+].+].pppp$Normal x6H6H$$tzVZxڅڅgA8yyyyyyy*$ Control Variables  SYMBOLS , * = Variable is needed for our PCS work  X{x} = x is a subscript. >$ {Logical(xx)} = LOGICAL variable (or array of size "xx"). >$ {Integer(xx)} = INTEGER variable (or array of size "xx"). 8$ {Real(xx)} = REAL variable (or array of size "xx").   References:  [1] "CONTIN: A General Purpose Constrained Regularization Program For Inverting Noisy Linear Algebraic and Integral Equations"; Provencher. (program summary) [2] "A Constrained Regularization Method For Inverting Data Represented By Linear Algebraic Or Integral Equations"; Provencher. (method summary) }[3] CONTIN Users Manual; Provencher. When citing this, usually only the section number, wthout the ref. Number, is given. |[4] CONTIN (Program); Provencher. When citing this, usually only the subprogram name, without the ref. number, is given.  $ Input Control  LAST Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Indicates whether or not another data set follows. LAST=1.0 (True) if this is the last set. If there is another then LAST=-1.0 (False).  NINTT Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. $Specifies the number of equally spaced sets of tk -- delay times T -- for NINTT>0. For NINTT<0 the T's are entered individually according to the FORMAT in IFORMT. 01 IFORMT Variable Type: Integer(70) Format: (1X,6A1,I5,E15.6) 'Use for QELS analysis: Yes, if NINTT<0 Default: (5E15.6). $Sets the FORMAT for the input of the delay times tk. Only the 6A1field ,for the variable name, is used . A second input line must immediately follow this one to enter the the FORMAT specification used to enter the table of delay times. FORMAT of the second line is (1X,70A1). 34 4See also: NINTT  IFORMY Variable Type: Integer(70) Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: (5E15.6). "$Sets the FORMAT for the input of the correlation function data yk. Only the 6A1field ,for the variable name, is used . A second input line must immediately follow this one to enter the the FORMAT specification used to enter the table of y values. FORMAT of the second card is (1X,70A1). @A  IFORMW Variable Type: Integer(70) Format: (1X,6A1,I5,E15.6) Use for QELS analysis: No Default: (5E15.6). '$Sets the FORMAT for the input of the least squares weights Wk. Only the 6A1field ,for the variable name, is used . A second input line must immediately follow this one to enter the the FORMAT specification used to enter the table of weighting values. FORMAT of the second card is (1X,70A1). <=  DOUSIN Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True). If DOUSIN=1.0 (True) then USERIN is called to preprocess the input data. If DOUSIN=-l.0 then USERIN is not called. USERIN converts the input correlation function to the normalized first-order correlation function as needed depending on the value of RUSER(10).  4See also: RUSER(10) 4 "$ Formation Of Linear Equations  NG Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 31. Specifies the number of grid points (N{g}) in the quadrature. These are the points over which the solution distribution is computed (in the quadrature). In our case these grid points are the particle radii. Default: 31.  *GMNMX R(2) Inputs the values of the first and last grid points. GMNMX(1)=g{1) and GMNMX(2)=g{NG). Again these points, in our application will be the particle radii (in cm) Default: 0.,0.. (Values of 0 will cause an error during program execution.)  *IQUAD I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. Specifies the quadrature method. For IQUAD=2 or 3 the trapezoidal or Simpson's rule, respectively, will be used to develop the system of linear equations. IF IQUAD=1 the problem already is in the form of linear algebraic equations. Default: 3.  *IGRID I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. Specifies the spacing of the points of the quadrature grid. IGRID=1 puts the grid in equal intervals of g from g{1} to g{NG}. IGRID=2 puts the grid in equal intervals of the monotonic function h(g) specified in USERTR. The default version of USERTR sets h(g)=ln(g) producing a logarithmic grid. IGRID=3 allows the user to specify each grid point individually using USERGR. Default: 2.  NLINF I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. HSpecifies the number of terms (N{L}) in a second optional (nonintegral) term in the original Fredholm equation. NLINF may not be < 0. If NLINF>0 USERLF is called to evaluate the NLINF additional known functions Li(tk) that are present in unknown amounts in the data. The equations to do the evaluation must be put into USERLF by the user. Currently USERLF is set up to allow the combination of two sets of data each with a different constant additive background (baseline). See USERLF subroutine in CONTIN for details. Default: 0.  $ Constraints  DOUSNQ L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Indicates whether or not USERNQ will be caled to evaluate inequality constraints. USERNQ is called if DOUSNQ=1.0 (True). Default: -1.0 (False).  *NONNEG L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Indicates whether or not the solution will be constrained to be everywhere nonnegative. If NONNEG=1.0 (True) then the solution is constrained. Default: 1.0 (True).  NEQ I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: No Default: 0. Specifies the number of equality constraints (N{eq}). If NEQ>0 then USEREQ is called to evaluate the constraints. Default: 0.  $ Least Squares Weights  *IWT I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. !Specifies the weighting scheme: [$IWT=1 sets wk=1. This is appropriate if the noise level is the same for all data points.  IWT=2 sets wk=1/YSAFEk. This is appropriate for Poisson statistics, ie the standard deviation of data point k is proportional to |y(tk)|1/2.  IWT=3 sets wk=[YSAFE)k]-2. This is appropriate for a constant relative error, ie where the standard deviation of data point k is proportional to |y(tk)|.  -$IWT=4 reads in the wk from Card Set 7. HIWT=5 computes the wk in USERWT. This is necessary only if none of the other IWT values are appropriate. The default version of USERWT computes statistical weights for the normalized first-order correlation fcn. assuming the second-order correlation fcn. follows Poisson statistics. See 4.2 [1]. **Note: YSAFEk uses the fit values of the Y's 'along with a safety margin to avoid very small values of the Y's from causing "disastrously" large w's, as would occur in IWT=2 or 3. See 4.2 [1] and 4.1.2.7. Default=1. 89 *NERFIT I Specifies the number of points used to calculate the safety margin used in determining the least squares weights. See IWT. Default=10.  $ Reqularizor  *NORDER I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. HSpecifies the order of the regularizor. NORDER=2 tends to give the "smoothest" solution that is consistent with the data. Here the regularizor is the sum of the squares of the second differences of the first Ng xj. The solution is smooth in the sense that an integral over its second derivative squared is a minimum. Other values of NORDER are possible; see 4.1.2.8. Default=2.  *NENDZ I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. Specifies the number of zero valued solutions, that lie outside the grid, to add to the regularizor. This is done if it is known that the solution outside the grid is zero. Adding the extra zeros ''tends to make the solution approach zero more smoothly at one or both ends of the grid, and this is often more natural and parsimonious." NENDZ(1) is for the low end of the grid and NENDZ(2) is for the high end. You must have: O<=NENDZ(J)<=NORDER, J=1,2. Then NENDZ(1)+NENDZ(2) extra differences are added to the regularizor. Default=2,2.  $ Alpha Grids  Alpha is the factor that multiplies the regularizor and so determines the extent to which it penalizes the solution. CONTIN chooses alpha, the regularization parameter, by determining solutions over two grids of alpha values. The first grid is widely spaced and is used to find the region where the selection criteria, PROB1 TO REJECT (Fisher's F-distribution, see 4.1.6.5), changes from small (near 0.0) to large (near 1.0). The second grid is more finely spaced and is concentrated on this region of changing PROB1. The chosen solution is the one with its PROB1 closest to 0.5. Alpha grid parameters listed below can be changed but if the PROB1 criteria is being used it should not be necessary to change them. See 4.1.3 and 4.1.6.5.  NQPROG I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. ASpecifies the number of points in the Alpha grids. Default=6,6.  RSVMNX R(2,2) ASpecifies the range of the alpha grids. User indirectly specifies the first and last points of each grid or of just the coarse grid and lets the fine grid scan the region of changing PROB1. The values are input using FORMAT (4E10.3). See 4.1.3. Default=1.,1.,0.,0.. (Here the fine grid searches the transition region.)  DFMIN R Specifies the minimum reasonable number of degrees of freedom. DFMIN>0 will reduce RSVvMNX(2,J), J=1,2, so that there will be approximately at least DFMIN Degrees of freedom in the regularized solution. DFMIN<=0 will cause no such action. See 4.1.3. Default=2..  