MISCELANEA.fjg

*   This file contains Rats FUNCTIONs for various things (MISCELANEA)
*   WinRATS 9.00
*   Paco Goerlich   02/03/2015

********************************************************************************

*   %SUMS - Sum the elements of a series

FUNCTION  %SUMS  X
TYPE REA  %SUMS
TYPE SER          X

LOCAL REAL A
LOCAL INT  I N

INQ(SER=X) * N
COM  A = %SUMS = 0, %DO(I,1,N,A = A + X(I)), %SUMS = A

END      %SUMS

********************************************************************************

*   %BLOCKDIAGSYM - Block diagonal symmetric matrix from a vector of symmetrics

FUNCTION      %BLOCKDIAGSYM  A
TYPE     SYM  %BLOCKDIAGSYM
TYPE VEC[SYM]                A

LOCA VEC[REC]  C

DIM  C(%ROWS(A))
EWI  C(I) = A(I)
COM  %BLOCKDIAGSYM = %BLOCKDIAG(C)

END  %BLOCKDIAGSYM

********************************************************************************

*   %AGREGA - Convert this PROC into a FUNCTION.

********************************************************************************

*   %DUPLICA - Operator to duplicate rows of a matrix.
*              To duplicate de columns post-multiply by TR(%DUPLICA(.))
*              Also to alter the order of the rows and/or columns of a matrix.

FUNCTION  %DUPLICA  V
TYPE REC  %DUPLICA
TYPE VEC            V

DIM  %DUPLICA(%ROWS(V),FIX(%MAXVALUE(V)))
EWI  %DUPLICA(I,J) = %IF(FIX(V(I))==J,1,0)

END  %DUPLICA

********************************************************************************

*   %COMPRESSV - Same as %COMPRESS(A,V) but with A type VEC[LAB]

FUNCTION       %COMPRESSV  A  V
TYPE VEC[LAB]  %COMPRESSV  A
TYPE VEC                      V

LOCAL INT I J

DIM  %COMPRESSV(%ROWS(%COMPRESS(V,V)))
COM I = 1
DO  J = 1,%ROWS(V)
    IF V(J).NE.0
       COM %COMPRESSV(I) = A(J), I = I + 1
END DO J

END  %COMPRESSV

********************************************************************************

*   %STRCOMPRESSV - Same as %COMPRESSV(A,V) but with A type VEC[STR]

FUNCTION       %STRCOMPRESSV  A  V
TYPE VEC[STR]  %STRCOMPRESSV  A
TYPE VEC                      V

LOCAL INT I J

DIM  %STRCOMPRESSV(%ROWS(%COMPRESS(V,V)))
COM I = 1
DO  J = 1,%ROWS(V)
    IF V(J).NE.0
       COM %STRCOMPRESSV(I) = A(J), I = I + 1
END DO J

END  %STRCOMPRESSV

********************************************************************************

*   %CPUTIMEHMS - Same as %CPUTIME() but in h:mm:ss format

FUNCTION  %CPUTIMEHMS N
TYPE STR  %CPUTIMEHMS
TYPE INT              N

COM %CPUTIMEHMS = %STRING(N/3600) + ' h  ' + %STRING(%MOD(N,3600)/60) + ' min  ' + %STRING(%MOD(%MOD(N,3600),60)) + ' sec'

END %CPUTIMEHMS

********************************************************************************

*   %INV - Inverse of a Real Number.

FUNCTION  %INV  X
TYPE REA  %INV  X

COM       %INV = 1./X

END       %INV

********************************************************************************

*   %NAN - Number of NA in a Series.

FUNCTION  %NAN  X
TYPE INT  %NAN
TYPE SER        X

LOCA INT   N1 N2 I

INQ(SER=X) N1 N2
COM %NAN = 0
DO I = N1,N2
   IF .NOT.%VALID(X(I))
      COM %NAN = %NAN + 1
END DO I

END       %NAN

********************************************************************************

*   %NEGATIVE - Number of Negative Values in a Series.

FUNCTION  %NEGATIVE  X
TYPE INT  %NEGATIVE
TYPE SER             X

LOCA SER  Z

SET  Z =  %IF(X<0,1,0)
COM       %NEGATIVE = FIX(%SUM(Z))

CLE  Z
END       %NEGATIVE

********************************************************************************

*   %POSITIVE - Number of Positive Values in a Series.

