Histograms and plots

CALL HPARAM (ID,IC,R2MIN,MAXPOW,COEFF*,ITERM*,NCO*)

Input parameters:

ID

Histogram or plot identifier.

IC

Control word (see below)

R2MIN

Maximum required value of multiple correlation coefficient

MAXPOW

Maximum degrees of standard polynomials (INTEGER array of size NDIM)

ITERM

Acceptable function codes (see explanation above) (INTEGER array of size $\le$ PNBF, see explanation above)

Output parameters:

NCO

number of regressors in final expression.

COEFF

Coefficients of terms (DOUBLE PRECISION array of size NCO)

ITERM

Accepted regressors codes (INTEGER array of size NDIM*NCO or NCO, see explanation above)

$IC\; =\; N*107\; +\; R*106\; +\; C*105\; +\; B*104\; +\; T*103\; +\; W*102\; +\; P*10\; +\; S$

S

This switch controls the superimposition of the result when printing the histogram, it is effective only for 1-dimensional histograms

1

Resulting parametric fit superimposed on histogram

0

No superposition

P

This switch controls the amount of information printed during the fitting process

0

Minimal output: the residual sum of squares is printed

1

Normal output: in addition, the problem characteristics and options are printed; also the standard deviations and confidence intervals of the coefficients

2

extensive output: the results of each iteration are printed with the normal output

W

This switch controls the weights to applied to the data during the fit

0

weights on histogram contents are already defined via HBARX or HPAKE. If not they are taken to be equal to the square-root of the contents

1

weights are equal to 1

T

This switch controls the system-defined elementary functions set to use

0

Monomials will be selected as the standard elementary functions

1

Chebyshev polynomials with a definition region: $[-1,1]$

2

Legendre polynomials with a definition region: $[-1,1]$

3

shifted Chebyshev polynomials with a definition region: $[0,1]$

4

Laguerre polynomials with a definition region:

5

Hermite polynomials with a definition region:

B

This switch controls the kind of regressor used in the fit

0

Regressors are products of standard polynomials (see preceeding switch)

1

Regressors are products of user-defined elementary functions. The user should write a DOUBLE PRECISION function [HELEFT]HELEFT(IEF,X) where IEF is the elementary function code in the sense explained above: 10 times the function code plus 1. The function code number can vary from 1 to PNEF, number of user supplied elementary functions. PNEF has to be specified by the user before calling HPARAM, via a call to the routine HSETPR described below. The seconf parameter X is the point where the function should be calculated.

2

Regressors are user-defined, in this case the variable PNBF, number of basic functions, must be set by the user via a call to HSETPR (see below). User regressors values are to be returned by the user-supplied DOUBLE PRECISION function [HBASFT]HBASFT(IBF,X) where IBF is the user-defined regressor code in the sense explained above: 10 times the regressor code plus 2. The regressor code number can vary from 1 to PNBF, number of basic functions used for the parametrization. PNBF has to be specified by the user before calling HPARAM, via a call to the routine HSETPR described below, in the case that the switches B or C of the control parameter IC have the value 2. The parameter X is an array of length NDIM defining the coordinate where the regressor should be calculated.

C

This switch controls the selection of the regressors

0

Regressors are selected by the system. The parameter PSEL and the array MAXPOW help the user in controlling the total degree of each regressor (see below).

1

for each elementary function or for each regressor, the logical function [HSELBF]HSELBF(ELEF) gets called once before the beginning of the actual fitting procedure to set up the table of available elementary functions or regressors. IELEF is the code of the regressor or of the function being tested for acceptance. A value of .TRUE. returned will cause the regressor/elementary function to be accepted. The default version of this function which is supplied in HBOOK always returns the value .TRUE., while the user may want to write his own version of this function to exclude some of the regressors or of the elementary functions (according to the value of the B switch he has selected).

