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SUBROUTINE CINVPR (EED,METHOD,NFOUND)
C
C GIVEN REAL OR COMPLEX MATRICIES, CINVPR WILL SOLVE FOR ALL OF
C THE EIGENVALUES AND EIGENVECTORS WITHIN A SPECIFIED REGION
C
C DEFINITION OF INPUT AND OUTPUT PARAMETERS
C
C FILEK(7) = MATRIX CONTROL BLOCK FOR THE INPUT STIFFNESS MATRIX K
C FILEM(7) = MATRIX CONTROL BLOCK FOR THE INPUT MASS MATRIX M
C FILEB(7) = MATRIX CONTROL BLOCK FOR THE INPUT DAMPING MATRIX B
C FILELM(7)= MATRIX CONTROL BLOCK FOR THE OUTPUT EIGENVALUES
C FILEVC(7)= MATRIX CONTROL BLOCK FOR THE OUTPUT EIGENVECTORS
C DMPFIL = FILE CONTAINING THE EIGENVALUE SUMMARY
C SR1FIL- = SCRATCH FILES USED INTERNALLY
C SR0FIL
C EPS = CONVERGENCE CRITERIA
C NOREG = NUMBER OF REGIONS INPUT
C REG(1,I) = X1 FOR REGION I
C REG(2,I) = Y1 FOR REGION I
C REG(3,I) = X2 FOR REGION I
C REG(4,I) = Y2 FOR REGION I
C REG(5,I) = L1 FOR REGION I
C REG(6,I) = NO. OF DESIRED ROOTS FOR REGION I
C REG(7,I) = NO. OF ESTIMATED ROOTS IN REGION I
C
C
LOGICAL NOLEFT
INTEGER METHOD ,EED ,EIGC(2) ,PHIDLI ,
1 SWITCH ,SCRFIL ,IHEAD(10),IREG(7,1)
INTEGER NAME(2) ,FILELM ,FILEVC ,
1 REAL ,RDP ,TYPEK ,TYPEM ,
2 TYPEB ,COMFLG ,IZ(1) ,DMPFIL ,
3 TIMED ,FILEK ,T1 ,T2 ,
4 FILEB ,FILEM
REAL L ,L1 ,MAXMOD
DOUBLE PRECISION LAM1 ,DZ(1) ,MINDIA
DOUBLE PRECISION LAMBDA ,LMBDA ,DTEMP(2)
CHARACTER UFM*23
COMMON /XMSSG / UFM
COMMON /CDCMPX/ IDUM(30) ,MINDIA
COMMON /CINVPX/ FILEK(7) ,FILEM(7) ,FILEB(7) ,FILELM(7),
1 FILEVC(7) ,DMPFIL ,SCRFIL(11),NOREG ,
2 EPS ,REG(7,10),PHIDLI
COMMON /NAMES / RD ,RDREW ,WRT ,WRTREW ,
1 REW ,NOREW ,EOFNRW ,RSP ,
1 RDP
COMMON /SYSTEM/ KSYSTM(65)
COMMON /ZZZZZZ/ Z(1)
COMMON /OUTPUT/ HEAD(1)
COMMON /CINVXX/ LAMBDA(2) ,SWITCH ,COMFLG ,LMBDA(2),
1 ITER ,TIMED ,NOCHNG ,RZERO ,
2 IND ,IVECT ,KREG ,REAL ,
3 LEFT ,NORTHO ,NOROOT ,NZERO ,
4 LAM1(2) ,MAXMOD ,NODES ,NOEST ,
5 ISTART ,IND1 ,ITERX ,ISYM
EQUIVALENCE (KSYSTM(1),ISYS ) ,(IREG(1,1),REG(1,1))
EQUIVALENCE (FILEK(5) ,TYPEK) ,(FILEM(5),TYPEM) ,
1 (FILEB(5) ,TYPEB) ,(IZ(1),Z(1))
EQUIVALENCE (ANODES ,NODES) ,(ANOEST,NOEST) ,
1 (Z(1) ,DZ(1)) ,(KSYSTM(2),NOUT )
DATA IHEAD/ 0,1009,2,7*0 /
DATA EIGC / 207,2 /
DATA NAME / 4HCINV,4HPR /
DATA SIGN / 1.0 /
C
C DEFINITION OF INTERNAL PARAMETERS
C
C REAL = 0 - ALL MATRICIES ARE REAL
C 1 - AT LEAST ONE MATRIX IS COMPLEX
