C#> gaussn.dc2
C
CFunction:     GAUSSN  
C
CPurpose:      GAUSSN computes the value of an N-component Gaussian
C
CFiles:        gaussn.dc2,gaussn.shl
C
CAuthor:       Peter Roelfsema
C
CCategory:     UTILITY
C
CCall:
C
C       GX=GAUSSN(X,PAR,NPAR)
C
C   Input parameters:
C                X     -R   -running coordinate.
C                PAR   -R   -array  defined  as  follows:  PAR(0:NPAR*3)  that
C                    contains the parameters for the Gaussian in the following
C                    order:
C
C                            PAR(0)        -zerolevel
C                       PAR(1)  -PAR(3)    -int, pos.  of peak, fwhm cmp.  1
C                             .                     .
C                     PAR(1+3*n)-PAR(3+3*n)-int, pos.  of peak, fwhm cmp.  n-1
C                                     etc
C                NPAR  -I   -number of components.
C
CUse:
C                  GAUSSN gives the value of a multi-component gaussian.
C                  Note  that  the Gaussian components are defined in terms of
C                  their Intensity, centre coordinate and Full Width  at  Half
C                  Maximum ( i.e.  not in terms of amplitude and sigma ! ).
C
C
C   Call:
C
C       CALL DGAUSN(X,PAR,DERIV,NPAR)          ( entry point in GAUSSN )
C
C   Input parameters:
C                X     -R   -running coordinate.
C                PAR   -R   -array  defined  as  follows:  PAR(0:NPAR*3)  that
C                    contains the parameters for the Gaussian in the following
C                    order:
C
C                            PAR(0)        -zerolevel
C                       PAR(1)  -PAR(3)    -int, pos.  of peak, fwhm cmp.  1
C                             .                     .
C                     PAR(1+3*n)-PAR(3+3*n)-int, pos.  of peak, fwhm cmp.  n-1
C                                     etc
C                NPAR  -I   -number of components.
C   Output parameters:
C                DERIV -R   -array defined as  follows:  DERIV(0:NPAR*3)  that
C                    contains the partial derivatives in the following order:
C                               DERIV(0)       -part.  deriv of zerolevel
C                         DERIV(1)-DERIV(3)    -part.  derivs.  of cmp.  1
C                                .                     .
C                     DERIV(1+3*n)-DERIV(3+3*n)-part.  derivs.  of cmp.  n-1
C                                          etc
C
C
CUse:
C                  DGAUSN gives the partial derivatives for the gaussian.
C                  Note  that  the Gaussian components are defined in terms of
C                  their Intensity, centre coordinate and Full Width  at  Half
C                  Maximum ( i.e.  not in terms of amplitude and sigma ! ).
C
C
C   Update History:
C      8- 7-85-PRR.-original document
C     16- 6-86-PRR.-converted for VAX8600
C     26- 2-92-PRR.-converted to new GIPSY
C#<
C
C@ real function gaussn( real , real , integer )
C@ subroutine dgausn( real , real , real , integer )
C
      REAL FUNCTION GAUSSN(X,PAR,NPAR)
C
C      ----------------------------------------------------------------
C
C      GAUSSN gives the value of a multi-component guassian
C
C      DGAUSN gives the partial derivatives for this gaussian
C
C      The parameters and deriavatives are defined as follows:
C             PAR(0)       -zerolevel
C            DERIV(0)      -part deriv zero level
C        PAR(1)  -PAR(3)   -int, pos. of peak and fwhm of component 1
C        DERIV(1)-DERIV(3) -part. derivs. of component 1
C              .                     .
C      PAR(1+3*n)-PAR(3+3*n)- int, pos. of peak, fwhm of comp. n-1
C                      etc
C
C      ----------------------------------------------------------------

N.natural logarithm of 2: LN(2)
      PARAMETER ( RLN2 = 0.6931472 )
N.factor to calculate the amplitude: 2*SQRT(LN(2)/PI)
      PARAMETER (  A0  = 0.9394373 )

