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UMAT_P_R.F90
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UMAT_P_R.F90
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! C
! UMAT_PCLI_R.for Plasticity Classical Theory C
! C
! LOCAL ARRAYS C
! C
! EELAS - ELASTIC STRAINS STATEV(1..NTENS) C
! EPLAS - PLASTIC STRAINS STATEV(NTENS+1...2*NTENS) C
! FLOW - PLASTIC FLOW DIRECTION C
! HARD - HARDENING MODULUS C
! C
! PROPS(1) - E C
! PROPS(2) - NU C
! PROPS(5..) - SYIELD AN HARDENING DATA C
! CALLS KUHARD FOR CURVE OF YIELD STRESS VS. PLASTIC STRAINS C
! EQPLAS - EQUIVALENT PLASTIC STRAIN STATEV(2*NTENS+1) C
! C
SUBROUTINE UMAT(STRESS, STATEV, DDSDDE, SSE, SPD, SCD, RPL,&
DDSDDT, DRPLDE, DRPLDT, STRAN, DSTRAN, TIME, DTIME, TEMP,&
DTEMP, PREDEF, DPRED, CMNAME, NDI, NSHR, NTENS, NSTATV,&
PROPS, NPROPS, COORDS, DROT, PNEWDT, CELENT, DFGRD0,&
DFGRD1, NOEL, NPT, LAYER, KSPT, KSTEP, KINC)
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 CMNAME
DIMENSION STRESS(NTENS), STATEV(NSTATV),DDSDDE(NTENS, NTENS),&
DDSDDT(NTENS),STRAN(NTENS),DSTRAN(NTENS),TIME(2),PROPS(NPROPS)
DIMENSION EELAS(NTENS), EPLAS(NTENS),DS(NTENS),DSTRESS(NTENS)
DIMENSION AUX1(1,NTENS),AUX2(NTENS,NTENS),AUX3(NTENS,NTENS),&
AUX4(NTENS,NTENS),AUX5(NTENS,NTENS),AUX6(NTENS,1),AUX7(1,NTENS),&
AUX8(1,1),AUX9(1,NTENS),AUX10(1,1),AUX11(NTENS,NTENS),&
AUX12(NTENS,1),AUX13(1,NTENS),AUX14(1,1),AUX15(1,NTENS),&
AUX16(NTENS,NTENS),AUX17(NTENS,NTENS),STRESST(1,NTENS),&
P(NTENS,NTENS),SINVAR(1,1),BI(NTENS,NTENS),STRESSUPD(NTENS,1),&
SDEV(NTENS,1),EM(NTENS,NTENS),B(NTENS,NTENS),Q(NTENS,NTENS),&
QT(NTENS,NTENS),DP(NTENS,NTENS),DC(NTENS,NTENS),DEL(NTENS,NTENS),&
BT(NTENS,NTENS),DIAG(NTENS,NTENS),GDIA(NTENS,NTENS)
PARAMETER (ZERO=0.D0, ONE=1.D0, TWO=2.D0, THREE=3.D0, SIX=6.0D0,&
ENUMAX=0.4999D0, NEWTON=10, TOLER=1.0D-7,MAXITER=30,&
FOUR=4.D0)
! Inititalize arrays
CALL KCLEAR(AUX1,1,NTENS)
CALL KCLEAR(AUX2,NTENS,NTENS)
CALL KCLEAR(AUX3,NTENS,NTENS)
CALL KCLEAR(AUX4,NTENS,NTENS)
CALL KCLEAR(AUX5,NTENS,NTENS)
CALL KCLEAR(AUX6,NTENS,1)
CALL KCLEAR(AUX7,1,NTENS)
CALL KCLEAR(AUX8,1,1)
CALL KCLEAR(AUX9,1,NTENS)
CALL KCLEAR(AUX10,1,1)
CALL KCLEAR(AUX11,NTENS,NTENS)
CALL KCLEAR(AUX12,NTENS,1)
CALL KCLEAR(AUX13,1,NTENS)
CALL KCLEAR(AUX14,1,1)
CALL KCLEAR(AUX15,1,NTENS)
CALL KCLEAR(AUX16,NTENS,NTENS)
CALL KCLEAR(AUX17,NTENS,NTENS)
CALL KCLEAR(P,NTENS,NTENS)
CALL KCLEAR(Q,NTENS,NTENS)
CALL KCLEAR(DP,NTENS,NTENS)
CALL KCLEAR(DC,NTENS,NTENS)
CALL KCLEAR(QT,NTENS,NTENS)
CALL KCLEAR(DEL,NTENS,NTENS)
CALL KCLEAR(STRESST,1,NTENS)
CALL KCLEAR(SINVAR,1,1)
CALL KCLEAR(STRESSUPD,NTENS,1)
CALL KCLEAR(AUX17,NTENS,NTENS)
CALL KCLEAR(B,NTENS,NTENS)
CALL KCLEAR(BT,NTENS,NTENS)
! Recover equivalent plastic strain, elastic strains, and plastic
! strains. Also initialize user definde data sets.
