SUBROUTINE TRI3 (M,A,B,C,K,Y1,Y2,Y3,TCOS,D,W1,W2,W3)
      DIMENSION       A(1)       ,B(1)       ,C(1)       ,K(4)       ,
     1                TCOS(1)    ,Y1(1)      ,Y2(1)      ,Y3(1)      ,
     2                D(1)       ,W1(1)      ,W2(1)      ,W3(1)
C
C     SUBROUTINE TO SOLVE THREE LINEAR SYSTEMS WHOSE COMMON COEFFICIENT
C     MATRIX IS A RATIONAL FUNCTION IN THE MATRIX GIVEN BY
C
C                  TRIDIAGONAL (...,A(I),B(I),C(I),...)
C
      MM1 = M-1
      K1 = K(1)
      K2 = K(2)
      K3 = K(3)
      K4 = K(4)
      F1 = K1+1
      F2 = K2+1
      F3 = K3+1
      F4 = K4+1
      K2K3K4 = K2+K3+K4
      IF (K2K3K4 .EQ. 0) GO TO 101
      L1 = F1/F2
      L2 = F1/F3
      L3 = F1/F4
      LINT1 = 1
      LINT2 = 1
      LINT3 = 1
      KINT1 = K1
      KINT2 = KINT1+K2
      KINT3 = KINT2+K3
  101 CONTINUE
      DO 115 N=1,K1
         X = TCOS(N)
         IF (K2K3K4 .EQ. 0) GO TO 107
         IF (N .NE. L1) GO TO 103
         DO 102 I=1,M
            W1(I) = Y1(I)
  102    CONTINUE
  103    IF (N .NE. L2) GO TO 105
         DO 104 I=1,M
            W2(I) = Y2(I)
  104    CONTINUE
  105    IF (N .NE. L3) GO TO 107
         DO 106 I=1,M
            W3(I) = Y3(I)
  106    CONTINUE
  107    CONTINUE
         Z = 1./(B(1)-X)
         D(1) = C(1)*Z
         Y1(1) = Y1(1)*Z
         Y2(1) = Y2(1)*Z
         Y3(1) = Y3(1)*Z
         DO 108 I=2,M
            Z = 1./(B(I)-X-A(I)*D(I-1))
            D(I) = C(I)*Z
            Y1(I) = (Y1(I)-A(I)*Y1(I-1))*Z
            Y2(I) = (Y2(I)-A(I)*Y2(I-1))*Z
            Y3(I) = (Y3(I)-A(I)*Y3(I-1))*Z
  108    CONTINUE
         DO 109 IP=1,MM1
            I = M-IP
            Y1(I) = Y1(I)-D(I)*Y1(I+1)
            Y2(I) = Y2(I)-D(I)*Y2(I+1)
            Y3(I) = Y3(I)-D(I)*Y3(I+1)
  109    CONTINUE
         IF (K2K3K4 .EQ. 0) GO TO 115
         IF (N .NE. L1) GO TO 111
         I = LINT1+KINT1
         XX = X-TCOS(I)
         DO 110 I=1,M
            Y1(I) = XX*Y1(I)+W1(I)
  110    CONTINUE
         LINT1 = LINT1+1
         L1 = (FLOAT(LINT1)*F1)/F2
  111    IF (N .NE. L2) GO TO 113
         I = LINT2+KINT2
         XX = X-TCOS(I)
         DO 112 I=1,M
            Y2(I) = XX*Y2(I)+W2(I)
  112    CONTINUE
         LINT2 = LINT2+1
         L2 = (FLOAT(LINT2)*F1)/F3
  113    IF (N .NE. L3) GO TO 115
         I = LINT3+KINT3
         XX = X-TCOS(I)
         DO 114 I=1,M
            Y3(I) = XX*Y3(I)+W3(I)
  114    CONTINUE
         LINT3 = LINT3+1
         L3 = (FLOAT(LINT3)*F1)/F4
  115 CONTINUE
      RETURN
      END

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