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SUBROUTINE FEC(NVCT,COORX,IEX,IPX,TCX,MUX,MLX,ALAM,CAY,FX,UX)
C THIS CODE USES QUADRILATERAL FINITE ELEMENTS TO SOLVE THE PROBLEM
C DEL(KDEL(U))-LAMBDA*U-F = 0 ,IN OMEGA
C KDU/DN+BETA*(U-U0)=Q ,ON OMEGA
C AA(.,.) AND AM(.,.) HAVE DIMENSION .GE. NVNP BY (ML+MU+1)
C PA(.,.) HAS DIMENSION .GE. NVNP BY (2*ML+MU+1)
C********FIRST DIMENSION OF PA MUST BE NDEN .GE. NVNP************
C********NDEN IS ENTERED BY PARAMETER STATEMENT******************
C V(.),U(.),IP1(.) HAVE DIMENSION .GE. NVNP
C UI(.),VI(.) HAVE DIMENSION .GE. NNP
C NDF .EQ. NUMBER OF DEGREES OF FREEDOM IN BASIS SET
C NE .EQ. NUMBER OF ELEMENTS
C NCN .EQ. CONSTANT NODES
C NNP .EQ. TOTAL NUMBER OF NODES
C NAXI .EQ. 0 FOR CARTESIAN FORMULATION
C NAXI .EQ. 1 FOR AXISYMMETRIC FORMULATION
C - FOR AXISYMMETRIC CASE: X=R AND Y=Z
C NGAU DETERMINES ORDER OF GAUSSIAN INTEGRATION
C NGAU=1 ]1 BY 1 GAUSS QUADRATURE
C NGAU=2 ]2 BY 2 GAUSS QUADRATURE
C NGAU=3 ]3 BY 3 GAUSS QUADRATURE
C NGAU=4 ]4 BY 4 GAUSS QUADRATURE
C NVNP= NNP-NCN .EQ. VARIABLE NODES
C D(.,.) HAS DIMENSION NNP BY 2
C IPRMAT .EQ. THE NUMBER OF ELEMENTS FOR WHICH ELEMENT MATRICES ARE TO BE
C PRINTED
C IPRGMA .EQ. 0 IF NO GLOBAL MATRICE PRINT IS DESIRED
C .EQ. 1 IF GLOBAL MATICE PRINT IS DESIRED
COMMON /TR/ FF
COMMON /BIG/ AA( 80,37),AM( 80,37)
COMMON VI(128),V( 80),IP1( 80),B( 80),UI(128),U( 80),D( 80,2)
COMMON ML,ML2,MU,MLM,MLL,NCN,NBDL,DELT,DELTP,EPSMAX,COORD(128,2),
1AE(9,9),BE(9,9),CE(9),BETA(30,3),T0(30,3),Q(30,3),TC(48),IE(32,9),
2IP(128,2),IPRMAT
DIMENSION COORX(128,2),IEX(32,9),IPX(128,2),UX(80),NVCT(8),TCX(48)
DIMENSION PA(80,55)
NDEN=80
ML=MLX
MU=MUX
FF=FX
NDF=4
NE=NVCT(1)
NNP=NVCT(2)
NCN=NVCT(3)
NGAU=NVCT(4)
NAXI=NVCT(5)
IPRMAT=NVCT(6)
IPRGMA=NVCT(7)
2257 NVNP=NNP-NCN
NBDL=1
MLM=ML+1
ML2=ML+2
MLL=MLM+MU
DO 5 I=1,NVNP
B(I)=0.0
DO 5 J=1,MLL
AM(I,J)=0.0
5 AA(I,J)=0.0
C INPUT GLOBAL COORDINATES OF NODE I ]COORDINATES ARE ORDERED IN
C INCREASING NODE NUMBER] COORD(I,1) .EQ.. X-COORDINATE OF NODE I ,
C COORD(I,2) .EQ. Y-COORDINATE OF NODE I
DO 8733 I=1,NNP
COORD(I,1)=COORX(I,1)
8733 COORD(I,2)=COORX(I,2)
C INPUT GLOBAL NODE NUMBERS IN ELEMENT I] NODES ARE TRAVERSED IN A
C COUNTERCLOCKWISE DIRECTION AROUND ELEMENT.