DO K1=1, NTENS
EELAS(K1)=STATEV(K1)
EPLAS(K1)=STATEV(K1+NTENS)
END DO
EQPLAS=STATEV(1+2*NTENS)
! Elastic properties
EMOD=PROPS(1)
ENU=MIN(PROPS(2),ENUMAX)
EBULK3=EMOD/(ONE-TWO*ENU)
EG2=EMOD/(ONE+ENU)
EG=EG2/TWO
EG3=THREE*EG
ELAM=(EBULK3-EG2)/THREE
CBETA2=EG2
! Elastic stiffness
DO K1=1, 3
DO K2=1, 3
DDSDDE(K2, K1)=ELAM
END DO
DDSDDE(K1, K1)=EG2+ELAM
END DO
DO K1=4, 4
DDSDDE(K1, K1)=EG
END DO
! Form proyector and diagonal decomposition matrices
CALL KPROYECTOR(P)
! Calculate predictor stress and elastic strains
CALL KMAVEC(DDSDDE,NTENS,NTENS,DSTRAN,DS)
CALL KUPDVEC(STRESS,NTENS,DS)
CALL KUPDVEC(EELAS,NTENS,DSTRAN)
! Calculate equivalent mises stress
CALL KMTRAN(STRESS,NTENS,1,STRESST)
CALL KMMULT(P,NTENS,NTENS,STRESS,NTENS,1,SDEV)
CALL KMMULT(STRESST,1,NTENS,SDEV,NTENS,1,SINVAR)
FBAR=DSQRT(SINVAR(1,1))
! Get the yield stress from the specifid hardening function.
CALL KUHARD(SYIEL0,EHARD,EQPLAS,2,PROPS(3))
! Determine if actively yielding
SYIELD=SYIEL0
IF(FBAR.GT.(ONE+TOLER)*SYIEL0) THEN
! Actively yielding-Perform local Newton iterations
! to find consistncy parameter and equivalent plastic
! strain
! Starts iterations
ITER=1
GAM_PAR=ZERO
IFLAG=0
DO
CALL KSPECTRAL(Q,DP,DC,DIAG,GDIA,GAM_PAR,EMOD,ENU)
CALL KMTRAN(Q,NTENS,NTENS,QT)
CALL KMMULT(STRESST,1,NTENS,Q,NTENS,NTENS,AUX1)
CALL KMMULT(QT,NTENS,NTENS,P,NTENS,NTENS,AUX2)
CALL KMMULT(AUX2,NTENS,NTENS,Q,NTENS,NTENS,AUX3)
CALL KMMULT(AUX3,NTENS,NTENS,DIAG,NTENS,NTENS,AUX4)
CALL KMMULT(AUX4,NTENS,NTENS,QT,NTENS,NTENS,AUX5)
CALL KMMULT(AUX5,NTENS,NTENS,STRESS,NTENS,1,AUX6)
CALL KMMULT(AUX1,1,NTENS,DIAG,NTENS,NTENS,AUX7)
CALL KMMULT(AUX7,1,NTENS,AUX6,NTENS,1,AUX8)
CALL KMMULT(AUX1,1,NTENS,GDIA,NTENS,NTENS,AUX9)
CALL KMMULT(AUX9,1,NTENS,AUX6,NTENS,1,AUX10)
FBAR=DSQRT(AUX8(1,1))
TETA2=ONE-(TWO/THREE)*EHARD*GAM_PAR
FJAC=TETA2*AUX10(1,1)/FBAR-(TWO/THREE)*EHARD*FBAR
FGAM=FBAR-SYIELD
! Updates
GAM_PAR=GAM_PAR-FGAM/FJAC
EQPLAS1=EQPLAS+DSQRT(TWO/THREE)*GAM_PAR*FBAR
CALL KUHARD(SYIELD,EHARD,EQPLAS1,2,PROPS(3))
IF(ABS(FGAM/FJAC).LT.TOLER) THEN
IFLAG=0
GOTO 801
ELSE
IF(ITER.GT.MAXITER) THEN
IFLAG=1
GOTO 802
END IF
END IF
ITER=ITER+1
END DO
801 CONTINUE
! Local Newton algorithm converged
! Update stresses, elastic and plastic strains, equivalent plastic
! strains
CALL KSPECTRAL(Q,DP,DC,DIAG,GDIA,GAM_PAR,EMOD,ENU)
CALL KMMULT(Q,NTENS,NTENS,DIAG,NTENS,NTENS,AUX17)
