double

Convert symbolic values to MATLAB double precision

Syntax

d = double(s)

Description

d = double(s) converts the symbolic values s to double precision. Converting symbolic values to double precision is useful when a MATLAB^® function does not accept symbolic values. For differences between symbolic and double-precision numbers, see Choose Numeric or Symbolic Arithmetic.

Examples

Convert Symbolic Number to Double Precision

Convert symbolic numbers to double precision by using double. Symbolic numbers are exact, while double-precision numbers have round-off errors.

Convert $\pi$ and $\frac{1}{3}$ from symbolic form to double precision.

symN = sym([pi 1/3])

symN = 
$$\left(\begin{array}{cc}\pi & \frac{1}{3}\end{array}\right)$$

doubleN = double(symN)

doubleN = 1×2

    3.1416    0.3333

For information on round-off errors, see Recognize and Avoid Round-Off Errors.

Convert Variable Precision to Double Precision

Variable-precision numbers created by vpa are symbolic values. When a MATLAB function does not accept symbolic values, convert variable precision to double precision by using double.

Convert $\pi$ and $\frac{1}{3}$ from variable-precision form to double precision.

vpaN = vpa([pi 1/3])

vpaN = $$\left(\begin{array}{cc}3.1415926535897932384626433832795& 0.33333333333333333333333333333333\end{array}\right)$$

doubleN = double(vpaN)

doubleN = 1×2

    3.1416    0.3333

Convert Symbolic Matrix to Double-Precision Matrix

Convert the symbolic numbers in matrix symM to double-precision numbers by using double.

a = sym(sqrt(2));
b = sym(2/3);
symM = [a b; a*b b/a]

symM = 
$$\left(\begin{array}{cc}\sqrt{2}& \frac{2}{3}\\ \frac{2\hspace{0.17em}\sqrt{2}}{3}& \frac{\sqrt{2}}{3}\end{array}\right)$$

doubleM = double(symM)

doubleM = 2×2

    1.4142    0.6667
    0.9428    0.4714

High-Precision Conversion

When converting symbolic expressions that suffer from internal cancellation or round-off errors, increase the working precision by using digits before converting the number.

Convert a numerically unstable expression Y with double. Then, increase precision to 100 digits by using digits and convert Y again. This high-precision conversion is accurate, while the low-precision conversion is not.

Y = ((exp(sym(200)) + 1)/(exp(sym(200)) - 1)) - 1;
lowPrecisionY = double(Y)

lowPrecisionY = 
0

digitsOld = digits(100);
highPrecisionY = double(Y) 

highPrecisionY = 
2.7678e-87

Restore the old precision used by digits for further calculations.

digits(digitsOld)

Convert Symbolic Results to Double Precision

Solve the trigonometric equation $\sin \left(2\mathit{x}\right)+\cos \left(\mathit{x}\right)=0$ by using solve. Set the ReturnConditions option to true to return the complete solution, parameters used in the solution, and conditions on those parameters.

syms x
eqn = sin(2*x) + cos(x) == 0;
[solx,params,conds] = solve(eqn,x,ReturnConditions=true)

solx = 
$$\left(\begin{array}{c}\frac{\pi }{2}+\pi \hspace{0.17em}k\\ 2\hspace{0.17em}\pi \hspace{0.17em}k-\frac{\pi }{6}\\ \frac{7\hspace{0.17em}\pi }{6}+2\hspace{0.17em}\pi \hspace{0.17em}k\end{array}\right)$$

params = $$k$$

conds = 
$$\left(\begin{array}{c}k\in \mathbb{Z}\\ k\in \mathbb{Z}\\ k\in \mathbb{Z}\end{array}\right)$$

The solver does not create the variable $\mathit{k}$ for the parameters in the MATLAB® workspace. Create this variable. Find the solutions for $\mathit{k}=2$ by using subs.

syms k
sols_k2 = subs(solx,k,2)

sols_k2 = 
$$\left(\begin{array}{c}\frac{5\hspace{0.17em}\pi }{2}\\ \frac{23\hspace{0.17em}\pi }{6}\\ \frac{31\hspace{0.17em}\pi }{6}\end{array}\right)$$

The solutions are exact symbolic numbers. Convert these numbers to double-precision numbers.

doublesols_k2 = double(sols_k2)

doublesols_k2 = 3×1

    7.8540
   12.0428
   16.2316

Convert Symbolic Matrix Variable of Numbers to Double Precision

Create a symbolic expression S that represents ${\mathit{A}}^2-2\mathit{A}+{\mathit{I}}_2$, where $\mathit{A}$ is a 2-by-2 symbolic matrix variable.

syms A 2 matrix
S = A*A - 2*A + eye(2)

S = $${\mathrm{I}}_2-2\hspace{0.17em}A+A^2$$

Substitute $\mathit{A}$ with symbolic numbers $\left[\begin{array}{cc}\cos \left(\frac{\pi }{5}\right)& \sin \left(\frac{\pi }{4}\right)\\ -1& 0\end{array}\right]$.

Aval = [cos(sym(pi)/5) sin(pi/4); -1 0];
symS = subs(S,A,Aval)

symS = 
$$\begin{array}{l}-2\hspace{0.17em}{\Sigma }_1+{{\Sigma }_1}^2+{\mathrm{I}}_2\\ \\ \mathrm{where}\\ \\ \mathrm{ }{\Sigma }_1=\left(\begin{array}{cc}\frac{\sqrt{5}}{4}+\frac{1}{4}& \frac{\sqrt{2}}{2}\\ -1& 0\end{array}\right)\end{array}$$

Convert the result to a double-precision matrix.

doubleS = double(symS)

doubleS = 2×2

   -0.6706   -0.8422
    1.1910    0.2929

Input Arguments

s — Symbolic input

symbolic number | array of symbolic numbers | symbolic matrix variable of numbers

Symbolic input, specified as a symbolic number, array of symbolic numbers, or symbolic matrix variable of numbers. If the input contains only numeric values (does not contain symbolic numbers), then the MATLAB double function is called.

Data Types: sym | symmatrix

Version History

Introduced before R2006a

R2022b: Convert symbolic matrix variables of numbers to double precision

You can convert a symbolic matrix variable of numbers of type symmatrix to a double-precision matrix of type double. For an example, see Convert Symbolic Matrix Variable of Numbers to Double Precision.