FUNCTION  %POSITIVE  X
TYPE INT  %POSITIVE
TYPE SER             X

LOCA SER  Z

SET  Z =  %IF(X>0,1,0)
COM       %POSITIVE = FIX(%SUM(Z))

CLE  Z
END       %POSITIVE

********************************************************************************

*   %NUMVALUE - Number of Values in a Series equal to VALUE.

FUNCTION  %NUMVALUE  X  V
TYPE INT  %NUMVALUE
TYPE SER             X
TYPE REA                V

LOCA SER  Z

SET  Z =  %IF(X==V,1,0)
COM       %NUMVALUE = FIX(%SUM(Z))

CLE  Z
END       %NUMVALUE

********************************************************************************

*   %NZEROS - Number of ZERO´s in a Series.

FUNCTION  %NZEROS  X
TYPE INT  %NZEROS
TYPE SER           X

COM       %NZEROS = %NUMVALUE(X,0)

END       %NZEROS

********************************************************************************

*   %NONES - Number of ONE´s in a Series.

FUNCTION  %NONES  X
TYPE INT  %NONES
TYPE SER          X

COM       %NONES = %NUMVALUE(X,1)

END       %NONES

********************************************************************************

*   %NLT - Number of Values in a Series LOWER THAN to VALUE.

FUNCTION  %NLT  X  V
TYPE INT  %NLT
TYPE SER        X
TYPE REA           V

LOCA SER  Z

SET  Z =  %IF(X<V,1,0)
COM       %NLT = FIX(%SUM(Z))

CLE  Z
END       %NLT

********************************************************************************

*   %NLE - Number of Values in a Series LOWER OR EQUAL THAN to VALUE.

FUNCTION  %NLE  X  V
TYPE INT  %NLE
TYPE SER        X
TYPE REA           V

LOCA SER  Z

SET  Z =  %IF(X<=V,1,0)
COM       %NLE = FIX(%SUM(Z))

CLE  Z
END       %NLE

********************************************************************************

*   %NGT - Number of Values in a Series GREATER THAN to VALUE.

FUNCTION  %NGT  X  V
TYPE INT  %NGT
TYPE SER        X
TYPE REA           V

LOCA SER  Z

SET  Z =  %IF(X>V,1,0)
COM       %NGT = FIX(%SUM(Z))

CLE  Z
END       %NGT

********************************************************************************

*   %NGE - Number of Values in a Series GREATER OR EQUAL THAN to VALUE.

FUNCTION  %NGE  X  V
TYPE INT  %NGE
TYPE SER        X
TYPE REA           V

LOCA SER  Z

SET  Z =  %IF(X>=V,1,0)
COM       %NGE = FIX(%SUM(Z))

CLE  Z
END       %NGE

********************************************************************************

*   %NEQV - Number of identical elements in a vector.

FUNCTION  %NEQV  X  V
TYPE INT  %NEQV
TYPE VEC         X
TYPE REA            V

LOCA VEC  Z

DIM Z(%ROWS(X))
EWI Z(I) = %IF(X(I)==V,1,0)
COM %NEQV = fix(%SUM(Z))

END %NEQV

********************************************************************************

*   %maxindexv - Returns a vector(integer) with the positions of the maximum value of a vector.
*                If the maximum value is unique then this is equivalent to %maxindex, type vector
*                of dimension 1, otherwise returns a vector of dimension %NEQV(V,%maxvalue(V))

function      %maxindexv  v
type vec[int] %maxindexv  v
type vec                  v

local int i j

dim %maxindexv(%neqv(v,%maxvalue(v)))
com j = 1
do i = 1,%rows(v)
   if v(i)==%maxvalue(v)
      com %maxindexv(j) = i, j += 1
end do i

end %maxindexv

********************************************************************************

*   %minindexv - Returns a vector(integer) with the positions of the minimum value of a vector.
*                If the minimum value is unique then this is equivalent to %minindex, type vector
*                of dimension 1, otherwise returns a vector of dimension %NEQV(V,%minvalue(V))

function      %minindexv  v
type vec[int] %minindexv  v
type vec                  v

local int i j

dim %minindexv(%neqv(v,%minvalue(v)))
com j = 1
do i = 1,%rows(v)
   if v(i)==%minvalue(v)
      com %minindexv(j) = i, j += 1
end do i

end %minindexv

********************************************************************************

*   %INTEGER - If a REAL is an INTEGER, 1, or NOT, 0.

