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SUBROUTINE qrdcmp(a,n,np,c,d,sing)
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INTEGER n,np
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REAL a(np,np),c(n),d(n)
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LOGICAL sing
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INTEGER i,j,k
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REAL scale,sigma,sum,tau
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sing=.false.
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do 17 k=1,n-1
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scale=0.
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do 11 i=k,n
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scale=max(scale,abs(a(i,k)))
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11 continue
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if(scale.eq.0.)then
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sing=.true.
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c(k)=0.
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d(k)=0.
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else
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do 12 i=k,n
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a(i,k)=a(i,k)/scale
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12 continue
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sum=0.
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do 13 i=k,n
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sum=sum+a(i,k)**2
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13 continue
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sigma=sign(sqrt(sum),a(k,k))
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a(k,k)=a(k,k)+sigma
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c(k)=sigma*a(k,k)
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d(k)=-scale*sigma
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do 16 j=k+1,n
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sum=0.
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do 14 i=k,n
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sum=sum+a(i,k)*a(i,j)
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14 continue
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tau=sum/c(k)
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do 15 i=k,n
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a(i,j)=a(i,j)-tau*a(i,k)
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15 continue
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16 continue
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endif
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17 continue
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d(n)=a(n,n)
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if(d(n).eq.0.)sing=.true.
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return
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END
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