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#COMPILE EXE "Cubic Spline.exe"
#DIM ALL
$S_MSGBOX_HDR = "Cubic Spline"
%T = -1
%F = 00
' Supports tridiagonal matrix solution
TYPE UDT_LDU
' Lower, diagonal and upper vectors
L AS DOUBLE
D AS DOUBLE
U AS DOUBLE
' Solution vector x<k> and x<k+1>
xk AS DOUBLE
xkp1 AS DOUBLE
' Right hand side source vector
b AS DOUBLE
END TYPE
' Supports tridiagonal matrix solver parameters
TYPE UDT_LDU_PARM
N_ITR_MAX AS LONG
e_ITR_MIN AS DOUBLE
END TYPE
' Supports cubic spline interpolation
TYPE UDT_CSP
' Spline coefficients
h AS DOUBLE
b AS DOUBLE
v AS DOUBLE
' Source vector
u AS DOUBLE
' Solution state
z AS DOUBLE
END TYPE
' Supports cubic spline input parameters
TYPE UDT_CSP_PARM
' References the input data
N_DATA AS LONG
pt_DATA AS DOUBLE POINTER
py_DATA AS DOUBLE POINTER
' References the interpolated data which forms the spline
N_INTP AS LONG
pt_INTP AS DOUBLE POINTER
py_INTP AS DOUBLE POINTER
' Supports tridiagonal coefficient solution
N_LDU AS LONG
pU_LDU AS UDT_LDU POINTER
U_LDU_PARM AS UDT_LDU_PARM
END TYPE
FUNCTION PBMAIN () AS LONG
' Call the test function
' Note this sets the interpolated data to the clipboard
CSP_TEST
END FUNCTION
FUNCTION GS_LDU_xkp1 ( _
N_LDU AS LONG , _
BYVAL pU_LDU AS UDT_LDU POINTER ) AS LONG
' Routine computes a Gauss Seidel single step iteration
DIM i AS LONG
DIM Lxk AS DOUBLE
DIM Uxk AS DOUBLE
IF N_LDU = 00 OR _
pU_LDU = 00 THEN
FUNCTION = %F
ELSE
FOR i = 00 TO N_LDU - 01
' Form the matrix (L+U)[x.k] noting boundaries for lower and upper
Lxk = IIF(i = 00 , %F, @pU_LDU[i].L * @pU_LDU[i - 01].xkp1) ' Uses most advance computed [x], Gauss Seidel method
Uxk = IIF(i = N_LDU - 01, %F, @pU_LDU[i].U * @pU_LDU[i + 01].xk)
' Solve [x.kp1]
IF NOT @pU_LDU[i].D = 0.0# THEN
@pU_LDU[i].xkp1 = 1.0# / @pU_LDU[i].D * (@pU_LDU[i].b - (Lxk + Uxk))
END IF
NEXT i
FUNCTION = %T
END IF
END FUNCTION
FUNCTION GS_LDU_BFR ( _
N_LDU AS LONG , _
BYVAL pU_LDU AS UDT_LDU POINTER ) AS LONG
' Routine computes a Gauss Seidel solution vector buffering step
DIM i AS LONG
IF N_LDU = 00 OR _
pU_LDU = 00 THEN
FUNCTION = %F
ELSE
FOR i = 00 TO N_LDU - 01
@pU_LDU[i].xk = @pU_LDU[i].xkp1
NEXT i
FUNCTION = %T
END IF
END FUNCTION
FUNCTION GS_LDU_e_ITR ( _
N_LDU AS LONG , _
BYVAL pU_LDU AS UDT_LDU POINTER ) AS DOUBLE
' Routine computes a Gauss Seidel solution vector error norm
