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SUBROUTINE INITP(IFLG1,N,NUMT,KDEG,COEF,NN,MMAXT,PAR,IPAR,
& IDEG,FACV,CL,PDG,QDG,R)
C
C INITP INITIALIZES THE CONSTANTS THAT DEFINE THE POLSYS HOMOTOPY,
C INITIALIZES THE CONSTANTS THAT DEFINE THE PROJECTIVE TRANSFORMATION,
C AND SCALES THE COEFFICIENTS (IF SCALING IS SPECIFIED).
C
C ON INPUT:
C
C IFLG1 IS A FLAG THAT SPECIFIES WHETHER THE COEFFICIENTS ARE TO
C BE SCALED OR NOT AND WHETHER THE PROJECTIVE TRANSFORMATION IS TO
C BE USED OR NOT. IFLG1=A*10+B. SCALING IS SPECIFIED WHEN B=1. THE
C PROJECTIVE TRANSFORMATION IS SPECIFIED WHEN A=1. OTHERWISE, A AND/OR
C B =0. SCALING IS EVOKED BY A CALL TO THE SUBROUTINE SCLGNP. THE
C PROJECTIVE TRANSFORMATION IS EVOKED BY SETTING THE CL ARRAY EQUAL
C TO RANDOM COMPLEX NUMBERS. OTHERWISE, CL IS SET TO NOMINAL VALUES.
C
C N IS THE NUMBER OF EQUATIONS AND VARIABLES.
C
C NUMT(J) IS THE NUMBER OF TERMS IN EQUATION J, FOR J=1 TO N.
C
C KDEG(J,L,K) IS THE DEGREE OF THE L-TH VARIABLE, X(L), IN THE K-TH
C TERM OF THE J-TH EQUATION, WHERE J=1 TO N, L=1 TO N+1, AND K=1 TO
C NUMT(J). THE CASE "L=N+1" IS SPECIAL, AND KDEG IS NOT AN INPUT
C VALUE TO POLSYS , BUT RATHER IS COMPUTED IN THIS SUBROUTINE.
C
C COEF(J,K) IS THE COEFFICIENT OF THE K-TH TERM FOR THE J-TH
C EQUATION, WHERE J=1 TO N AND K=1 TO NUMT(J).
C
C NN IS THE DECLARED DIMENSION OF SEVERAL ARRAY INDICES.
C
C MMAXT IS AN UPPER BOUND FOR NUMT(J) FOR J=1 TO N.
C
C PAR AND IPAR ARE WORKSPACE ARRAYS.
C
C ON OUTPUT:
C
C IDEG(J) IS THE DEGREE OF THE J-TH EQUATION FOR J=1 TO N.
C
C FACV(J) IS THE SCALE FACTOR FOR THE J-TH VARIABLE.
C
C CL(2,1:N+1) IS AN ARRAY USED TO DEFINE THE PROJECTIVE
C TRANSFORMATION. IT IS USED IN SUBROUTINES FFUNP AND OTPUTP
C TO DEFINE THE PROJECTIVE COORDINATE, XNP1.
C
C PDG IS USED IN SUBROUTINE GFUNP TO DEFINE THE INITIAL SYSTEM,
C G(X)=0.
C
C QDG IS USED IN SUBROUTINE GFUNP TO DEFINE THE INITIAL SYSTEM,
C G(X)=0.
C
C R IS USED IN SUBROUTINE STRPTP TO GENERATE SOLUTIONS TO G(X)=0.
C
C
C DECLARATIONS OF INPUT AND OUTPUT:
INTEGER IFLG1,N,NUMT,KDEG,NN,MMAXT,IPAR,IDEG
DOUBLE PRECISION COEF,PAR,FACV,CL,PDG,QDG,R
DIMENSION NUMT(NN),KDEG(NN,NN+1,MMAXT),IDEG(N),COEF(NN,MMAXT),
& PAR(2 + 28*N + 6*N**2 + 7*N*MMAXT + 4*N**2*MMAXT),
& IPAR(42 + 2*N + N*(N+1)*MMAXT),
& FACV(N),CL(2,N+1),PDG(2,N),QDG(2,N),R(2,N)
C
C DECLARATIONS OF VARIABLES:
INTEGER I,IERR,IIDEG,J,JJ,K,L,N2,NP1
DOUBLE PRECISION P,Q,CCL,ZERO
DIMENSION P(2,10),Q(2,10),CCL(2,11)
C
ZERO=0.0
N2 =2*N
NP1=N+1
DO 15 J=1,N
IDEG(J)=0
DO 15 K=1,NUMT(J)
IIDEG=0
DO 12 L=1,N
IIDEG=IIDEG+KDEG(J,L,K)
12 CONTINUE
IF(IIDEG.GT.IDEG(J))IDEG(J)=IIDEG
15 CONTINUE
DO 25 J=1,N
DO 25 K=1,NUMT(J)
IIDEG=0
DO 22 L=1,N
IIDEG=IIDEG+KDEG(J,L,K)
22 CONTINUE
KDEG(J,NP1,K)=IDEG(J)-IIDEG
25 CONTINUE
IF ( IFLG1 .EQ. 10 .OR. IFLG1 .EQ. 00) THEN
C
C DON'T SCALE THE COEFFICIENTS. SET FACV EQUAL TO NOMINAL
C VALUES.
C
DO 30 I=1,N
FACV(I)=0.0
30 CONTINUE
ELSE
C
C SET UP THE WORKSPACE FOR SUBROUTINE SCLGNP AND CALL SCLGNP TO
C SCALE THE COEFFICIENTS.
C
C*****************************************************************
C VARIABLES THAT ARE PASSED IN ARRAY PAR.
