real*4 rm(3,3),v(3)
	character*40 MATNAME
	do 10 i=1,3
	do 10 j=1,3
10	rm(i,j)=0.
	n=0
20     TYPE *,'ENTER FILE NAME OF next MATRIX to include(CR to stop):'
       read(5,40)MATNAME
 40    FORMAT (A40)
	if (matname(1:5).eq.'     ') goto 100
       OPEN(UNIT=4,FILE=MATNAME,STATUS='OLD')
	n=n+1
	DO 41 I=1,3
	READ(4,*)(v(J),J=1,3)
	write(6,*)(v(j),j=1,3)
	do 41 j=1,3
	if (n.ne.2*(n/2)) then
c	change sign of each element of odd matrices:
	v(j)=-v(j)
	write(6,*)' negating this matrix:',n
	endif
41	rm(i,j)=rm(i,j)+v(j)
	CLOSE(UNIT=4)
   	goto 20

100	do 200 i=1,3
	do 200 j=1,3
200	rm(i,j)=rm(i,j)/n


C	NOW ORTHONORMALIZE, PRESERVING DIRECTION OF 3'D ROW (VECTOR THAT WILL BE TAKEN TO Z)

C	NORMALIZE 3'D ROW:
	SUM=0.
	DO 400 J=1,3
400	SUM=SUM+RM(3,J)*RM(3,J)
	SUM=SQRT(SUM)
	DO 420 J=1,3
420	RM(3,J)=RM(3,J)/SUM


C	NOW REMOVE COMPONENT OF 3RD ROW FROM 2ND, FIRST:
	DO 450 I=1,2
	SUM=0
	DO 440 J=1,3
440	SUM=SUM+RM(3,J)*RM(I,J)
	DO 450 J=1,3
450	RM(I,J)=RM(I,J)-SUM*RM(3,J)


C	NOW NORMALIZE 2ND ROW:
	I=2
	SUM=0.
	DO 480 J=1,3
480	SUM=SUM+RM(I,J)*RM(I,J)
	SUM=SQRT(SUM)
	DO 500 J=1,3
500	RM(I,J)=RM(I,J)/SUM


C	NOW REMOVE COMPONENT OF 2ND ROW FROM FIRST:
	I=1
	SUM=0
	DO 540 J=1,3
540	SUM=SUM+RM(2,J)*RM(I,J)
	DO 550 J=1,3
550	RM(I,J)=RM(I,J)-SUM*RM(2,J)


C	NOW NORMALIZE 1ST ROW:
	I=1
	SUM=0.
	DO 580 J=1,3
580	SUM=SUM+RM(I,J)*RM(I,J)
	SUM=SQRT(SUM)
	DO 600 J=1,3
600	RM(I,J)=RM(I,J)/SUM


C	CHECK ORTHONORMALITY:
	DO 700 I=1,3
	DO 680 J=1,3
	V(J)=0.
	DO 680 K=1,3
680	V(J)=V(J)+RM(I,K)*RM(J,K)
700	WRITE(6,301)(V(J),J=1,3)


C	WRITE ORTHONORMAL MATRIX THAT TAKES ORIG THIRD ROW TO Z TO FILE:
	OPEN (UNIT=3,FILE='AVEROT.MAT',STATUS='NEW')
	DO 300 I=1,3
300	WRITE(3,301) (RM(I,J),J=1,3)
	CLOSE (UNIT=3)	
301	format(' ',2(3f15.8,3x))
	end