C COUNTERCLOCKWISE DIRECTION AROUND ELEMENT(CORNER NODES FIRST THEN
C MIDSIDE NODES IN THE CASE OF QUADRATIC BASIS SET).
DO 8734 I=1,NE
DO 8734 J=1,4
8734 IE(I,J)=IEX(I,J)
C INPUT NODE TYPE] IP(I,1) .EQ. 0 IF U IS SPECIFIED AT BOUNDARY NODE I]
C IP(I,1) .EQ. 1 IF NODE I IS AN INTERIOR NODE] IP(I,1) .EQ. 2 IF THE
C FLUX IS ZERO AT BOUNDARY NODE I] IP(I,1) .EQ. 3 IF THE GENERAL FLUX
C BOUNDARY CONDITION APPLIES AT BOUNDARY NODE I.
C DETERMINATION OF THE NUMBER OF SPECIFIED BOUNDARY NODES ABOVE ACTIVE NODE I
C INPUT OF U VALUES AT SPECIFIED BOUNDARY NODES. THE ELEMENTS OF TC(.)
C ARE ORDERED IN INCREASING GLOBAL NODE NUMBER
DO 8735 I=1,NNP
8735 IP(I,1)=IPX(I,1)
DO 8736 I=1,NCN
8736 TC(I)=TCX(I)
IP(1,2)=0
IF(IP(1,1) .EQ. 0)IP(1,2)=1
DO 62 I=2,NNP
IP(I,2)=IP(I-1,2)
IF(IP(I,1) .EQ. 0)IP(I,2)=IP(I,2)+1
62 CONTINUE
DO 2 M=1,NE
C CONSTRUCT ELEMENT MATRICES
CALL MAKE(NAXI,NDF,NGAU,M,NTRAN)
C CONSTRUCTION OF GLOBAL CAPACITY AND DISSIPATION MATRICES AND FORCE VECTOR
DO 523 K=1,NDF
I=IE(M,K)
I1=IP(I,2)
IF(IP(I,1) .EQ. 0)GO TO 524
I2=I-I1
B(I2)=B(I2)-CE(K)
524 DO 523 L=1,NDF
J=IE(M,L)
IF(IP(J,1) .EQ. 0)GO TO 523
J1=IP(J,2)
J2=J-J1
IF(IP(I,1) .EQ. 0)GO TO 522
K1=J2-I2
K2=K1+MLM
IF(K2 .LT. 1 .OR. K1 .GT. MU)GO TO 523
AA(I2,K2)=AA(I2,K2)+AE(K,L)+ALAM*BE(K,L)
AM(I2,K2)=AM(I2,K2)+BE(K,L)
GO TO 523
522 B(J2)=B(J2)-(AE(L,K)+ALAM*BE(L,K))*TC(I1)
523 CONTINUE
2 CONTINUE
IF(IPRGMA .EQ. 0)GO TO 589
WRITE(6,601)
WRITE(6,502)((AA(I,J),J=1,MLL),I=1,NVNP)
WRITE(6,602)
WRITE(6,502)((AM(I,J),J=1,MLL),I=1,NVNP)
WRITE(6,603)
WRITE(6,502)(B(I),I=1,NVNP)
589 CONTINUE
C CALCULATION OF STEADY STATE SOLUTION
DO 82 I=1,NVNP
DO 82 J=1,MLL
PA(I,J)=AA(I,J)
82 CONTINUE
CALL DECB(NDEN,NVNP,ML,MU,PA,IP1,IER)
IF(IER .EQ. 0)GO TO 98
WRITE(6,700)IER
GO TO 1000
98 DO 20 I=1,NVNP
20 U(I)=B(I)
CALL SOLB(NDEN,NVNP,ML,MU,PA,U,IP1)
IF(IPRMAT.NE.0)WRITE(6,901)
C RECONSTRUCTION AND OUTPUT OF FULL NODAL SOLUTION VECTOR
NA=1
DO 107 I=1,NNP
IF(IP(I,1) .EQ. 0)GO TO 108
I1=I-IP(I,2)
VI(I)=U(I1)
GO TO 107
108 VI(I)=TC(NA)
NA=NA+1
107 CONTINUE
DO 7119 I=1,NNP
7119 UX(I)=VI(I)
IF(IPRMAT.EQ.0)GO TO 99
WRITE(6,500)(VI(I),I=1,NNP)