C NSHIFT = NO. OF SHIFT POINTS IN A REGION
C NODES = NO. OF DESIRED ROOTS IN A REGION
C NOEST = NO. OF ESTIMATED ROOTS IN A REGION
C SHIFT = INDEX OF THE CURRENT SHIFT POINT
C ISHIFT = INDEX OF THE CURRENT SHIFT POINT
C IMIN = LOWEST INDEX OF THE COMPLETED SHIFT POINTS
C IMAX = HIGHEST INDEX OF COMPLETED SHIFT POINTS
C
C FILE ALLOCATION
C
C SR1FIL CONTAINS (LAMBDA**2*M + LAMBDA*B + K)
C SR2FIL CONTAINS -(B+LAMBDA*M)
C SR3FIL CONTAINS THE LOWER TRIANGLE OF THE DECOMPOSED DYNAMIC MTRX
C SR4FIL CONTAINS THE UPPER TRIANGLE OF THE DECOMPOSED DYNAMIC MTRX
C SR5FIL IS USED AS A SCRATCH FOR CDCOMP
C SR6FIL IS USED AS A SCRATCH FOR CDCOMP
C SR7FIL IS USED AS A SCRATCH FOR CDCOMP
C SR8FIL CONTAINS THE LOWER TRIANGLE L
C SR9FIL CONTAINS THE UPPER TRIANGLE U
C SR0FIL CONTAINS THE LEFT EIGENVECTORS
C S11FIL CONTAINS -(B + LAMBDA*M)
C
C DEFINITION OF INTERNAL PARAMETERS
C
C IND = AN INDEX FOR GENERATING VARIOUS STARTING VECTORS
C ITER = TOTAL NUMBER OF ITERATIONS
C NODCMP = TOTAL NUMBER OF DECOMPOSITIONS
C NOSTRT = NUMBER OF STARTING POINTS USED
C NOMOVS = NUMBER OF TIMES A STARTING POINT HAD TO BE MOVED
C RZERO = DISTANCE FROM THE STARTING POINT TO THE CORNER OF THE
C PARALELOGRAM
C NOCHNG = COUNT OF THE NUMBER OF MOVES WHILE LOOKING FOR ONE ROO
C COMFLG = 0 -
C = 1 -
C = 2 -
C = 3 -
C = 4 -
C = 5 -
C = 6 -
C SWITCH =
C IVECT =
C KREG = 0-NO VECTORS FOUND IN SEARCH AREA YET
C 1- A VECTOR HAS BEEN FOUND IN THE SEARCH AREA
C ISING = SINGULARITY FLAG
C ITERM = REASON FOR TERMINATING
C = 1 - 2SINGULARITIES IN A ROW
C = 2 - 4 MOVES WHILE TRACKING ONE ROOT
C = 3 - ALL REGIONS COMPLETED
C = 4 - 3*NOEST FOUND
C = 5 - ALL ROOTS FOUND
C = 8 - 200 ITERATIONS WITH ONE MOVE WITHOUR CONVERGING
C TIMED = TIME TOO FORM AND DECOMPOSE THE DYNAMIC MATRIX
C LEFT = 1 - DECOMPOSE MATRIX FOR THE COMPUTATION OF THE LEFT
C EIGENVECTORS
C
CALL SSWTCH (12,IDIAG)
IND1 = 0
NZ = KORSZ(Z)
CALL KLOCK (ISTART)
IBUF = NZ - ISYS - 2
IFILE= FILELM(1)
CALL OPEN (*500,FILELM,Z(IBUF),WRTREW)
CALL CLOSE (FILELM,REW)
IFILE = FILEVC (1)
CALL OPEN (*500,FILEVC,Z(IBUF),WRTREW)
CALL CLOSE (FILEVC,REW)
CALL GOPEN (DMPFIL,Z(IBUF),WRTREW)
CALL CLOSE (DMPFIL,EOFNRW)
IFILE = SCRFIL(10)
CALL OPEN (*500,IFILE,Z(IBUF),WRTREW)
CALL CLOSE (IFILE,REW)
NOLEFT = .FALSE.
IZ(1) = 204
CALL RDTRL (IZ)
IF (IZ(1) .LT. 0) NOLEFT = .TRUE.
