question about UMAT

I have read Pro Huang's UMAT for many times and one of its subprogramme I can't understand.

Can anybody help me ?

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      SUBROUTINE LUDCMP (A, N, NP, INDX, D)

 

C-----  LU decomposition

 

C-----  Use single precision on cray

C

      IMPLICIT REAL*8 (A-H,O-Z)

      PARAMETER (NMAX=200, TINY=1.0E-20)

      DIMENSION A(NP,NP), INDX(N), VV(NMAX)

 

      D=1.

      DO I=1,N

         AAMAX=0.

 

         DO J=1,N

            IF (ABS(A(I,J)).GT.AAMAX)
AAMAX=ABS(A(I,J))

         END DO

 

         IF (AAMAX.EQ.0.) PAUSE 'Singular
matrix.'

         VV(I)=1./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=0.

 

         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=1./A(J,J)

            DO I=J+1,N

               A(I,J)=A(I,J)*DUM

            END DO

         END IF

 

      END DO

 

      RETURN

      END