N.running coordinate
      REAL       X
N.parameter array
      REAL       PAR(0:*)
N.array with derivatives
      REAL       DERIV(0:*)
N.buffer variables
      REAL       GAUSS,A

N.number of parameters
      INTEGER    NPAR
N.number of components
      INTEGER    NCOMP
N.loop counter
      INTEGER    I

E *** Main code ***
N.determine number of components
      NCOMP=(NPAR-1)/3

N.zero level
      GAUSS=PAR(0)
N.loop on all components
      FOR I=0,(NCOMP-1)
N.argument of exponential
      IF (PAR(I*3+3) .NE. 0.0)
      THEN
      A=(X-PAR(I*3+2))/PAR(I*3+3)
N.add component to what we had already
      GAUSS=GAUSS+A0*PAR(I*3+1)/PAR(I*3+3)*EXP(-4*RLN2*A*A)
      CIF
      CFOR

      GAUSSN=GAUSS
      RETURN


C#> dgausn.dc2
C
CName:          DGAUSN  
C
C
CPurpose:       DGAUSN computes the partial derivatives of that Gaussian
C
CFiles:         dgaussn.dc2,gaussn.shl
C
CAuthor:        Peter Roelfsema
C
C
C   Call:
C
C       CALL DGAUSN(X,PAR,DERIV,NPAR)          ( entry point in GAUSSN )
C
C   Input parameters:
C                X     -R   -running coordinate.
C                PAR   -R   -array  defined  as  follows:  PAR(0:NPAR*3)  that
C                    contains the parameters for the Gaussian in the following
C                    order:
C
C                            PAR(0)        -zerolevel
C                       PAR(1)  -PAR(3)    -int, pos.  of peak, fwhm cmp.  1
C                             .                     .
C                     PAR(1+3*n)-PAR(3+3*n)-int, pos.  of peak, fwhm cmp.  n-1
C                                     etc
C                NPAR  -I   -number of components.
C   Output parameters:
C                DERIV -R   -array defined as  follows:  DERIV(0:NPAR*3)  that
C                    contains the partial derivatives in the following order:
C                               DERIV(0)       -part.  deriv of zerolevel
C                         DERIV(1)-DERIV(3)    -part.  derivs.  of cmp.  1
C                                .                     .
C                     DERIV(1+3*n)-DERIV(3+3*n)-part.  derivs.  of cmp.  n-1
C                                          etc
C
C
C   Use:
C                  DGAUSN gives the partial derivatives for the gaussian.
C                  Note  that  the Gaussian components are defined in terms of
C                  their Intensity, centre coordinate and Full Width  at  Half
C                  Maximum ( i.e.  not in terms of amplitude and sigma ! ).
C
C
C   Update History:
C      8- 7-85-PRR.-original document
C     16- 6-86-PRR.-converted for VAX8600
C     26- 2-92-PRR.-converted to new GIPSY
C#<
      ENTRY DGAUSN(X,PAR,DERIV,NPAR)

N.determine number of components
      NCOMP=(NPAR-1)/3

N.zero-level
      DERIV(0)=1.0
N.loop on all components
      FOR I=0,(NCOMP-1)
N.argument of exponential
      IF (PAR(I*3+3) .NE. 0.0)
      THEN   
      A=(X-PAR(I*3+2))/PAR(I*3+3)
N.calculate this component
      GAUSS=A0/PAR(I*3+3)*EXP(-4*RLN2*A*A)
N.derivative of integral
      DERIV(I*3+1)=GAUSS
N.derivative of centre coordinate
      DERIV(I*3+2)=GAUSS*8*RLN2*A*PAR(I*3+1)/PAR(I*3+3)
N.derivative of FWHM
      DERIV(I*3+3)=GAUSS*(8*RLN2*A*A-1)*PAR(I*3+1)/PAR(I*3+3)
      ELSE
      DERIV(I*3+1)=0.0
      DERIV(I*3+2)=0.0
      DERIV(I*3+3)=0.0
      CIF
      CFOR

      RETURN
      END