NORTHO = 0
NROW = 2*FILEK(3)
NROW2 = 2*NROW
ISYM = 1
IF (FILEK(1).NE.0 .AND. FILEK(4).NE.6) GO TO 2
IF (FILEM(1).NE.0 .AND. FILEM(4).NE.6) GO TO 2
IF (FILEB(1).NE.0 .AND. FILEB(4).NE.6) GO TO 2
ISYM = 0
2 CONTINUE
C
C PICK UP REGION PARAMETERS
C
CALL PRELOC (*500,Z(IBUF),EED)
CALL LOCATE (*500,Z(IBUF),EIGC(1),FLAG)
6 CALL FREAD (EED,IREG,10,0)
IF (METHOD.EQ.IREG(1,1) .OR. METHOD.EQ.-1) GO TO 8
7 CALL FREAD (EED,IREG,7,0)
IF (IREG(6,1) .NE. -1) GO TO 7
GO TO 6
8 JREG = 1
EPS = .0001
IF (REG(1,2) .NE. 0.) EPS = REG(1,2)
11 CALL FREAD (EED,IREG(1,JREG),7,0)
IF (IREG(6,JREG) .EQ. -1) GO TO 9
JREG = JREG + 1
IF (JREG .GT. 10) GO TO 9
GO TO 11
9 CALL CLOSE (EED,REW)
NOREG = JREG - 1
JREG = 0
C
C PICK UP PARAMETERS FOR REGION I
C
5 JREG = JREG + 1
ITER = 0
NODCMP = 0
NOSTRT = 0
NOMOVS = 0
X1 = REG(1,JREG)
Y1 = REG(2,JREG)
X2 = REG(3,JREG)
Y2 = REG(4,JREG)
L = REG(5,JREG)
ANOEST = REG(6,JREG)
ANODES = REG(7,JREG)
IF (NODES.EQ. 0) NODES = 3*NOEST
NSHIFT = SQRT((X1-X2)**2+(Y1-Y2)**2)/L + 1.
L1 = L*.5
NOROOT = 0
C
C
C FIND SHIFT POINT CLOSEST TO THE ORIGIN
C
R = SQRT((X1-X2)**2 + (Y1-Y2)**2)
IF (R) 10,10,15
10 WRITE (NOUT,12) UFM
12 FORMAT (A23,' 2366, REGION IMPROPERLY DEFINED ON EIGC CARD.')
CALL MESAGE (-61,0,0)
15 CONTINUE
D = (FLOAT(NSHIFT)*L-R)/2.0
XX = X1 + D*(X1-X2)/R
X2 = X2 + D*(X2-X1)/R
X1 = XX
YY = Y1 + D*(Y1-Y2)/R
Y2 = Y2 + D*(Y2-Y1)/R
Y1 = YY
IF (IDIAG .EQ. 0) GO TO 7000
WRITE (NOUT,1000) X1,Y1,X2,Y2,L1,NODES,NOEST,NSHIFT
1000 FORMAT (1H1,5F10.2,3I5)
7000 CONTINUE
DELTX = (X1-X2)/FLOAT(NSHIFT)
DELTY = (Y1-Y2)/FLOAT(NSHIFT)
XX = X2 + DELTX/2.
YY = Y2 + DELTY/2.
RANGE = XX**2 + YY**2
N = NSHIFT - 1
SHIFT = 1.
IF (DELTX .NE. 0.) GO TO 20
ANUM1 = L1
ANUM2 = 0.