FUNCTION  %INTEGER  X
TYPE INT  %INTEGER
TYPE REAL           X

COM       %INTEGER = %IF(%FRAC(X)==0,1,0)

END       %INTEGER

********************************************************************************

*   %IEVEN - If an INTEGER is EVEN, 1, or NOT, 0.

FUNCTION  %IEVEN  X
TYPE INT  %IEVEN  X

COM       %IEVEN = %IF(%mod(X,2)==0,1,0)

END       %IEVEN

********************************************************************************

*   %IODD - If an INTEGER is ODD, 1, or NOT, 0.

FUNCTION  %IODD  X
TYPE INT  %IODD  X

COM       %IODD = 1 - %IEVEN(X)

END       %IODD

********************************************************************************

*   %EVEN - If a REAL is an EVEN INTEGER, 1, or NOT, 0.

FUNCTION  %EVEN  X
TYPE REAL %EVEN  X

COM       %EVEN = %IF(%INTEGER(X),%IEVEN(FIX(X)),%NA)

END       %EVEN

********************************************************************************

*   %ODD - If a REAL is an ODD INTEGER, 1, or NOT, 0.

FUNCTION  %ODD  X
TYPE REAL %ODD  X

COM       %ODD = %IF(%INTEGER(X),1-%EVEN(X),%NA)

END       %ODD

********************************************************************************

*   %FRACV - %FRAC for vectors.

FUNCTION  %FRACV  V
TYPE VEC  %FRACV  V

DIM %FRACV(%ROWS(V))
EWI %FRACV(I) = %FRAC(V(I))

END       %FRACV

********************************************************************************

*   %FRACM - %FRAC for matrices (rectangular).

FUNCTION  %FRACM  V
TYPE REC  %FRACM  V

DIM %FRACM(%ROWS(V),%COLS(V))
EWI %FRACM(I,J) = %FRAC(V(I,J))

END       %FRACM

********************************************************************************

*   %FIXV - FIX for vectors.
*           In fact, it does a TRUNCATION, because returned type is VEC[REAL]

FUNCTION  %FIXV  V
TYPE VEC  %FIXV  V

DIM %FIXV(%ROWS(V))
EWI %FIXV(I) = FIX(V(I))

END       %FIXV

********************************************************************************

*   %FIXM - %FIX for matrices (rectangular).
*           In fact, it does a TRUNCATION, because returned type is VEC[REAL]

FUNCTION  %FIXM  V
TYPE REC  %FIXM  V

DIM %FIXM(%ROWS(V),%COLS(V))
EWI %FIXM(I,J) = FIX(V(I,J))

END       %FIXM

********************************************************************************

*   %ROUNDV - %ROUND for vectors.

FUNCTION  %ROUNDV  V  S
TYPE VEC  %ROUNDV  V
TYPE INT              S

LOCA INT I

DIM %ROUNDV(%ROWS(V))
EWI %ROUNDV(I) = %ROUND(V(I),S)

END       %ROUNDV

********************************************************************************

*   %ROUNDM - %ROUND for matrices (rectangular).

FUNCTION  %ROUNDM  V  S
TYPE REC  %ROUNDM  V
TYPE INT              S

LOCA INT I J

DIM %ROUNDM(%ROWS(V),%COLS(V))
EWI %ROUNDM(I,J) = %ROUND(V(I,J),S)

END       %ROUNDM

********************************************************************************

*   %UNITM - %UNITV for matrices (rectangular).

FUNCTION  %UNITM  M N I J
TYPE REC  %UNITM
TYPE INT          M N I J

COM %UNITM = %ZEROS(M,N), %UNITM(I,J) = 1.

END       %UNITM

********************************************************************************

*   %ANY - Creates and m x n matrix with all elements equal to a given real, A.
*          Same as %CONST(A) without dimensioning the matrix.

FUNCTION  %ANY  M N A
TYPE REC  %ANY
TYPE INT        M N
TYPE REA            A

DIM %ANY(M,N)
COM %ANY = %CONST(A)

END       %ANY

********************************************************************************

*   %PROPORTIONAL - Adjust proportionally a vector V to a given quantity, S.

