SUBROUTINE D7RPLY(UU, VV, NZ, P, QP, K, QK, SVK)
C VARIABLE-SHIFT K-POLYNOMIAL ITERATION FOR A
C QUADRATIC FACTOR CONVERGES ONLY IF THE ZEROS ARE
C EQUIMODULAR OR NEARLY SO.
C UU,VV - COEFFICIENTS OF STARTING QUADRATIC
C NZ - NUMBER OF ZERO FOUND
C
      COMMON /P77PLY/ SR, SI, U,
     1 V, A, B, C, D, A1, A2, A3, A6, A7, E, F, G,
     2 H, SZR, SZI, LZR, LZI, ETA, ARE, MRE, N, NN
C
      INTEGER N, NN
      INTEGER NZ, TYPE, I, J
C
      DOUBLE PRECISION ETA, ARE, MRE
      DOUBLE PRECISION MP, OMP, EE, RELSTP, T, ZM
C
      DOUBLE PRECISION P(1), QP(1), K(1),
     1   QK(1), SVK(1), SR, SI, U, V, A, B, C, D,
     2   A1, A2, A3, A6, A7, E, F, G, H, SZR, SZI,
     3   LZR, LZI
C
      DOUBLE PRECISION UI, VI, UU, VV
      LOGICAL TRIED
C
      NZ = 0
      TRIED = .FALSE.
      U = UU
      V = VV
      J = 0
C MAIN LOOP
   10 CALL D6RPLY(1.D0, U, V, SZR, SZI, LZR, LZI)
C RETURN IF ROOTS OF THE QUADRATIC ARE REAL AND NOT
C CLOSE TO MULTIPLE OR NEARLY EQUAL AND  OF OPPOSITE
C SIGN
      IF (DABS(DABS(SZR)-DABS(LZR)).GT..01D0*
     1   DABS(LZR)) RETURN
C EVALUATE POLYNOMIAL BY QUADRATIC SYNTHETIC DIVISION
      CALL D8RPLY(NN, U, V, P, QP, A, B)
      MP = DABS(A-SZR*B) + DABS(SZI*B)
C COMPUTE A RIGOROUS  BOUND ON THE ROUNDING ERROR IN
C EVALUTING P
      ZM = SQRT(ABS(V))
      EE = 2.*ABS(QP(1))
      T = -SZR*B
      DO 20 I=2,N
        EE = EE*ZM + ABS(QP(I))
   20 CONTINUE
      EE = EE*ZM + ABS(A)+T
      EE = (5.*MRE+4.*ARE)*EE - (5.*MRE+2.*ARE)*
     2   (ABS(A+T)+ABS(B)*ZM) +
     3   2.*ARE*ABS(T)
C ITERATION HAS CONVERGED SUFFICIENTLY IF THE
C POLYNOMIAL VALUE IS LESS THAN 20 TIMES THIS BOUND
      IF (MP.GT.20.*EE) GO TO 30
      NZ = 2
      RETURN
   30 J = J + 1
C STOP ITERATION AFTER 20 STEPS
      IF (J.GT.20) RETURN
      IF (J.LT.2) GO TO 50
      IF (RELSTP.GT..01 .OR. MP.LT.OMP .OR. TRIED)
     1   GO TO 50
C A CLUSTER APPEARS TO BE STALLING THE CONVERGENCE.
C FIVE FIXED SHIFT STEPS ARE TAKEN WITH A U,V CLOSE
C TO THE CLUSTER
      IF (RELSTP.LT.ETA) RELSTP = ETA
      RELSTP = SQRT(RELSTP)
      U = U - U*RELSTP
      V = V + V*RELSTP
      CALL D8RPLY(NN, U, V, P, QP, A, B)
      DO 40 I=1,5
        CALL D2RPLY(TYPE, K, QK)
        CALL D5RPLY(TYPE, P, QP, K, QK)
   40 CONTINUE
      TRIED = .TRUE.
      J = 0
   50 OMP = MP
C CALCULATE NEXT K POLYNOMIAL AND NEW U AND V
      CALL D2RPLY(TYPE, K, QK)
      CALL D5RPLY(TYPE, P, QP, K, QK)
      CALL D2RPLY(TYPE, K, QK)
      CALL D4RPLY(TYPE, UI, VI, P, K)
C IF VI IS ZERO THE ITERATION IS NOT CONVERGING
      IF (VI.EQ.0.D0) RETURN
      RELSTP = DABS((VI-V)/VI)
      U = UI
      V = VI
      GO TO 10
      END

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