99 CONTINUE
GO TO 1000
9998 WRITE(6,700)IER
1000 CONTINUE
100 FORMAT(12I5,F10.5)
150 FORMAT(4F10.5,E10.3)
200 FORMAT(3I5,2F10.7)
202 FORMAT(20I4)
203 FORMAT(8F10.7)
204 FORMAT(15X,2F10.7)
300 FORMAT(5E15.8)
400 FORMAT(3E15.8)
500 FORMAT(6(3X,E15.8))
502 FORMAT(7(2X,E15.8))
600 FORMAT(/)
601 FORMAT(20X,37HAA(I,J):7(2X,E15.8):SUMMED ON I FIRST)
602 FORMAT(20X,37HAM(I,J):7(2X,E15.8):SUMMED ON I FIRST)
603 FORMAT(20X,16HB(I):7(2X,E15.8))
700 FORMAT(10X,I2,16HTH PIVOT IS ZERO)
901 FORMAT(46X,21HSTEADY STATE SOLUTION)
902 FORMAT(33X,25HCONSISTENT MASS TRANSIENT,10H(EPS*UMAX=,E10.3,1H))
903 FORMAT(35X,21HLUMPED MASS TRANSIENT,10H(EPS*UMAX=,E10.3,1H))
2002 FORMAT(50X,20HEXECUTION STARTED AT,4X,A10)
2003 FORMAT(49X,21HEXECUTION FINISHED AT,4X,A10)
RETURN
END
SUBROUTINE MAKE(NAXI,NDF,NGAU,M,NTRAN)
C FF(X,Y) IS THE HEAT SOURCE FUNCTION AND MUST BE SUPPLIED HERE
C FK1 IS THE X-DIFFUSIVITY FUNCTION AND MUST BE SUPPLIED AS A FUNCTION
C FK2 IS THE Y-DIFFUSIVITY FUNCTION AND MUST BE SUPPLIED AS A FUNCTION
C V1(X,Y) IS THE X-COMPONENT OF VELOCITY VECTOR AND MUST BE SUPPLIED HERE
C V2(X,Y) IS THE Y-COMPONENT OF VELOCITY VECTOR AND MUST BE SUPPLIED HERE
COMMON /TR/ FXF
COMMON /BIG/ AA( 80,37),AM( 80,37)
COMMON VI(128),V( 80),IP1( 80),B( 80),UI(128),U( 80),D(80,2)
COMMON ML,ML2,MU,MLM,MLL,NCN,NBDL,DELT,DELTP,EPSMAX,COORD(128,2),
1AE(9,9),BE(9,9),CE(9),BETA(30,3),T0(30,3),Q(30,3),TC(48),IE(32,9),
2IP(128,2),IPRMAT
DIMENSION P(4,4),W(4,4),DBAA(9,2),BAA(9),DMAP(2,2),DELBA(9,2)
DIMENSION BA(9,4,4),DBA(9,2,4,4),DE(9)
REAL JAC,JAC1,L1,L2,JACI,JAC2
DATA P/0.0,0.57735026918963,0.77459666924148,0.86113631159405,0.0,
1-.57735026918963,-.77459666924148,-.86113631159405,0.0,0.0,0.0,
20.33998104358486,0.0,0.0,0.0,-0.33998104358486/
DATA W/2.0,1.0,0.55555555555556,0.34785484513745,1.0,1.0,
10.55555555555556,0.34785484513745,0.0,0.0,0.88888888888889,
20.65214515486255,0.0,0.0,0.0,0.65214515486255/
FK1(X,Y)=1.0
FK2(X,Y)=1.0
FF(X,Y)=FXF
V1(X,Y)=0.0
V2(X,Y)=0.0
50 DO 5 I=1,NDF
CE(I)=0.0
DO 5 J=1,NDF
BE(I,J)=0.0
5 AE(I,J)=0.0
C GAUSSIAN INTEGRATION
DO 100 I20=1,NGAU
DO 100 J20=1,NGAU
IF(M .GT. 1)GO TO 31
L1=P(NGAU,I20)