FUNCTION  %PROPORTIONAL  V  S
TYPE VEC  %PROPORTIONAL  V
TYPE REAL                   S

COM %PROPORTIONAL = %IF(%MIN(%MINVALUE(V),S)<0,%NA,%IF(%SUM(V)==0.AND.S==0,1,S/%SUM(V)))*V

END       %PROPORTIONAL

********************************************************************************

*   %IPROPORTIONAL - Integer version of %PROPORTIONAL.
*                    Rule for integer asiggment 'controled rounding' of Cox (1982-JASA), as implemented in
*                    Balinski & Rachev (1997-MS,p.-5).
*                    This is essentially the 'method of greatest remainders'
*                    After %proportional() adjustment with standard rounding, truncate the vector to integers
*                    and add 1 at a time to the max fractional of the remaining part.
*                    In case of max fractional is NOT unique we signal this as a multiple solution, and a
*                    random choice in made between the max elements. In this case different results for
*                    the same input is possible, and a global variable, %%Multiple, is set to >= 1.

FUNCTION  %IPROPORTIONAL  V  S
TYPE VEC  %IPROPORTIONAL  V
TYPE REAL                    S

loca int i
loca vec Real

* If S in not integer it is rounded to integer using standard rounding.
* Proportional adjustment (Real) and truncation
com Real = %PROPORTIONAL(V,%round(S,0)), %IPROPORTIONAL = %fixv(Real), %%Multiple = 0

* If the sum of integers is < S then iterate until = S
while %sum(%IPROPORTIONAL)<%round(S,0)
   {
   if %neqv(Real-%IPROPORTIONAL,%maxvalue(Real-%IPROPORTIONAL))==1
      com %IPROPORTIONAL(%maxindex(Real-%IPROPORTIONAL)) += 1
   else
      com i = %raninteger(1,%rows(%maxindexv(Real-%IPROPORTIONAL))),                       $
                   %IPROPORTIONAL(%maxindexv(Real-%IPROPORTIONAL)(i)) += 1, %%Multiple = 1
   }
end       %IPROPORTIONAL

********************************************************************************

*   %DivBaseProp - Integer version of %PROPORTIONAL using divisor based methods.
*                  It implements the algorithm in Dorfleiter & Klein (1999-SP) Section 3,
*                  with standard rounding.
*                  After %proportional() adjustment with standard rounding, we enter the discrepancy
*                  loop and eventually we handle ties (multiple solutions).
*                  If multiple solutions exist a global variable, %%Multiple, is set to 1.
*                  The algorithm returns in %DivBaseProp a given solution, which depends on the order of the
*                  elements in the vector, %%z is the vector of signs to obtain the full set of solutions
*                  and %%zstr is the short hand for such set. See Dorfleiter & Klein (1999-SP) Section 4.

function  %DivBaseProp  v  s
type vec  %DivBaseProp  v
type real                  s

loca real discrepancy max min
loca int  i
loca vec  Lower Upper

* Globals
dec vec[int] %%z
dec vec[str] %%zstr
dim Lower(%rows(v)) Upper(%rows(v)) %%z(%rows(v)) %%zstr(%rows(v))

* MULTIPLIER STEP: Standard rounding on %proportional()
* If S in not integer it is rounded to integer using standard rounding.
com %DivBaseProp = %roundv(%proportional(v,%round(s,0)),0)

* DISCREPANCY LOOP
com discrepancy = %sum(%DivBaseProp) - %round(s,0)
if      discrepancy < 0
   com %do(i,1,%rows(v),Upper(i) = (%DivBaseProp(i)+0.5)/v(i)), %DivBaseProp(%minindex(Upper)) += 1
else if discrepancy > 0
   com %do(i,1,%rows(v),Lower(i) = (%DivBaseProp(i)-0.5)/v(i)), %DivBaseProp(%maxindex(Lower)) -= 1

* MULTIPLE SOLUTIONS STEP
ewi Lower(i) = (%DivBaseProp(i)-0.5)/v(i); com max = %maxvalue(Lower)
ewi Upper(i) = (%DivBaseProp(i)+0.5)/v(i); com min = %minvalue(Upper)
ewi %%z(i)   = 0
if max==min
   ewi %%z(i) = %if(Upper(i)==min,1,%if(Lower(i)==max,-1,0))
com %%Multiple = %if(max==min,1,0)
ewi %%zstr(i)  = %string(fix(%DivBaseProp(i)))+%if(%%z(i)==1,'+',%if(%%z(i)==-1,'-',''))

end       %DivBaseProp

********************************************************************************

*   %MAXINDEXROW - %MAXINDEX row for a rectangular matrix.