DIM i AS LONG
DIM e_ITR AS DOUBLE
IF N_LDU = 00 OR _
pU_LDU = 00 THEN
FUNCTION = %F
ELSE
FOR i = 00 TO N_LDU - 01
e_ITR += ABS(@pU_LDU[i].xkp1 - @pU_LDU[i].xk)
NEXT i
FUNCTION = e_ITR
END IF
END FUNCTION
FUNCTION GS_LDU_SOLVE ( _
N_LDU AS LONG , _
BYVAL pU_LDU AS UDT_LDU POINTER , _
BYVAL pU_LDU_PARM AS UDT_LDU_PARM POINTER ) AS LONG
' Routine computes a Gauss Seidel solution to the GS LDU parameters
DIM k_ITR AS LONG
DIM e_ITR AS DOUBLE
IF N_LDU = 00 OR _
pU_LDU = 00 OR _
pU_LDU_PARM = 00 THEN
FUNCTION = %F
ELSE
DO
INCR k_ITR
GS_LDU_xkp1 N_LDU, pU_LDU ' Comute single step
GS_LDU_e_ITR N_LDU, pU_LDU TO e_ITR ' Compute error norm
GS_LDU_BFR N_LDU, pU_LDU ' Back buffer [x.k] = [x.kp1]
#IF %F
MSGBOX "k_ITR, e_ITR " + STR$(k_itr) + " " + STR$(e_itr) + $CRLF + GS_LDU_GET_S(N_LDU, pU_LDU), %MB_ICONINFORMATION OR %MB_TASKMODAL OR %MB_TOPMOST, $S_MSGBOX_HDR
#ENDIF
LOOP WHILE (k_ITR < @pU_LDU_PARM.N_ITR_MAX) AND (e_ITR > @pU_LDU_PARM.e_ITR_MIN)
FUNCTION = %T
END IF
END FUNCTION
FUNCTION GS_LDU_GET_S ( _
N_LDU AS LONG , _
BYVAL pU_LDU AS UDT_LDU POINTER ) AS STRING
DIM i AS LONG
DIM S_LDU AS STRING
IF N_LDU = 00 OR _
pU_LDU = 00 THEN
FUNCTION = ""
ELSE
FOR i = 00 TO N_LDU - 01
S_LDU += TRIM$("x.kp1[" + STR$(i+1) + "]") + " " + STR$(@pU_LDU[i].xkp1) + $CRLF
NEXT i
FUNCTION = S_LDU
END IF
END FUNCTION
FUNCTION GS_LDU_TEST ( ) AS LONG
' Routine computes an Gauss Seidel test function
DIM N_LDU AS LONG
DIM U_LDU() AS UDT_LDU
DIM U_LDU_PARM AS UDT_LDU_PARM
N_LDU = 3
REDIM U_LDU(00 TO N_LDU - 01)
U_LDU(00).L = %F
U_LDU(01).L = 1.0#
U_LDU(02).L = 1.0#
U_LDU(00).D = 8.0#
U_LDU(01).D = -7.0#
U_LDU(02).D = 9.0#
U_LDU(00).U = 1.0#
U_LDU(01).U = 2.0#
U_LDU(02).U = %F
U_LDU(00).b = 8.0#
U_LDU(01).b = -4.0#
U_LDU(02).b = 12.0#
U_LDU(00).xk = 0.0#
U_LDU(01).xk = 0.0#
U_LDU(02).xk = 0.0#
U_LDU_PARM.N_ITR_MAX = 10
U_LDU_PARM.e_ITR_MIN = 1.0E-6#
'GS_LDU_xkp1 N_LDU, VARPTR(U_LDU(00))
GS_LDU_SOLVE N_LDU, VARPTR(U_LDU(00)), VARPTR(U_LDU_PARM)
MSGBOX GS_LDU_GET_S(N_LDU, VARPTR(U_LDU(00))), %MB_ICONINFORMATION OR %MB_TASKMODAL OR %MB_TOPMOST, $S_MSGBOX_HDR
END FUNCTION
FUNCTION CSP_FIND_INDEX( _
N_CSP AS LONG , _
BYVAL pU_CSP AS UDT_CSP POINTER , _
BYVAL pU_CSP_PARM AS UDT_CSP_PARM POINTER , _
t_INTP AS DOUBLE ) AS LONG
' Routine finds the ith index that an interpolated data point would lie between
