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====== Linear interpolation background functions ======
A set of linear interpolation background functions, similar to GSAS background function 7 (p130 of GSAS manual), with 6, 12, 24 and 36 parameters.
The function splits the pattern into N equal segments with N+1 refined background intensity points with straight lines describing the background between each point.
These functions use nested IF loops to significantly decrease the calculation time compared to subsequent IF statements.
The macros can be used to draw your own background by fixing the background intensity values at the observed value...
e.g. Bkg_LinInterpol_N6(!bk0, 370, !bk1, 309, !bk2, 171, !bk3, 88, !bk4, 72, !bk5, 42, !bk6, 30)
...or just used to refine even the most tricky of backgrounds which are not well served by gradually changing mathematical functions.
Example of use: Bkg_LinInterpol_N36(bk0, 0, bk1, 500, bk2, 0, bk3, 500, bk4, 0, bk5, 500, bk6, 0, bk7, 500, bk8, 0, bk9, 500, bk10, 0, bk11, 500, bk12, 0, bk13, 500, bk14, 0, bk15, 500, bk16, 0, bk17, 500, bk18, 0, bk19, 500, bk20, 0, bk21, 500, bk22, 0, bk23, 500, bk24, 0, bk25, 500, bk26, 0, bk27, 500, bk28, 0, bk29, 500, bk30, 0, bk31, 500, bk32, 0, bk33, 500, bk34, 0, bk35, 500, bk36, 0)
Linear interpolation background function with 6 parameters
macro Bkg_LinInterpol_N6(bk0, b0v, bk1, b1v, bk2, b2v, bk3, b3v, bk4, b4v, bk5, b5v, bk6, b6v)
{
prm pStep =((X*0)+X2-X1)/6;
prm pStart =((X*0)+X1);
prm Xval0 = pStart;
prm Xval1 = pStart+pStep;
prm Xval2 = pStart+(pStep*2);
prm Xval3 = pStart+(pStep*3);
prm Xval4 = pStart+(pStep*4);
prm Xval5 = pStart+(pStep*5);
prm bk0 b0v
prm bk1 b1v
prm bk2 b2v
prm bk3 b3v
prm bk4 b4v
prm bk5 b5v
prm bk6 b6v
fit_obj =
IF (X < Xval3) THEN
IF (X < Xval1) THEN
((bk1-bk0)/pStep)*(X-Xval0)+bk0
ELSE IF (X < Xval2) THEN
((bk2-bk1)/pStep)*(X-Xval1)+bk1
ELSE
((bk3-bk2)/pStep)*(X-Xval2)+bk2
ENDIF
ENDIF
ELSE IF (X < Xval4) THEN
((bk4-bk3)/pStep)*(X-Xval3)+bk3
ELSE IF (X < Xval5) THEN
((bk5-bk4)/pStep)*(X-Xval4)+bk4
ELSE
((bk6-bk5)/pStep)*(X-Xval5)+bk5
ENDIF
ENDIF
ENDIF
;
}
Linear interpolation background function with 12 parameters
macro Bkg_LinInterpol_N12(bk0, b0v, bk1, b1v, bk2, b2v, bk3, b3v, bk4, b4v, bk5, b5v, bk6, b6v, bk7, b7v, bk8, b8v, bk9, b9v, bk10, b10v, bk11, b11v, bk12, b12v)
{
prm pStep =((X*0)+X2-X1)/12;
prm pStart =((X*0)+X1);
prm Xval0 = pStart; prm Xval6 = pStart+(pStep*6);
prm Xval1 = pStart+pStep; prm Xval7 = pStart+(pStep*7);
prm Xval2 = pStart+(pStep*2); prm Xval8 = pStart+(pStep*8);
prm Xval3 = pStart+(pStep*3); prm Xval9 = pStart+(pStep*9);
prm Xval4 = pStart+(pStep*4); prm Xval10 = pStart+(pStep*10);
prm Xval5 = pStart+(pStep*5); prm Xval11 = pStart+(pStep*11);
prm bk0 b0v prm bk7 b7v
prm bk1 b1v prm bk8 b8v
prm bk2 b2v prm bk9 b9v
prm bk3 b3v prm bk10 b10v
prm bk4 b4v prm bk11 b11v