CALL KMMULT(AUX17,NTENS,NTENS,QT,NTENS,NTENS,B)
CALL KMMULT(B,NTENS,NTENS,STRESS,NTENS,1,STRESSUPD)
CALL KCLEAR(STRESS,NTENS,1)
DO K1=1,NTENS
STRESS(K1)=STRESSUPD(K1,1)
END DO
CALL KCLEAR(STRESST,1,NTENS)
CALL KCLEAR(SDEV,NTENS,1)
CALL KMTRAN(STRESS,NTENS,1,STRESST)
CALL KMMULT(P,NTENS,NTENS,STRESS,NTENS,1,SDEV)
CALL KMMULT(STRESST,1,NTENS,SDEV,NTENS,1,SINVAR)
FBAR=DSQRT(SINVAR(1,1))
DO K1=1,NTENS
EPLAS(K1)=EPLAS(K1)+GAM_PAR*SDEV(K1,1)
EELAS(K1)=EELAS(K1)-EPLAS(K1)
END DO
EQPLAS=EQPLAS1
! Formulate the consistent material Jacobian (tangent)
CALL KCLEAR(EM,NTENS,NTENS)
CALL KMMULT(B,NTENS,NTENS,DDSDDE,NTENS,NTENS,EM)
CALL KMMULT(EM,NTENS,NTENS,P,NTENS,NTENS,AUX11)
CALL KMMULT(AUX11,NTENS,NTENS,STRESS,NTENS,1,AUX12)
CALL KMMULT(STRESST,1,NTENS,P,NTENS,NTENS,AUX13)
CALL KMMULT(AUX13,1,NTENS,AUX12,NTENS,1,AUX14)
CALL KMTRAN(AUX12,NTENS,1,AUX15)
CALL KMMULT(AUX12,NTENS,1,AUX15,1,NTENS,AUX16)
SCALAR1=ONE/AUX14(1,1)
CALL KSMULT(AUX16,NTENS,NTENS,SCALAR1)
TETA2=ONE-(TWO/THREE)*EHARD*GAM_PAR
CBETA=(TWO/THREE/TETA2/AUX14(1,1))*FBAR*FBAR*EHARD
SCALAR2=ONE/(ONE+CBETA)
CALL KSMULT(AUX16,NTENS,NTENS,SCALAR2)
CALL KCLEAR(DDSDDE,NTENS,NTENS)
CALL KMATSUB(EM,NTENS,NTENS,AUX16,DDSDDE,0)
END IF
! Store elastic strains, (equivalent) plastic strains
! in state variable array
DO K1=1,NTENS
STATEV( K1)=EELAS(K1)
STATEV(NTENS+K1)=EPLAS(K1)
END DO
STATEV(2*NTENS+1)=EQPLAS
STATEV(2*NTENS+2)=DSQRT(THREE/TWO)*FBAR
802 IF (IFLAG.EQ.1) THEN
WRITE(*,*)
WRITE(*,*) 'LOCAL PLASTICITY ALGORITHM DID NOT CONVREGED'
WRITE(*,*) 'AT GAUSS POINT=',NPT, 'ELEMENT=',NOEL
WRITE(*,*) 'AFTER=',ITER,' ITERATIONS'
WRITE(*,*) 'LAST CORRECTION=',FGAM/FJAC
CALL XIT
END IF
END SUBROUTINE UMAT
! C
! SUBROUTINE UHARD C
! C
SUBROUTINE KUHARD(SYIELD,EHARD,EQPLAS,NVALUE,TABLE)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION TABLE(2,NVALUE)
PARAMETER(ZERO=0.D0,TWO=2.D0,THREE=3.D0)
SYIEL0=TABLE(1,1)
! Compute hardening modulus
EHARD=(TABLE(1,2)-TABLE(1,1))/TABLE(2,2)
! Compute yield stress corresponding to EQPLAS
SYIELD=DSQRT(TWO/THREE)*(SYIEL0+EHARD*EQPLAS)
RETURN
END
! C
! SUBROUTINE SPECTRAL C
! C
SUBROUTINE KSPECTRAL(Q,DP,DC,DIAG,GDIA,GAM_PAR,E,ENU)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER(ZERO=0.D0,ONE=1.D0,TWO=2.D0,THREE=3.D0,FOUR=4.D0,&
SIX=6.D0)
DIMENSION Q(4,4),DP(4,4),DC(4,4),DIAG(4,4),GDIA(4,4)
CALL KCLEAR(Q,4,4)
CALL KCLEAR(DP,4,4)
CALL KCLEAR(DC,4,4)