' Note this ranges 00 to n - 01 - 01, thus returns -1 on fail which is tested
DIM i AS LONG
IF N_CSP = 00 OR _
pU_CSP = 00 OR _
pU_CSP_PARM = 00 THEN
FUNCTION = -1
ELSEIF @pU_CSP_PARM.N_DATA = 00 OR _ ' Test all allocations and pointers
@pU_CSP_PARM.pt_DATA = 00 OR _
@pU_CSP_PARM.py_DATA = 00 OR _
@pU_CSP_PARM.N_INTP = 00 OR _
@pU_CSP_PARM.pt_INTP = 00 OR _
@pU_CSP_PARM.py_INTP = 00 OR _
@pU_CSP_PARM.N_LDU = 00 OR _
@pU_CSP_PARM.pU_LDU = 00 THEN
ELSEIF NOT @pU_CSP_PARM.N_DATA = @pU_CSP_PARM.N_LDU THEN ' LDU allocation must match the input data size
FUNCTION = -1
ELSE
' Trap the boundaries
IF t_INTP <= @[email protected]_DATA[00] THEN
FUNCTION = 00
ELSEIF t_INTP >= @[email protected]_DATA[N_CSP - 01 - 01] THEN
FUNCTION = N_CSP - 01 - 01
ELSE
FOR i = 00 TO N_CSP - 01 - 01
IF t_INTP >= @[email protected]_DATA[i] AND _
t_INTP < @[email protected]_DATA[i + 01] THEN
FUNCTION = i
EXIT FUNCTION
END IF
NEXT i
' Fail condition is encountered
FUNCTION = -1
END IF
END IF
END FUNCTION
FUNCTION CSP_SOLVE ( _
N_CSP AS LONG , _
BYVAL pU_CSP AS UDT_CSP POINTER , _
BYVAL pU_CSP_PARM AS UDT_CSP_PARM POINTER ) AS LONG
' Routine computes a cubic spline solution to a set of input data by pointer
DIM i AS LONG
DIM i_INTP AS LONG
IF N_CSP = 00 OR _
pU_CSP = 00 OR _
pU_CSP_PARM = 00 THEN
FUNCTION = %F
ELSEIF @pU_CSP_PARM.N_DATA = 00 OR _ ' Test all allocations and pointers
@pU_CSP_PARM.pt_DATA = 00 OR _
@pU_CSP_PARM.py_DATA = 00 OR _
@pU_CSP_PARM.N_INTP = 00 OR _
@pU_CSP_PARM.pt_INTP = 00 OR _
@pU_CSP_PARM.py_INTP = 00 OR _
@pU_CSP_PARM.N_LDU = 00 OR _
@pU_CSP_PARM.pU_LDU = 00 THEN
ELSEIF NOT @pU_CSP_PARM.N_DATA = @pU_CSP_PARM.N_LDU THEN ' LDU allocation must match the input data size
FUNCTION = %F
ELSE
' Compute b and h coefficients
FOR i = 00 TO N_CSP - 01 - 01
@pU_CSP[i].h = @[email protected]_DATA[i + 01] - @[email protected]_DATA[i]
IF NOT @pU_CSP[i].h = 0.0# THEN
@pU_CSP[i].b = 1.0# / @pU_CSP[i].h * (@[email protected]_DATA[i + 01] - @[email protected]_DATA[i])
END IF
NEXT i
' Compute v and u coefficients
FOR i = 01 TO N_CSP - 01 - 01
@pU_CSP[i].v = 2.0# * (@pU_CSP[i - 01].h + @pU_CSP[i].h)
@pU_CSP[i].u = 6.0# * (@pU_CSP[i].b - @pU_CSP[i - 01].b)
NEXT i
' Load the LDU coefficients to prepare for the tridiagonal solution
FOR i = 00 TO @pU_CSP_PARM.N_LDU - 01
' Load the LDU vectors
