ROOT

ROOT low, high, segs, maxerr, BYREF result, BYREF errcode USE expr

Roots of f(x).

ROOT will find the first x-intercept of the given function ( where f(x) = 0 ) in the interval [low, high]

low: the lower limit
high: the upper limit
segs: the number of segments (spaces)
maxerr: tolerance (IF ABS(f(x)) < maxerr THEN OK)
errcode: 0 for success; otherwise calculation error
result: the result
expr: the given function

Example 1

def f1(x) = x - 2 
' Theory: x - 2 = 0 -> x = 2

ROOT 0, 5, 500, 0.001, result, errcode USE f1(x)

if(errcode) then
    print("No root found")
else
    print "Root at "; result
endif

' Output: Root at 1.99951171875

Example 2

def f2(x) = x^2 - 2
' Theory: x^2 - 2 = 0 -> x^2 = 2 -> x = +/-sqr(2) = +/-1.41

ROOT -1, 2, 500, 0.001, result, errcode USE f2(x)

if(errcode) then
    print("No root found")
else
    print "Root at "; result 
endif

' Output: Root at 1.4140625

002 numeric variables.bas 004 loops.bas bairstow.bas dogstar5.bas newtonraphson.bas scales132.bas

ABS ABSMAX ABSMIN ACOS ACOSH ACOT ACOTH ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATAN2 ATANH ATN CEIL COS COSH COT COTH CSC CSCH DEG DERIV DETERM DIFFEQN EXP EXPRSEQ FIX FLOOR FRAC INT INTERSECT INVERSE LINEQN LOG LOG10 M3APPLY M3IDENT M3ROTATE M3SCALE M3TRANS MAX MIN POLYAREA POLYCENT POLYEXT POW PTDISTLN PTDISTSEG PTSIGN RAD RND ROOT ROUND SEC SECH SEGCOS SEGLEN SEGSIN SEQ SGN SIN SINH SQR STATMEAN STATMEANDEV STATMEDIAN STATSPREADP STATSPREADS STATSTD SUM SUMSQ TAN TANH

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ROOT

Example 1

Example 2