FUNCTION  %MAXINDEXROW  V
TYPE INT  %MAXINDEXROW
TYPE REC                V

COM %MAXINDEXROW = %CLOCK(%MAXINDEX(%VEC(V)),%ROWS(V))

END       %MAXINDEXROW

********************************************************************************

*   %MININDEXROW - %MININDEX row for a rectangular matrix.

FUNCTION  %MININDEXROW  V
TYPE INT  %MININDEXROW
TYPE REC                V

COM %MININDEXROW = %CLOCK(%MININDEX(%VEC(V)),%ROWS(V))

END       %MININDEXROW

********************************************************************************

*   %MAXINDEXCOL - %MAXINDEX column for a rectangular matrix.

FUNCTION  %MAXINDEXCOL  V
TYPE INT  %MAXINDEXCOL
TYPE REC                V

COM %MAXINDEXCOL = %MAXINDEXROW(TR(V))

END       %MAXINDEXCOL

********************************************************************************

*   %MININDEXCOL - %MININDEX column for a rectangular matrix.

FUNCTION  %MININDEXCOL  V
TYPE INT  %MININDEXCOL
TYPE REC                V

COM %MININDEXCOL = %MININDEXROW(TR(V))

END       %MININDEXCOL

********************************************************************************

*   %BINRIGHT - %BIN with right closed intervals.
*               Returns n = %BINRIGHT(x,V) where V(n-1) < x <= V(n)

FUNCTION  %BINRIGHT  X  V
TYPE INT  %BINRIGHT
TYPE REA             X
TYPE VEC                V

COM %BINRIGHT = FIX(%IF(X>%MAXVALUE(V),0,%BIN(X,V)+%IF(X==V(%BIN(X,V)),0,1)))

END %BINRIGHT

********************************************************************************

*   %DOMINANCE - Checks the dominance of two curves (series = ordinates).
*                0 No dominance
*                1 if Y1 (strong) dominates Y2
*                2 if Y2 (strong) dominates Y1
*                (Strong) dominance is defined as Y1>=Y2, with at least one strict inequality.

FUNCTION  %DOMINANCE  Y1  Y2
TYPE INT  %DOMINANCE
TYPE SER              Y1  Y2

LOCA INT N
LOCA SER Z

INQ(REG) * N
# Y1 Y2

SET Z = Y1 - Y2
IF      (%POSITIVE(Z)+%NZEROS(Z)==N).AND.%NZEROS(Z)<N;   COM %DOMINANCE = 1
ELSE IF (%NEGATIVE(Z)+%NZEROS(Z)==N).AND.%NZEROS(Z)<N;   COM %DOMINANCE = 2
ELSE                                                 ;   COM %DOMINANCE = 0

END %DOMINANCE

********************************************************************************

*   %PADDING - Pads an integer with zeros to the left. Type: String
*              N is the length of the returned string.

FUNCTION  %PADDING  N  I
TYPE STR  %PADDING
TYPE INT            N  I

COM %PADDING = %STRREP('0',N-%STRLEN(%STRING(I)))+%STRING(I)

END %PADDING

********************************************************************************

*   %PROV2CA - Returns, as INTEGER, the CCAA code from a PROVINCIA code
*              It is assumed that the order is the one in the EPF's

FUNCTION  %PROV2CA  P
TYPE INT  %PROV2CA  P

IF      P==4.OR.P==11.OR.P==14.OR.P==18.OR.P==21.OR.P==23.OR.P==29.OR.P==41
   COM %PROV2CA =  1
ELSE IF P==22.OR.P==44.OR.P==50
   COM %PROV2CA =  2
ELSE IF P==33
   COM %PROV2CA =  3
ELSE IF P==7
   COM %PROV2CA =  4
ELSE IF P==35.OR.P==38
   COM %PROV2CA =  5
ELSE IF P==39
   COM %PROV2CA =  6
ELSE IF P==5.OR.P==9.OR.P==24.OR.P==34.OR.P==37.OR.P==40.OR.P==42.OR.P==47.OR.P==49
   COM %PROV2CA =  7
ELSE IF P==2.OR.P==13.OR.P==16.OR.P==19.OR.P==45
   COM %PROV2CA =  8
ELSE IF P==8.OR.P==17.OR.P==25.OR.P==43
   COM %PROV2CA =  9
ELSE IF P==3.OR.P==12.OR.P==46
   COM %PROV2CA = 10
ELSE IF P==6.OR.P==10
   COM %PROV2CA = 11
ELSE IF P==15.OR.P==27.OR.P==32.OR.P==36
   COM %PROV2CA = 12
ELSE IF P==28
   COM %PROV2CA = 13
ELSE IF P==30
   COM %PROV2CA = 14
ELSE IF P==31
   COM %PROV2CA = 15
ELSE IF P==1.OR.P==20.OR.P==48
   COM %PROV2CA = 16
ELSE IF P==26
   COM %PROV2CA = 17
ELSE IF P==51.OR.P==52
   COM %PROV2CA = 18
ELSE
   COM %PROV2CA = 0