' Note the IIF operator for the boundary condition (i = 00 OR i = N_CSP - 01) which processes S''(x) = 0 by setting L, U = 0 and D = 1
@[email protected]_LDU[i].L = IIF(i = 00 OR i = N_CSP - 01, 0.0#, IIF(i = 01 , %F, @pU_CSP[i - 01].h))
@[email protected]_LDU[i].D = IIF(i = 00 OR i = N_CSP - 01, 1.0#, @pU_CSP[i].v )
@[email protected]_LDU[i].U = IIF(i = 00 OR i = N_CSP - 01, 0.0#, IIF(i = N_CSP - 01 - 01, %F, @pU_CSP[i].h) )
' Load the b solution source vector which in this case is the [u] vector
@[email protected]_LDU[i].b = @pU_CSP[i].u
NEXT i
' Solve the cubic spline [z] vector for S.i''(x) using the tridiagonal Gauss Seidel LDU solver
GS_LDU_SOLVE @pU_CSP_PARM.N_LDU, @pU_CSP_PARM.pU_LDU, VARPTR(@pU_CSP_PARM.U_LDU_PARM)
#IF %F
MSGBOX GS_LDU_GET_S(@pU_CSP_PARM.N_LDU, @pU_CSP_PARM.pU_LDU), %MB_ICONINFORMATION OR %MB_TASKMODAL OR %MB_TOPMOST, $S_MSGBOX_HDR
#ENDIF
' Range over the span of the interpolated t points
FOR i_INTP = 00 TO @pU_CSP_PARM.N_INTP - 01
' Create the uniform interpolation points
@[email protected]_INTP[i_INTP] = @[email protected]_DATA[00] + (@[email protected]_DATA[@pU_CSP_PARM.N_DATA - 01] - @[email protected]_DATA[00]) * i_INTP / (@pU_CSP_PARM.N_INTP - 01)
' Find the data index that each point lies in
CSP_FIND_INDEX N_CSP , _
pU_CSP , _
pU_CSP_PARM , _
@[email protected]_INTP[i_INTP] TO i
' Error check the index for -1 from the find index function
IF NOT i = -1 THEN
' Compute the cubic spline interpolation y = ao + a1 t + a2 t^2 + a3 t^3
' Note the LDU solved [x]kp1 term replaces the [z] solution vector by variable name
@[email protected]_INTP[i_INTP] = @[email protected]_LDU[i + 01].xkp1 / (6.0# * @pU_CSP[i].h) * (@[email protected]_INTP[i_INTP] - @[email protected]_DATA[i]) ^ 3 + _
@[email protected]_LDU[i].xkp1 / (6.0# * @pU_CSP[i].h) * (@[email protected]_DATA[i + 01] - @[email protected]_INTP[i_INTP]) ^ 3 + _
(@[email protected]_DATA[i + 01] / @pU_CSP[i].h - @[email protected]_LDU[i + 01].xkp1 / 6.0# * @pU_CSP[i].h) * (@[email protected]_INTP[i_INTP] - @[email protected]_DATA[i]) + _
(@[email protected]_DATA[i] / @pU_CSP[i].h - @[email protected]_LDU[i].xkp1 / 6.0# * @pU_CSP[i].h) * (@[email protected]_DATA[i + 01] - @[email protected]_INTP[i_INTP])
END IF
NEXT i_INTP
FUNCTION = %T
END IF
END FUNCTION
FUNCTION CSP_SET_CLIP ( _
N_CSP AS LONG , _
BYVAL pU_CSP AS UDT_CSP POINTER , _
