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SUBROUTINE WILVEC (D,O,VAL,VLOC,V,F,P,Q,R,VEC,NX,SVEC)
C
C WILKINSON EIGENVECTOR SOLUTION FOR LARGE SYM MATRICES
C
INTEGER VLOC(1),ENTRY,V2,XENTRY,PV,VECTOR,VV,V1,MCB(7),
1 SYSBUF,MCB1(7),PHIA,SVEC(1),PATH
DOUBLE PRECISION D(1),O(1),VAL(1),V(1),P(1),F(1),Q(1),R(1),
1 VEC(NX,1),VALUE,W,X,Y,Z,DLMDAS,
2 RMULT,RRMULT,SFT,SFTINV,DEPS,VMULT,ZERO,ONE
CHARACTER UFM*23,UWM*25,UIM*29
COMMON /XMSSG / UFM,UWM,UIM
COMMON /GIVN / TITLE(1),MO,T3,MR,MT1,T6,MV1,T8(3),ENTRY,T12(5),
1 RSTRT,V2,T19,XENTRY,T21(80),VCOM(30),T131(20)
COMMON /PACKX / IT1,IT2,II,JJ,INCR
COMMON /UNPAKX/ IT3,III,JJJ,INCR1
COMMON /SYSTEM/ SYSBUF,IOTPE,KSYS(52),IPREC
COMMON /REIGKR/ IOPTN
COMMON /MGIVXX/ DLMDAS
EQUIVALENCE (N ,VCOM( 1)), (PV ,VCOM( 5)),
1 (NV ,VCOM( 7)), (NRIGID,VCOM(10)),
2 (PHIA ,VCOM(12)), (NVER ,VCOM(13)),
3 (MAXITR,VCOM(15)), (ITERM ,VCOM(16))
DATA MUL3 , MCB1,MCB / 0, 0,0,0,2,2,0,0, 7*0 /
DATA ZERO , ONE / 0.0D+0, 1.0D+0 /
DATA MGIV / 4HMGIV /
C
C D = DIAGONAL TERMS OF THE TRIDIAGONAL MATRIX (N)
C O = OFF-DIAGONAL TERMS OF THE TRIDIAGONAL MATRIX (N)
C VAL = EIGENVALUES (NV)
C VLOC = ORIGINAL ORDERING OF THE EIGENVALUES (NV)
C V,F,P,Q,R= N DIMENSIONAL ARRAYS
C VEC = THE REST OF OPEN CORE
C
C MT = TRANSFORMATION TAPE
C N = ORDER OF PROBLEM
C NV = NUMBER OF EIGENVECTORS
C RSTRT
C V2 = NUMBER OF EIGENVECTORS ALREADY CLLCULATED
C VV = POINTER TO CURRENT VECTOR IN CORE VEC(1,VV)
C NM2X = MIDPOINT OF PROBLEM (SWITCH SINE SAVE TAPES)
C
C
C INITALIZE VARIABLES
C
DEPS = 1.0D-35
SFT = 1.0D+20
SFTINV= 1.0D+0/SFT
VMULT = 1.0D-02
NZ = KORSZ(SVEC)
IBUF1 = NZ - SYSBUF + 1
IBUF2 = IBUF1 - SYSBUF
IM = 1
CALL MAKMCB (MCB1,PHIA,N,2,IPREC)
IM1 = 2
NZ = IBUF2 - 1
PATH = 0
NV1 = (NZ-1)/(N+N)
IM2 = 2
NM1 = N - 1
NM2 = N - 2
NVER = 0
V2 = NRIGID
C
C REARRANGE EIGENVALUES AND EXTRACTION ORDER FOR MULTIPLE ROOTS
C TO GUARANTEE THAT THEY ARE IN SUBMATRIX ORDER FOR PURPOSES
C OF TRIAL VECTOR AND ORTHOGONOLIZATION COMPUTATIONS
C
RMULT = VMULT
RRMULT= VMULT/100.0D0
ICLOS = 0
I = NRIGID + 1
10 IF (DABS(VAL(I))+DABS(VAL(I+1)) .LT. RMULT) GO TO 20
IF (VAL(I) .EQ. ZERO) GO TO 90
IF (DABS(ONE-VAL(I)/VAL(I+1)) .GT. RRMULT) GO TO 80
20 IF (ICLOS .NE. 0) GO TO 90
ICLOS = I
GO TO 90
30 CONTINUE
DO 50 I1 = ICLOS,I
MIN = VLOC(I1)
VALUE = VAL(I1)
K = I1
DO 40 J = I1,I
IF (VLOC(J) .GE. MIN) GO TO 40
K = J
MIN = VLOC(J)
VALUE= VAL(J)
40 CONTINUE
VLOC(K) = VLOC(I1)
VAL(K) = VAL(I1)
VLOC(I1)= MIN
VAL(I1) = VALUE
50 CONTINUE
ICLOS = 0
80 IF (ICLOS .NE. 0) GO TO 30
90 I = I + 1
IF (I .LT. NV) GO TO 10
IF (ICLOS .NE. 0) GO TO 30
C
C START LOOP FOR CORE LOADS OF VECTORS
C
100 CALL KLOCK (IST)
V1 = V2 + 1
V2 = V2 + NV1
MUL2 = MUL3
MULP2= 0
MUL3 = 0
IF (NV-V2) 101,110,102
101 V2 = NV
GO TO 110
C
C SEARCH FOR MULTIPLICITIES OF EIGENVALUES V2 AND V2+1.
