'**************************************************** '* Parabolic Least Squares Demonstration Program * '* ------------------------------------------------ * '* Reference: BASIC Scientific Subroutines, Vol. II * '* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 * '* [BIBLI 01]. * '* ------------------------------------------------ * '* SAMPLE RUN: * '* * '* This program calculates a parabolic * '* least squares fit to a given data set. * '* * '* INSTRUCTIONS * '* ------------ * '* * '* The number of data coordinates provided must be * '* greater than three. Otherwise, a divide by zero * '* error may result. * '* * '* Number of data points : 4 * '* * '* There are two input options: * '* 1. input coordinate pairs * '* 2. first input the independant variable values, * '* then input dependant ones. * '* Your choice (1 or 2): 1 * '* * '* ? 1 1 * '* ? 2 2 * '* ? 3 3 * '* ? 5 5.01 * '* * '* Fitted equation is: * '* Y = -4.573E-003 + 1.002571 X * '* * '* Standard deviation of fit: 2.9E-003 * '* * '**************************************************** DEFINT I-N DEFDBL A-H, O-Z 10 CLS PRINT PRINT "LEAST SQUARES CURVE FIT ROUTINE" PRINT PRINT "This program calculates a parabolic" PRINT "least squares fit to a given data set" PRINT PRINT "INSTRUCTIONS" PRINT "------------" PRINT PRINT " The number of data coordinates provided" PRINT " must be greater than three. Otherwise, a" PRINT " divide by zero error may result." PRINT INPUT " Number of data points : ", n IF n < 4 THEN GOTO 10 DIM x(n + 1), y(n + 1) 20 CLS : PRINT PRINT " There are two input options:" PRINT " 1. input coordinate pairs" PRINT " 2. first input the independant variable values, then input dependant ones." INPUT " Your choice (1 or 2) : ", iz PRINT IF iz < 1 THEN GOTO 20 IF iz > 2 THEN GOTO 20 IF iz = 1 THEN GOTO 30 FOR m = 0 TO n - 1 PRINT m + 1; : INPUT x(m) NEXT m PRINT FOR m = 0 TO n - 1 PRINT m + 1; : INPUT y(m) NEXT m GOTO 50 30 FOR m = 0 TO n - 1 PRINT m + 1; : INPUT x(m), y(m) NEXT m REM Call linear least squares subroutine 50 GOSUB 1000 PRINT PRINT " Fitted equation is:" PRINT " Y = "; INT(1000000 * a) / 1000000; " "; IF b > 0 THEN PRINT "+"; PRINT INT(1000000 * b) / 1000000; "X"; IF c > 0 THEN PRINT " +"; PRINT INT(1000000 * c) / 1000000; "X^2"; PRINT:PRINT PRINT " Standard deviation of fit: "; INT(10000 * d) / 10000 END '************************************************ '* Parabolic least squares subroutine * '* -------------------------------------------- * '* The input data set is X(m), Y(m). The number * '* of data points is n (n>3). The returned para-* '* meters are a,b,c, coefficients of equation * '* Y = a + b X + c X^2, d, standard deviation * '* of fit. * '************************************************ 1000 a0 = 1: a1 = 0: a2 = 0: a3 = 0: a4 = 0 b0 = 0: b1 = 0: b2 = 0 FOR m = 0 TO n - 1 a1 = a1 + x(m) a2 = a2 + x(m) * x(m) a3 = a3 + x(m) * x(m) * x(m) a4 = a4 + x(m) * x(m) * x(m) * x(m) b0 = b0 + y(m) b1 = b1 + y(m) * x(m) b2 = b2 + y(m) * x(m) * x(m) NEXT m a1 = a1 / n: a2 = a2 / n: a3 = a3 / n: a4 = a4 / n b0 = b0 / n: b1 = b1 / n: b2 = b2 / n d = a0 * (a2 * a4 - a3 * a3) - a1 * (a1 * a4 - a2 * a3) + a2 * (a1 * a3 - a2 * a2) a = b0 * (a2 * a4 - a3 * a3) + b1 * (a2 * a3 - a1 * a4) + b2 * (a1 * a3 - a2 * a2) a = a / d b = b0 * (a2 * a3 - a1 * a4) + b1 * (a0 * a4 - a2 * a2) + b2 * (a1 * a2 - a0 * a3) b = b / d c = b0 * (a1 * a3 - a2 * a2) + b1 * (a2 * a1 - a0 * a3) + b2 * (a0 * a2 - a1 * a1) c = c / d 'Evaluation of standard deviation d d = 0 FOR m = 0 TO n - 1 d1 = y(m) - a - b * x(m) - c * x(m) * x(m) d = d + d1 * d1 NEXT m d = SQR(d / (n - 3)) RETURN 'End lstsqr2.bas 