BYVAL pU_CSP_PARM AS UDT_CSP_PARM POINTER ) AS LONG
' Routine sets cubic spline solution to the clipboard for easy plotting
DIM i AS LONG
DIM i_INTP AS LONG
DIM S_CLIP AS STRING
IF N_CSP = 00 OR _
pU_CSP = 00 OR _
pU_CSP_PARM = 00 THEN
FUNCTION = %F
ELSEIF @pU_CSP_PARM.N_DATA = 00 OR _ ' Test all allocations and pointers
@pU_CSP_PARM.pt_DATA = 00 OR _
@pU_CSP_PARM.py_DATA = 00 OR _
@pU_CSP_PARM.N_INTP = 00 OR _
@pU_CSP_PARM.pt_INTP = 00 OR _
@pU_CSP_PARM.py_INTP = 00 OR _
@pU_CSP_PARM.N_LDU = 00 OR _
@pU_CSP_PARM.pU_LDU = 00 THEN
ELSEIF NOT @pU_CSP_PARM.N_DATA = @pU_CSP_PARM.N_LDU THEN ' LDU allocation must match the input data size
FUNCTION = %F
ELSE
' Range over the span of the interpolated t points
FOR i_INTP = 00 TO @pU_CSP_PARM.N_INTP - 01
S_CLIP += STR$(@[email protected]_INTP[i_INTP]) + " " + STR$(@[email protected]_INTP[i_INTP]) + $CRLF
NEXT i_INTP
CLIPBOARD SET TEXT S_CLIP
FUNCTION = %T
END IF
END FUNCTION
FUNCTION CSP_GET_S ( _
N_CSP AS LONG , _
BYVAL pU_CSP AS UDT_CSP POINTER , _
BYVAL pU_CSP_PARM AS UDT_CSP_PARM POINTER ) AS STRING
DIM i AS LONG
DIM i_INTP AS LONG
DIM S_CSP AS STRING
IF N_CSP = 00 OR _
pU_CSP = 00 OR _
pU_CSP_PARM = 00 THEN
FUNCTION = ""
ELSEIF @pU_CSP_PARM.N_DATA = 00 OR _ ' Test all allocations and pointers
@pU_CSP_PARM.pt_DATA = 00 OR _
@pU_CSP_PARM.py_DATA = 00 OR _
@pU_CSP_PARM.N_INTP = 00 OR _
@pU_CSP_PARM.pt_INTP = 00 OR _
@pU_CSP_PARM.py_INTP = 00 OR _
@pU_CSP_PARM.N_LDU = 00 OR _
@pU_CSP_PARM.pU_LDU = 00 THEN
ELSEIF NOT @pU_CSP_PARM.N_DATA = @pU_CSP_PARM.N_LDU THEN ' LDU allocation must match the input data size
FUNCTION = ""
ELSE
#IF 00
FOR i = 00 TO N_CSP - 01
S_CSP += TRIM$("b[" + STR$(i+1) + "]") + " " + STR$(@pU_CSP[i].b) + " " + _
TRIM$("v[" + STR$(i+1) + "]") + " " + STR$(@pU_CSP[i].v) + " " + _
TRIM$("u[" + STR$(i+1) + "]") + " " + STR$(@pU_CSP[i].u) + $CRLF
NEXT i
#ENDIF
#IF 00
FOR i = 00 TO @pU_CSP_PARM.N_LDU - 01
S_CSP += TRIM$("L[" + STR$(i+1) + "]") + " " + STR$(@[email protected]_LDU[i].L) + " " + _
TRIM$("D[" + STR$(i+1) + "]") + " " + STR$(@[email protected]_LDU[i].D) + " " + _
TRIM$("U[" + STR$(i+1) + "]") + " " + STR$(@[email protected]_LDU[i].U) + $CRLF
NEXT i
#ENDIF
#IF -1
FOR i_INTP = 00 TO @pU_CSP_PARM.N_INTP - 01
S_CSP += "[i INTP, t_INTP, y_INTP] " + STR$(i_INTP) + " " + STR$(@[email protected]_INTP[i_INTP]) + " " + STR$(@[email protected]_INTP[i_INTP]) + $CRLF
