\hspace{0.17em}{\mathrm{e}}^{2\hspace{0.17em}t}\hspace{0.17em}\left(\frac{{\mathrm{e}}^{\sqrt{3}\hspace{0.17em}t}}{2}+\frac{{\mathrm{e}}^{-\sqrt{3}\hspace{0.17em}t}}{2}-\frac{18\hspace{0.17em}\sqrt{3}\hspace{0.17em}\left(\frac{{\mathrm{e}}^{\sqrt{3}\hspace{0.17em}t}}{2}-\frac{{\mathrm{e}}^{-\sqrt{3}\hspace{0.17em}t}}{2}\right)}{19}\right)}{39}$$