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C Copied from Thomas Lumley's leaps 2.9 package for earth 3.2-6 to avoid
C use of external routines in earth causing complaints from CRAN check.
C Code which writes to the console has been commented out.
C Original Fortran code from Alan Miller.
C
C PROGRAM START
C
C This is the starting program for the SUBSETS package of programs.
C It forms the upper-triangular Banachiewicz factorization of the
C input data.
C Free-format input is assumed, i.e. with data fields separated by
C spaces, CR's, tabs or commas. N.B. Some Fortran compilers will
C not accept tabs and/or commas as delimiters.
C Warning: Some Fortran compilers will not allow free format input
C of character data. This program inputs the names of variables
C in free format.
C
C Latest revision - 16 August 1992
C
C Stephen Milborrow 5 Sep 2016: tweaked code to eliminate warnings:
C Warning: Obsolescent feature: DO termination statement which is
C not END DO or CONTINUE with label
C
c___c IMPLICIT NONE
c___ integer npmax, dimu
c___ parameter (npmax=50, dimu=npmax*(npmax+1)/2)
c___ DOUBLE PRECISION U(dimu), EL(0:npmax), RHS(0:npmax), X(0:npmax),
c___ + WT, ONE, Y, RESSQ
c___ CHARACTER ANS, FNAME*20, VNAME(0:npmax)*8, YNAME*8, TEXT*79
c___ INTEGER LIN, YPOS, IPOS, I, K, ICONST, NCOLS, NOBS, NRBAR, IER,
c___ + LINE1, LOUT
c___ LOGICAL OK, LSEL
c___ DATA WT/1.D0/, ONE/1.D0/, LSEL/.FALSE./
c___
c___C
c___C Set unit numbers for I/O in the data statement below.
c___C
c___ DATA LIN/5/, LOUT/6/
c___C
c___C Ask for details of the data file.
c___C
c___ 10 WRITE(LOUT, 900)
c___ 900 FORMAT(' Name of data file = ? ')
c___ READ(LIN, *) FNAME
c___C
c___C Add extension .dat if none has been entered,
c___C detected by the lack of a '.'
c___C
c___ IF (INDEX(FNAME, '.') .EQ. 0) THEN
c___ IPOS = INDEX(FNAME, ' ')
c___ FNAME = FNAME(1:IPOS-1) // '.dat'
c___ END IF
c___C
c___C Check that file exists.
c___C
c___ INQUIRE(FILE=FNAME, EXIST=OK)
c___ IF (.NOT. OK) THEN
c___ WRITE(*, 910) FNAME
c___ 910 FORMAT(' *** File not found - ', a, ' **')
c___ GO TO 10
c___ END IF
c___C
c___C Display first part of file.
c___C
c___ OPEN(10, FILE=FNAME, STATUS='OLD')
c___ WRITE(*, *)'Start of your data file follows'
c___ DO 20 I = 1, 12
c___ READ(10, '(A)') TEXT
c___ WRITE(*, '(1X, A)') TEXT
c___ 20 CONTINUE
c___ REWIND 10
c___C
c___ WRITE(LOUT, 920)
c___ 920 FORMAT(' How many X-variables ? ')
c___ READ(LIN, *) K
c___ WRITE(LOUT, 930)
c___ 930 FORMAT('+Do you want a constant in the model ? ')
c___ READ(LIN, *) ANS
c___ ICONST = 0
c___ IF(ANS.EQ.'Y' .OR. ANS .EQ. 'y') ICONST = 1
c___ NCOLS = K + ICONST
c___ NRBAR = NCOLS * (NCOLS - 1) / 2
c___C
c___C Get position of dependant variable.
c___C
c___ WRITE(*, *)'Is dependant variable at end ? (Y/N): '
c___ READ(*, *) ANS
c___ IF (ANS .EQ. 'Y' .OR. ANS .EQ. 'y') THEN
c___ YPOS = K+1
c___ ELSE
c___ WRITE(*, *)'Enter no. of position of dependant variable: '
c___ READ(*, *) YPOS
c___ IF (YPOS .LT. 1) YPOS = 1
c___ IF (YPOS .GT. K) YPOS = K + 1
c___ END IF
c___C
c___C Enter variable names, read them from file, or set defaults.
c___C
c___ VNAME(0) = 'Constant'
c___ WRITE(*, *)'Are variable names in data file ? (Y/N): '
c___ READ(*, *) ANS
c___ IF (ANS .EQ. 'Y' .OR. ANS .EQ. 'y') THEN
c___ WRITE(*, *)'Which line do names start on ? '
c___ READ(*, *) LINE1
c___ IF (LINE1 .GT. 1) THEN
c___ DO 30 I = 1, LINE1-1
c___ 30 READ(10, *)
c___ END IF
c___ IF (YPOS .GT. K) THEN
c___ READ(10, *) (VNAME(I),I=1,K), YNAME
c___ ELSE IF (YPOS .EQ. 1) THEN
c___ READ(10, *) YNAME, (VNAME(I),I=1,K)
c___ ELSE
c___ READ(10, *) (VNAME(I),I=1,YPOS-1), YNAME,
c___ + (VNAME(I),I=YPOS,K)
c___ END IF
c___ REWIND 10
c___ ELSE
c___ WRITE(*, *)'Do you want to name variables ? (Y/N): '
c___ READ(*, '(a)') ANS
c___ IF (ANS .EQ. 'Y' .OR. ANS .EQ. 'y') THEN
c___ WRITE(*, *)'Variable names may contain up to 8 characters'
c___ WRITE(*, *)'Name for dependant (Y) variable = ? '
c___ READ(*, '(a)') YNAME
c___ DO 40 I = 1, K
c___ WRITE(*, *)'Name for variable', I, ' = ? '
c___ READ(*, '(a)') VNAME(I)
c___ 40 CONTINUE
c___ ELSE
c___ DO 50 I = 1, K
c___ WRITE(VNAME(I), 940) I
c___ 940 FORMAT('XVAR(', I2, ')')
c___ 50 CONTINUE
c___ YNAME = 'Dept.var'
c___ END IF
c___ END IF
c___C
c___ WRITE(*, *)'Which line does the data start on ? '
c___ READ(*, *) LINE1
c___ IF (LINE1 .GT. 1) THEN
c___ DO 60 I = 1, LINE1-1
c___ 60 READ(10, *)
c___ END IF
c___C
c___C Read in data and form the upper-triangular factorization.
c___C
c___ IF (ICONST .EQ. 1) THEN
c___ CALL CLEAR(NCOLS, NRBAR, EL, U, RHS, RESSQ, IER)
c___ ELSE
c___ CALL CLEAR(NCOLS, NRBAR, EL(1), U, RHS(1), RESSQ, IER)
c___ END IF
c___ NOBS = 1
c___ X(0) = ONE
c___C
c___C Case is skipped if spurious characters are found (e.g. for
c___C missing values).
c___C
c___ 70 CONTINUE
c___ IF (YPOS .GT. K) THEN
c___ READ(10, *, ERR=70, END=80) (X(I),I=1,K), Y
c___ ELSE IF (YPOS .EQ. 1) THEN
c___ READ(10, *, ERR=70, END=80) Y, (X(I),I=1,K)
c___ ELSE
c___ READ(10, *, ERR=70, END=80) (X(I),I=1,YPOS-1), Y,
c___ + (X(I),I=YPOS,K)
c___ END IF
c___ IF (ICONST .EQ. 1) THEN
c___ CALL INCLUD(NCOLS, NRBAR, WT, X, Y, EL, U, RHS, RESSQ, IER)
c___ ELSE
c___ CALL INCLUD(NCOLS, NRBAR, WT, X(1), Y, EL(1), U, RHS(1), RESSQ,
c___ + IER)
c___ END IF
c___ NOBS = NOBS + 1
c___ GO TO 70
c___C
c___C Change extension to .red for output file.
c___C
c___ 80 IPOS = INDEX(FNAME, '.')
c___ FNAME(IPOS+1:IPOS+3) = 'red'
c___ NOBS = NOBS - 1
c___C
c___C Write U, EL, RHS & the residual sum of squares (RESSQ) to disk.
c___C
c___ OPEN(9, FILE=FNAME, STATUS='NEW', ACCESS='SEQUENTIAL',
c___ + FORM='UNFORMATTED')
c___ WRITE(9) K, ICONST, NCOLS, NOBS, NRBAR, LSEL
c___ IF (ICONST .EQ. 0) THEN
c___ WRITE(9) YNAME, (VNAME(I),I=1,K)
c___ WRITE(9) (U(I),I=1,NRBAR), (EL(I),I=1,K), (RHS(I),I=1,K), RESSQ
c___ ELSE
c___ WRITE(9) YNAME, (VNAME(I),I=0,K)
c___ WRITE(9) (U(I),I=1,NRBAR), (EL(I),I=0,K), (RHS(I),I=0,K), RESSQ
c___ END IF
c___ ENDFILE 9
c___C
c___ END
SUBROUTINE CLEAR(NP, NRBAR, D, RBAR, THETAB, SSERR, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
C
C Sets arrays to zero prior to calling INCLUD
C
INTEGER NP, NRBAR, IER
DOUBLE PRECISION D(NP), RBAR(*), THETAB(NP), SSERR
C
C Local variables
C
INTEGER I
DOUBLE PRECISION ZERO
C
DATA ZERO/0.D0/
C
C Some checks.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (IER .NE. 0) RETURN
C
DO 10 I = 1, NP
D(I) = ZERO
THETAB(I) = ZERO
10 CONTINUE
DO 20 I = 1, NRBAR
RBAR(I) = ZERO
20 END DO
SSERR = ZERO
RETURN
END
c___ SUBROUTINE INCLUD(NP, NRBAR, WEIGHT, XROW, YELEM, D,
c___ + RBAR, THETAB, SSERR, IER)
c___C
c___C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
c___C Modified from algorithm AS 75.1
c___C
c___C Calling this routine updates d, rbar, thetab and sserr by the
c___C inclusion of xrow, yelem with the specified weight. The number
c___C of columns (variables) may exceed the number of rows (cases).
c___C
c___C**** WARNING: The elements of XROW are overwritten ****
c___C
c___ INTEGER NP, NRBAR, IER
c___ DOUBLE PRECISION WEIGHT, XROW(NP), YELEM, D(NP), RBAR(*),
c___ + THETAB(NP), SSERR
c___C
c___C Local variables
c___C
c___ INTEGER I, K, NEXTR
c___ DOUBLE PRECISION ZERO, W, Y, XI, DI, WXI, DPI, CBAR, SBAR, XK
c___C
c___ DATA ZERO/0.D0/
c___C
c___C Some checks.
c___C
c___ IER = 0
c___ IF (NP .LT. 1) IER = 1
c___ IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
c___ IF (IER .NE. 0) RETURN
c___C
c___ W = WEIGHT
c___ Y = YELEM
c___ NEXTR = 1
c___ DO 30 I = 1, NP
c___C
c___C Skip unnecessary transformations. Test on exact zeros must be
c___C used or stability can be destroyed.
c___C
c___ IF (W .EQ. ZERO) RETURN
c___ XI = XROW(I)
c___ IF (XI .EQ. ZERO) THEN
c___ NEXTR = NEXTR + NP - I
c___ GO TO 30
c___ END IF
c___ DI = D(I)
c___ WXI = W * XI
c___ DPI = DI + WXI*XI
c___ CBAR = DI / DPI
c___ SBAR = WXI / DPI
c___ W = CBAR * W
c___ D(I) = DPI
c___ IF (I .EQ. NP) GO TO 20
c___ DO 10 K = I+1, NP
c___ XK = XROW(K)
c___ XROW(K) = XK - XI * RBAR(NEXTR)
c___ RBAR(NEXTR) = CBAR * RBAR(NEXTR) + SBAR * XK
c___ NEXTR = NEXTR + 1
c___ 10 CONTINUE
c___ 20 XK = Y
c___ Y = XK - XI * THETAB(I)
c___ THETAB(I) = CBAR * THETAB(I) + SBAR * XK
c___ 30 CONTINUE
c___C
c___C Y * SQRT(W) is now equal to Brown & Durbin's recursive residual.
c___C
c___ SSERR = SSERR + W * Y * Y
c___C
c___ RETURN
c___ END
SUBROUTINE ADD1(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST, TOL, SS,
+ SXX, SXY, SMAX, JMAX, IER)
C
C Calculate the reduction in residual sum of squares when one
C variable, selected from those in positions FIRST .. LAST, is
C added, given that the variables in positions 1 .. FIRST-1 (if
C any) are already included.