C
102 VV = V2
103 IF (DABS(VAL(V2))+DABS(VAL(V2+1)) .LT. RMULT) GO TO 1041
IF (DABS(ONE-VAL(V2)/VAL(V2+1)) .GT. RMULT) GO TO 110
1041 CONTINUE
L1 = VLOC(V2 )
L2 = VLOC(V2+1)
N1 = MIN0(L1,L2)
N2 = MAX0(L1,L2) - 1
DO 104 K = N1,N2
IF (O(K) .EQ. ZERO) GO TO 110
104 CONTINUE
V2 = V2 - 1
IF (V2+6.GT.N1 .AND. V2.GT.V1) GO TO 103
V2 = VV
MUL3 = 1
C
C FIND EIGENVECTORS V1 - V2.
C
110 N1 = 0
N2 = 0
NV2= V2 - V1 + 1
DO 175 VV = 1,NV2
VECTOR = V1 + VV - 1
VALUE = VAL (VECTOR)
C
C FOR MGIV METHOD, USE ORIGINAL LAMBDA COMPUTED BY QRITER
C IN EIGENVECTOR COMPUTATIONS
C
IF (IOPTN .EQ. MGIV) VALUE = 1.0D0/(VALUE + DLMDAS)
LOC = VLOC(VECTOR)
IF (LOC.GE.N1 .AND. LOC.LE.N2) GO TO 120
C
C SEARCH FOR A DECOUPLED SUBMATRIX.
C
MUL1 = 0
IF (LOC .EQ. 1) GO TO 112
DO 111 K = 2,LOC
N1 = LOC - K + 2
IF (O(N1-1) .EQ. ZERO) GO TO 113
111 CONTINUE
112 N1 = 1
113 IF (LOC .EQ. N) GO TO 115
DO 114 K = LOC,NM1
IF (O(K) .EQ. ZERO) GO TO 116
114 CONTINUE
115 N2 = N
GO TO 120
116 N2 = K
120 IF (MUL1.NE.0 .OR. MUL2.NE.0) GO TO 122
DO 121 I = 1,N
V(I) = ZERO
121 CONTINUE
IF (N1 .NE. N2) GO TO 122
V(LOC) = ONE
GO TO 152
122 N2M1 = N2 - 1
N2M2 = N2 - 2
C
C SET UP SIMULTANEOUS EQUATIONS
C
X = D(N1) - VALUE
Y = O(N1)
DO 131 K = N1,N2M1
IF (X .EQ. ZERO) GO TO 125
F(K) = -O(K)/X
GO TO 126
125 F(K) = -SFT*O(K)
126 IF (DABS(X)-DABS(O(K))) 127,128,129
C
C PIVOT.
C
127 P(K) = O(K)
Q(K) = D(K+1) - VALUE
R(K) = O(K+1)
Z =-X/P(K)
X = Z*Q(K) + Y
Y = Z*R(K)
GO TO 130
C
C DO NOT PIVOT.
C
128 IF (X .EQ. ZERO) X = SFTINV
129 P(K) = X
Q(K) = Y
R(K) = ZERO
X = D(K+1) - (VALUE+O(K)*(Y/X))
Y = O(K+1)
130 CONTINUE
131 CONTINUE
IF (MUL1.NE.0 .OR. MUL2.NE.0) GO TO 135
DO 134 K = N1,N2M1
134 V(K) = ONE
W = ONE/DSQRT(DBLE(FLOAT(N2-N1+1)))
V(N2)= ONE
C
C SOLVE FOR AN EIGENVECTOR OF THE TRIDIAGONAL MATRIX.