GO TO 25
20 SLOPE = DELTY/DELTX
ARG = SQRT(1.+SLOPE**2)
ANUM1 = SLOPE*L1/ARG
ANUM2 = L1/ARG
25 CONTINUE
IF (N .EQ. 0) GO TO 40
DO 30 I = 1,N
XX = XX + DELTX
YY = YY + DELTY
RANG = XX**2 + YY**2
IF (RANG .GE. RANGE) GO TO 40
RANGE = RANG
30 SHIFT = I + 1
C
C COMPUTE COORDINATES OF CORNERS OF THE REGION
C
40 XL2 = X2 + ANUM1
YL2 = Y2 - ANUM2
IMIN = SHIFT
IMAX = SHIFT
C
C FIND THE MAXIMUM MODULUS OF THE SEARCH REGION
C
MAXMOD = XL2**2 + YL2**2
XX = X2 - ANUM1
YY = Y2 + ANUM2
MAXMOD = AMAX1(MAXMOD,XX**2+YY**2)
XX = X1 + ANUM1
YY = Y1 - ANUM2
MAXMOD = AMAX1(MAXMOD,XX**2+YY**2)
XX = X1 - ANUM1
YY = Y1 + ANUM2
MAXMOD = AMAX1(MAXMOD,XX**2+YY**2)
C
C INITIALIZE
C
IND = 0
LEFT = 0
45 ISHIFT = SHIFT
C
C EVALUATE THE VALUE OF LAMBDA IN THE CENTER OF THE CURRENT SEARCH
C REGION
C
LAMBDA(1) = X2 + (SHIFT-.5)*DELTX
LAMBDA(2) = Y2 + (SHIFT-.5)*DELTY
IF (LAMBDA(2) .EQ. 0.0D0) LAMBDA(2) = .01*DELTY
C
C COMPUTE DISTANCE TO FARTHEST CORNER OF THE SQUARE SEARCH REGION
C
XX = XL2 + SHIFT*DELTX
YY = YL2 + SHIFT*DELTY
RZERO = (LAMBDA(1)-XX)**2 + (LAMBDA(2)-YY)**2
RZERO = SQRT(RZERO)*1.05
IF (IDIAG .EQ. 0) GO TO 7001
WRITE (NOUT,1216)RZERO
1216 FORMAT (//,10H RZERO = ,F10.4)
7001 CONTINUE
NOSTRT = NOSTRT + 1
COMFLG = 0
61 LMBDA(1) = LAMBDA(1)
LMBDA(2) = LAMBDA(2)
NOCHNG = 0
SWITCH = 0
IVECT = 0
KREG = 0
IND = IND + 1
IF (IABS (IND) .EQ. 13) IND = 1
ISING = 0
GO TO 100
80 ISING = 0
SWITCH = 1
100 IF (NOCHNG .GE. 4) GO TO 220
NOCHNG = NOCHNG + 1
CALL KLOCK (T1)
C
C CALL IN ADD LINK TO FORM (LAMBDA**2*M + LAMBDA*B + K)
C
CALL CINVP1
C
C CALL IN CD COMP TO DECOMPOSE THE MATRIX
C
IF (IDIAG .EQ. 0) GO TO 7002
WRITE (NOUT,1001) LAMBDA
1001 FORMAT (10H1LAMBDA = ,2D15.5)
7002 CONTINUE
NODCMP = NODCMP + 1
CALL CINVP2 (*110)
CALL KLOCK (T2)
GO TO 120
110 IF (ISING .EQ. 1) GO TO 210
C
C SINGULAR MATRIX. INCREMENT LAMBDA AND TRY ONCE MORE
C
ISING = 1
LAMBDA(1) = LAMBDA(1) + .02*RZERO
LAMBDA(2) = LAMBDA(2) + .02*RZERO
GO TO 100
C
C DETERMINE THE TIME REQUIRED TO FORM AND DECOMPOSE THE DYNAMIC
C MATRIX
C
120 TIMED = T2 - T1
IF (TIMED .EQ. 0) TIMED = 1
C
C CALL IN MAIN LINK TO ITERATE FOR EIGENVALUES
C
121 CALL CINVP3
IF (LEFT .EQ. 1) GO TO 130
IF (COMFLG .EQ. 2) GO TO 125
IF (COMFLG .EQ. 1) GO TO 80
GO TO 140
125 NOMOVS = NOMOVS + 1
GO TO 61
C
C CALL IN LINK TO COMPUTE THE LEFT EIGENVECTOR
C
130 DTEMP(1) = LAMBDA(1)
DTEMP(2) = LAMBDA(2)
LAMBDA(1) = LAM1(1)
LAMBDA(2) = LAM1(2)
131 SWITCH = -1
CALL CINVP1
C
C DECOMPOSE THE DYNAMIC MATRIX AT THE EIGENVALUE TO OBTAIN THE LEFT
C EIGENVECTOR BY THE DETERMINATE METHOD
C
IF (IDIAG .EQ. 0) GO TO 132
WRITE (NOUT,1001) LAMBDA
132 CALL CINVP2 (*138)
C
C BUILD LOAD FOR FBS
C
D1 = NROW/2