C
INTEGER NP, NRBAR, FIRST, LAST, JMAX, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), TOL(NP), SS(NP),
+ SXX(NP), SXY(NP), SMAX
C
C Local variables
C
INTEGER J, INC, POS, ROW, COL
DOUBLE PRECISION ZERO, DIAG, DY, SSQX
DATA ZERO/0.D0/
C
C Check call arguments
C
JMAX = 0
SMAX = ZERO
IER = 0
IF (FIRST .GT. NP) IER = 1
IF (LAST .LT. FIRST) IER = IER + 2
IF (FIRST .LT. 1) IER = IER + 4
IF (LAST .GT. NP) IER = IER + 8
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
IF (IER .NE. 0) RETURN
C
C Accumulate sums of squares & products from row FIRST
C
DO 10 J = FIRST, LAST
SXX(J) = ZERO
SXY(J) = ZERO
10 CONTINUE
INC = NP - LAST
POS = (FIRST-1) * (NP+NP-FIRST)/2 + 1
DO 30 ROW = FIRST, LAST
DIAG = D(ROW)
DY = DIAG * THETAB(ROW)
SXX(ROW) = SXX(ROW) + DIAG
SXY(ROW) = SXY(ROW) + DY
DO 20 COL = ROW+1, LAST
SXX(COL) = SXX(COL) + DIAG * RBAR(POS)**2
SXY(COL) = SXY(COL) + DY * RBAR(POS)
POS = POS + 1
20 CONTINUE
POS = POS + INC
30 CONTINUE
C
C Incremental sum of squares for a variable = SXY * SXY / SXX.
C Calculate whenever sqrt(SXX) > TOL for that variable.
C
DO 40 J = FIRST, LAST
SSQX = SXX(J)
IF (SQRT(SSQX) .GT. TOL(J)) THEN
SS(J) = SXY(J)**2 / SXX(J)
IF (SS(J) .GT. SMAX) THEN
SMAX = SS(J)
JMAX = J
END IF
ELSE
SS(J) = ZERO
END IF
40 CONTINUE
C
RETURN
END
SUBROUTINE BAKWRD(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST,
* VORDER, TOL, RSS, BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* WK, IWK, IER)
C
C Backward elimination from variables in positions FIRST .. LAST.
C If FIRST > 1, variables in positions prior to this are forced in.
C If LAST < NP, variables in positions after this are forced out.
C On exit, the array VORDER contains the numbers of the variables
C in the order in which they were deleted.
C
INTEGER NP, NRBAR, FIRST, LAST, VORDER(NP), NVMAX, IR, NBEST,
* IL, LOPT(IL, *), IWK, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), TOL(NP), RSS(NP),
* BOUND(NVMAX), RESS(IR, *), WK(IWK)
C
C Local variables
C
INTEGER NEED, POS, J1, JMIN, I
DOUBLE PRECISION SMIN
C
C Check call arguments
C
IER = 0
IF (FIRST .GE. NP) IER = 1
IF (LAST .LE. 1) IER = IER + 2
IF (FIRST .LT. 1) IER = IER + 4
IF (LAST .GT. NP) IER = IER + 8
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
IF (IWK .LT. 2*LAST) IER = IER + 32
IF (NBEST .GT. 0) THEN
NEED = NVMAX*(NVMAX+1)/2
IF (IR .LT. NVMAX) IER = IER + 64
IF (IL .LT. NEED) IER = IER + 128
END IF
IF (IER .NE. 0) RETURN
C
C For POS = LAST, ..., FIRST+1 call DROP1 to find best variable to
C find which variable to drop next.
C
J1 = LAST + 1
DO 20 POS = LAST, FIRST+1, -1
CALL DROP1(NP, NRBAR, D, RBAR, THETAB, FIRST, POS, TOL, WK,
* WK(J1), SMIN, JMIN, IER)
IF (JMIN .GT. 0 .AND. JMIN .LT. POS) THEN
CALL VMOVE(NP, NRBAR, VORDER, D, RBAR, THETAB, RSS, JMIN, POS,
* TOL, IER)
IF (NBEST .GT. 0) THEN
DO 10 I = JMIN, POS-1
CALL REPORT(I, RSS(I), BOUND, NVMAX, RESS, IR, NBEST, LOPT,
* IL, VORDER)
10 END DO
END IF
END IF
20 CONTINUE
C
RETURN
END
SUBROUTINE DROP1(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST, TOL,
* SS, WK, SMIN, JMIN, IER)
C
C Calculate the increase in the residual sum of squares when
C variable J is dropped from the model, for J = FIRST, ..., LAST.
C
INTEGER NP, NRBAR, FIRST, LAST, JMIN, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), TOL(NP),
* SS(LAST), WK(LAST), SMIN
C
C Local variables
C
INTEGER J, POS1, INC, POS, ROW, COL, I
DOUBLE PRECISION LARGE, ZERO, D1, RHS, D2, X
DATA LARGE/1.D+35/, ZERO/0.D0/
C
C Check call arguments
C
JMIN = 0
SMIN = LARGE
IER = 0
IF (FIRST .GT. NP) IER = 1
IF (LAST .LT. FIRST) IER = IER + 2
IF (FIRST .LT. 1) IER = IER + 4
IF (LAST .GT. NP) IER = IER + 8
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
IF (IER .NE. 0) RETURN
C
C POS1 = position of first element of row FIRST in RBAR.
C
POS1 = (FIRST - 1) * (NP + NP - FIRST)/2 + 1
INC = NP - LAST
C
C Start of outer cycle for the variable to be dropped.
C
DO 60 J = FIRST, LAST
D1 = D(J)
IF (SQRT(D1) .LT. TOL(J)) THEN
SS(J) = ZERO
SMIN = ZERO
JMIN = J
GO TO 50
END IF
RHS = THETAB(J)
IF (J .EQ. LAST) GO TO 40
C
C Copy row J of RBAR into WK.
C
POS = POS1
DO 10 I = J+1, LAST
WK(I) = RBAR(POS)
POS = POS + 1
10 CONTINUE
POS = POS + INC
C
C Lower the variable past each row.
C
DO 30 ROW = J+1, LAST
X = WK(ROW)
D2 = D(ROW)
IF (ABS(X) * SQRT(D1) .LT. TOL(ROW) .OR. D2 .EQ. ZERO) THEN
POS = POS + NP - ROW
GO TO 30
END IF
D1 = D1 * D2 / (D2 + D1 * X**2)
DO 20 COL = ROW+1, LAST
WK(COL) = WK(COL) - X * RBAR(POS)
POS = POS + 1
20 CONTINUE
RHS = RHS - X * THETAB(ROW)
POS = POS + INC
30 CONTINUE
40 SS(J) = RHS * D1 * RHS
IF (SS(J) .LT. SMIN) THEN
JMIN = J
SMIN = SS(J)
END IF
C
C Update position of first element in row of RBAR.
C
50 IF (J .LT. LAST) POS1 = POS1 + NP - J
C
60 CONTINUE
C
RETURN
END
SUBROUTINE EXADD1(IVAR, RSS, BOUND, NVMAX, RESS, IR, NBEST,
1 LOPT, IL, VORDER, SMAX, JMAX, SS, WK, LAST)
C
C Update the NBEST subsets of IVAR variables found from a call
C to subroutine ADD1.
C
INTEGER IVAR, NVMAX, IR, NBEST, IL, LOPT(IL, NBEST), LAST,
* VORDER(LAST), JMAX
DOUBLE PRECISION RSS(LAST), BOUND(NVMAX), RESS(IR, NBEST), SMAX,
* SS(LAST), WK(LAST)
C
C Local variables
C
DOUBLE PRECISION ZERO, SSBASE, SM, TEMP
INTEGER I, J, LTEMP, JM
DATA ZERO/0.D0/
C
IF (JMAX .EQ. 0) RETURN
IF (IVAR .LE. 0) RETURN
IF (IVAR .GT. NVMAX) RETURN
LTEMP = VORDER(IVAR)
JM = JMAX
SM = SMAX
IF (IVAR .GT. 1) SSBASE= RSS(IVAR-1)
IF (IVAR .EQ. 1) SSBASE= RSS(IVAR) + SS(1)
DO 10 J = IVAR, LAST
WK(J) = SS(J)
10 END DO
C
DO 30 I = 1, NBEST
TEMP = SSBASE - SM
IF (TEMP .GE. BOUND(IVAR)) GO TO 40
VORDER(IVAR) = VORDER(JM)
IF (JM .EQ. IVAR) VORDER(IVAR) = LTEMP
CALL REPORT(IVAR, TEMP, BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* VORDER)
IF (I .GE. NBEST) GO TO 40
WK(JM) = ZERO
SM = ZERO
JM = 0
DO 20 J = IVAR, LAST
IF (WK(J) .LE. SM) GO TO 20
JM = J
SM = WK(J)
20 CONTINUE
IF (JM .EQ. 0) GO TO 40
30 CONTINUE
C
C Restore VORDER(IVAR)
C
40 VORDER(IVAR) = LTEMP
C
RETURN
END
SUBROUTINE FORWRD(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST,
* VORDER, TOL, RSS, BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* WK, IWK, IER)
C
C Forward selection from variables in positions FIRST .. LAST.
C If FIRST > 1, variables in positions prior to this are forced in.
C If LAST < NP, variables in positions after this are forced out.
C On exit, the array VORDER contains the numbers of the variables
C in the order in which they were added.
