`vpa`

Variable-precision evaluation of numbers and symbolic expressions.

Category: Symbolic Computations in MATLAB > Conversion Between Symbolic and Numeric

Syntax

r = vpa(x)

Evaluates x with digits significant decimal digits (32 by default).

r = vpa(x, d)

Evaluates with d digits for this call only.

Description

vpa turns exact quantities like sqrt(sym(2)) or sym(1)/3 into decimal numbers with far more digits than a double offers, while symbols stay symbolic: vpa(sin(x) + sym(pi), 5) gives sin(x) + 3.1416. The global precision is set by digits.

The result is of class sym; convert it to a double with double when ordinary arithmetic is needed.

Input arguments

x: Number, symbolic expression or array.
d: Number of significant digits.

Output arguments

r: Symbolic result in which numeric parts are decimals with the requested precision.

Example

Different precisions

vpa(sqrt(sym(2)), 20)
vpa(sym(1)/3, 5)
vpa(sym(pi))
syms x
vpa(sin(x) + sym(pi), 5)

Output

ans = 1.4142135623730950488
ans = 0.33333
ans = 3.1415926535897932384626433832795
ans = sin(x) + 3.1416

Notes

In MatLivre an explicit d larger than the current digits setting is not honored; raise digits first. A double argument such as vpa(pi) or vpa(1/3) is treated as the exact constant or fraction, whereas MATLAB shows the digits of the stored double (for example 0.33333333333333331483); use vpa(sym(...)) for portable results.

vpa