D2 = NORTHO
DO 133 I = 1,NROW,2
K = (I+1)/2
DZ(I) = SIGN*MINDIA/(1.D0+(1.D0-FLOAT(K)/D1)*D2)
133 DZ(I+1) = 0.0D0
SIGN = -SIGN
CALL CDIFBS (DZ(1),Z(IBUF))
LAMBDA(1) = DTEMP(1)
LAMBDA(2) = DTEMP(2)
SWITCH = 0
C
C NORMALIZE AND STORE THE LEFT EIGENVECTOR
C
CALL CNORM1 (DZ(1),FILEK(2))
IF (IDIAG .EQ. 0) GO TO 135
WRITE (NOUT,134) (DZ(I),I=1,NROW)
134 FORMAT (///,15H LEFT VECTOR ,//,(10D12.4))
135 CONTINUE
IF (NOLEFT .OR. ISYM.EQ.0) GO TO 136
IFILE = PHIDLI
CALL OPEN (*500,IFILE,Z(IBUF),WRT)
CALL WRITE (IFILE,DZ(1),NROW2,1)
CALL CLOSE (IFILE,NOREW)
136 IFILE = SCRFIL(10)
CALL GOPEN (IFILE,Z(IBUF),RD)
CALL BCKREC (IFILE)
CALL FREAD (IFILE,DZ(NROW+2),NROW2,1)
CALL BCKREC (IFILE)
CALL CLOSE (IFILE,NOREW)
C
C COMPUTE REAL LEFT VECTOR SCALED
C
CALL CX TRN Y (DZ(1),DZ(NROW+2),DTEMP)
CALL CDIVID (DZ(1),DZ(1),DTEMP,NROW)
CALL OPEN (*500,IFILE,Z(IBUF),WRT)
CALL WRITE (IFILE,DZ(1),NROW2,1)
CALL CLOSE (IFILE,REW)
GO TO 121
138 LAMBDA(1) = 1.01*LAMBDA(1)
LAMBDA(2) = 1.01*LAMBDA(2)
GO TO 131
140 IF (COMFLG .GE. 3) GO TO 200
IF (COMFLG .EQ. 0) GO TO 160
IF (IDIAG .EQ. 0) GO TO 150
WRITE (NOUT,145) NOREG,JREG
145 FORMAT (2I10)
150 IF (NOREG .EQ. JREG) RETURN
GO TO 5
C
C FIND NEXT SHIFT POINT WHICH IS CLOSEST TO THE ORIGIN
C
160 IF (IMIN .NE. 1) GO TO 170
IF (IMAX .EQ. NSHIFT) GO TO 250
165 SHIFT = SHIFT + 1.
IMAX = IMAX + 1
LAMBDA(1) = LMBDA(1) + DELTX
LAMBDA(2) = LMBDA(2) + DELTY
GO TO 45
170 IF (IMAX .NE. NSHIFT) GO TO 180
175 SHIFT = SHIFT - 1.
IMIN = IMIN - 1
LAMBDA(1) = LMBDA(1) - DELTX
LAMBDA(2) = LMBDA(2) - DELTY
GO TO 45
180 XX = LMBDA(1) - DELTX
YY = LMBDA(2) - DELTY
RANG = XX**2 + YY**2
XX = LMBDA(1) + DELTX
YY = LMBDA(2) + DELTY
RANGE= XX**2 + YY**2
IF (RANGE-RANG) 175,175,165
200 ITERM = COMFLG
GO TO 260
C
C SINGULARITY ENCOUNTERED TWICE IN A ROW
C
210 ITERM = 1
GO TO 260
C
C 4 MOVES WHILE TRACKING ONE ROOT
C
220 ITERM = 2
GO TO 260
C
C REGIONS COMPLETED
C
250 ITERM = 3
C
C SET UP THE SUMMARY FILE
C
260 IFILE = DMPFIL
CALL OPEN (*500,DMPFIL,Z(IBUF),WRT)
CALL WRITE (DMPFIL,IHEAD(1),10,0)
I = 0
IZ(I+2) = NORTHO
IZ(I+3) = NOSTRT
IZ(I+4) = NOMOVS
IZ(I+5) = NODCMP
IZ(I+6) = ITER
IZ(I+7) = ITERM
DO 270 I = 8,12
270 IZ(I) = 0
I = 2
CALL WRITE (DMPFIL,IZ(I),40,0)
CALL WRITE (DMPFIL,HEAD(1),96,1)
CALL WRITE (DMPFIL,IZ(1),0,1)
CALL CLOSE (DMPFIL,EOFNRW)
C
C WRITE DUMMY TRAILER
IXX = FILEK(1)
FILEK(1) = DMPFIL
CALL WRTTRL (FILEK(1))
FILEK(1) = IXX
NFOUND = NORTHO
IF (IDIAG .EQ. 0) GO TO 350
J = 12
WRITE (NOUT,300)(IZ(I),I=1,J)
300 FORMAT (///,12I10)
350 CONTINUE
IF (ITERM .EQ. 5) RETURN
GO TO 150
C
500 CALL MESAGE (-1,IFILE,NAME)
RETURN
END
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