C
INTEGER NP, NRBAR, FIRST, LAST, VORDER(NP), NVMAX, IR, NBEST,
* IL, LOPT(IL, *), IWK, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), TOL(NP), RSS(NP),
* BOUND(NVMAX), RESS(IR, *), WK(IWK)
C
C Local variables
C
INTEGER NEED, POS, J1, J2, JMAX
DOUBLE PRECISION SMAX
C
C Check call arguments
C
IER = 0
IF (FIRST .GE. NP) IER = 1
IF (LAST .LE. 1) IER = IER + 2
IF (FIRST .LT. 1) IER = IER + 4
IF (LAST .GT. NP) IER = IER + 8
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
IF (IWK .LT. 3*LAST) IER = IER + 32
IF (NBEST .GT. 0) THEN
NEED = NVMAX*(NVMAX+1)/2
IF (IR .LT. NVMAX) IER = IER + 64
IF (IL .LT. NEED) IER = IER + 128
END IF
IF (IER .NE. 0) RETURN
C
C For POS = FIRST .. LAST-1, call ADD1 to find best variable to put
C into position POS.
C
J1 = LAST + 1
J2 = LAST + J1
DO 10 POS = FIRST, LAST-1
CALL ADD1(NP, NRBAR, D, RBAR, THETAB, POS, LAST, TOL, WK,
* WK(J1), WK(J2), SMAX, JMAX, IER)
IF (NBEST .GT. 0) CALL EXADD1(POS, RSS, BOUND, NVMAX, RESS,
* IR, NBEST, LOPT, IL, VORDER, SMAX, JMAX, WK, WK(J1), LAST)
C
C Move the best variable to position POS.
C
IF (JMAX .GT. POS) CALL VMOVE(NP, NRBAR, VORDER, D, RBAR,
* THETAB, RSS, JMAX, POS, TOL, IER)
10 CONTINUE
C
RETURN
END
SUBROUTINE INITR(NP, NVMAX, NBEST, BOUND, RESS, IR, LOPT, IL,
* VORDER, RSS, IER)
C
C Initialize the recording of best subsets
C
INTEGER NP, NVMAX, NBEST, IR, IL, LOPT(IL,NBEST), VORDER(NP), IER
DOUBLE PRECISION BOUND(NP), RESS(IR,NBEST), RSS(NP)
C
C Local variables
C
INTEGER BEST, POS, NVAR, I
DOUBLE PRECISION LARGE
DATA LARGE/1.D+35/
C
C Check call arguments
C
IER = 0
IF (NBEST .LE. 0) IER = 1
IF (NVMAX .LE. 0) IER = IER + 2
IF (NVMAX .GT. NP) IER = IER + 4
IF (IR .LT. NVMAX) IER = IER + 8
IF (IL .LT. NVMAX*(NVMAX+1)/2) IER = IER + 16
IF (IER .NE. 0) RETURN
C
C Initialize arrays BOUND, RESS & LOPT
C
DO 30 BEST = 1, NBEST
POS = 1
DO 20 NVAR = 1, NVMAX
IF (BEST .EQ. 1) THEN
RESS(NVAR,BEST) = RSS(NVAR)
ELSE
RESS(NVAR,BEST) = LARGE
END IF
IF (BEST .EQ. NBEST) BOUND(NVAR) = RESS(NVAR,NBEST)
DO 10 I = 1, NVAR
IF (BEST .EQ. 1) THEN
LOPT(POS,BEST) = VORDER(I)
ELSE
LOPT(POS,BEST) = 0
END IF
POS = POS + 1
10 CONTINUE
20 CONTINUE
30 CONTINUE
C
RETURN
END
SUBROUTINE REPORT(POS, SSQ, BOUND, NVMAX, RESS, IR, NBEST, LOPT,
* IL, VORDER)
C
C Update record of the best NBEST subsets of POS variables, if
C necessary, using SSQ.
C
INTEGER POS, NVMAX, IR, IL, NBEST, LOPT(IL,NBEST), VORDER(POS)
DOUBLE PRECISION SSQ, BOUND(NVMAX), RESS(IR,NBEST)
C
C Local variables
C
INTEGER RANK, L0, JJ, J, LISTJ, L, I, K
DOUBLE PRECISION UNDER1, OVER1
DATA UNDER1/0.9999D0/, OVER1/1.0001D0/
C
C If residual sum of squares (SSQ) for the new subset > the
C appropriate bound, return.
C
IF (POS .GT. NVMAX) RETURN
IF (SSQ .GE. BOUND(POS)) RETURN
C
C Find rank of the new subset
C
DO 30 RANK = 1,NBEST
IF (SSQ .LE. RESS(POS,RANK)) GO TO 40
30 CONTINUE
40 L0 = (POS*(POS-1))/2
C
C Check that the subset is not a duplicate of one which has already
C been recorded.
C
JJ = RANK
IF (SSQ .GT. UNDER1*RESS(POS,RANK)) GO TO 50
IF (RANK .EQ. 1) GO TO 90
IF (SSQ .GT. OVER1*RESS(POS,RANK-1)) GO TO 90
JJ = RANK-1
50 DO 70 J = 1, POS
LISTJ = VORDER(J)
L = L0
DO 60 I = 1, POS
L = L + 1
IF (LISTJ .EQ. LOPT(L,JJ)) GO TO 70
60 CONTINUE
GO TO 80
70 CONTINUE
RETURN
80 JJ = JJ - 1
IF (JJ .GT. 0 .AND. JJ .EQ. RANK-1) GO TO 50
C
C Record new subset, and move down the other records.
C
90 IF (RANK .EQ. NBEST) GO TO 110
J = NBEST - RANK
DO 101 I = 1, J
JJ = NBEST - I
RESS(POS,JJ+1) = RESS(POS,JJ)
L = L0
DO 100 K = 1, POS
L = L + 1
LOPT(L,JJ+1) = LOPT(L,JJ)
100 END DO
101 END DO
110 RESS(POS,RANK) = SSQ
L = L0
DO 120 K = 1, POS
L = L + 1
LOPT(L,RANK) = VORDER(K)
120 CONTINUE
BOUND(POS) = RESS(POS,NBEST)
END
SUBROUTINE SEQREP(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST,
* VORDER, TOL, RSS, BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* WK, IWK, IER)
C
C Sequential replacement algorithm applied to the variables in
C positions FIRST, ..., LAST.
C If FIRST > 1, variables in positions prior to this are forced in.
C If LAST < NP, variables in positions after this are forced out.
C
INTEGER NP, NRBAR, FIRST, LAST, VORDER(NP), NVMAX, IR, NBEST,
* IL, LOPT(IL, *), IWK, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), TOL(NP), RSS(NP),
* BOUND(NVMAX), RESS(IR, *), WK(IWK)
C
C Local variables
C
INTEGER NEED, J1, J2, NV, SIZE, START, BEST, FROM, I, JMAX, COUNT
DOUBLE PRECISION ZERO, SSRED, SMAX
DATA ZERO/0.D0/
C
C Check call arguments
C
IER = 0
IF (FIRST .GE. NP) IER = 1
IF (LAST .LE. 1) IER = IER + 2
IF (FIRST .LT. 1) IER = IER + 4
IF (LAST .GT. NP) IER = IER + 8
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
IF (IWK .LT. 3*LAST) IER = IER + 32
IF (NBEST .GT. 0) THEN
NEED = NVMAX*(NVMAX+1)/2
IF (IR .LT. NVMAX) IER = IER + 64
IF (IL .LT. NEED) IER = IER + 128
END IF
IF (IER .NE. 0 .OR. NBEST .LE. 0) RETURN
C
J1 = 1 + LAST
J2 = J1 + LAST
NV = MIN(NVMAX, LAST-1)
C
C Outer loop; SIZE = current size of subset being considered.
C
DO 30 SIZE = FIRST, NV
COUNT = 0
START = FIRST
10 SSRED = ZERO
BEST = 0
FROM = 0
C
C Find the best variable from those in positions SIZE+1, ..., LAST
C to replace the one in position SIZE. Then rotate variables in
C positions START, ..., SIZE.
C
DO 20 I = START, SIZE
CALL ADD1(NP, NRBAR, D, RBAR, THETAB, SIZE, LAST, TOL, WK,
* WK(J1), WK(J2), SMAX, JMAX, IER)
IF (JMAX .GT. SIZE) THEN
CALL EXADD1(SIZE, RSS, BOUND, NVMAX, RESS, IR, NBEST,
* LOPT, IL, VORDER, SMAX, JMAX, WK, WK(J1), LAST)
IF (SMAX .GT. SSRED) THEN
SSRED = SMAX
BEST = JMAX
IF (I .LT. SIZE) THEN
FROM = SIZE + START - I - 1
ELSE
FROM = SIZE
END IF
END IF
END IF
IF (I .LT. SIZE) CALL VMOVE(NP, NRBAR, VORDER, D, RBAR,
* THETAB, RSS, SIZE, START, TOL, IER)
20 CONTINUE
C
C If any replacement reduces the RSS, make the best one.
C Move variable from position FROM to SIZE.
C Move variable from position BEST to FIRST.
C
IF (BEST .GT. SIZE) THEN
IF (FROM .LT. SIZE) CALL VMOVE(NP, NRBAR, VORDER, D, RBAR,
* THETAB, RSS, FROM, SIZE, TOL, IER)
CALL VMOVE(NP, NRBAR, VORDER, D, RBAR, THETAB, RSS, BEST,
* FIRST, TOL, IER)
COUNT = 0
START = FIRST + 1
ELSE
COUNT = COUNT + 1
END IF
C
C Repeat until COUNT = SIZE - START + 1
C
IF (COUNT .LE. SIZE - START) GO TO 10
30 CONTINUE
C
RETURN
END
SUBROUTINE XHAUST(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST,
* VORDER, TOL, RSS, BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* WK, DIMWK, IWK, DIMIWK, IER)
C
C Exhaustive search algorithm, using leaps and bounds, applied to
C the variables in positions FIRST, ..., LAST.
C If FIRST > 1, variables in positions prior to this are forced in.
C If LAST < NP, variables in positions after this are forced out.
C
INTEGER NP, NRBAR, FIRST, LAST, VORDER(NP), NVMAX, IR, NBEST,
* IL, LOPT(IL, *), DIMWK, DIMIWK, IWK(DIMIWK), IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), TOL(NP), RSS(NP),
* BOUND(NVMAX), RESS(IR, *), WK(DIMWK)
C
C Local variables
C
INTEGER NEED, J1, J2, ROW, I, JMAX, IPT, NEWPOS
DOUBLE PRECISION SMAX, TEMP
C
C Check call arguments
C
IER = 0
IF (FIRST .GE. NP) IER = 1
IF (LAST .LE. 1) IER = IER + 2
IF (FIRST .LT. 1) IER = IER + 4
IF (LAST .GT. NP) IER = IER + 8
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
IF (DIMWK .LT. 3*LAST .OR. DIMIWK .LT. NVMAX) IER = IER + 32
IF (NBEST .GT. 0) THEN
NEED = NVMAX*(NVMAX+1)/2
IF (IR .LT. NVMAX) IER = IER + 64
IF (IL .LT. NEED) IER = IER + 128
END IF
IF (IER .NE. 0 .OR. NBEST .LE. 0) RETURN
C
J1 = 1 + LAST
J2 = J1 + LAST
C
C Record subsets contained in the initial ordering, including check
C for variables which are linearly related to earlier variables.
C This should be redundant if the user has first called SING and
C INITR.