ALPST R(2) *Specifies a particular value for alpha and turns off the grid searching routine if ALPST>O. If ALPST<=0 the grid searching routine is used. ALPST(1) specifies the action for the preliminary unweighted analysis and ALPST(2) specifies the action for the final analysis. See 4.1.3. Default=0.,0..  $ Miscellaneous  SIMULA L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) $Indicates that data is to be simulated if SIMULA=1.0 (True). USEREX produces noise-free values for the yk and USERI adds pseudo-random normal deviates to the noise-free data. The default versions of USEREX and USERSI simulate a delta function distribution for the data corresponding to a second-order correlation function in dynamic light scattering. Use RUSER 25 to 40 and IUSER 3 and 11 for inputs. See 4.1.6.2. Default=-1.0 (False). hi IUNIT I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. xSpecifies a device number for a scratch file. If If IUNIT>=0 then the scratch file numbered IUNIT will be used. This cuts down on run time especially if the kernel requires much computation time. With a scratch file the kernel is computed once and stored otherwise it is recomputed twice for each solution. If IUNIT<0 then no scratch file is used. See 4.1.6.1. Default=-1.  ICRIT I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. VSpecifies the criterion for choosing alpha. DO NOT CHANGE. See 4.1.6.5. Default=1,1.  PLEVEL R(2,2) Specifies the probalility level for choosing alpha. DO NOT CHANGE. These values are input using FORMAT (4F5.2). See 4.1.6.5. Default=0.5,0.5,0.5,0.5.  $ Peak Constraints See 4.1.6.4.  NNSGN I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. PSpecifies the number of peak constrained analyses. NNSGN(x)<=4. Default=0,0.  NSGN I(4) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. ISpecifies the number of monotonic regions. 1<=NSGN<=4. Default=0,0,0,0.  LSIGN I(4,4) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. wSpecifies the starting locations of the monotonic regions. Input using FORMAT (16I5). Default=0 for all 16 elements.  NFL0T I(4,2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. vSpecifies the number of attempts to eliminate plateaus. Input using FORMAT (8I5). Default=0 for all eight elements.  SRMIN R JSpecifies the relative threshold for defining plateaus. Default=0.01.  MQPITR I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. ZSpecifies the maximum number of iterations for a peak-constrained analysis. Default=35.  $ Output Control  *LINEPG I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. Specifies the number of lines per page of printed output. Use the number of lines per page available on users output device. This is used to plan certain outputs (residuals) so that plots are not broken up in going from one page to the next. Default=60.  *NEWPG1 L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) FIndicates that a blank page will be printed at the start of a run if mNEWPG1=1.0 (True). If this is not needed or desired then set NEWPG1=-1.0 (False). Default=-l.0 (False).  *MIOERR I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. Specifies the number of messages indicating errors in the users input format that will be printed before the run is aborted. Default=5.  *PRY L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) e$Indicates that the T (delay time) and Y (correlation function) arrays will be printed if PRY=1.0 (True). If IWT=4 then the square roots of the wk (least squares weights) will also be output. If SIMULA=True then the simulated (noise-free and "noisey") values will also be printed. If PRY=-1.0 (False) then none of -these will be output. Default=1.0.  *PRWT L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Indicates that the square roots of the least squares weights are to be output if PRWT=1.0 (True) and if IWT=2, 3 or 5. If PRWT=-1.0 (False) then the weights will not be output. Default=1.0.  *IPRINT I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. [Indicates the frequency and spacing of the output of the plots of the solutions. IPRINT= 0 for never printing them. A1 for printing them only after the peak-constrained solution. 72 for printing them also after the Chosen Solution. *3 for printing them after every solution. 44 for also starting a new page for each solution. xIPRINT(1) does this for the Preliminary Unweighted Analysis and IPRINT(2) for the Final Analysis. Default=4,4.  *ONLY1 L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Specifies whether or not a second curve is to be plotted along with the solution (ie with the size distribution). "X"=solution. "O"=second curve. If ONLY1=1.0 (True) only the solution is printed. IF 0NLY1=-1.0 (False) then two curves are printed. See 4.1.6.3. Default=1.0.  *IPLRES I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. DIndicates the frequency of plots of the weighted residuals. IPLRES= 0 for never plotting them. B1 for plotting them only after the peak-constrained solutions. 82 for also plotting them before the Chosen Solution. 23 for also plotting them after every solution. tIPLRES(1) does this for the Preliminary Unweighted Analysis and IPLRES(2) for the Final Analysis. Default=2,2.  *IPLFIT I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. fIndicates the frequency of the plots of the fit to the data in the same way as IPLRES. Default=2,2.  *IUSROU I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. pIndicates the frequency of calls to USEROU for special purpose outputs in the same way as IPRINT. Default=0,0  *DOMOM L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Indicates that Moments of the Solution are to be computed and output if DOMOM=1.0 (True). If DOMOM=-1.0 (False) then this will not be done. Default=1.0.  *MOMNMX I(2) Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. Specifies the minimum and maximum degrees of the moments, respectively MOMNMX(1) and MOMNMX(2), to be computed. If MOMNMX(1)>MOMNMX(2) then the moment computation is not done. Default=-1.3.  *MPKMOM I Variable Type: Integer Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. 1Specifies number of individual peaks for which the moments are to be computed. If there are more than MPKMOM peaks, then peak MPKMOM and all following peaks along the g-axis are considered together as peak MPKMOM. If MPKMOM<=1, then only the moments of the entire solution are computed. Default=5.  *DOCHOS L Variable Type: Logical Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 1.0 (True) Indicates that the Chosen Solution is to be printed at the end of the analysis if DOCHOS=1.0 (True). If DOCHOS=-1.0 (False), then this is not done. Default=1.0.  EFor more information on these Output Control Variables see 4.1.5.  $ USER Arrays Arrays of Control Variables available to the user to input data that will be used in any of the USER subprograms or to store intermediate results produced in the USER subprograms for later use. All three arrays have some room (or can be enlarged) to store special user values.  n4See also: Contin Users Manual Sec. 4.1.1 and comment lines in the program listing for additional information.   RUSER Array Variable Type: Real(100) Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. for all elements. WArray of real values used to input equation, fit and some program control parameters.  RUSER(1) Variable Type: Real Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. ESets the value of the solution at the first grid point if NEQ>=1.  El4See also: NEQ, RUSER(2), RUSER(6), Contin Users Manual Sec. 4.1.2.6.  ! RUSER(2) Variable Type: Real Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. ASets the value of the solution at the last grid point if NEQ>=2.  Fl4See also: NEQ, RUSER(1), RUSER(6), Contin Users Manual Sec. 4.1.2.6.  !4  RUSER(3) Variable Type: Real Format: (1X,6A1,I5,E15.6) Use for QELS analysis: No Default: 0. Sets noise level of the simulated data if SIMULA=True. Values of the standard deviations depends on the weighting statistics used (IWT).  \l4See also: IWT, RUSER(25), IUSER(3), Contin Users Manual Sec. 4.1.6.2. and Ref [1] sec 4.3.  "4  RUSER(6) Variable Type: Real Format: (1X,6A1,I5,E15.6) Use for QELS analysis: No Default: 0. hSets the value of the integral over the solution (using the quadrature as an approximation ) if NEQ>=3.  El4See also: NEQ, RUSER(1), RUSER(2), Contin Users Manual Sec. 4.1.2.6.  !4  RUSER(8) Variable Type: Real Format: (1X,6A1,I5,E15.6) Use for QELS analysis: No Default: 0. 9((g^R(8))*(e-g)/G(R(8)+1) is plotted. G=Gamma function.   & ' RUSER(10) Variable Type: Real Format: (1X,6A1,I5,E15.6) Use for QELS analysis: Yes Default: 0. 7Specifies the normalization for the correlation fcn.: `lR(10)>0 then R(10) is the baseline or background and the yk are replaced by +(yk /R(10)-1)1/2. :;OPZ]&$R(10)=0 then the yk are not changed. R(1O)p & j r !@!h!!#F$$&&''''' (@(t((j*r**** +2+T-\---00000"1J1111233"4*4<4l5t555556(6B6&8.8>8n8888h:p::::;.;;;;D<L<<<<<<=<=d====>$>X>>>>>?>D<4!*h+WINSPOOLSeymour Krelboine (0N160)\\PROCTER_GAMBLE\.Q0141_LJ6MP.MVL.CIN.NA.PGSeymour Krelboine (0N160)Letter (8 x 11 in))X)ә @X