2

The input array ITERM contains a list of selected regressors or elementary functions according to the value of the switch B. The array has to be at least NDIM*PNBF words and the variable PNBF, maximum number of elementary functions or regressors, should have been set via a call to HSETPR. In the case of elementary functions, the element ITERM(IDIM+(IBF-1)*NDIM) is the function of the variable $x$_IDIM

to be multiplied by the coefficent number IBF, given a maximum expected number of PNBF coefficents. This can be of course reduced by the fitting program under considerations of linear dependency, as stated above, returning only NCO coefficents, thus after the fit ITERM will identify which regressors were actually used. In the case of user-defined regressors, only the first PNBF position of the ITERM array need to be filled, and the array will contain directly the code of the selected user-defined regressors.

R

This switch controls the system selection mechanism for the regressors:

0

Stepwise regression, the regression is calculated as explained before, and selected regressors may be eliminated in a further step of the procedure

1

Forward regression. The backward stage is suppressed: a regressor included at one time will always remain in the regression later on

2

Fixed-term regression: all selected regressors will appear in the final expression

N

This switch controls the normalization of the X range during the computation.

0

No normalization of X-range

1

X scaled in the range $[-1,1]$

2

X scaled in the range $[0,1]$

3

X scaled in the range

The value of R2MIN is used to determine the satisfactory end of the fitting process. If 0<R2MIN<1, this value will be compared to the current sum of the squares of the residuals to determine whether the fit should be stopped or continued. If R2MIN$\ge 1$ , the fitting process will be halted when the residual variance is minimal.

Various parameters which are relevant for the parametrization can be set via the routine HSETPR.

CALL HSETPR (CHNAME,VALUE)

Input parameters:

CHNAME

Name of the parameter to be set (of type CHARACTER)

VALUE

Value assigned to parameter CHNAME (of type REAL)

Possible values for CHNAME are:

'PNEF'

This parameter specifies to the system the number of elementary functions that are supplied by the user, in case the switch B of the IC parameter is set to 1. The system will build PNBF basic regressors made up by products of NDIM elementary functions, possibly user selected, as specified by the switch C of the parameter IC.

'PNBF'

This parameter must be specified in case user regressors are used (B switch of IC set to 2), or in case the ITERM contains on input the selected regressors or basic elementary functions (C switch of IC parameter set to 2). The parameter is ignored in the other cases. This is the total number of user-defined regressors or elementary functions which the system will use for the parametrization process. Please note that in case of user given regressors, if the C switch of the IC parameter is either 0 or 1, the logical function [HSELBF]HSELBF(ELEF) will always be called in order to verify the inclusion of the regressor IELEF in the list for the current fitting operation.

'PSEL'

This parameter is used only in case of system-supplied elementary functions. It is the maximum limit for the sum of the terms POW(I)/MAXPOW(I) in each regressor, where POW(I) is the power of the system-supplied elementary function for the $Ith$ variable ($1\le$ I<NDIM) and MAXPOW(I) is the user supplied maximum value for the degree of the system-supplied elementary functions for the $Ith$ variable. This value must be 0<VALUE<NDIM. Note that setting PSEL to 0 selects the constant term for all the regressors. Setting PSEL to a value $\ge$ NDIM has the effect of removing any limitation on the total degree of the regressors, leaving MAXPOW(I) as the only effective limitation on the degree of the the elementary functions. This means that the total degree of the regressors can be equal to the sum of the NDIM elements of MAXPOW(I). The system supplied default is 1.

'PFLV'

This parameter determines the F-test significance level for rejection of already included regressors; by default it is set to 1. A higher value makes it more difficult for regressors to remain in the regression. The value of PFLV has to be >0.

'PLUN'

This parameter indicates the logical unit for writing the Fortran code of the function [FPARAM]FPARAM(X). which gives the value of the parametrization at point X. This Fortran code can be compiled and used in subsequent jobs. By default no code is written.

'PNBX'

Maximum number of regressors that may be entered as input to the fitting process (after selection). By default PNBX is set to 500; setting PNBX to an appropriate value will avoid wasting space in dynamic area /PAWC/.    This parameter may be set to the same value of PNBF or PNEF whichever is appropriate to save space.

'PNCX'

Maximum number of regressors that may appear in the final expression of the parametrization (this number has to be $\le 50$ ). Default setting is 50. The same remark applies as for PNBX.