C
DO 10 ROW = FIRST, NVMAX
IF (D(ROW) .LE. TOL(ROW)) THEN
IER = -999
RETURN
END IF
CALL REPORT(ROW, RSS(ROW), BOUND, NVMAX, RESS, IR, NBEST, LOPT,
* IL, VORDER)
10 CONTINUE
C
C IWK(I) contains the upper limit for the I-th simulated DO-loop for
C I = FIRST, ..., NVMAX-1.
C IPT points to the current DO loop.
C
DO 20 I = FIRST, NVMAX
IWK(I) = LAST
20 END DO
C
C Innermost loop.
C Find best possible variable for position NVMAX from those in
C positions NVMAX, .., IWK(NVMAX).
C
30 CALL ADD1(NP, NRBAR, D, RBAR, THETAB, NVMAX, IWK(NVMAX), TOL, WK,
* WK(J1), WK(J2), SMAX, JMAX, IER)
CALL EXADD1(NVMAX, RSS, BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* VORDER, SMAX, JMAX, WK, WK(J1), IWK(NVMAX))
C
C Move to next lower numbered loop which has not been exhausted.
C
IPT = NVMAX - 1
40 IF (IPT .GE. IWK(IPT)) THEN
IPT = IPT - 1
IF (IPT .GE. FIRST) GO TO 40
RETURN
END IF
C
C Lower variable from position IPT to position IWK(IPT).
C Record any good new subsets found by the move.
C
NEWPOS = IWK(IPT)
CALL VMOVE(NP, NRBAR, VORDER, D, RBAR, THETAB, RSS, IPT, NEWPOS,
* TOL, IER)
DO 50 I = IPT, MIN(NVMAX, NEWPOS-1)
CALL REPORT(I, RSS(I), BOUND, NVMAX, RESS, IR, NBEST, LOPT, IL,
* VORDER)
50 END DO
C
C Reset all ends of loops for I >= IPT.
C
DO 60 I = IPT, NVMAX
IWK(I) = NEWPOS - 1
60 END DO
C
C If residual sum of squares for all variables above position NEWPOS
C is greater than BOUND(I), no better subsets of size I can be found
C inside the current loop.
C
TEMP = RSS(NEWPOS-1)
DO 70 I = IPT, NVMAX
IF (TEMP .GT. BOUND(I)) GO TO 80
70 CONTINUE
IF (IWK(NVMAX) .GT. NVMAX) GO TO 30
IPT = NVMAX - 1
GO TO 40
80 IPT = I - 1
IF (IPT .LT. FIRST) RETURN
GO TO 40
C
END
C
C___ SUBROUTINE EFROYM(NP, NRBAR, D, RBAR, THETAB, FIRST, LAST,
C___ * FIN, FOUT, SIZE, NOBS, VORDER, TOL, RSS, BOUND, NVMAX, RESS,
C___ * IR, NBEST, LOPT, IL, WK, IWK, IER)
C___C
C___C Efroymson's stepwise regression from variables in positions FIRST,
C___C ..., LAST. If FIRST > 1, variables in positions prior to this are
C___C forced in. If LAST < NP, variables in positions after this are
C___C forced out.
C___C
C___c IMPLICIT NONE
C___ INTEGER NP, NRBAR, FIRST, LAST, SIZE, NOBS, VORDER(NP), NVMAX, IR,
C___ * NBEST, IL, LOPT(IL, *), IWK, IER
C___ DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), FIN, FOUT,
C___ * TOL(NP), RSS(NP), BOUND(NVMAX), RESS(IR, *), WK(IWK)
C___C
C___C Local variables
C___C
C___ INTEGER NEED, J1, J2, JMAX, JMIN, I
C___ DOUBLE PRECISION ONE, EPS, ZERO, SMAX, BASE, VAR, F, SMIN
C___ DATA ONE/1.D0/, EPS/1.D-16/, ZERO/0.D0/
C___C
C___C Check call arguments
C___C
C___ IER = 0
C___ IF (FIRST .GE. NP) IER = 1
C___ IF (LAST .LE. 1) IER = IER + 2
C___ IF (FIRST .LT. 1) IER = IER + 4
C___ IF (LAST .GT. NP) IER = IER + 8
C___ IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 16
C___ IF (IWK .LT. 3*LAST) IER = IER + 32
C___ IF (NBEST .GT. 0) THEN
C___ NEED = NVMAX*(NVMAX+1)/2
C___ IF (IR .LT. NVMAX) IER = IER + 64
C___ IF (IL .LT. NEED) IER = IER + 128
C___ END IF
C___ IF (FIN .LT. FOUT .OR. FIN .LE. ZERO) IER = IER + 256
C___ IF (NOBS .LE. NP) IER = IER + 512
C___ IF (IER .NE. 0) RETURN
C___C
C___C EPS approximates the smallest quantity such that the calculated
C___C value of (1 + EPS) is > 1. It is used to test for a perfect fit
C___C (RSS = 0).
C___C
C___ 10 IF (ONE + EPS .LE. ONE) THEN
C___ EPS = EPS + EPS
C___ GO TO 10
C___ END IF
C___C
C___C SIZE = number of variables in the current subset
C___C
C___ SIZE = FIRST - 1
C___ J1 = LAST + 1
C___ J2 = LAST + J1
C___C
C___C Find the best variable to add next
C___C
C___ 20 CALL ADD1(NP, NRBAR, D, RBAR, THETAB, SIZE+1, LAST, TOL, WK,
C___ * WK(J1), WK(J2), SMAX, JMAX, IER)
C___ IF (NBEST .GT. 0) CALL EXADD1(SIZE+1, RSS, BOUND, NVMAX, RESS,
C___ * IR, NBEST, LOPT, IL, VORDER, SMAX, JMAX, WK, WK(J1), LAST)
C___ write(*, *) 'Best variable to add: ', VORDER(JMAX)
C___C
C___C Calculate 'F-to-enter' value
C___C
C___ IF (SIZE .GT. 0) THEN
C___ BASE = RSS(SIZE)
C___ ELSE
C___ BASE = RSS(1) + WK(1)
C___ END IF
C___ VAR = (BASE - SMAX) / (NOBS - SIZE - 1)
C___ IF (VAR .LT. EPS*BASE) THEN
C___ IER = -1
C___ F = ZERO
C___ ELSE
C___ F = SMAX / VAR
C___ END IF
C___ write(*, 900) F
C___ 900 format(' F-to-enter = ', f10.2)
C___C
C___C Exit if F < FIN or IER < 0 (perfect fit)
C___C
C___ IF (F .LT. FIN .OR. IER .LT. 0) RETURN
C___C
C___C Add the variable to the subset (in position FIRST).
C___C
C___ SIZE = SIZE + 1
C___ IF (JMAX .GT. FIRST) CALL VMOVE(NP, NRBAR, VORDER, D, RBAR,
C___ * THETAB, RSS, JMAX, FIRST, TOL, IER)
C___C
C___C See whether a variable entered earlier can be deleted now.
C___C
C___ 30 IF (SIZE .LE. FIRST) GO TO 20
C___ CALL DROP1(NP, NRBAR, D, RBAR, THETAB, FIRST+1, SIZE, TOL, WK,
C___ * WK(J1), SMIN, JMIN, IER)
C___ VAR = RSS(SIZE) / (NOBS - SIZE)
C___ F = SMIN / VAR
C___ write(*, 910) VORDER(JMIN), F
C___ 910 format(' F-to-drop variable: ', i4, ' = ', f10.2)
C___ IF (F .LT. FOUT) THEN
C___ CALL VMOVE(NP, NRBAR, VORDER, D, RBAR, THETAB, RSS, JMIN, SIZE,
C___ * TOL, IER)
C___ IF (NBEST .GT. 0) THEN
C___ DO 40 I = JMIN, SIZE-1
C___ 40 CALL REPORT(I, RSS(I), BOUND, NVMAX, RESS, IR, NBEST, LOPT,
C___ * IL, VORDER)
C___ END IF
C___ SIZE = SIZE - 1
C___ GO TO 30
C___ END IF
C___C
C___ GO TO 20
C___ END
SUBROUTINE REGCF(NP, NRBAR, D, RBAR, THETAB, TOL, BETA,
+ NREQ, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL 41, NO. x
C
C Modified version of AS75.4 to calculate regression coefficients
C for the first NREQ variables, given an orthogonal reduction from
C AS75.1.
C
INTEGER NP, NRBAR, NREQ, IER
DOUBLE PRECISION D(NP), RBAR(*), THETAB(NP), TOL(NP),
+ BETA(NP)
C
C Local variables
C
INTEGER I, J, NEXTR
DOUBLE PRECISION ZERO
C
DATA ZERO/0.D0/
C
C Some checks.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (NREQ .LT. 1 .OR. NREQ .GT. NP) IER = IER + 4
IF (IER .NE. 0) RETURN
C
DO 20 I = NREQ, 1, -1
IF (SQRT(D(I)) .LT. TOL(I)) THEN
BETA(I) = ZERO
D(I) = ZERO
GO TO 20
END IF
BETA(I) = THETAB(I)
NEXTR = (I-1) * (NP+NP-I)/2 + 1
DO 10 J = I+1, NREQ
BETA(I) = BETA(I) - RBAR(NEXTR) * BETA(J)
NEXTR = NEXTR + 1
10 CONTINUE
20 CONTINUE
C
RETURN
END
C
SUBROUTINE SING(NP, NRBAR, D, RBAR, THETAB, SSERR, TOL,
+ LINDEP, WORK, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
C
C Checks for singularities, reports, and adjusts orthogonal
C reductions produced by AS75.1.
C
INTEGER NP, NRBAR, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), SSERR,
+ TOL(NP), WORK(NP)
LOGICAL LINDEP(NP)
C
C Local variables
C
DOUBLE PRECISION ZERO, TEMP
INTEGER COL, POS, ROW, NC2, POS2
C
DATA ZERO/0.D0/
C
C Check input parameters
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (IER .NE. 0) RETURN
C
DO 10 COL = 1, NP
WORK(COL) = SQRT(D(COL))
10 END DO
C
DO 40 COL = 1, NP
C
C Set elements within RBAR to zero if they are less than TOL(COL) in
C absolute value after being scaled by the square root of their row
C multiplier.
C
TEMP = TOL(COL)
POS = COL - 1
DO 30 ROW = 1, COL-1
IF (ABS(RBAR(POS)) * WORK(ROW) .LT. TEMP) RBAR(POS) = ZERO
POS = POS + NP - ROW - 1
30 CONTINUE
C
C If diagonal element is near zero, set it to zero, set appropriate
C element of LINDEP, and use INCLUD to augment the projections in
C the lower rows of the orthogonalization.
C
LINDEP(COL) = .FALSE.
IF (WORK(COL) .LE. TEMP) THEN
LINDEP(COL) = .TRUE.
IER = IER - 1
IF (COL .LT. NP) THEN
NC2 = NP - COL
POS2 = POS + NP - COL + 1
CALL INCLUD(NC2, NC2*(NC2-1)/2, D(COL), RBAR(POS+1),
+ THETAB(COL), D(COL+1), RBAR(POS2), THETAB(COL+1),
+ SSERR, IER)
ELSE
SSERR = SSERR + D(COL) * THETAB(COL)**2
END IF
D(COL) = ZERO
WORK(COL) = ZERO
THETAB(COL) = ZERO
END IF
40 CONTINUE
RETURN
END
C
SUBROUTINE SSLEAPS(NP, D, THETAB, SSERR, RSS, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL. 41, NO. 2
C
C Calculates partial residual sums of squares from an orthogonal
C reduction from AS75.1.