CALL KCLEAR(DIAG,4,4)
CALL KCLEAR(GDIA,4,4)
EG2=E/(ONE+ENU)
EG=EG2/TWO
ELAM=EG2*ENU/(ONE-TWO*ENU)
CBETA2=EG2
CALFA2=EG2
Q(1,1)=ZERO
Q(1,2)=TWO/DSQRT(SIX)
Q(1,3)=ONE/DSQRT(THREE)
Q(2,1)=-DSQRT(TWO)/TWO
Q(2,2)=-ONE/DSQRT(SIX)
Q(2,3)=ONE/DSQRT(THREE)
Q(3,1)=DSQRT(TWO)/TWO
Q(3,2)=-ONE/DSQRT(SIX)
Q(3,3)=ONE/DSQRT(THREE)
Q(4,4)=ONE
DP(1,1)=ONE
DP(2,2)=ONE
DP(3,3)=ZERO
DP(4,4)=TWO
DC(1,1)=EG2
DC(2,2)=EG2
DC(3,3)=THREE*ELAM+EG2
DC(4,4)=EG
DIAG(1,1)=ONE/(ONE+CBETA2*GAM_PAR)
DIAG(2,2)=ONE/(ONE+CBETA2*GAM_PAR)
DIAG(3,3)=ONE
DIAG(4,4)=ONE/(ONE+CBETA2*GAM_PAR)
GDIA(1,1)=-(CBETA2/((ONE+CBETA2*GAM_PAR)**2))
GDIA(2,2)=-(CBETA2/((ONE+CBETA2*GAM_PAR)**2))
GDIA(3,3)=ZERO
GDIA(4,4)=-(CBETA2/((ONE+CBETA2*GAM_PAR)**2))
RETURN
END
! C
! SUBROUTINE PROYECTOR C
! C
SUBROUTINE KPROYECTOR(P)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER(ZERO=0.D0,ONE=1.D0,TWO=2.D0,THREE=3.D0)
DIMENSION P(4,4)
CALL KCLEAR(P,4,4)
P(1,1)=TWO/THREE
P(1,2)=-ONE/THREE
P(1,3)=-ONE/THREE
P(2,1)=-ONE/THREE
P(2,2)=TWO/THREE
P(2,3)=-ONE/THREE
P(3,1)=-ONE/THREE
P(3,2)=-ONE/THREE
P(3,3)=TWO/THREE
P(4,4)=TWO
RETURN
END
! C
! M A T R I X H A N D L I N G C
!-------------U T I L I T I E S B L O C K-------------- C
! C
! C
! SUBROUTINE KCLEAR(A,N,M) C
! Clear a real matrix C
! C
SUBROUTINE KCLEAR(A,N,M)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER(ZERO=0.0D0)
DIMENSION A(N,M)
DO I=1,N
DO J=1,M
A(I,J)=ZERO
END DO
END DO
RETURN
END
! C
! SUBROUTINE KMMULT(A,NRA,NCA,B,NRB,NCB,C) C
! Real matrix product C
! C
SUBROUTINE KMMULT(A,NRA,NCA,B,NRB,NCB,C)
IMPLICIT REAL*8 (A-H,O-Z)
PARAMETER(ZERO=0.D0)
DIMENSION A(NRA,NCA),B(NRB,NCB),C(NRA,NCB)
CALL KCLEAR(C,NRA,NCB)
DUM=ZERO
DO I=1,NRA
DO J=1,NCB
DO K=1,NCA
DUM=DUM+A(I,K)*B(K,J)
END DO
C(I,J)=DUM
DUM=ZERO
END DO
END DO
RETURN
END
! C
! SUBROUTINE KSMULT(A,NR,NC,S) C
! Matrix times a scalar. C
! C
SUBROUTINE KSMULT(A,NR,NC,S)
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION A(NR,NC)
DO I=1,NR
DO J=1,NC
DUM=A(I,J)
A(I,J)=S*DUM
DUM=0.D0
END DO
END DO
RETURN
END
! C
! SUBROUTINE KUPDMAT(A,NR,NC,B) C
! Updates an existing matrix with an incremental matrix. C
! C
SUBROUTINE KUPDMAT(A,NR,NC,B)
IMPLICIT REAL*8 (A-H,O-Z)
PARAMETER(ZERO=0.D0)
DIMENSION A(NR,NC),B(NR,NC)
DO I=1,NR
DO J=1,NC
DUM=A(I,J)
A(I,J)=ZERO
A(I,J)=DUM+B(I,J)
DUM=ZERO
END DO
END DO
RETURN
END
! C
! SUBROUTINE KMTRAN(A,NRA,NCA,B) !