prm bk5 b5v prm bk12 b12v
prm bk6 b6v
fit_obj =
IF (X < Xval6) THEN
IF (X < Xval3) THEN
IF (X < Xval1) THEN
((bk1-bk0)/pStep)*(X-Xval0)+bk0
ELSE IF (X < Xval2) THEN
((bk2-bk1)/pStep)*(X-Xval1)+bk1
ELSE
((bk3-bk2)/pStep)*(X-Xval2)+bk2
ENDIF
ENDIF
ELSE
IF (X < Xval4) THEN
((bk4-bk3)/pStep)*(X-Xval3)+bk3
ELSE IF (X < Xval5) THEN
((bk5-bk4)/pStep)*(X-Xval4)+bk4
ELSE
((bk6-bk5)/pStep)*(X-Xval5)+bk5
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval9) THEN
IF (X < Xval7) THEN
((bk7-bk6)/pStep)*(X-Xval6)+bk6
ELSE IF (X < Xval8) THEN
((bk8-bk7)/pStep)*(X-Xval7)+bk7
ELSE
((bk9-bk8)/pStep)*(X-Xval8)+bk8
ENDIF
ENDIF
ELSE
IF (X < Xval10) THEN
((bk10-bk9)/pStep)*(X-Xval9)+bk9
ELSE IF (X < Xval11) THEN
((bk11-bk10)/pStep)*(X-Xval10)+bk10
ELSE
((bk12-bk11)/pStep)*(X-Xval11)+bk11
ENDIF
ENDIF
ENDIF
ENDIF
;
}
Linear interpolation background function with 24 parameters
macro Bkg_LinInterpol_N24(bk0, b0v, bk1, b1v, bk2, b2v, bk3, b3v, bk4, b4v, bk5, b5v, bk6, b6v, bk7, b7v, bk8, b8v, bk9, b9v, bk10, b10v, bk11, b11v, bk12, b12v, bk13, b13v, bk14, b14v, bk15, b15v, bk16, b16v, bk17, b17v, bk18, b18v, bk19, b19v, bk20, b20v, bk21, b21v, bk22, b22v, bk23, b23v, bk24, b24v)
{
prm pStep =((X*0)+X2-X1)/24;
prm pStart =((X*0)+X1);
prm Xval0 = pStart; prm Xval12 = pStart+(pStep*12);
prm Xval1 = pStart+pStep; prm Xval13 = pStart+(pStep*13);
prm Xval2 = pStart+(pStep*2); prm Xval14 = pStart+(pStep*14);
prm Xval3 = pStart+(pStep*3); prm Xval15 = pStart+(pStep*15);
prm Xval4 = pStart+(pStep*4); prm Xval16 = pStart+(pStep*16);
prm Xval5 = pStart+(pStep*5); prm Xval17 = pStart+(pStep*17);
prm Xval6 = pStart+(pStep*6); prm Xval18 = pStart+(pStep*18);
prm Xval7 = pStart+(pStep*7); prm Xval19 = pStart+(pStep*19);
prm Xval8 = pStart+(pStep*8); prm Xval20 = pStart+(pStep*20);
prm Xval9 = pStart+(pStep*9); prm Xval21 = pStart+(pStep*21);
prm Xval10 = pStart+(pStep*10); prm Xval22 = pStart+(pStep*22);
prm Xval11 = pStart+(pStep*11); prm Xval23 = pStart+(pStep*23);
prm bk0 b0v prm bk10 b10v prm bk20 b20v
prm bk1 b1v prm bk11 b11v prm bk21 b21v
prm bk2 b2v prm bk12 b12v prm bk22 b22v
prm bk3 b3v prm bk13 b13v prm bk23 b23v
prm bk4 b4v prm bk14 b14v prm bk24 b24v
prm bk5 b5v prm bk15 b15v
prm bk6 b6v prm bk16 b16v
prm bk7 b7v prm bk17 b17v
prm bk8 b8v prm bk18 b18v
prm bk9 b9v prm bk19 b19v
fit_obj =
IF (X < Xval12) THEN
IF (X < Xval6) THEN
IF (X < Xval3) THEN
IF (X < Xval1) THEN
((bk1-bk0)/pStep)*(X-Xval0)+bk0
ELSE IF (X < Xval2) THEN
((bk2-bk1)/pStep)*(X-Xval1)+bk1
ELSE
((bk3-bk2)/pStep)*(X-Xval2)+bk2
ENDIF
ENDIF
ELSE
IF (X < Xval4) THEN
((bk4-bk3)/pStep)*(X-Xval3)+bk3
ELSE IF (X < Xval5) THEN
((bk5-bk4)/pStep)*(X-Xval4)+bk4
ELSE
((bk6-bk5)/pStep)*(X-Xval5)+bk5
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval9) THEN
IF (X < Xval7) THEN
((bk7-bk6)/pStep)*(X-Xval6)+bk6
ELSE IF (X < Xval8) THEN
((bk8-bk7)/pStep)*(X-Xval7)+bk7