END    %PROV2CA

********************************************************************************

*   List of functions

*   %SUMS          - Sum the elements of a series
*   %BLOCKDIAGSYM  - Block diagonal symmetric matrix from a vector of symmetrics
*   %AGREGA        - Convert this PROC into a FUNCTION (pending)
*   %DUPLICA       - Operator to duplicate rows of a matrix.
*   %COMPRESSV     - Same as %COMPRESS(A,V) but with A type VEC[LAB]
*   %STRCOMPRESSV  - Same as %COMPRESSV(A,V) but with A type VEC[STR]
*   %CPUTIMEHMS    - Same as %CPUTIME() but in h:mm:ss format
*   %INV           - Inverse of a Real Number.
*   %NAN           - Number of NA in a Series.
*   %NEGATIVE      - Number of Negative Values in a Series.
*   %POSITIVE      - Number of Positive Values in a Series.
*   %NUMVALUE      - Number of Values in a Series equal to VALUE.
*   %NZEROS        - Number of ZERO´s in a Series.
*   %NONES         - Number of ONE´s in a Series.
*   %NLT           - Number of Values in a Series LOWER THAN to VALUE.
*   %NLE           - Number of Values in a Series LOWER OR EQUAL THAN to VALUE.
*   %NGT           - Number of Values in a Series GREATER THAN to VALUE.
*   %NGE           - Number of Values in a Series GREATER OR EQUAL THAN to VALUE.
*   %NEQV          - Number of identical elements in a vector.
*   %maxindexv     - Vector(integer) with the positions of the maximum value of a vector
*   %minindexv     - Vector(integer) with the positions of the minimum value of a vector
*   %INTEGER       - If a REAL is an INTEGER, 1, or NOT, 0.
*   %IEVEN         - If an INTEGER is EVEN, 1, or NOT, 0.
*   %IODD          - If an INTEGER is ODD, 1, or NOT, 0.
*   %EVEN          - If a REAL is an EVEN INTEGER, 1, or NOT, 0.
*   %ODD           - If a REAL is an ODD INTEGER, 1, or NOT, 0.
*   %FRACV         - %FRAC for vectors.
*   %FRACM         - %FRAC for matrices (rectangular).
*   %FIXV          -  FIX  for vectors.
*   %FIXM          -  FIX  for matrices (rectangular).
*   %ROUNDV        - %ROUND for vectors.
*   %ROUNDM        - %ROUND for matrices (rectangular).
*   %UNITM         - %UNITV for matrices (rectangular).
*   %ANY           - Creates and m x n matrix with all elements equal to a given real, A.
*                    Same as %CONST(A) without dimensioning the matrix.
*   %PROPORTIONAL  - Adjust proportionally a vector V to a given quantity, S.
*   %IPROPORTIONAL - Integer version of %PROPORTIONAL: 'control rounding'
*   %DivBaseProp   - Integer version of %PROPORTIONAL: 'divisor based methods'
*   %MAXINDEXROW   - %MAXINDEX row for a rectangular matrix.
*   %MININDEXROW   - %MININDEX row for a rectangular matrix.
*   %MAXINDEXCOL   - %MAXINDEX column for a rectangular matrix.
*   %MININDEXCOL   - %MININDEX column for a rectangular matrix.
*   %BINRIGHT      - %BIN with right closed intervals.
*                    Returns n = %BINRIGHT(X,V) where V(n-1) < x <= V(n)
*   %DOMINANCE     - Checks the dominance of two curves (series = ordinates).
*   %PADDING       - Pads an integer with zeros to the left. Type: String
*   %PROV2CA       - Returns the CCAA code from a PROVINCIA code (EPF´s order)

********************************************************************************