separateUnits

Separate units from expression

Syntax

[Data,Units] = separateUnits(expr)

Data = separateUnits(expr)

Description

[Data,Units] = separateUnits(expr) returns the symbolic units of the symbolic expression expr in Units and the rest of expr in Data.

Data = separateUnits(expr) removes symbolic units from expr and then returns the rest.

Examples

Separate Units and Expression

Separate the units from the expression 10*t*u.m/u.s, where u = symunit, by providing two output arguments for separateUnits.

u = symunit;
syms t
speed = 10*t*u.m/u.s;
[Data,Units] = separateUnits(speed)

Data = $$10\hspace{0.17em}t$$

Units = 
$$\frac{\mathrm{m}\mathrm{"meter\; -\; a\; physical\; unit\; of\; length."}}{\mathrm{s}\mathrm{"second\; -\; a\; physical\; unit\; of\; time."}}$$

Return only the expression with the units removed by providing one output argument.

Data = separateUnits(speed)

Data = $$10\hspace{0.17em}t$$

Separate Compatible Units

If the input has compatible units that can be converted to the same unit, then separateUnits performs the conversion and returns the separated result. Units are compatible when they have the same dimensions (although the conversion factor may not necessarily be 1).

Separate the units from 2*u.m + 30*u.cm + 12*u.in. Even though the units differ, separateUnits converts them to the same unit and returns the separated result.

u = symunit;
[Data,Units] = separateUnits(2*u.m + 30*u.cm + 12*u.in)

Data = 
$$\frac{1628}{625}$$

Units = $$\mathrm{m}\mathrm{"meter\; -\; a\; physical\; unit\; of\; length."}$$

Input Arguments

expr — Input

number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic equation | symbolic multidimensional array | symbolic function | symbolic expression

Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, equation, multidimensional array, function, or expression.

When adding or subtracting quantities with different units in expr, the units must be compatible. Units are compatible when they have the same dimensions. For example, see Separate Compatible Units.

Output Arguments

Data — Expression after removing units

number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic equation | symbolic multidimensional array | symbolic function | symbolic expression

Expression after removing units, returned as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, equation, multidimensional array, function, or expression.

Units — Units from input

symbolic units

Units from input, returned as symbolic units.

Tips

• If an expression has incompatible units, then separateUnits errors. Units are incompatible when they do not have the same dimensions, such as length and time.

  For example, this code will error.

  u = symunit;
  [Data,Units] = separateUnits(2*u.m + 3*u.s)

  Instead, to return the units in the input, use findUnits.

  Units = findUnits(2*u.m + 3*u.s)

  Units = 
  [[m], [s]]

Version History

Introduced in R2017a

R2022b: separateUnits returns simplified expression after separating units

Starting in R2022b, separateUnits returns a simplified expression after separating units. For example, separate the units from an expression expr, and return the remaining expression as Data and the units as Units.

u = symunit;
syms t tau;
t_s = t*u.s;
t_0 = 0.01*u.s;
tau_s = tau*u.s;
a = 2*u.V;
b = 6*u.V;
expr = a + b*exp(-(t_s-t_0)/tau_s)
[Data,Units] = separateUnits(expr)

expr = 
2*[V] + 6*exp((((1/100)*[s] + (-t)*[s])/tau)*(1/[s]))*[V] 
 
Data = 
6*exp(-(100*t - 1)/(100*tau)) + 2

Units = 
[V]

In previous releases, separateUnits returns an unsimplified expression: Data = 6*exp((((1/100)*[s] - t*[s])/tau)*(1/[s])) + 2.