C
C VARIABLE NAME LENGTH OFFSET
C
C 1 CCOEF N*MMAXT 1
C 2 ALPHA 4*N**2 1+N*MMAXT
C 3 BETA 2*N 1+N*MMAXT+4*N**2
C 4 RWORK N*(2*N+1) 1+N*MMAXT+4*N**2+2*N
C 5 XWORK 2*N 1+N*MMAXT+4*N**2+2*N+N*(2*N+1)
C 6 FACE N 1+N*MMAXT+4*N**2+4*N+N*(2*N+1)
C 7 COESCL N*MMAXT 1+N*MMAXT+4*N**2+5*N+N*(2*N+1)
C
C*****************************************************************
C VARIABLES THAT ARE PASSED IN ARRAY IPAR.
C
C VARIABLE NAME LENGTH OFFSET
C
C 1 NNUMT N 1
C 2 KKDEG N*(N+1)*MMAXT 1+N
C
C*****************************************************************
C
CALL SCLGNP(N,NN,MMAXT,NUMT,KDEG,0,ZERO,COEF,
& IPAR(1),
& IPAR(1+N),
& PAR(1),
& PAR(1+N*MMAXT),
& PAR(1+N*MMAXT+4*N**2),
& PAR(1+N*MMAXT+4*N**2+2*N),
& PAR(1+N*MMAXT+4*N**2+2*N+N*(2*N+1)),
& FACV,
& PAR(1+N*MMAXT+4*N**2+4*N+N*(2*N+1)),
& PAR(1+N*MMAXT+4*N**2+5*N+N*(2*N+1)),
& IERR)
C
C SET COEF EQUAL TO THE SCALED COEFFICIENTS
C
IF (IERR .EQ. 0) THEN
DO 40 J=1,N
DO 40 K=1,NUMT(J)
COEF(J,K)=PAR(N*MMAXT+4*N**2+5*N+N*(2*N+1) + J + N*(K-1))
40 CONTINUE
END IF
END IF
C
P(1, 1)= .12324754231D0
P(2, 1)= .76253746298D0
P(1, 2)= .93857838950D0
P(2, 2)=-.99375892810D0
P(1, 3)=-.23467908356D0
P(2, 3)= .39383930009D0
P(1, 4)= .83542556622D0
P(2, 4)=-.10192888288D0
P(1, 5)=-.55763522521D0
P(2, 5)=-.83729899911D0
P(1, 6)=-.78348738738D0
P(2, 6)=-.10578234903D0
P(1, 7)= .03938347346D0
P(2, 7)= .04825184716D0
P(1, 8)=-.43428734331D0
P(2, 8)= .93836289418D0
P(1, 9)=-.99383729993D0
P(2, 9)=-.40947822291D0
P(1,10)= .09383736736D0
P(2,10)= .26459172298D0
C
Q(1, 1)= .58720452864D0
Q(2, 1)= .01321964722D0
Q(1, 2)= .97884134700D0
Q(2, 2)=-.14433009712D0
Q(1, 3)= .39383737289D0
Q(2, 3)= .41543223411D0
Q(1, 4)=-.03938376373D0
Q(2, 4)=-.61253112318D0
Q(1, 5)= .39383737388D0
Q(2, 5)=-.26454678861D0
Q(1, 6)=-.00938376766D0
Q(2, 6)= .34447867861D0
Q(1, 7)=-.04837366632D0
Q(2, 7)= .48252736790D0
Q(1, 8)= .93725237347D0
Q(2, 8)=-.54356527623D0
Q(1, 9)= .39373957747D0
Q(2, 9)= .65573434564D0
Q(1,10)=-.39380038371D0
Q(2,10)= .98903450052D0
C
CCL(1, 1)=-.03485644332D0
CCL(2, 1)= .28554634336D0
CCL(1, 2)= .91453454766D0
CCL(2, 2)= .35354566613D0
CCL(1, 3)=-.36568737635D0
CCL(2, 3)= .45634642477D0
CCL(1, 4)=-.89089767544D0
CCL(2, 4)= .34524523544D0
CCL(1, 5)= .13523462465D0
CCL(2, 5)= .43534535555D0
CCL(1, 6)=-.34523544445D0
CCL(2, 6)= .00734522256D0
CCL(1, 7)=-.80004678763D0
CCL(2, 7)=-.009387123644D0
CCL(1, 8)=-.875432124245D0
CCL(2, 8)= .00045687651D0
CCL(1, 9)= .65256352333D0
CCL(2, 9)=-.12356777452D0
CCL(1,10)= .09986798321548D0
CCL(2,10)=-.56753456577D0
CCL(1,11)= .29674947394739D0
CCL(2,11)= .93274302173D0
C
C IF THE PROJECTIVE TRANSFORMATION IS TO BE USED, THEN CL IS
C SET EQUAL TO THE CCL VALUES. OTHERWISE, CL IS SET
C EQUAL TO NOMINAL VALUES.
C
IF (IFLG1 .EQ. 01 .OR. IFLG1 .EQ. 00) THEN
DO 50 I=1,2
DO 50 J=1,N
CL(I,J)=0.0
50 CONTINUE
CL(1,NP1)=1.0
CL(2,NP1)=0.0
ELSE
DO 60 J=1,NP1
JJ=MOD(J-1,11)+1
DO 60 I=1,2
CL(I,J)=CCL(I,JJ)
60 CONTINUE
END IF
C
C COMPUTE POWERS OF P AND Q, AND R=Q/P
DO 70 J=1,N
JJ=MOD(J-1,10)+1
CALL POWP(IDEG(J),P(1,JJ),PDG(1,J))
CALL POWP(IDEG(J),Q(1,JJ),QDG(1,J))
CALL DIVP(Q(1,JJ),P(1,JJ),R(1,J),IERR)
70 CONTINUE
RETURN
END
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