L2=P(NGAU,J20)
C GENERATE AND STORE DERIVATIVES OF BASIS FNCS. AT GAUSS POINTS
C GENERATE AND STORE BASIS FNCS. AT GAUSS POINTS
CALL BASIS(L1,L2,NDF,BAA,DBAA)
DO 32 IJ=1,NDF
BA(IJ,I20,J20)=BAA(IJ)
DO 32 IK=1,2
32 DBA(IJ,IK,I20,J20)=DBAA(IJ,IK)
31 X=0.0
Y=0.0
DO 30 I=1,NDF
KA=IE(M,I)
X=X+COORD(KA,1)*BA(I,I20,J20)
30 Y=Y+COORD(KA,2)*BA(I,I20,J20)
C DERIVATIVES OF COORDINATE MAPPING
DO 71 K3=1,2
DO 71 K2=1,2
DMAP(K2,K3)=0.0
DO 71 K1=1,NDF
KA=IE(M,K1)
71 DMAP(K2,K3)=DMAP(K2,K3)+COORD(KA,K2)*DBA(K1,K3,I20,J20)
C CALCULATION OF AREA JACOBIAN
JAC=DMAP(1,1)*DMAP(2,2)-DMAP(1,2)*DMAP(2,1)
JACI=1.0/JAC
JAC2=(X**NAXI)*JAC
C GRADIENT OPERATOR
DO 6 I1=1,NDF
DELBA(I1,1)=JACI*(DMAP(2,2)*DBA(I1,1,I20,J20)-DMAP(1,2)*
1DBA(I1,2,I20,J20))
6 DELBA(I1,2)=JACI*(-DMAP(2,1)*DBA(I1,1,I20,J20)+DMAP(1,1)*
1DBA(I1,2,I20,J20))
C CONSTRUCTION OF BULK CONTRIBUTIONS TO ELEMENT MATRICES
DO 81 I=1,NDF
CE(I)=CE(I)+FF(X,Y)*JAC2*BA(I,I20,J20)*W(NGAU,I20)*W(NGAU,J20)
DO 81 J=1,NDF
AE(I,J)=AE(I,J)+JAC2*(FK1(X,Y)*DELBA(I,1)*DELBA(J,1)+FK2(X,Y)*
1DELBA(I,2)*DELBA(J,2)+(V1(X,Y)*DELBA(J,1)+V2(X,Y)*DELBA(J,2))*
2BA(I,I20,J20))*W(NGAU,J20)*W(NGAU,I20)
81 BE(I,J)=BE(I,J)+JAC2*BA(I,I20,J20)*BA(J,I20,J20)*W(NGAU,I20)*
1W(NGAU,J20)
100 CONTINUE
KB=2
IF(NDF .EQ. 8)KB=3
DO 21 K=1,4
KA=IE(M,K)
IF(IP(KA,1) .LT. 3)GO TO 21
READ(5,*)(Q(NBDL,I),I=1,KB)
IF(IP(KA,1) .NE. 4)GO TO 278
READ(5,*)(BETA(NBDL,I),I=1,KB)
READ(5,*)(T0(NBDL,I),I=1,KB)
278 NBDL=NBDL+1
C GAUSSIAN INTEGRATION
DO 7 I20=1,NGAU
GO TO (8,9,10,11),K
8 L2=-1.
L1=P(NGAU,I20)
GO TO 12
9 L1=1.
L2=P(NGAU,I20)
GO TO 12
10 L2=1.
L1=P(NGAU,I20)
GO TO 12
11 L1=-1.
L2=P(NGAU,I20)
C GENERATE BASIS FNCS. AT GAUSS POINTS
C GENERATE DERIVATIVES OF BASIS FNCS. AT GAUSS POINTS
12 CALL BASIS(L1,L2,NDF,BAA,DBAA)
C GENERATE DERIVATIVES OF COORDINATE MAPPING
DO 14 K3=1,2
DO 14 K2=1,2
DMAP(K2,K3)=0.0
DO 14 K1=1,NDF
KA=IE(M,K1)
14 DMAP(K2,K3)=DMAP(K2,K3)+COORD(KA,K2)*DBAA(K1,K3)
C CALCULATION OF LINE JACOBIAN
19 GO TO (15,16,15,16),K
15 JAC1=SQRT(DMAP(1,1)**2+DMAP(2,1)**2)
GO TO 17
16 JAC1=SQRT(DMAP(2,2)**2+DMAP(1,2)**2)
17 CONTINUE
C INTERPOLATION OF BETA, Q, AND T0 ON BDRY.