C
INTEGER NP, IER
DOUBLE PRECISION D(NP), THETAB(NP), SSERR, RSS(NP)
C
C Local variables
C
INTEGER I
DOUBLE PRECISION SUM
C
C Some checks.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (IER .NE. 0) RETURN
C
SUM = SSERR
RSS(NP) = SSERR
DO 10 I = NP, 2, -1
SUM = SUM + D(I) * THETAB(I)**2
RSS(I-1) = SUM
10 CONTINUE
RETURN
END
C
SUBROUTINE TOLSET(NP, NRBAR, D, RBAR, TOL, WORK, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
C
C Sets up array TOL for testing for zeros in an orthogonal
C reduction formed using AS75.1.
C
INTEGER NP, NRBAR, IER
DOUBLE PRECISION D(NP), RBAR(*), TOL(NP), WORK(NP)
C
C Local variables.
C
INTEGER COL, ROW, POS
DOUBLE PRECISION EPS, SUM, ZERO
C
C EPS is a machine-dependent constant. For compilers which use
C the IEEE format for floating-point numbers, recommended values
C are 1.E-06 for single precision and 1.D-12 for double precision.
C
c changed EPS from 10^-12 to 5x10^-10 to try to fix a bug
DATA EPS/5.D-10/, ZERO/0.D0/
C
C Some checks.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (IER .NE. 0) RETURN
C
C Set TOL(I) = sum of absolute values in column I of RBAR after
C scaling each element by the square root of its row multiplier.
C
DO 10 ROW = 1, NP
WORK(ROW) = SQRT(D(ROW))
10 END DO
DO 30 COL = 1, NP
POS = COL - 1
IF (COL .LE. NP) THEN
SUM = WORK(COL)
ELSE
SUM = ZERO
END IF
DO 20 ROW = 1, MIN(COL-1, NP)
SUM = SUM + ABS(RBAR(POS)) * WORK(ROW)
POS = POS + NP - ROW - 1
20 CONTINUE
TOL(COL) = EPS * SUM
30 CONTINUE
C
RETURN
END
C
SUBROUTINE PCORR(NP, NRBAR, D, RBAR, THETAB, SSERR, IN,
+ WORK, CORMAT, DIMC, YCORR, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL. 41, NO. 2
C
C Calculate partial correlations after the first IN variables
C have been forced into the regression.
C
C Auxiliary routine called: COR
C
INTEGER NP, NRBAR, IN, DIMC, IER
DOUBLE PRECISION D(NP), RBAR(*), THETAB(NP), SSERR,
+ WORK(NP), CORMAT(*), YCORR(NP)
C
C Local variables.
C
INTEGER START, IN1, I
DOUBLE PRECISION ZERO
C
DATA ZERO/0.D0/
C
C Some checks.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (IN .LT. 0 .OR. IN .GT. NP-1) IER = IER + 4
IF (DIMC .LT. (NP-IN)*(NP-IN-1)/2) IER = IER + 8
IF (IER .NE. 0) RETURN
C
START = IN * (NP+NP-IN-1)/2 + 1
IN1 = IN + 1
CALL COR(NP-IN, D(IN1), RBAR(START), THETAB(IN1),
+ SSERR, WORK, CORMAT, YCORR)
C
C Check for zeros.
C
DO 10 I = 1, NP-IN
IF (WORK(I) .LE. ZERO) IER = -I
10 CONTINUE
C
RETURN
END
C
SUBROUTINE COR(NP, D, RBAR, THETAB, SSERR, WORK, CORMAT,
+ YCORR)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL. 41, NO. 2
C
C Calculate correlations from an orthogonal reduction. This
C routine will usually be called from PCORR, which will have
C removed the appropriate number of rows at the start.
C
INTEGER NP
DOUBLE PRECISION D(NP), RBAR(*), THETAB(NP), SSERR,
+ WORK(NP), CORMAT(*), YCORR(NP)
C
C Local variables.
C
INTEGER ROW, POS, COL1, POS1, COL2, POS2, DIFF
DOUBLE PRECISION SUMY, SUM, ZERO
C
DATA ZERO/0.D0/
C
C Process by columns, including the projections of the dependent
C variable (THETAB).
C
SUMY = SSERR
DO 10 ROW = 1, NP
SUMY = SUMY + D(ROW) * THETAB(ROW)**2
10 END DO
SUMY = SQRT(SUMY)
POS = NP*(NP-1)/2
DO 70 COL1 = NP, 1, -1
C
C Calculate the length of column COL1.
C
SUM = D(COL1)
POS1 = COL1 - 1
DO 20 ROW = 1, MIN(COL1-1, NP)
SUM = SUM + D(ROW) * RBAR(POS1)**2
POS1 = POS1 + NP - ROW - 1
20 CONTINUE
WORK(COL1) = SQRT(SUM)
C
C If SUM = 0, set all correlations with this variable to zero.
C
IF (SUM .EQ. ZERO) THEN
YCORR(COL1) = ZERO
DO 30 COL2 = NP, COL1+1, -1
CORMAT(POS) = ZERO
POS = POS - 1
30 CONTINUE
GO TO 70
END IF
C
C Form cross-products, then divide by product of column lengths.
C
SUM = D(COL1) * THETAB(COL1)
POS1 = COL1 - 1
DO 40 ROW = 1, MIN(COL1-1, NP)
SUM = SUM + D(ROW) * RBAR(POS1) * THETAB(ROW)
POS1 = POS1 + NP - ROW - 1
40 CONTINUE
YCORR(COL1) = SUM / (SUMY * WORK(COL1))
C
DO 60 COL2 = NP, COL1+1, -1
IF (WORK(COL2) .GT. ZERO) THEN
POS1 = COL1 - 1
POS2 = COL2 - 1
DIFF = COL2 - COL1
SUM = ZERO
DO 50 ROW = 1, MIN(COL1-1, NP)
SUM = SUM + D(ROW) * RBAR(POS1) * RBAR(POS2)
POS1 = POS1 + NP - ROW - 1
POS2 = POS1 + DIFF
50 CONTINUE
SUM = SUM + D(COL1) * RBAR(POS2)
CORMAT(POS) = SUM / (WORK(COL1) * WORK(COL2))
ELSE
CORMAT(POS) = ZERO
END IF
POS = POS - 1
60 CONTINUE
70 CONTINUE
C
RETURN
END
C
SUBROUTINE VMOVE(NP, NRBAR, VORDER, D, RBAR, THETAB,
+ RSS, FROM, TO, TOL, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
C
C Move variable from position FROM to position TO in an
C orthogonal reduction produced by AS75.1.
C
INTEGER NP, NRBAR, VORDER(NP), FROM, TO, IER
DOUBLE PRECISION D(NP), RBAR(*), THETAB(NP), RSS(NP),
+ TOL(NP)
C
C Local variables
C
DOUBLE PRECISION ZERO, D1, D2, X, ONE, D1NEW, D2NEW, CBAR, SBAR, Y
INTEGER M, FIRST, LAST, INC, M1, M2, MP1, COL, POS, ROW
C
DATA ZERO/0.D0/, ONE/1.D0/
C
C Check input parameters
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (FROM .LT. 1 .OR. FROM .GT. NP) IER = IER + 4
IF (TO .LT. 1 .OR. TO .GT. NP) IER = IER + 8
IF (IER .NE. 0) RETURN
C
IF (FROM .EQ. TO) RETURN
C
IF (FROM .LT. TO) THEN
FIRST = FROM
LAST = TO - 1
INC = 1
ELSE
FIRST = FROM - 1
LAST = TO
INC = -1
END IF
DO 70 M = FIRST, LAST, INC
C
C Find addresses of first elements of RBAR in rows M and (M+1).
C
M1 = (M-1)*(NP+NP-M)/2 + 1
M2 = M1 + NP - M
MP1 = M + 1
IF (M .LE. NP) THEN
D1 = D(M)
IF (MP1 .LE. NP) THEN
D2 = D(MP1)
ELSE
D2 = ZERO
END IF
ELSE
D1 = ZERO
D2 = ZERO
END IF
C
C Special cases.
C
IF (D1 .EQ. ZERO .AND. D2 .EQ. ZERO) GO TO 40
X = RBAR(M1)
IF (ABS(X) * SQRT(D1) .LT. TOL(MP1)) THEN
X = ZERO
END IF
IF (D1 .EQ. ZERO .OR. X .EQ. ZERO) THEN
D(M) = D2
D(MP1) = D1
RBAR(M1) = ZERO
DO 10 COL = M+2, NP
M1 = M1 + 1
X = RBAR(M1)
RBAR(M1) = RBAR(M2)
RBAR(M2) = X
M2 = M2 + 1
10 CONTINUE
X = THETAB(M)
THETAB(M) = THETAB(MP1)
THETAB(MP1) = X
GO TO 40
ELSE IF (D2 .EQ. ZERO) THEN
D(M) = D1 * X**2
RBAR(M1) = ONE / X
DO 20 COL = M+2, NP
M1 = M1 + 1
RBAR(M1) = RBAR(M1) / X
20 CONTINUE
THETAB(M) = THETAB(M) / X
GO TO 40
END IF
C
C Planar rotation in regular case.
C
D1NEW = D2 + D1*X**2
CBAR = D2 / D1NEW
SBAR = X * D1 / D1NEW
D2NEW = D1 * CBAR
D(M) = D1NEW
D(MP1) = D2NEW
RBAR(M1) = SBAR
DO 30 COL = M+2, NP
M1 = M1 + 1
Y = RBAR(M1)
RBAR(M1) = CBAR*RBAR(M2) + SBAR*Y
RBAR(M2) = Y - X*RBAR(M2)
M2 = M2 + 1
30 CONTINUE
Y = THETAB(M)
THETAB(M) = CBAR*THETAB(MP1) + SBAR*Y
THETAB(MP1) = Y - X*THETAB(MP1)
C
C Swap columns M and (M+1) down to row (M-1).
C
40 IF (M .EQ. 1) GO TO 60
POS = M
DO 50 ROW = 1, M-1
X = RBAR(POS)
RBAR(POS) = RBAR(POS-1)
RBAR(POS-1) = X
POS = POS + NP - ROW - 1
50 CONTINUE
C
C Adjust variable order (VORDER), the tolerances (TOL) and
C the vector of residual sums of squares (RSS).
C
60 M1 = VORDER(M)
VORDER(M) = VORDER(MP1)
VORDER(MP1) = M1
X = TOL(M)
TOL(M) = TOL(MP1)
TOL(MP1) = X
RSS(M) = RSS(MP1) + D(MP1) * THETAB(MP1)**2
70 CONTINUE
C
RETURN
END
C
SUBROUTINE REORDR(NP, NRBAR, VORDER, D, RBAR, THETAB,
+ RSS, TOL, LIST, N, POS1, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
C
C Re-order the variables in an orthogonal reduction produced by
C AS75.1 so that the N variables in LIST start at position POS1,
C though will not necessarily be in the same order as in LIST.
C Any variables in VORDER before position POS1 are not moved.
