Convert Symbolic Number to Double Precision

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

Convertpiand1/3from symbolic form to double precision.

symN = sym([pi 1/3])

symN = [ pi, 1/3]

doubleN = double(symN)

doubleN = 3.1416 0.3333

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

Convert Variable Precision to Double Precision

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

Convertpiand1/3from variable-precision form to double precision.

vpaN = vpa([pi 1/3])

vpaN = [ 3.1415926535897932384626433832795, 0.33333333333333333333333333333333]

doubleN = double(vpaN)

doubleN = 3.1416 0.3333

Convert Symbolic Matrix to Double-Precision Matrix

Convert the symbolic numbers in matrixsymMto double-precision numbers by usingdouble.

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

symM = [ 2^(1/2), 2/3] [ (2*2^(1/2))/3, 2^(1/2)/3]

doubleM = double(symM)

doubleM = 1.4142 0.6667 0.9428 0.4714

High-Precision Conversion

When converting symbolic expressions that suffer from internal cancelation or round-off errors, increase the working precision by usingdigitsbefore converting the number.

Convert a numerically unstable expressionYwithdouble. Then, increase precision to100digits by usingdigitsand convertYagain. 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 bydigitsfor further calculations.

digits(digitsOld)