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SUBROUTINE lubksb(a,n,np,indx,b)
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INTEGER n,np,indx(n)
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REAL a(np,np),b(n)
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INTEGER i,ii,j,ll
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REAL sum
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ii=0
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do 12 i=1,n
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ll=indx(i)
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sum=b(ll)
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b(ll)=b(i)
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if (ii.ne.0)then
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do 11 j=ii,i-1
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sum=sum-a(i,j)*b(j)
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11 continue
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else if (sum.ne.0.) then
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ii=i
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endif
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b(i)=sum
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12 continue
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do 14 i=n,1,-1
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sum=b(i)
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do 13 j=i+1,n
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sum=sum-a(i,j)*b(j)
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13 continue
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b(i)=sum/a(i,i)
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14 continue
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return
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END
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