C
C Auxiliary routine called: VMOVE
C
INTEGER NP, NRBAR, VORDER(NP), N, LIST(N), POS1, IER
DOUBLE PRECISION D(NP), RBAR(NRBAR), THETAB(NP), RSS(NP),
+ TOL(NP)
C
C Local variables.
C
INTEGER NEXT, I, L, J
C
C Check N.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (N .LT. 1 .OR. N .GT. NP+1-POS1) IER = IER + 4
IF (IER .NE. 0) RETURN
C
C Work through VORDER finding variables which are in LIST.
C
NEXT = POS1
I = POS1
10 L = VORDER(I)
DO 20 J = 1, N
IF (L .EQ. LIST(J)) GO TO 40
20 CONTINUE
30 I = I + 1
IF (I .LE. NP) GO TO 10
C
C If this point is reached, one or more variables in LIST has not
C been found.
C
IER = NEXT - N - 1
RETURN
C
C Variable L is in LIST; move it up to position NEXT if it is not
C already there.
C
40 IF (I .GT. NEXT) CALL VMOVE(NP, NRBAR, VORDER, D, RBAR,
+ THETAB, RSS, I, NEXT, TOL, IER)
NEXT = NEXT + 1
IF (NEXT .LT. N+POS1) GO TO 30
C
RETURN
END
SUBROUTINE INCLUD(NP, NRBAR, WEIGHT, XROW, YELEM, D,
+ RBAR, THETAB, SSERR, IER)
C
C ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2
C Modified from algorithm AS 75.1
C
C Calling this routine updates d, rbar, thetab and sserr by the
C inclusion of xrow, yelem with the specified weight. The number
C of columns (variables) may exceed the number of rows (cases).
C
C**** WARNING: The elements of XROW are overwritten ****
C
INTEGER NP, NRBAR, IER
DOUBLE PRECISION WEIGHT, XROW(NP), YELEM, D(NP), RBAR(*),
+ THETAB(NP), SSERR
C
C Local variables
C
INTEGER I, K, NEXTR
DOUBLE PRECISION ZERO, W, Y, XI, DI, WXI, DPI, CBAR, SBAR, XK
C
DATA ZERO/0.D0/
C
C Some checks.
C
IER = 0
IF (NP .LT. 1) IER = 1
IF (NRBAR .LT. NP*(NP-1)/2) IER = IER + 2
IF (IER .NE. 0) RETURN
C
W = WEIGHT
Y = YELEM
NEXTR = 1
DO 30 I = 1, NP
C
C Skip unnecessary transformations. Test on exact zeros must be
C used or stability can be destroyed.
C
IF (W .EQ. ZERO) RETURN
XI = XROW(I)
IF (XI .EQ. ZERO) THEN
NEXTR = NEXTR + NP - I
GO TO 30
END IF
DI = D(I)
WXI = W * XI
DPI = DI + WXI*XI
CBAR = DI / DPI
SBAR = WXI / DPI
W = CBAR * W
D(I) = DPI
IF (I .EQ. NP) GO TO 20
DO 10 K = I+1, NP
XK = XROW(K)
XROW(K) = XK - XI * RBAR(NEXTR)
RBAR(NEXTR) = CBAR * RBAR(NEXTR) + SBAR * XK
NEXTR = NEXTR + 1
10 CONTINUE
20 XK = Y
Y = XK - XI * THETAB(I)
THETAB(I) = CBAR * THETAB(I) + SBAR * XK
30 CONTINUE
C
C Y * SQRT(W) is now equal to Brown & Durbin's recursive residual.
C
SSERR = SSERR + W * Y * Y
C
RETURN
END
c___C PROGRAM SUBSET
c___C
c___C Interactive program to perform regressions on subsets of
c___C variables. Max. no. of variables, excl. constant = 50.
c___C
c___C Subroutines called:-
c___C ADD1, BAKWRD, EFROYM, XHAUST, FORWRD, EXADD1, INITR, REGCF,
c___C REORDR, LSORT, PCORR, REPORT, SEQREP, SHELL, SS, TOLSET.
c___C
c___C Latest revision - 10 November 1993
c___C
c___C IMPLICIT NONE
c___ INTEGER MAXCOL, MAXSUB, MAXBST, MAXL, MAXR
c___ PARAMETER (MAXCOL=50, MAXSUB=25, MAXBST=20, MAXL=1000,
c___ + MAXR=MAXSUB*MAXBST)
c___ INTEGER UDIM, IIW, IW
c___ PARAMETER (UDIM=MAXCOL*(MAXCOL+1)/2, IIW=3*MAXCOL, IW=UDIM+IIW)
c___ CHARACTER FNAME*30, ANS, OPTION(22), VNAME(0:MAXCOL)*8, YNAME*8
c___ LOGICAL LSEL, OK
c___ INTEGER LIN, LOUT, LPR, LOPT(MAXL), IWK(IIW), K, IRTN, LINE,
c___ + ICONST, NCOLS, I1, IPOS, I, NOBS, VORDER(0:MAXCOL), IL,
c___ + NRBAR, NVMAX, NVMX, NBEST, IOPT, IER, NDF, J, NV, NB,
c___ + IPRINT, IR, L, IPROC, FIRST, LAST, SIZE, M, ILNB
c___ DOUBLE PRECISION U(UDIM), EL(0:MAXCOL), RHS(0:MAXCOL), RESSQ,
c___ + SSQ(0:MAXCOL), TOL(0:MAXCOL), BOUND(MAXSUB), RESS(MAXR),
c___ + WK(IW), TEMP, FIN, FOUT
c___ REAL VAR
c___ DATA OPTION/'C', 'c', 'F', 'f', 'B', 'b', 'R', 'r', 'E', 'e',
c___ + 'P', 'p', 'I', 'i', 'O', 'o', 'L', 'l', 'X', 'x', 'Q', 'q'/
c___C
c___C Set unit numbers for I/O in LIN & LOUT below.
c___C
c___ DATA LIN/5/, LOUT/6/
c___C
c___C Ask for name of the data set.
c___C
c___ 10 WRITE(LOUT,9000)
c___ 9000 FORMAT(' Enter name of .RED file for data (e.g. B:myfile): ')
c___ READ(LIN,8000) FNAME
c___ 8000 FORMAT(A)
c___C
c___C Add the .RED extension if necessary.
c___C
c___ IF (INDEX(FNAME, '.RED') .EQ. 0) THEN
c___ IPOS = INDEX(FNAME, ' ')
c___ IF (IPOS .EQ. 0 .OR. IPOS .GT. 11) THEN
c___ WRITE(LOUT, 9010) FNAME
c___ 9010 FORMAT(' ** Illegal filename entered - ', A, ' **')
c___ GO TO 10
c___ END IF
c___ FNAME(IPOS: IPOS+3) = '.RED'
c___ END IF
c___C
c___C Check that file exists.
c___C
c___ INQUIRE(FILE=FNAME, EXIST=OK)
c___ IF (.NOT. OK) THEN
c___ WRITE(LOUT, 9020) FNAME
c___ 9020 FORMAT(' ** File not found - ', A, ' **')
c___ GO TO 10
c___ END IF
c___ OPEN(9, FILE=FNAME, STATUS='OLD', ACCESS='SEQUENTIAL',
c___ + FORM='UNFORMATTED')
c___C
c___C Read contents of file.
c___C
c___ READ(9) K, ICONST, NCOLS, NOBS, NRBAR, LSEL
c___ IF (ICONST .EQ. 0) THEN
c___ READ(9) YNAME, (VNAME(I),I=1,K)
c___ READ(9) (U(I),I=1,NRBAR), (EL(I),I=1,K), (RHS(I),I=1,K), RESSQ
c___ ELSE
c___ READ(9) YNAME, (VNAME(I),I=0,K)
c___ READ(9) (U(I),I=1,NRBAR), (EL(I),I=0,K), (RHS(I),I=0,K), RESSQ
c___ END IF
c___ I1 = 1 + ICONST
c___ WRITE(LOUT, 9030) K, NOBS, YNAME
c___ 9030 FORMAT(' No. of predictors = ', I3, 5X, 'No. of cases = ', I5/
c___ + ' Dependant variable is ', A)
c___ WRITE(LOUT, 9930) (I, VNAME(I),I=1,K)
c___C
c___C Initially, all variables except the constant (if there is one)
c___C are considered candidates for either inclusion or exclusion
c___C
c___ FIRST = I1
c___ LAST = NCOLS
c___C
c___C Set up array VORDER.
c___C
c___ DO 30 I = 0, K
c___ VORDER(I) = I
c___ 30 CONTINUE
c___C
c___C Ask for values of NVMAX & NBEST.
c___C
c___ 50 WRITE(LOUT, 9040)
c___ 9040 FORMAT(' Enter max. size of subsets (excl. constant): ')
c___ READ(LIN, 8010) NVMAX
c___ 8010 FORMAT(I3)
c___ NVMX = NVMAX + ICONST
c___ IF(NVMX .LE. MAXBST) GO TO 70
c___ 60 WRITE(LOUT, 9050)
c___ 9050 FORMAT(' *** Too many, sorry, try again')
c___ GO TO 50
c___ 70 IL = NVMX*(NVMX + 1)/2
c___ L = MIN(MAXL/IL, MAXR/NVMX, MAXBST)
c___ WRITE(LOUT, 9060) L, NVMAX
c___ 9060 FORMAT('+How many subsets of each size to be recorded ?'/
c___ + ' Max. = ', I4, ' with NVMAX =', I3, ' : ')
c___ READ(LIN, 8010) NBEST
c___ IF(NBEST .GT. L) GO TO 60
c___C
c___C Call TOLSET, SS & INITR to initialize arrays.
c___C
c___ IF (ICONST .EQ. 1) THEN
c___ CALL TOLSET(NCOLS, NRBAR, EL, U, TOL, WK, IER)
c___ CALL SS(NCOLS, EL, RHS, RESSQ, SSQ, IER)
c___ CALL INITR(NCOLS, NVMX, NBEST, BOUND, RESS, NVMX, LOPT, IL,
c___ + VORDER, SSQ, IER)
c___ ELSE
c___ CALL TOLSET(NCOLS, NRBAR, EL(1), U, TOL(1), WK, IER)
c___ CALL SS(NCOLS, EL(1), RHS(1), RESSQ, SSQ(1), IER)
c___ CALL INITR(NCOLS, NVMX, NBEST, BOUND, RESS, NVMX, LOPT, IL,
c___ + VORDER(1), SSQ(1), IER)
c___ END IF
c___ WRITE(LOUT, 9065) NCOLS, RESSQ
c___ 9065 FORMAT(' Initially NCOLS = ', I4,' RESSQ = ', G13.5)
c___ IF (NOBS .GT. NCOLS) THEN
c___ NDF = NOBS - NCOLS
c___ VAR = RESSQ / NDF
c___ WRITE(*, 9068) VAR, NDF
c___ 9068 FORMAT(' Resid. variance estimate = ', g11.4, ' with ', i4,
c___ + ' deg. of freedom'/)
c___ END IF
c___ IPROC = 0
c___C
c___C Display menu & ask for choice.