! Matrix transpose C
! C
SUBROUTINE KMTRAN(A,NRA,NCA,B)
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION A(NRA,NCA),B(NCA,NRA)
CALL KCLEAR(B,NCA,NRA)
DO I=1,NRA
DO J=1,NCA
B(J,I)=A(I,J)
END DO
END DO
RETURN
END
! C
! SUBROUTINE KMAVEC(A,NRA,NCA,B,C) C
! Real matrix times vector C
! C
SUBROUTINE KMAVEC(A,NRA,NCA,B,C)
IMPLICIT REAL*8 (A-H,O-Z)
PARAMETER(ZERO=0.D0)
DIMENSION A(NRA,NCA),B(NCA),C(NRA)
CALL KCLEARV(C,NRA)
DO K1=1,NRA
DO K2=1,NCA
C(K1)=C(K1)+A(K1,K2)*B(K2)
END DO
END DO
RETURN
END
! C
! SUBROUTINE KCLEARV(A,N) C
! Clear a real vector C
! C
SUBROUTINE KCLEARV(A,N)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER(ZERO=0.0D0)
DIMENSION A(N)
DO I=1,N
A(I)=ZERO
END DO
RETURN
END
! C
! SUBROUTINE KUPDVEC(A,NR,B) C
! Updates an existing vector with an incremental vector. C
! C
SUBROUTINE KUPDVEC(A,NR,B)
IMPLICIT REAL*8 (A-H,O-Z)
PARAMETER(ZERO=0.D0)
DIMENSION A(NR),B(NR)
DO I=1,NR
DUM=A(I)
A(I)=ZERO
A(I)=DUM+B(I)
DUM=ZERO
END DO
RETURN
END
! C
! SUBROUTINE KVECSUB(A,NRA,B,NRB,C) C
! Substracts one column vector from another column vector C
! IFLAG=0 for substraction C
! IFLAG=1 for addition C
! C
SUBROUTINE KVECSUB(A,NRA,B,NRB,C,IFLAG)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER (ONE=1.0D0, ONENEG=-1.0D0)
DIMENSION A(NRA,1),B(NRB,1),C(NRB,1)
SCALAR=ONENEG
IF (IFLAG.EQ.1) SCALAR=ONE
DO I=1,NRA
C(I,1)=A(I,1)+B(I,1)*SCALAR
END DO
RETURN
END
! C
! SUBROUTINE KMATSUB(A,NRA,NCA,B,C,IFLAG) C
! Substracts one rectangular matrix from another rectangular C
! matrix C
! IFLAG=0 for substraction C
! IFLAG=1 for addition C
! C
SUBROUTINE KMATSUB(A,NRA,NCA,B,C,IFLAG)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER (ONE=1.0D0, ONENEG=-1.0D0)
DIMENSION A(NRA,NCA),B(NRA,NCA),C(NRA,NCA)
CALL KCLEAR(C,NRA,NCA)
SCALAR=ONENEG
IF (IFLAG.EQ.1) SCALAR=ONE
DO I=1,NRA
DO J=1,NCA
C(I,J)=A(I,J)+B(I,J)*SCALAR
END DO
END DO
RETURN
END
! C
! SUBROUTINE IDENTITY C
! CREATES AN IDENTITY MATRIX OF DIMENSIONS NDIM,NDIM C
! C
SUBROUTINE KIDENTITY(DEL,NDIM)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER(ONE=1.D0)
DIMENSION DEL(NDIM,NDIM)
CALL KCLEAR(DEL,NDIM,NDIM)
DO K1=1,NDIM
DEL(K1,K1)=ONE
END DO
RETURN
END
! C