ELSE
((bk9-bk8)/pStep)*(X-Xval8)+bk8
ENDIF
ENDIF
ELSE
IF (X < Xval10) THEN
((bk10-bk9)/pStep)*(X-Xval9)+bk9
ELSE IF (X < Xval11) THEN
((bk11-bk10)/pStep)*(X-Xval10)+bk10
ELSE
((bk12-bk11)/pStep)*(X-Xval11)+bk11
ENDIF
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval18) THEN
IF (X < Xval15) THEN
IF (X < Xval13) THEN
((bk13-bk12)/pStep)*(X-Xval12)+bk12
ELSE IF (X < Xval14) THEN
((bk14-bk13)/pStep)*(X-Xval13)+bk13
ELSE
((bk15-bk14)/pStep)*(X-Xval14)+bk14
ENDIF
ENDIF
ELSE
IF (X < Xval16) THEN
((bk16-bk15)/pStep)*(X-Xval15)+bk15
ELSE IF (X < Xval17) THEN
((bk17-bk16)/pStep)*(X-Xval16)+bk16
ELSE
((bk18-bk17)/pStep)*(X-Xval17)+bk17
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval21) THEN
IF (X < Xval19) THEN
((bk19-bk18)/pStep)*(X-Xval18)+bk18
ELSE IF (X < Xval20) THEN
((bk20-bk19)/pStep)*(X-Xval19)+bk19
ELSE
((bk21-bk20)/pStep)*(X-Xval20)+bk20
ENDIF
ENDIF
ELSE
IF (X < Xval22) THEN
((bk22-bk21)/pStep)*(X-Xval21)+bk21
ELSE IF (X < Xval23) THEN
((bk23-bk22)/pStep)*(X-Xval22)+bk22
ELSE
((bk24-bk23)/pStep)*(X-Xval23)+bk23
ENDIF
ENDIF
ENDIF
ENDIF
ENDIF
;
}
Linear interpolation background function with 36 parameters
macro Bkg_LinInterpol_N36(bk0, b0v, bk1, b1v, bk2, b2v, bk3, b3v, bk4, b4v, bk5, b5v, bk6, b6v, bk7, b7v, bk8, b8v, bk9, b9v, bk10, b10v, bk11, b11v, bk12, b12v, bk13, b13v, bk14, b14v, bk15, b15v, bk16, b16v, bk17, b17v, bk18, b18v, bk19, b19v, bk20, b20v, bk21, b21v, bk22, b22v, bk23, b23v, bk24, b24v, bk25, b25v, bk26, b26v, bk27, b27v, bk28, b28v, bk29, b29v, bk30, b30v, bk31, b31v, bk32, b32v, bk33, b33v, bk34, b34v, bk35, b35v, bk36, b36v)
{
prm pStep =((X*0)+X2-X1)/36;
prm pStart =((X*0)+X1);
prm Xval0 = pStart; prm Xval12 = pStart+(pStep*12); prm Xval24 = pStart+(pStep*24);
prm Xval1 = pStart+pStep; prm Xval13 = pStart+(pStep*13); prm Xval25 = pStart+(pStep*25);
prm Xval2 = pStart+(pStep*2); prm Xval14 = pStart+(pStep*14); prm Xval26 = pStart+(pStep*26);
prm Xval3 = pStart+(pStep*3); prm Xval15 = pStart+(pStep*15); prm Xval27 = pStart+(pStep*27);
prm Xval4 = pStart+(pStep*4); prm Xval16 = pStart+(pStep*16); prm Xval28 = pStart+(pStep*28);
prm Xval5 = pStart+(pStep*5); prm Xval17 = pStart+(pStep*17); prm Xval29 = pStart+(pStep*29);
prm Xval6 = pStart+(pStep*6); prm Xval18 = pStart+(pStep*18); prm Xval30 = pStart+(pStep*30);
prm Xval7 = pStart+(pStep*7); prm Xval19 = pStart+(pStep*19); prm Xval31 = pStart+(pStep*31);
prm Xval8 = pStart+(pStep*8); prm Xval20 = pStart+(pStep*20); prm Xval32 = pStart+(pStep*32);
prm Xval9 = pStart+(pStep*9); prm Xval21 = pStart+(pStep*21); prm Xval33 = pStart+(pStep*33);
prm Xval10 = pStart+(pStep*10); prm Xval22 = pStart+(pStep*22); prm Xval34 = pStart+(pStep*34);
prm Xval11 = pStart+(pStep*11); prm Xval23 = pStart+(pStep*23); prm Xval35 = pStart+(pStep*35);
prm bk0 b0v prm bk10 b10v prm bk20 b20v prm bk30 b30v
prm bk1 b1v prm bk11 b11v prm bk21 b21v prm bk31 b31v