c___C
c___ 100 WRITE(LOUT, 9070)
c___ 9070 FORMAT(' Options:-'/
c___ 1 ' C Corrlns. & partial corrlns. F Forward selection'/
c___ 2 ' B Backward elimination R Sequential replacement'/
c___ 3 ' E Efroymson stepwise P Print summary of subsets'/
c___ 4 ' I Specify IN variables O Specify OUT variables'/
c___ 5 ' L Least-squares regn.coeffs. X Exhaustive search'/
c___ 6 ' Q Quit ENTER YOUR OPTION : ')
c___ READ(LIN, *) ANS
c___C
c___C Compare ANS with currently available options.
c___C
c___ DO 110 IOPT = 1,22
c___ IF(ANS .EQ. OPTION(IOPT)) GO TO 120
c___ 110 CONTINUE
c___ WRITE(LOUT, 9080) ANS
c___ 9080 FORMAT(' Option ', A, ' not available')
c___ GO TO 100
c___ 120 L = (IOPT + 1)/2
c___C
c___C C F B R E P I O L X Q
c___ GO TO (200, 300, 400, 500, 550, 700, 800, 900, 250, 600, 850), L
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 1. Correlations.
c___C
c___ 200 WRITE(LOUT, 9200)
c___ 9200 FORMAT('+Do you want partial correlations ? (Y or N) ')
c___ NV = 0
c___ READ(LIN, *) ANS
c___ IF(ANS .EQ. 'N' .OR. ANS .EQ. 'n') GO TO 210
c___ IF(ANS .NE. 'Y' .AND. ANS .NE. 'y') GO TO 200
c___ ASSIGN 210 TO IRTN
c___ WRITE(LOUT, 9210)
c___ 9210 FORMAT(' Partial corrlns. on how many variables (excl.const.) ? ')
c___ READ(LIN, 8010) NV
c___ IF(NV .GT. 0) GO TO 1000
c___ 210 WRITE(LOUT, 9220)
c___ 9220 FORMAT('+Correlations amongst all variables (A) or with Y only',
c___ + 1X,'(Y) ? ')
c___ IOPT = 0
c___ READ(LIN, *) ANS
c___ IF(ANS .EQ. 'A' .OR. ANS .EQ. 'a') IOPT = 1
c___ NB = NV + ICONST
c___ CALL PCORR(NCOLS, NRBAR, EL, U, RHS, RESSQ, NB, WK(UDIM+NCOLS+1),
c___ + WK, IW, WK(UDIM+1), IER)
c___C
c___C Display the (partial) correlations.
c___C Correlations amongst the X-variables start at WK(1); correlations
c___C with Y start at WK(UDIM+1).
c___C
c___ CALL PRINTC(NCOLS, NB, WK, UDIM, WK(UDIM+1), VORDER, VNAME(1),
c___ + YNAME, IOPT, LOUT, IER)
c___ GO TO 100
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 9. Least - squares regression coefficients.
c___C
c___ 250 WRITE(LOUT, 9850)
c___ READ(LIN, 8010) NV
c___ ASSIGN 260 TO IRTN
c___ GO TO 1000
c___ 260 IF (ICONST .EQ. 1) THEN
c___ CALL REGCF(NCOLS, NRBAR, EL, U, RHS, TOL, WK, NV, IER)
c___ ELSE
c___ CALL REGCF(NCOLS, NRBAR, EL(1), U, RHS(1), TOL(1), WK, NV, IER)
c___ END IF
c___ IER = -IER
c___ IF(IER .NE. 0) WRITE(LOUT, 9250) IER
c___ 9250 FORMAT(' Variables linearly dependant, rank deficiency =',I4)
c___ WRITE(LOUT, 9260)(VORDER(I-ICONST),WK(I),I=1,NV)
c___ 9260 FORMAT(' Least-squares regn.coeffs.',
c___ + 7(/1X, I5, G13.5, 2X, I5, G13.5, 2X, I5, G13.5, 2X, I5, G13.5))
c___ WRITE(LOUT, 9270) SSQ(NV-ICONST)
c___ 9270 FORMAT(' Resid. sum of sq. =',G13.5/)
c___ GO TO 100
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 2. Forward selection.
c___C
c___ 300 IF (ICONST .EQ. 1) THEN
c___ CALL FORWRD(NCOLS, NRBAR, EL, U, RHS, FIRST, LAST, VORDER, TOL,
c___ + SSQ, BOUND, NVMX, RESS, NVMX, NBEST, LOPT, IL, WK, IW, IER)
c___ ELSE
c___ CALL FORWRD(NCOLS, NRBAR, EL(1), U, RHS(1), FIRST, LAST,
c___ + VORDER(1), TOL(1), SSQ(1), BOUND, NVMX, RESS, NVMX, NBEST,
c___ + LOPT, IL, WK, IW, IER)
c___ END IF
c___ NV = NVMX
c___ IF (IPROC .EQ. 2*(IPROC/2)) IPROC = IPROC + 1
c___ GO TO 1100
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 3. Backward elimination.
c___C
c___ 400 IF (ICONST .EQ. 1) THEN
c___ CALL BAKWRD(NCOLS, NRBAR, EL, U, RHS, FIRST, LAST, VORDER, TOL,
c___ + SSQ, BOUND, NVMX, RESS, NVMX, NBEST, LOPT, IL, WK, IW, IER)
c___ ELSE
c___ CALL BAKWRD(NCOLS, NRBAR, EL(1), U, RHS(1), FIRST, LAST,
c___ + VORDER(1), TOL(1), SSQ(1), BOUND, NVMX, RESS, NVMX, NBEST,
c___ + LOPT, IL, WK, IW, IER)
c___ END IF
c___ NV = LAST
c___ I = IPROC/2
c___ IF (I .EQ. 2*(I/2)) IPROC = IPROC + 2
c___ GO TO 1100
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 4. Sequential replacement.
c___C
c___ 500 IF (ICONST .EQ. 1) THEN
c___ CALL SEQREP(NCOLS, NRBAR, EL, U, RHS, FIRST, LAST, VORDER, TOL,
c___ + SSQ, BOUND, NVMX, RESS, NVMX, NBEST, LOPT, IL, WK, IW, IER)
c___ ELSE
c___ CALL SEQREP(NCOLS, NRBAR, EL(1), U, RHS(1), FIRST, LAST,
c___ + VORDER(1), TOL(1), SSQ(1), BOUND, NVMX, RESS, NVMX, NBEST,
c___ + LOPT, IL, WK, IW, IER)
c___ END IF
c___ I = IPROC/8
c___ IF (I .EQ. 2*(I/2)) IPROC = IPROC + 8
c___ NV = NVMX
c___ GO TO 1100
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 5. Efroymson (stepwise)
c___C
c___ 550 WRITE(LOUT, 9550)
c___ 9550 FORMAT(' Enter F-to-enter value : ')
c___ READ(LIN, 8550) FIN
c___ 8550 FORMAT(F10.0)
c___ WRITE(LOUT, 9560)
c___ 9560 FORMAT(' Enter F-to-remove value : ')
c___ READ(LIN, 8550) FOUT
c___ IF (ICONST .EQ. 1) THEN
c___ CALL EFROYM(NCOLS, NRBAR, EL, U, RHS, FIRST, LAST, FIN, FOUT,
c___ + SIZE, NOBS, VORDER, TOL, SSQ, BOUND, NVMX, RESS, NVMX, NBEST,
c___ + LOPT, IL, WK, IW, IER)
c___ ELSE
c___ CALL EFROYM(NCOLS, NRBAR, EL(1), U, RHS(1), FIRST, LAST, FIN,
c___ + FOUT, SIZE, NOBS, VORDER(1), TOL(1), SSQ(1), BOUND, NVMX, RESS,
c___ + NVMX, NBEST, LOPT, IL, WK, IW, IER)
c___ END IF
c___ IF (IER .NE. 0) THEN
c___ WRITE(LOUT, 9570) IER
c___ 9570 FORMAT(' Error code',I4,' returned by EFROYM')
c___ GO TO 100
c___ ELSE
c___ NV = SIZE
c___ I = IPROC/4
c___ IPROC = IPROC + 4
c___ GO TO 1100
c___ END IF
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 10. Exhaustive search.
c___C
c___ 600 IF (ICONST .EQ. 1) THEN
c___ CALL XHAUST(NCOLS, NRBAR, EL, U, RHS, FIRST, LAST, VORDER, TOL,
c___ + SSQ, BOUND, NVMX, RESS, NVMX, NBEST, LOPT, IL, WK, IW, IWK,
c___ + IIW, IER)
c___ ELSE
c___ CALL XHAUST(NCOLS, NRBAR, EL(1), U, RHS(1), FIRST, LAST,
c___ + VORDER(1), TOL(1), + SSQ(1), BOUND, NVMX, RESS, NVMX,
c___ + NBEST, LOPT, IL, WK, IW, IWK, IIW, IER)
c___ END IF
c___ IF (IPROC .LT. 16) IPROC = IPROC + 16
c___ GO TO 100
c___C
c___C-----------------------------------------------------------------------
c___C
c___C Option 6. Print summary of best subsets found so far.
c___C
c___ 700 CALL LSORT(LOPT, IL, NBEST, NVMX)
c___ L = FIRST*(FIRST-1)/2 + 1
c___ LINE = 1
c___ M = FIRST - ICONST
c___ DO 730 NV = FIRST, NVMX
c___ WRITE(LOUT,9700) M
c___ 9700 FORMAT(20X,'Best subsets found of',I3,' variables')
c___ LINE = LINE + 1
c___ DO 720 NB = 1,NBEST
c___ J = (NB-1)*NVMX + NV
c___ TEMP = RESS(J)
c___ IF(TEMP .GT. 1.E+35) GO TO 720
c___ IPOS = L
c___ DO 710 I = 1,NV
c___ J = (NB-1)*IL + IPOS
c___ IWK(I) = LOPT(J)
c___ IPOS = IPOS + 1
c___ 710 CONTINUE
c___ WRITE(LOUT,9710) TEMP,(IWK(I),I=FIRST,NV)
c___ LINE = LINE + 1 + (NV-1)/10
c___ 9710 FORMAT(' RSS =',G14.6,3X,'Variables:',10I4,4(/10X,10I4))
c___ 720 CONTINUE
c___ IF (LINE .GE. 25 - NB) THEN
c___ PAUSE
c___ LINE = 1
c___ END IF
c___ L = L + NV
c___ M = M + 1
c___ 730 CONTINUE
c___ GO TO 100
c___C
c___C----------------------------------------------------------------------
c___C
c___C Option 7. Force variables into models.
c___C
c___ 800 WRITE(LOUT, 9800)
c___ 9800 FORMAT('+How many variables, excl. constant ? ')
c___ READ(LIN, 8010) NV
c___ ASSIGN 810 TO IRTN
c___ GO TO 1000
c___ 810 GO TO 1100
c___C
c___C----------------------------------------------------------------------
c___C
c___C Option 11. Exit.