NEXT i_INTP
#ENDIF
FUNCTION = S_CSP
END IF
END FUNCTION
FUNCTION CSP_TEST ( ) AS LONG
' Routine computes an cubic spline test function
DIM N_CSP AS LONG
DIM U_CSP() AS UDT_CSP
DIM U_CSP_PARM AS UDT_CSP_PARM
DIM N_DATA AS LONG
DIM t_DATA() AS DOUBLE
DIM y_DATA() AS DOUBLE
DIM N_INTP AS LONG
DIM t_INTP() AS DOUBLE
DIM y_INTP() AS DOUBLE
DIM N_LDU AS LONG
DIM U_LDU() AS UDT_LDU
' Create a test input data set
' Note the assumption is that the load data is sorted
' 0.9 0
' 1.3 1.5
' 1.9 1.85
' 2.1 2.1
N_DATA = 04
REDIM t_DATA(00 TO N_DATA - 01) : ARRAY ASSIGN t_DATA() = 0.9# , 1.3# , 1.9# , 2.1#
REDIM y_DATA(00 TO N_DATA - 01) : ARRAY ASSIGN y_DATA() = 0.0# , 1.5# , 1.85#, 2.1#
U_CSP_PARM.N_DATA = N_DATA
U_CSP_PARM.pt_DATA = VARPTR(t_DATA(00))
U_CSP_PARM.py_DATA = VARPTR(y_DATA(00))
' Allocate the LDU solution data structure
N_LDU = N_DATA
REDIM U_LDU(00 TO N_LDU - 01)
U_CSP_PARM.N_LDU = N_DATA
U_CSP_PARM.pU_LDU = VARPTR(U_LDU(00))
' Allocate the cubic spline coefficients to the number of data points
N_CSP = N_DATA
REDIM U_CSP(00 TO N_CSP - 01)
' Set the LDU solve parameters
U_CSP_PARM.U_LDU_PARM.N_ITR_MAX = 10
U_CSP_PARM.U_LDU_PARM.e_ITR_MIN = 1.0E-6#
' Create a test input interpolation set
' Note this is larger than the input data set to create smoothness
N_INTP = 10
REDIM t_INTP(00 TO N_INTP - 01)
REDIM y_INTP(00 TO N_INTP - 01)
U_CSP_PARM.N_INTP = N_INTP
U_CSP_PARM.pt_INTP = VARPTR(t_INTP(00))
U_CSP_PARM.py_INTP = VARPTR(y_INTP(00))
' Solve for cubic spline
CSP_SOLVE N_CSP, VARPTR(U_CSP(00)), VARPTR(U_CSP_PARM)
CSP_SET_CLIP N_CSP, VARPTR(U_CSP(00)), VARPTR(U_CSP_PARM)
' When interpolated to 10 interpolation points, this data should produce the following spline result
' 0.90000 0.00000
' 1.03333 0.59125
' 1.16667 1.11407
' 1.30000 1.50000
' 1.43333 1.70412
' 1.56667 1.77553
' 1.70000 1.78685
' 1.83333 1.81069
' 1.96667 1.91647
' 2.10000 2.10000
#IF %T
MSGBOX CSP_GET_S(N_CSP, VARPTR(U_CSP(00)), VARPTR(U_CSP_PARM)), %MB_ICONINFORMATION OR %MB_TASKMODAL OR %MB_TOPMOST, $S_MSGBOX_HDR
#ENDIF
END FUNCTION
' Range over the span of the interpolated t points FOR i_INTP = 00 TO @pU_CSP_PARM.N_INTP - 01 S_CLIP += STR$(@[email protected]_INTP[i_INTP]) + " " + STR$(@[email protected]_INTP[i_INTP]) + $CRLF NEXT i_INTP
#COMPILE EXE
#DIM ALL