prm bk2 b2v prm bk12 b12v prm bk22 b22v prm bk32 b32v
prm bk3 b3v prm bk13 b13v prm bk23 b23v prm bk33 b33v
prm bk4 b4v prm bk14 b14v prm bk24 b24v prm bk34 b34v
prm bk5 b5v prm bk15 b15v prm bk25 b25v prm bk35 b35v
prm bk6 b6v prm bk16 b16v prm bk26 b26v prm bk36 b36v
prm bk7 b7v prm bk17 b17v prm bk27 b27v
prm bk8 b8v prm bk18 b18v prm bk28 b28v
prm bk9 b9v prm bk19 b19v prm bk29 b29v
fit_obj =
IF (X < Xval12) THEN
IF (X < Xval6) THEN
IF (X < Xval3) THEN
IF (X < Xval1) THEN
((bk1-bk0)/pStep)*(X-Xval0)+bk0
ELSE IF (X < Xval2) THEN
((bk2-bk1)/pStep)*(X-Xval1)+bk1
ELSE
((bk3-bk2)/pStep)*(X-Xval2)+bk2
ENDIF
ENDIF
ELSE
IF (X < Xval4) THEN
((bk4-bk3)/pStep)*(X-Xval3)+bk3
ELSE IF (X < Xval5) THEN
((bk5-bk4)/pStep)*(X-Xval4)+bk4
ELSE
((bk6-bk5)/pStep)*(X-Xval5)+bk5
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval9) THEN
IF (X < Xval7) THEN
((bk7-bk6)/pStep)*(X-Xval6)+bk6
ELSE IF (X < Xval8) THEN
((bk8-bk7)/pStep)*(X-Xval7)+bk7
ELSE
((bk9-bk8)/pStep)*(X-Xval8)+bk8
ENDIF
ENDIF
ELSE
IF (X < Xval10) THEN
((bk10-bk9)/pStep)*(X-Xval9)+bk9
ELSE IF (X < Xval11) THEN
((bk11-bk10)/pStep)*(X-Xval10)+bk10
ELSE
((bk12-bk11)/pStep)*(X-Xval11)+bk11
ENDIF
ENDIF
ENDIF
ENDIF
ELSE IF (X < Xval24) THEN
IF (X < Xval18) THEN
IF (X < Xval15) THEN
IF (X < Xval13) THEN
((bk13-bk12)/pStep)*(X-Xval12)+bk12
ELSE IF (X < Xval14) THEN
((bk14-bk13)/pStep)*(X-Xval13)+bk13
ELSE
((bk15-bk14)/pStep)*(X-Xval14)+bk14
ENDIF
ENDIF
ELSE
IF (X < Xval16) THEN
((bk16-bk15)/pStep)*(X-Xval15)+bk15
ELSE IF (X < Xval17) THEN
((bk17-bk16)/pStep)*(X-Xval16)+bk16
ELSE
((bk18-bk17)/pStep)*(X-Xval17)+bk17
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval21) THEN
IF (X < Xval19) THEN
((bk19-bk18)/pStep)*(X-Xval18)+bk18
ELSE IF (X < Xval20) THEN
((bk20-bk19)/pStep)*(X-Xval19)+bk19
ELSE
((bk21-bk20)/pStep)*(X-Xval20)+bk20
ENDIF
ENDIF
ELSE
IF (X < Xval22) THEN
((bk22-bk21)/pStep)*(X-Xval21)+bk21
ELSE IF (X < Xval23) THEN
((bk23-bk22)/pStep)*(X-Xval22)+bk22
ELSE
((bk24-bk23)/pStep)*(X-Xval23)+bk23
ENDIF
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval30) THEN
IF (X < Xval27) THEN
IF (X < Xval25) THEN
((bk25-bk24)/pStep)*(X-Xval24)+bk24
ELSE IF (X < Xval26) THEN
((bk26-bk25)/pStep)*(X-Xval25)+bk25
ELSE
((bk27-bk26)/pStep)*(X-Xval26)+bk26
ENDIF
ENDIF
ELSE
IF (X < Xval28) THEN
((bk28-bk27)/pStep)*(X-Xval27)+bk27
ELSE IF (X < Xval29) THEN
((bk29-bk28)/pStep)*(X-Xval28)+bk28
ELSE
((bk30-bk29)/pStep)*(X-Xval29)+bk29
ENDIF
ENDIF
ENDIF
ELSE
IF (X < Xval33) THEN
IF (X < Xval31) THEN
((bk31-bk30)/pStep)*(X-Xval30)+bk30
ELSE IF (X < Xval32) THEN
((bk32-bk31)/pStep)*(X-Xval31)+bk31
ELSE
((bk33-bk32)/pStep)*(X-Xval32)+bk32
ENDIF
ENDIF
ELSE
IF (X < Xval34) THEN
((bk34-bk33)/pStep)*(X-Xval33)+bk33
ELSE IF (X < Xval35) THEN
((bk35-bk34)/pStep)*(X-Xval34)+bk34
ELSE
((bk36-bk35)/pStep)*(X-Xval35)+bk35
ENDIF
ENDIF
ENDIF
ENDIF
ENDIF
ENDIF
;
}