KK=K+1
IF(KK .EQ. 5)KK=1
KKK=K+4
Q1=Q(NBDL,1)*BAA(K)+Q(NBDL,2)*BAA(KK)
IF(NDF .EQ. 4)GO TO 35
Q1=Q1+Q(NBDL,3)*BAA(KKK)
35 IF(IP(KA,1) .EQ. 3)GO TO 36
BET=BETA(NBDL,1)*BAA(K)+BETA(NBDL,2)*BAA(KK)
T01=T0(NBDL,1)*BAA(K)+T0(NBDL,2)*BAA(KK)
IF(NDF .EQ. 4)GO TO 19
BET=BET+BETA(NBDL,3)*BAA(KKK)
T01=T01+T0(NBDL,3)*BAA(KKK)
C CONSTRUCTION OF BDRY. CONTRIBUTIONS TO ELEMENT MATRICES
36 DO 18 I=K,K+1
K4=I
IF(I .EQ. 5)K4=1
IF(IP(KA,1) .NE. 3)GO TO 37
CE(K4)=CE(K4)-Q1*BAA(K4)*JAC1*W(NGAU,I20)
IF(I .GT. K)GO TO 18
IF(NDF .GE. 9)CE(KKK)=CE(KKK)-Q1*BAA(KKK)*JAC1*W(NGAU,I20)
GO TO 18
37 CE(K4)=CE(K4)-(Q1+BET*T01)*BAA(K4)*JAC1*W(NGAU,I20)
IF(I .GT. K)GO TO 27
IF(NDF .GE. 9)CE(KKK)=CE(KKK)-(Q1+BET*T01)*BAA(KKK)*JAC1*
1W(NGAU,I20)
IF(NDF .GE. 9)AE(KKK,KKK)=AE(KKK,KKK)+BET*BAA(KKK)*BAA(KKK)*
1JAC1*W(NGAU,I20)
27 DO 28 J=K,K+1
K5=J
IF(J .EQ. 5)K5=1
AE(K4,K5)=AE(K4,K5)+BET*BAA(K4)*BAA(K5)*JAC1*W(NGAU,I20)
IF(J .GT. K)GO TO 28
IF(NDF .EQ. 4)GO TO 28
AE(K4,KKK)=AE(K4,KKK)+BET*BAA(K4)*BAA(KKK)*JAC1*W(NGAU,I20)
AE(KKK,K4)=AE(K4,KKK)
28 CONTINUE
18 CONTINUE
7 CONTINUE
21 CONTINUE
IF(M .GT. IPRMAT) GO TO 9987
WRITE(6,9003)
WRITE(6,9001)
WRITE(6,9000)((AE(I,J),J=1,NDF),I=1,NDF)
WRITE(6,9003)
WRITE(6,9002)
WRITE(6,9000)(CE(I),I=1,NDF)
WRITE(6,9003)
9000 FORMAT(4(2X,E15.8))
9001 FORMAT(20X,37HAE(I,J):4(2X,E15.8):SUMMED ON I FIRST)
9002 FORMAT(20X,17HCE(I):4(2X,E15.8))
9003 FORMAT(/)
9987 IF(NTRAN .NE. 2)GO TO 22
S=0.0
DO 101 I=1,NDF
DE(I)=BE(I,I)
DO 101 J=1,NDF
101 S=S+BE(I,J)
T=0.0
DO 102 I=1,NDF
102 T=T+DE(I)
DO 103 I=1,NDF
DO 103 J=1,NDF
103 BE(I,J)=0.0
DO 104 I=1,NDF
104 BE(I,I)=S*DE(I)/T
22 CONTINUE
IF (M .GT. IPRMAT) GO TO 23
WRITE(6,9004)
WRITE(6,9000)((BE(I,J),J=1,NDF),I=1,NDF)
9004 FORMAT(20X,37HBE(I,J):4(2X,E15.8):SUMMED ON I FIRST)
WRITE(6,9003)
201 FORMAT(3F10.7)
23 CONTINUE
RETURN
END
SUBROUTINE BASIS(L1,L2,NDF,BA,DBA)
REAL L1,L2
C LINEAR AND QUADRATIC APPROXIMATION ON QUADRILATERALS
DIMENSION BA(9),DBA(9,2),S(9),T(9)
DATA S /-1.,1.,1.,-1.,0.,1.,0.,-1.,0./
DATA T /-1.,-1.,1.,1.,-1.,0.,1.,0.,0./
C LINEAR BASIS FNCS.
