Sample 10 Interpolation & Co


SYSTEM(BackGround=99, Run = 1) DLG(TI='interpolation, integration, and differentiation', Edit='#Describe', Button='OK')
#Describe . The Akima-algorithm is used for numerical . interpolation, integration, and differentiation Call: . result = IPOL(xi, xyMTX [, parm3]) with: . xi interpolation x-value, no parm3 . integration: parm3 = upper limit, xi = lower limit . dy/dx: parm3 = xi - 1 . d2y/dx2: parm3 = xi - 2 . xyMTX matrix: . column 1 = x values . column 2 = y values .
DO SET($max=10, yi=0, xA=0, xZ=100, dX=1, yA=-1, yZ=2) xymtx(10,2) = 0 ! define a 10 rows, 2 column xy-matrix xymtx($,1) = $^2 ! x is set to a number 1...100 xymtx($,2) = RAN(0, 100) ! y is set to random 0 +- 100 checks($) = ('Blue: Interpolate y(x)', 'Red: Integrate(0,x)', 'Cyan: dy/dx', 'Dash: d2y/dx2') DLG(L=0,W=1/4, Button='OK', CHeckbox=checks, Value=CHECKED) DLG(TI='Akima-interpolation, -integration, -differentation1*+2*', L=1/4, W=3/4, H=1, AX=2, TI='Blue=interpolate, Red=Integrate/100, Cyan=dy/dx, Magenta broken=d2y/dx2*10', Y=0, MIN=-100, MAX=100) LINE(Ax=2, COL=1, XV=xymtx, Col=2, YV=xymtx, S='🔴', D=-1) IF(INDEX(CHECKED, 'Interpolate')) DO xi = xA, xZ, dX yi = IPOL(xi, xymtx) ! interpolation for xi LINE(Ax=2, OneWayX=1, X=xi,Y=yi,W=3,D=9) ENDDO ENDIF IF(INDEX(CHECKED, 'Integrate')) DO xi = xA, xZ, dX yi = IPOL(xA, xymtx, xi) ! integral from start to xi yi = yi / 100 LINE(Ax=2, OneWayX=1, X=xi,Y=yi,W=3,D=900) ENDDO ENDIF IF(INDEX(CHECKED, 'dy/dx')) DO xi = xA, xZ, dX yi = IPOL(xi, xymtx, xi - 1) ! dy/dx at position xi yi = yi LINE(Ax=2, OneWayX=1, X=xi,Y=yi,W=3,D=99) ENDDO ENDIF IF(INDEX(CHECKED, 'd2y/dx2')) DO xi = xA, xZ yi = IPOL(xi, xymtx, xi - 2) ! d2y/dx2 at position xi yi = yi * 10 LINE(Ax=2, OneWayX=1, X=xi,Y=yi,W=3,Brok=1.2, D=909) ENDDO ENDIF ENDDO END