C
135 MUL2 = 0
MAXITR = 3
DO 150 ITER = 1,MAXITR
C
C BACK SUBSTITUTION
C
IF (X .EQ. ZERO) GO TO 136
V(N2) = V(N2)/X
GO TO 137
136 V(N2 ) = V(N2)*SFT
137 V(N2-1) = (V(N2-1) - Q(N2-1)*V(N2))/P(N2-1)
MAX = N2
IF (DABS(V(N2)) .LT. DABS(V(N2-1))) MAX = N2M1
IF (N2M2 .LT. N1) GO TO 140
DO 138 K = N1,N2M2
L = N2M2 - (K-N1)
V(L) = (V(L)-Q(L)*V(L+1) - R(L)*V(L+2))/P(L)
IF (DABS(V(L)) .GT. DABS (V(MAX))) MAX = L
138 CONTINUE
C
C NORMALIZE THE VECTOR.
C
140 Y = DABS(V(MAX))
Z = ZERO
DO 141 I = N1,N2
V(I) = V(I)/Y
IF (DABS(V(I)) .LT. DEPS) GO TO 141
Z = Z + V(I)*V(I)
141 CONTINUE
Z = DSQRT(Z)
DO 142 I = N1,N2
V(I) = V(I)/Z
142 CONTINUE
C
C CHECK CONVERGENCE OF THE LARGEST COMPONENT OF THE VECTOR.
C
Y = DABS(V(MAX))
IF (SNGL(W) .EQ. SNGL(Y)) GO TO 152
IF (ITER .EQ. MAXITR) GO TO 150
W = Y
C
C PIVOT V.
C
DO 145 I = N1,N2M1
IF (P(I) .EQ. O(I)) GO TO 144
V(I+1) = V(I+1) + V(I)*F(I)
GO TO 145
144 Z = V(I+1)
V(I+1) = V(I) + Z/F(I)
V(I ) = Z
145 CONTINUE
150 CONTINUE
C
C TOO MANY ITERATIONS.
C
C THE ACCURACY OF EIGENVECTOR XXXX CORRESPONDING TO THE EIGENVALUE
C XXXXXXX IS IN DOUBT.
C
152 DO 153 I = 1,N
VEC(I,VV) = V(I)
153 CONTINUE
C
C CHECK MULTIPLICITY OF THE NEXT EIGENVALUE IF IT IS IN THE SAME
C SUBMATRIX AS THIS ONE.
C
IF (VECTOR .EQ. V2) GO TO 160
C
C FOR MGIV METHOD, USE ADJUSTED LAMBDA COMING OUT OF QRITER
C IN THE FOLLOWING CHECKS
C
IF (DABS(VAL(VECTOR+1))+DABS(VAL(VECTOR)) .LT. RMULT) GO TO 154
IF (DABS(VAL(VECTOR+1)-VAL(VECTOR)) .GT.RMULT*DABS(VAL(VECTOR+1)))
1 GO TO 160
154 CONTINUE
L1 = VLOC(VECTOR+1)
IF (L1.LT.N1 .OR. L1.GT.N2) GO TO 160
C
C A MULTIPLICITY DOES EXIT...THE INITIAL APPROXIMATION OF THE NEXT
C EIGENVECTOR SHOULD BE ORTHOGONAL TO THE ONE JUST CALCULATED.
C
IF (MUL1 .EQ. 0) MUL1 = VV
MULP2 = MULP2 + 1
MULP3 = MULP2 + MUL1 - 1
DO 4001 KKK = N1,N2
4001 V(KKK) = ONE
DO 4003 JJJ = MUL1,MULP3
Z = ZERO
DO 4004 KK = N1,N2
DO 4005 II = N1,N2
4005 Z = Z + VEC(II,JJJ)*V(II)
4004 V(KK) = V(KK) - Z*VEC(KK,JJJ)
4003 CONTINUE
GO TO 175
C
C DOES THIS EIGENVALUE = PREVIOUS ONE(S) IN THIS SUBMATRIX
C
160 IF (MUL1 .EQ. 0) GO TO 175
C
C A MULTIPLICITY OF EIGENVALUES OCCURRED...IMPROVE THE ORTHOGONALITY
C OF THE CORRESPONDING EIGENVECTORS.