BASL(X,Y,XI,YI)=0.25*(1.+X*XI)*(1.+Y*YI)
DBAL(X,Y,XI,YI)=0.25*XI*(1.+Y*YI)
C SERENDIPITY QUADRATIC FNCS.
BASQC(X,Y,XI,YI)=0.25*(1.+XI*X)*(1.+YI*Y)*(XI*X+YI*Y-1.)
DBAQC(X,Y,XI,YI)=0.25*(1.+YI*Y)*(XI*YI*Y+2.*X*XI*XI)
BASQM(X,Y,XI,YI)=0.5*((1.-X*X)*(1.+YI*Y)*YI*YI+(1.+XI*X)*(1.-Y*Y)*
1XI*XI)
DBAQM(X,Y,XI,YI)=-X*(1.+Y*YI)*YI*YI+0.5*(1.-Y*Y)*XI*XI*XI
C LAGRANGE QUADRATIC BASIS FNCS.
BASLC(X,Y,XI,YI)=0.25*(XI+X)*(YI+Y)*X*Y
DBALC(X,Y,XI,YI)=0.25*(XI+2.*X)*(YI+Y)*Y
BASLM(X,Y,XI,YI)=0.5*(X*(XI+X)*(1.-Y*Y)*XI*XI+Y*(YI+Y)*(1.
1-X*X)*YI*YI)
DBALM(X,Y,XI,YI)=0.5*(XI+2.*X)*(1.-Y*Y)*XI*XI-X*Y*(YI+Y)
1*YI*YI
BASL0(X,Y)=(1.-Y*Y)*(1.-X*X)
DBAL0(X,Y)=-2.*X*(1.-Y*Y)
C LINEAR
IF(NDF .NE. 4) GO TO 1
DO 5 I=1,4
BA(I)=BASL(L1,L2,S(I),T(I))
DBA(I,1)=DBAL(L1,L2,S(I),T(I))
5 DBA(I,2)=DBAL(L2,L1,T(I),S(I))
RETURN
1 IF (NDF .NE. 8) GO TO 2
C QUADRATIC SERENDIPTY
DO 6 I=1,4
BA(I)=BASQC(L1,L2,S(I),T(I))
DBA(I,1)=DBAQC(L1,L2,S(I),T(I))
6 DBA(I,2)=DBAQC(L2,L1,T(I),S(I))
DO 7 I=5,8
BA(I)=BASQM(L1,L2,S(I),T(I))
DBA(I,1)=DBAQM(L1,L2,S(I),T(I))
7 DBA(I,2)=DBAQM(L2,L1,T(I),S(I))
RETURN
2 DO 8 I=1,4
BA(I)=BASLC(L1,L2,S(I),T(I))
DBA(I,1)=DBALC(L1,L2,S(I),T(I))
8 DBA(I,2)=DBALC(L2,L1,T(I),S(I))
DO 9 I=5,8
BA(I)=BASLM(L1,L2,S(I),T(I))
DBA(I,1)=DBALM(L1,L2,S(I),T(I))
9 DBA(I,2)=DBALM(L2,L1,T(I),S(I))
BA(9)=BASL0(L1,L2)
DBA(9,1)=DBAL0(L1,L2)
DBA(9,2)=DBAL0(L2,L1)
RETURN
END
SUBROUTINE DECB(NDIM,N,ML,MU,B,IP,IER)
DIMENSION B(NDIM,1),IP(N)
C LU DECOMPOSITION OF BAND MATRIX A.. L*U = P*A , WHERE P IS A
C PERMUTATION MATRIX, L IS A UNIT LOWER TRIANGULAR MATRIX, AND U IS AN
C UPPER TRIANGULAR MATRIX
C N = ORDER OF MATRIX
C B = N BY (2*ML+MU+1) ARRAY CONTAINING THE MATRIX A ON INPUT
C AND ITS FACTORED FORM ON OUTPUT.
C ON INPUT, B(I,K) (1 .LE. N) CONTAINS THE K-TH DIAGONAL OF A, OR
C A(I,J) IS STORED IN B(I,J-I+ML+1).