c___C
c___ 850 IF (IPROC .EQ. 0) STOP
c___ WRITE(LOUT, 9860)
c___ 9860 FORMAT(' Do you want to save the best subsets found ? (Y/N) ')
c___ READ(LIN, *) ANS
c___ IF (ANS .EQ. 'Y' .OR. ANS .EQ. 'y') THEN
c___ REWIND(9)
c___ CALL LSORT(LOPT, IL, NBEST, NVMX)
c___ READ(9) K, ICONST, NCOLS, NOBS, NRBAR, LSEL
c___ IF (ICONST .EQ. 0) THEN
c___ READ(9) YNAME, (VNAME(I),I=1,K)
c___ READ(9) (U(I),I=1,NRBAR), (EL(I),I=1,K), (RHS(I),I=1,K), RESSQ
c___ ELSE
c___ READ(9) YNAME, (VNAME(I),I=0,K)
c___ READ(9) (U(I),I=1,NRBAR), (EL(I),I=0,K), (RHS(I),I=0,K), RESSQ
c___ END IF
c___ LSEL = .TRUE.
c___ REWIND(9)
c___ ILNB = IL*NBEST
c___ IR = NVMX*NBEST
c___ WRITE(9) K, ICONST, NCOLS, NOBS, NRBAR, LSEL
c___ IF (ICONST .EQ. 0) THEN
c___ WRITE(9) YNAME, (VNAME(I),I=1,K)
c___ WRITE(9) (U(I),I=1,NRBAR), (EL(I),I=1,K), (RHS(I),I=1,K),
c___ + RESSQ
c___ ELSE
c___ WRITE(9) YNAME, (VNAME(I),I=0,K)
c___ WRITE(9) (U(I),I=1,NRBAR), (EL(I),I=0,K), (RHS(I),I=0,K),
c___ + RESSQ
c___ END IF
c___ WRITE(9) NVMAX, NBEST, IL, ILNB, IR, IPROC
c___ WRITE(9) (LOPT(L),L=1,ILNB)
c___ WRITE(9) (RESS(I),I=1,IR)
c___ END IF
c___ STOP
c___C
c___C----------------------------------------------------------------------
c___C
c___C Simulated subroutine to force variables into starting positions.
c___C NV = no. of variables to be forced in.
c___C
c___ 1000 WRITE(LOUT, 9930) (I, VNAME(I),I = 1,K)
c___ 9930 FORMAT('+Variables & their numbers:', 10(/1X, 5(I3, 1X, A8, 3X)))
c___ IF(NV .LE. 0) GO TO 100
c___ WRITE(LOUT, 9920)
c___ 9920 FORMAT(' List variable nos. : ')
c___ READ(LIN, *) (IWK(I),I = 1,NV)
c___C
c___C Find variables in VORDER which are in the input list and move up
c___C to the next available position.
c___C
c___ IF (ICONST .EQ. 1) THEN
c___ CALL REORDR(NCOLS, NRBAR, VORDER, EL, U, RHS, SSQ, TOL, IWK, NV,
c___ + 2, IER)
c___ ELSE
c___ CALL REORDR(NCOLS, NRBAR, VORDER(1), EL(1), U, RHS(1), SSQ(1),
c___ + TOL(1), IWK, NV, 1, IER)
c___ END IF
c___ NV = NV + ICONST
c___ FIRST = NV + 1
c___ GO TO IRTN,(210, 260, 810)
c___C
c___C----------------------------------------------------------------------
c___C
c___C Option 8. Force variables out of models.
c___C
c___ 900 WRITE(LOUT, 9850)
c___ 9850 FORMAT('+How many variables ? ')
c___ READ(LIN, 8010) NV
c___ WRITE(LOUT, 9920)
c___ DO 910 I = 1, NV
c___ 910 READ(LIN, *) IWK(I)
c___ LAST = NCOLS
c___ J = LAST
c___ 920 L = VORDER(J)
c___ DO 930 M = 1, NV
c___ IF(L .EQ. IWK(M)) GO TO 940
c___ 930 CONTINUE
c___ GO TO 960
c___ 940 IF(J .EQ. LAST) GO TO 950
c___ CALL VMOVE(NCOLS, NRBAR, VORDER, EL, U, RHS, SSQ, J, LAST, TOL,
c___ + IER)
c___ 950 LAST = LAST - 1
c___ IF(J .LT. FIRST) FIRST = FIRST - 1
c___ 960 J = J - 1
c___ IF(J .GT. 0) GO TO 920
c___ GO TO 100
c___C
c___C----------------------------------------------------------------------
c___C
c___C Print current order of the first NV variables and their RSS's.
c___C
c___ 1100 WRITE(LOUT, 9900)
c___ 9900 FORMAT(' Order Variable Resid.sumsq.')
c___ DO 1110 I = 1-ICONST, NV-ICONST
c___ J = VORDER(I)
c___ WRITE(LOUT, 9910) I, VNAME(J), SSQ(I)
c___ 9910 FORMAT(I5, 3X, A8, 1X, G14.6)
c___ 1110 CONTINUE
c___ GO TO 100
c___ END
c___C
c___C
c___C
c___C
SUBROUTINE LSORT(LOPT, IL, NBEST, NVMX)
C
C Sort the variable numbers in LOPT into increasing order.
C
C Latest revision - 12 February 1986
C
DIMENSION LOPT(IL, NBEST)
INTEGER COL, SIZE, TEMP, START
C
IF (NVMX .LT. 2) RETURN
DO 20 COL = 1, NBEST
TEMP = LOPT(2, COL)
IF (TEMP .GT. LOPT(3,COL)) THEN
LOPT(2,COL) = LOPT(3,COL)
LOPT(3,COL) = TEMP
END IF
IF (IL .LE. 3) GO TO 20
START = 4
DO 10 SIZE = 3, NVMX
CALL SHELL(LOPT(START,COL), SIZE)
START = START + SIZE
10 CONTINUE
20 CONTINUE
RETURN
END
C
C
C
C
SUBROUTINE SHELL(L, N)
C
C Perform a SHELL-sort on integer array L, sorting into
C increasing order.
C
C Latest revision - 12 February 1986
C
DIMENSION L(N)
INTEGER START, END, TEMP
C
INCR = N
10 INCR = INCR/3
IF (INCR .EQ. 2*(INCR/2)) INCR = INCR + 1
DO 50 START = 1, INCR
END = N
C
C TEMP contains the element being compared; IT holds its current
C location. It is compared with the elements in locations
C IT+INCR, IT+2.INCR, ... until a larger element is found. All
C smaller elements move INCR locations towards the start. After
C each time through the sequence, the END is decreased by INCR
C until END <= INCR.
C
20 I1 = START
TEMP = L(I1)
IT = I1
C
C I2 = location of element NEW to be compared with TEMP.
C Test I2 <= END.
C
30 I2 = I1 + INCR
IF (I2 .GT. END) THEN
IF (I1 .GT. IT) L(I1) = TEMP
END = END - INCR
GO TO 40
END IF
NEW = L(I2)
C
C If TEMP > NEW, move NEW to lower-numbered position.
C
IF (TEMP .GT. NEW) THEN
L(I1) = NEW
I1 = I2
GO TO 30
END IF
C
C TEMP <= NEW so do not swap.
C Use NEW as the next TEMP.
C
IF (I1 .GT. IT) L(I1) = TEMP
I1 = I2
TEMP = NEW
IT = I1
GO TO 30
C
C Repeat until END <= INCR.
C
40 IF (END .GT. INCR) GO TO 20
50 CONTINUE
C
C Repeat until INCR = 1.
C
IF (INCR .GT. 1) GO TO 10
RETURN
END
C
C
C
c___ SUBROUTINE PRINTC(NP, IN, CORMAT, DIMC, YCORR, VORDER, VNAME,
c___ + YNAME, IOPT, LOUT, IER)
c___C
c___C Print (partial) correlations calculated using PCORR.
c___C If IOPT = 0, print correlations with the Y-variable only.
c___C
c___C IMPLICIT NONE
c___ INTEGER NP, IN, DIMC, VORDER(NP), IOPT, LOUT, IER
c___ DOUBLE PRECISION CORMAT(DIMC), YCORR(NP)
c___ CHARACTER VNAME(NP)*8, YNAME*8
c___C
c___C Local variables.
c___C
c___ INTEGER NROWS, J1, J2, J, I1, I2, I, ROW, UPOS, TPOS, LAST
c___ CHARACTER TEXT*74, EMPTY*65, CHAR1*9
c___
c___ DATA EMPTY/' '/, CHAR1/' 1.0'/
c___C
c___C Check validity of arguments
c___C
c___ IER = 0
c___ IF (IN .GE. NP) IER = 1
c___ IF (NP .LE. 1) IER = IER + 2
c___ NROWS = NP - IN
c___ IF (DIMC .LE. NROWS*(NROWS-1)/2) IER = IER + 4
c___ IF (IER .NE. 0) RETURN
c___C
c___C If IOPT.NE.0 output heading
c___C
c___ IF(IOPT .EQ. 0) GO TO 30
c___ WRITE(LOUT, 900)
c___ 900 FORMAT(/5X, 'Correlation matrix')
c___ J1 = IN + 1
c___ 10 J2 = MIN(J1+6, NP)
c___ I1 = J1 - IN
c___ I2 = J2 - IN
c___ WRITE(LOUT, 910)(VNAME(VORDER(J)), J=J1,J2)
c___ 910 FORMAT(11X, 7(A8, 1X))
c___C
c___C Print correlations for rows 1 to I2, columns I1 to I2.
c___C
c___ DO 20 ROW = 1, I2
c___ TEXT = ' ' // VNAME(VORDER(ROW+IN)) // EMPTY
c___ IF (I1 .GT. ROW) THEN
c___ UPOS = (ROW-1) * (NROWS+NROWS-ROW) /2 + (I1-ROW)
c___ LAST = UPOS + I2 - I1
c___ WRITE(TEXT(12:74), '(7(F8.5,1X))')(CORMAT(I),I=UPOS,LAST)
c___ ELSE
c___ UPOS = (ROW-1) * (NROWS+NROWS-ROW) /2 + 1
c___ TPOS = 12 + 9*(ROW-I1)
c___ TEXT(TPOS:TPOS+8) = CHAR1
c___ LAST = UPOS + I2 - ROW - 1
c___ IF (ROW .LT. I2) WRITE(TEXT(TPOS+9:74), '(6(F8.5, 1X))')
c___ + (CORMAT(I),I=UPOS, LAST)
c___ END IF
c___ WRITE(LOUT, '(A)') TEXT
c___ 20 CONTINUE
c___C
c___C Move onto the next block of columns.
c___C
c___ J1 = J2 + 1
c___ IF (J1 .LE. NP) GO TO 10
c___C
c___C Correlations with the Y-variable.
c___C
c___ 30 WRITE(LOUT, 920) YNAME
c___ 920 FORMAT(/5X, 'Correlations with the dependent variable: ', A)
c___ J1 = IN + 1
c___ 40 J2 = MIN(J1+7, NP)
c___ I1 = J1 - IN
c___ I2 = J2 - IN
c___ WRITE(LOUT, 930)(VNAME(VORDER(J)), J=J1,J2)
c___ 930 FORMAT(/1X, 8(A8, 1X))
c___ WRITE(LOUT, 940)(YCORR(I),I=I1,I2)
c___ 940 FORMAT(1X, 8(F8.5, 1X))
c___ J1 = J2 + 1
c___ IF (J1 .LE. NP) GO TO 40
c___C
c___C Put extra blank line into output
c___C
c___ WRITE(LOUT, *)
c___C
c___ RETURN
c___ END
c include 'subs.for'
|