C
MULP1 = MUL1 + 1
DO 170 L = MULP1,VV
DO 161 I = N1,N2
P(I) = VEC(I,L)
Q(I) = ZERO
161 CONTINUE
LM1 = L - 1
DO 164 K = MUL1,LM1
Z = ZERO
DO 162 I = N1,N2
Z = Z + P(I)*VEC(I,K)
162 CONTINUE
DO 163 I = N1,N2
Q(I) = Q(I) + Z*VEC(I,K)
163 CONTINUE
164 CONTINUE
Z = ZERO
DO 165 K = N1,N2
Q(K) = P(K) - Q(K)
IF (DABS(Q(K)) .LT. DEPS) GO TO 165
Z = Z + Q(K)*Q(K)
165 CONTINUE
Z = DSQRT(Z)
DO 166 K = N1,N2
VEC(K,L) = Q(K)/Z
166 CONTINUE
170 CONTINUE
MUL1 = 0
MULP2 = 0
175 CONTINUE
C
C CORE IS NOW FULL OF EIGENVECTORS OF THE TRIDIAGONAL MATRIX.
C CONVERT THEM TO EIGENVECTORS OF THE ORIGINAL MATRIX.
C
IT1 = 2
IT2 = 2
JJ = N
INCR= 1
C
C IS THE ORIGINAL MATRIX A 2X2
C
IF (NM2 .EQ. 0) GO TO 186
MT = MT1
IF (PATH .NE. 0) GO TO 176
MT = MO
176 CALL GOPEN (MT,SVEC(IBUF1),IM2)
IF (PATH.EQ.0 .AND. V2.NE.NV) CALL GOPEN (MT1,SVEC(IBUF2),1)
IT3 = 2
JJJ = N
INCR1= 1
DO 185 M = 1,NM2
L1 = N - M
III = L1+ 1
IF (PATH .EQ. 0) CALL BCKREC (MT)
CALL UNPACK (*167,MT,P)
GO TO 180
167 DO 179 I = 1,M
P(I) = ZERO
179 CONTINUE
180 IF (PATH.NE.0 .OR. V2.EQ.NV) GO TO 177
II = L1+1
CALL PACK (P,MT1,MCB)
177 IF (PATH .EQ. 0) CALL BCKREC (MT)
DO 182 K = 1,M
L2 = N - K + 1
I = M - K + 1
Y = P(I)
IF (Y .EQ. ZERO) GO TO 182
X = ZERO
IF (DABS(Y) .LT. ONE) X = DSQRT(ONE-Y**2)
DO 181 VV = 1,NV2
Z = X*VEC(L1,VV) -Y*VEC(L2,VV)
VEC(L2,VV) = X*VEC(L2,VV) + Y*VEC(L1,VV)
VEC(L1,VV) = Z
181 CONTINUE
182 CONTINUE
185 CONTINUE
CALL CLOSE (MT,1)
IF (PATH .NE. 0) GO TO 186
IF (V2 .NE. NV) WRITE (IOTPE,1001) UIM,N,NV,NV1
1001 FORMAT (A29,' 2016A, WILVEC EIGENVECTOR COMPUTATIONS.', /37X,
1 'PROBLEM SIZE IS',I6,', NUMBER OF EIGENVECTORS TO BE ',
2 'RECOVERED IS',I6 , /37X,'SPILL WILL OCCUR FOR THIS ',
3 'CORE AT RECOVERY OF',I6,' EIGENVECTORS.')
PATH = 1
CALL CLOSE (MT1,1)
IM2 = 0
C
C WRITE THE EIGENVECTORS ONTO PHIA
C
186 CALL GOPEN (PHIA,SVEC(IBUF1),IM)
II = 1
IT2 = IPREC
IF (IM.NE.1 .OR. NRIGID.LE.0) GO TO 205
C
C PUT OUT ZERO VECTORS FOR RIGID BODY MODES
C
JJ = 1
DO 206 VV = 1,NRIGID
CALL PACK (ZERO,PHIA,MCB1)
206 CONTINUE
JJ = N
205 CONTINUE
IM = 3
IF (N .EQ. 1) GO TO 250
DO 192 VV = 1,NV2
CALL PACK (VEC(1,VV),PHIA,MCB1)
192 CONTINUE
250 IF (V2 .EQ. NV) IM1 = 1
CALL CLOSE (PHIA,IM1)
XENTRY = -ENTRY
C
C ANY TIME LEFT TO FIND MORE
C
CALL TMTOGO (ITIME)
CALL KLOCK (IFIN)
IF (2*(IFIN-IST) .GE. ITIME) GO TO 200
IF (V2 .NE. NV) GO TO 100
201 CALL WRTTRL (MCB1)
RETURN
C
C MAX TIME
C
200 ITERM = 3
GO TO 201
END
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