FUNCTION PBMAIN() AS LONG
LOCAL x AS LONG 'loopcount
LOCAL lngDatapoint AS LONG
LOCAL strFile,strT AS STRING
LOCAL minY,maxY AS EXT
minY = 1.2*10^4932
maxY = -1.2*10^4932
DIM arrX(1 TO 100) AS EXT ' Use separate arrays for ease of sort
DIM arrY(1 TO 100) AS EXT ' If initial data is not sorted
DISPLAY OPENFILE , , , "Select data file", EXE.PATH$, CHR$("All Files", 0, "*.*", 0),"Mannishdata.tab","" , 0 TO strFile
IF NOT ISFILE(strFIle) THEN
? "File Not Found - Exiting"
EXIT FUNCTION
END IF
OPEN strFile FOR INPUT AS #1
WHILE NOT EOF(#1)
INCR lngDatapoint
IF UBOUND(arrX()) < lngDatapoint THEN REDIM PRESERVE arrX(lngDataPoint + 100):REDIM PRESERVE arrY(lngDataPoint + 100)
LINE INPUT #1, strT
arrx(lngDatapoint) = VAL(PARSE$(strT,$TAB,1))
arrY(lngDatapoint) = VAL(PARSE$(strT,$TAB,2))
IF arrY(lngDatapoint) > MaxY THEN MaxY = arrY(lngDatapoint)
IF arrY(lngDatapoint) < MinY THEN MinY = arrY(lngDatapoint)
WEND
CLOSE #1
REDIM PRESERVE arrX(1 TO lngDatapoint)
REDIM PRESERVE arrY(1 TO lngDatapoint)
ARRAY SORT ArrX(), TAGARRAY ArrY()
Plotit ArrX(),ArrY(), MinY,MaxY, strFile
END FUNCTION
FUNCTION Plotit(ArrX() AS EXT, arrY() AS EXT ,minY AS EXT,MaxY AS EXT,strF AS STRING) AS LONG
LOCAL hWin AS DWORD
LOCAL minX,maxX, x AS EXT
LOCAL SMinX,SMinY,SMaxX,SMaxY AS EXT
'Get graph bounds
minX = ArrX(LBOUND(arrx()))
maxX = ArrX(UBOUND(arrx()))
'put 10% margins round data
SMinX = minx - (maxX-minX) *.1
sMinY = miny - (maxy-miny) *.1
sMaxX = maxx + (maxX-minX) *.1
sMaxY = maxy + (maxy-miny) *.1
GRAPHIC WINDOW NEW strF , 50, 50, 800, 400 TO hWin
GRAPHIC SCALE (Sminx,Smaxy) - (SmaxX,SMinY)
'Draw the axes
GRAPHIC COLOR %BLACK,-1
GRAPHIC WIDTH 2
GRAPHIC LINE (MinX,MinY)-(Minx,MAxY)
GRAPHIC LINE (Minx,MinY)-(MaxX,MinY)
'Plot the data
GRAPHIC COLOR %BLUE,-1
GRAPHIC SET POS (arrx(1),arry(1))
FOR x = 2 TO UBOUND(arrx())
GRAPHIC LINE - (arrX(x),arrY(x))
NEXT
GRAPHIC WAITKEY$
GRAPHIC DETACH
GRAPHIC WINDOW END hWin
END FUNCTION
'
'instead of - graphic set pixel (arrX(jj),arrY(jj)+deltaY), %rgb_darkred 'try - graphic box (arrX(jj) - 1,arrY(jj)+deltaY - 1) - (arrX(jj) + 1,arrY(jj)+deltaY + 1), _ 50, %rgb_darkred, %rgb_darkred, 0
' Draw circular boxes with very tiny dimensions
GRAPHIC BOX (arrX(jj) - 0.05,arrY(jj)+deltaY - 0.05) - _
(arrX(jj) + 0.05,arrY(jj)+deltaY + 0.05), _
100, %RGB_DARKRED, %RGB_DARKRED, 0
Comment