C ON OUTPUT, B CONTAINS THE L AND U FACTORS, WITH U IN COLUMNS 1 TO ML+MU+1,
C AND L IN COLUMNS ML+MU+2 TO 2*ML+MU+1.
C ML,MU= WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, NOT
C COUNTING THE MAIN DIAGONAL. TOTAL BANDWIDTH IS ML+MU+1.
C NDIM = THE FIRST DIMENSION (COLUMN LENGTH) OF THE ARRAY B.
C NDIM MUST BE .GE. N.
C IP = ARRAY OF LENGTH N CONTAINING PIVOT INFORMATION.
C IER = ERROR INDICATOR.
C = 0 IF NO ERRORS
C = K IF THE K-TH PIVOT CHOSEN WAS ZERO (A IS SINGULAR).
C THE INPUT ARGUMENTS ARE NDIM, N, ML, MU, B.
C THE OUTPUT ARGUMENTS ARE B, IP, IER.
IER=0
IF (N .EQ. 1) GO TO 92
LL=ML+MU+1
N1=N-1
IF (ML .EQ. 0) GO TO 32
DO 30 I=1,ML
II=MU+I
K=ML+1-I
DO 10 J=1,II
10 B(I,J)=B(I,J+K)
K=II+1
DO 20 J=K,LL
20 B(I,J)=0.0
30 CONTINUE
32 LR=ML
DO 90 NR=1,N1
NP=NR+1
IF(LR .NE. N)LR=LR+1
MX=NR
XM=ABS(B(NR,1))
IF(ML .EQ. 0)GO TO 42
DO 40 I=NP,LR
IF(ABS(B(I,1)) .LE. XM)GO TO 40
MX=I
XM=ABS(B(I,1))
40 CONTINUE
42 IP(NR)=MX
IF(MX .EQ. NR)GO TO 60
DO 50 I=1,LL
XX=B(NR,I)
B(NR,I)=B(MX,I)
50 B(MX,I)=XX
60 XM=B(NR,1)
IF(XM .EQ. 0.0)GO TO 100
B(NR,1)=1./XM
IF(ML .EQ. 0)GO TO 90
XM=-B(NR,1)
KK=MIN0(N-NR,LL-1)
DO 80 I=NP,LR
J=LL+I-NR
XX=B(I,1)*XM
B(NR,J)=XX
DO 70 II=1,KK
70 B(I,II)=B(I,II+1)+XX*B(NR,II+1)
80 B(I,LL)=0.0
90 CONTINUE
92 NR=N
IF(B(N,1) .EQ. 0.)GO TO 100
B(N,1)=1./B(N,1)
RETURN
100 IER=NR
RETURN
END
SUBROUTINE SOLB(NDIM,N,ML,MU,B,Y,IP)
C THE FOLLOWING CARD IS FOR OPTIMIZED COMPILATION UNDER CHAT.
DIMENSION B(NDIM,1),Y(N),IP(N)
C SOLUTION OF A*X = C GIVEN LU DECOMPOSITION OF A FROM DECB.
C Y = RIGHT-HAND VECTOR C, OF LENGTH N, ON INPUT,
C = SOLUTION VECTOR X ON OUTPUT.
C ALL THE ARGUMENTS ARE INPUT ARGUMENTS.
C THE OUTPUT ARGUMENT IS Y.
IF(N .EQ. 1)GO TO 60
N1=N-1
LL=ML+MU+1
IF(ML .EQ. 0)GO TO 32
DO 30 NR=1,N1
IF(IP(NR) .EQ. NR)GO TO 10
J=IP(NR)
XX=Y(NR)
Y(NR)=Y(J)
Y(J)=XX
10 KK=MIN0(N-NR,ML)
DO 20 I=1,KK
20 Y(NR+I)=Y(NR+I)+Y(NR)*B(NR,LL+I)
30 CONTINUE
32 LL=LL-1
Y(N)=Y(N)*B(N,1)
KK=0
DO 50 NB=1,N1
NR=N-NB
IF(KK .NE. LL)KK=KK+1
DP=0.0
IF(LL .EQ. 0)GO TO 50
DO 40 I=1,KK
40 DP=DP+B(NR,I+1)*Y(NR+I)
50 Y(NR)=(Y(NR)-DP)*B(NR,1)
RETURN
60 Y(1)=Y(1)*B(1,1)
RETURN
END