! SUBROUTINE KINVERSE C
! C
! IVEERSE OF A MATRIX USING LU DECOMPOSITION C
! TAKEN FROM NUMERICAL RECIPES By Press et al C
! C
! A Matrix to be inverted. C
! Y Inverse of A C
! N Dimension C
! C
! C
! C
SUBROUTINE KINVERSE(A,Y,NP,N)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER (ZERO=0.D0,ONE=1.D0)
DIMENSION A(NP,NP),Y(NP,NP),INDX(NP),AUX(NP,NP)
CALL KCLEAR(AUX,NP,NP)
CALL KCOPYMAT(A,AUX,N)
DO I=1,N
DO J=1,N
Y(I,J)=ZERO
END DO
Y(I,I)=ONE
END DO
CALL KLUDCMP(AUX,N,NP,INDX,D)
DO J=1,N
CALL KLUBKSB(AUX,N,NP,INDX,Y(1,J))
END DO
RETURN
END
! C
! SUBROUTINE KLUDCMP C
! C
! LU MATRIX DECOMPOSITION C
! TAKEN FROM NUMERICAL RECIPES By Press et al C
! C
! C
! C
SUBROUTINE KLUDCMP(A,N,NP,INDX,D)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER(NMAX=500,TINY=1.0E-20,ZERO=0.D0,ONE=1.D0)
DIMENSION INDX(N),A(NP,NP),VV(NMAX)
D=ONE
DO I=1,N
AAMAX=ZERO
DO J=1,N
IF(ABS(A(I,J)).GT.AAMAX) AAMAX=ABS(A(I,J))
END DO
IF(AAMAX.EQ.0.) write(*,*) 'SINGULAR MATRIX IN LUDCMP'
VV(I)=ONE/AAMAX
END DO
DO J=1,N
DO I=1,J-1
SUM=A(I,J)
DO K=1,I-1
SUM=SUM-A(I,K)*A(K,J)
END DO
A(I,J)=SUM
END DO
AAMAX=ZERO
DO I=J,N
SUM=A(I,J)
DO K=1,J-1
SUM=SUM-A(I,K)*A(K,J)
END DO
A(I,J)=SUM
DUM=VV(I)*ABS(SUM)
IF(DUM.GE.AAMAX) THEN
IMAX=I
AAMAX=DUM
END IF
END DO
IF(J.NE.IMAX) THEN
DO K=1,N
DUM=A(IMAX,K)
A(IMAX,K)=A(J,K)
A(J,K)=DUM
END DO
D=-D
VV(IMAX)=-VV(J)
END IF
INDX(J)=IMAX
IF(A(J,J).EQ.0.) A(J,J)=TINY
IF(J.NE.N) THEN
DUM=ONE/A(J,J)
DO I=J+1,N
A(I,J)=A(I,J)*DUM
END DO
END IF
END DO
RETURN
END
! C
! SUBROUTINE KLUBKSB C
! C
! FORWARD SUBSTITUTION C
! TAKEN FROM NUMERICAL RECIPES By Press et al C
! C
! C
! C
SUBROUTINE KLUBKSB(A,N,NP,INDX,B)
IMPLICIT REAL*8(A-H,O-Z)
PARAMETER (ZERO=0.D0)
DIMENSION INDX(N),A(NP,NP),B(NP)
II=0
DO I=1,N
LL=INDX(I)
SUM=B(LL)
B(LL)=B(I)
IF(II.NE.0) THEN
DO J=II,I-1
SUM=SUM-A(I,J)*B(J)
END DO
ELSE IF(SUM.NE.ZERO) THEN
II=I
END IF
B(I)=SUM
END DO
DO I=N,1,-1
SUM=B(I)
DO J=I+1,N
SUM=SUM-A(I,J)*B(J)
END DO
B(I)=SUM/A(I,I)
END DO
RETURN
END
! C
! SUBROUTINE KCOPYMAT C
! C
SUBROUTINE KCOPYMAT(A,B,N)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(N,N),B(N,N)
CALL KCLEAR(B,N,N)
DO K1=1,N
DO K2=1,N
B(K1,K2)=A(K1,K2)
END DO
END DO
RETURN
END